ftp.xmission.com/2014.06.ftp.xmission.com.tar/ftp.xmission.com/pub/lists/fractint/archive/fractint.200106

Internet Message Format | 2001-06-30 | 471KB

From: [e-mail]
Subject: (fractint) C-FOTD  01-06-01  (A Fractal Jewel [8])
Date: 01 Jun 2001 09:30:46 EDT


Classic FOTD -- June 01, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

Today's image, the first of the month of June, is a real jewel.
So I named it "A Fractal Jewel".  A jewel of such magnitude
certainly deserves some recognition, which I feel that the
rating of a superior 8 supplies.

To achieve the effect, I uncorked the outside=fmod option,
which, though it is somewhat difficult to use, can produce some
stunning effects with certain fractals.  The good-old
MandelbrotMix4 formula did the footwork as it iterated the
expression -3.5Z^(0.7)+3.5Z^(-0.7)+(1/C).

This expression draws a parent fractal that at first appears to
be a total failure, since it consists of no more than a few tiny
patches of color on a black background.  Today's scene lies
along the shoreline of a mis-shapen bud at the edge of one of
these tiny patches.

All good things take time, and today's image is no exception.
The parameter file takes 22-1/2 minutes to render.  But unlike
so many natural processes, the rendering of today's image can be
bypassed by visiting Paul's web site at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

and downloading the already-rendered image from there.

The fractal weather today was near perfect but bland, with hazy
sun and a temperature of 72F (22C).  The fractal cats, who are
habitually bland, approved blandly.

As for me, I've got to get going on more profitable things.
Until next time, take care, and row your boat down the stream.
Life is but a dream.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

A_Fractal_Jewel    { ; time=0:22:37.10--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.01550644258372/-0.0139521159263/4.35\
  8122e+009/1/-160 params=-3.5/0.7/3.5/-0.7/0/5000
  float=y maxiter=3600 inside=0 proximity=0.5
  outside=fmod periodicity=10
  colors=000000000QMUPOWPQZPS`PUaTVdWXf_YicZkf_niapl\
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  cIPZFUUDYPBaK9fF6jA5o53s00x00z00y00x00v00u00t00s22\
  q22p32o32n32l42k42j53i53h
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================

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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  02-06-01  (Fractal Feathers [8])
Date: 02 Jun 2001 11:08:04 -0400 (EDT)


Classic FOTD -- June 02, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

Though it's not a work day, I seem to have a hundred tasks that
need to be done.  So this FOTD will have to be hasty.

Today's fractal is the second consecutive one to rate an 8.
Either I'm becoming a better fractalist, or more likely, I'm
having a string of good luck.  Actually, most of the worth of
today's image lies in the color palette.  A minute or two trying
to find better colors will show this.

To produce an image (not this particular image, which I was not
yet aware of), I took Z^1.333 and subtracted Z^1.618 from it
before adding C.  I named the picture "Fractal Feathers" because
the pattern reminds me of feathers.  I rated it an 8 because I
like it.

But pictures speak louder than words, and the way to see the
picture is to run the parameter file and wait 25 minutes, or to
give Paul and Scott a chance to render and post the image, and
then download it in one minute.

The image file will be available for downloading at the web sites:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather was cloudy with heavy rain and all the
unpleasant things that accompany heavy rain.  The cats
complained and the basement took on water, etc.  The temperature
of 64F (18C) was irrelevant.

I'll return with more fractal stuff in about 12 hours.  Until
then, take care, and stay sharp.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Fractal_Feathers   { ; time=0:24:50.13--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+5.32964478731053700/+0.155415801184001\
  90/2.561639e+007/1/135 params=1/1.333/-1/1.618/0/0
  float=y maxiter=3200 inside=0
  logmap=460 periodicity=10
  colors=0000D60D60E60E60F60F60G60G41H41H41I41I41J41\
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  zv0zv0zv0zv0zv0zv0zv0zv0z
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Thaddaeus Parker <[e-mail]>
Subject: RE: (fractint) C-FOTD  02-06-01  (Fractal Feathers [8])
Date: 02 Jun 2001 09:54:03 -0700

Jim:
I would name it Peacock, but still the same it is a fantastic rendering.
Keep it up.  Love the antics of the Fractal Cats, got one myself and know
exactly how they react to the weather and such.  Keep up the good work.

Thaddaeus Parker
San Diego CA
ICQ# 3304633

-----Original Message-----
[mailto:[e-mail]]On Behalf Of Jim Muth
Sent: Saturday, June 02, 2001 8:08 AM
Cc: [e-mail]



Classic FOTD -- June 02, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

Though it's not a work day, I seem to have a hundred tasks that
need to be done.  So this FOTD will have to be hasty.

Today's fractal is the second consecutive one to rate an 8.
Either I'm becoming a better fractalist, or more likely, I'm
having a string of good luck.  Actually, most of the worth of
today's image lies in the color palette.  A minute or two trying
to find better colors will show this.

To produce an image (not this particular image, which I was not
yet aware of), I took Z^1.333 and subtracted Z^1.618 from it
before adding C.  I named the picture "Fractal Feathers" because
the pattern reminds me of feathers.  I rated it an 8 because I
like it.

But pictures speak louder than words, and the way to see the
picture is to run the parameter file and wait 25 minutes, or to
give Paul and Scott a chance to render and post the image, and
then download it in one minute.

The image file will be available for downloading at the web sites:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather was cloudy with heavy rain and all the
unpleasant things that accompany heavy rain.  The cats
complained and the basement took on water, etc.  The temperature
of 64F (18C) was irrelevant.

I'll return with more fractal stuff in about 12 hours.  Until
then, take care, and stay sharp.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Fractal_Feathers   { ; time=0:24:50.13--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+5.32964478731053700/+0.155415801184001\
  90/2.561639e+007/1/135 params=1/1.333/-1/1.618/0/0
  float=y maxiter=3200 inside=0
  logmap=460 periodicity=10
  colors=0000D60D60E60E60F60F60G60G41H41H41I41I41J41\
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  zv0zv0zv0zv0zv0zv0zv0zv0z
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Morgan L. Owens" <[e-mail]>
Subject: (fractint) Re: [philofractal] C-FOTD  02-06-01  (Fractal Feathers [8])
Date: 03 Jun 2001 12:00:58 +1200

At 03:08 03/06/2001, Jim Muth wrote:

>The fractal weather was cloudy with heavy rain and all the
>unpleasant things that accompany heavy rain.  The cats
>complained and the basement took on water, etc.  The temperature
>of 64F (18C) was irrelevant.

Eeh, you're really going to have to do something about that basement. Next
thing, you'll have your house rotting out from under you.

Morgan L. Owens
"Just be glad your house isn't made of polystyrene."


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  03-06-01  (Julia mandelbrot [6])
Date: 02 Jun 2001 23:03:29 -0400 (EDT)


Classic FOTD -- June 03, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Three FOTD images in a row, all rating an 8, is too much to hope
for.  So I had no hopes of producing another 8-rated image when
I sat down for my daily search for fractals this evening.  Then,
when the day's effort yielded only a 6-rated image, I was not
disappointed.

But a rating of 6 is still above average, and well worth the 7
minutes required to render the scene from the parameter file.
The formula that created the image is totally whimsical --
1.3Z^(1.3)+0.13Z^(-13)+(1/C).  I found the parameters by turning
off my thinking (quite an easy task) and letting my fingers roam
where they wished.

The name "Julia Mandelbrot" came to me as I studied the picture.
The pattern around the central midget is that of julia sets
located in the East Valley area of Mandelbrot midgets, yet the
midget itself is pure Mandel stuff.  The combination inspired
the name.  The rating of 6 is honest, since the image has too
many imperfections for a higher rating.

Other than running the parameter file, an alternate way of
viewing the image is to download the GIF file from the Web at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was variably cloudy but so far dry,
with a temperature of 77F (25C).  The fractal cats must have
approved, for they spent much time in the yard, trying to stay
out of trouble.

Now it's my turn to try to stay out of trouble.  It's hard to
imagine how I could get into trouble watching a junky old sci-fi
movie, so that's what I'll do.  Until next time, take care, and
take two fractals at bedtime for a good night's sleep.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Julia_Mandelbrot   { ; time=0:06:47.82--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-2.485951411296012/+0.00097323098757938\
  /3.036155e+007/1/102.5 params=1.3/1.3/0.13/-13/0/0
  float=y maxiter=850 inside=0
  logmap=-137 periodicity=10 sound=off
  colors=000F00J00L00S80WB0_F0cJ0gM1kQ5oU8sZCudHwjLy\
  pPzvSzzWozVhvV`qUUjUMdUF_S7US0PS0RR0SQ0UP0VO0WM0YL\
  0ZK0_K0`J0bH0cG0dF0eE555555555555555555656757858A5\
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  RBWSASV8PW7MZ7J_6Fb5Bc48d4Ac7BbBCbFE`JF`MF_PGZSHZW\
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  MrEMrEMrEMrEor0nr0nr0nr0mr0mr0mr0mr0kr0kr0kr0kr0jr\
  0jr0jr0ir0ir0ir0ir0hr0hr0
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 31-05-01 (Fractal Fractles [7])
Date: 03 Jun 2001 09:01:10 -0000

>From: Jim Muth <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  31-05-01  (Fractal Fractles [7])
>Date: Thu, 31 May 2001 10:59:51 -0400 (EDT)
>
>
>Classic FOTD -- May 31, 2001 (Rating 7)

Erm... Wow! That is one *trippy* image! I really really dIg those colours!
Very nice work, Jim!

Thanks.
Andrew.

PS. One day (when I have web space) I think I may start doing a fractal of
the month...

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 03-06-01 (Julia mandelbrot [6])
Date: 03 Jun 2001 09:06:06 -0000

>From: Jim Muth <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  03-06-01  (Julia mandelbrot [6])
>Date: Sat, 2 Jun 2001 23:03:29 -0400 (EDT)
>
>
>Classic FOTD -- June 03, 2001 (Rating 6)

I'd rate this one higher than that, perhaps 7, on account of the elegant
simplicity of the image and the very nice, harmonious colours.

Thanks.
Andrew.

_________________________________________________________________________
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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) Re: Wet basement
Date: 03 Jun 2001 09:55:03 -0400 (EDT)

At 12:00 PM 6/3/01 +1200, Morgan Owens wrote:

>Eeh, you're really going to have to do something about that
>basement. Next thing, you'll have your house rotting out from
>under you.

As long as it's not brain rot, I can live with it.  The brick
house is in pretty good shape -- foundation sitting on solid rock
-- and the water comes in only with very heavy rain, like the 10cm
in 8 hours downpour we had Friday.  To fix the problem, it would be
necessary to dig up my yard and the garden of the elderly widow
next door, which would upset not only the widow, but the cats as
well.  I have installed a sump pump, and that keeps the wetness
down to a wet floor, so I guess I can live with the dampness a
while -- just as long as some alien fractal fungus doesn't develop
and start growing down there.

Jim M.


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  04-06-01  (Cometary Impression [8])
Date: 04 Jun 2001 01:24:32 -0400 (EDT)


Classic FOTD -- June 04, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

The hot streak continues unabated.  Not only is my fractal
philosophy once again active, but my fractal images are active
also.  And all this action piled up on a day with so many
mundane chores needing to be done.

With today's image we're back up to a superior rating of 8.  If
the present trend continues, we may reach one of the very rare
9's, or possibly even an unheard-of 10 before long.

To create today's fractal I entered the parameters for
-2Z^(-1.1)-0.0002Z^(-11)+(1/C) into the MandelbrotMix4 formula,
and let her rip.  Today's scene lies at the end of a curving
filament extending from a bud, very near the point where many
filaments converge into a starlike object.

I named the image "Cometary Impression" when I saw the eight
elements around the midgets and imagined eight circling comets.
The parameter file render time of 13 minutes is slow.  The
download is fast, and will be available shortly on the Web at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was variably cloudy and breezy.  The
wind and temperature of 75F (24C) kept the fractal cats indoors
most of the day, frequently checking the door to see whether it
was still breezy outside.  Later in the afternoon the wind died
down and the cats went out, scolding me for not turning down the
wind earlier.

The time is now after 1am -- most certainly time to shut down
the fractal shoppe and throw the big switch.  Until next time,
take care, and have faith in your fractals.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

CometaryImpression { ; time=0:13:25.10--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-6.312863840603067/-8.071658728774926/1\
  80586.5/1/147.5 params=-2/-1.1/-0.0002/-11/0/300
  float=y maxiter=1500 inside=0
  logmap=261 periodicity=10
  colors=000002000000000000000000zzz000zzc000zzI20Lm\
  cP52UcUW97`99cCCgEEkGGmGIrILtLNyLPzWZrgekrkczrWzm`\
  zkczggzejz`mzZozUtzSvzNzzLzzGzzEzz9zz7zz2zz0zz0zz0\
  zz0zz0zz0zz0zt0zm0ze5zZ9zPGzINz9Uz2Zz0Pz0Gz07v00m0\
  0g02c05W07S09L0CG2E97G5CL5GP5LU5PZ5Uc5Wg5`k5eo5jt5\
  my5zz7oz5`z2Lv25t00o00o00m00m00k00k00k00j00j20j20g\
  20g20e50e50e50c70c70c70`70`90Z90Z90ZC0WC0WC0ZE0WC0\
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  vzzyzyyzvzvvzttzorzkozgmzcmzZkzUjzSgzNezIezEcz9`z5\
  Zz0Wz0Pz0Wz7czGgzPmzZtzgyzozzvzzyzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
  zzzzzzzzzzzzzzzzzzzzzzzzz
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  05-06-01  (A Raspy Old Midget [9])
Date: 04 Jun 2001 22:54:11 -0400 (EDT)


Classic FOTD -- June 05, 2001 (Rating 9)

Fractal visionaries and enthusiasts:

Things have been going well here at fractal central lately.  I'm
in one of those periods where I seem to automatically pick the
right places to look for those hard-to-find midgets, and equally
important, good color palettes seem to appear almost by magic.

I named today's image "A Raspy Old Midget".  The eight rasp-like
elements surrounding the midget inspired the name.  Undecided as
to what rating I might bestow upon the picture, I decided on a
rather liberal 9.  An 8-1/2 might be more accurate, but we need
at least a few 9's in the archives.

The formula -5(Z^(-1.15))-0.02(Z^(-11.5))+(1/C) drew the parent
fractal, which is a rather interesting but oversized figure by
itself, with a prominent fan-like element extending eastward
from the origin.  Today's midget lies on the south border of
this fractal fan.

The 11-minute parameter file is a bit slow.  I advise visiting
Paul's web site or Scott's site, and downloading the GIF image
file from there.  Paul's FOTD site can be found at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

Scott's is at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was virtually perfect, with sunny
skies, a temperature of 77F (25C), and happy cats.

And having found such a fine fractal, I'm happy too.  Until next
time, take care, and I wonder whether fractal seeds will grow.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

A_Raspy_Old_Midget { ; time=0:11:41.29--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.77096187026955700/-2.487403802992336\
  00/3.864825e+009/1/92.499/0.003
  params=-5/-1.15/-0.02/-11.5/0/0 float=y
  maxiter=1200 inside=0 logmap=205 periodicity=10
  colors=000zSuzTrzUuzVuzWuzXuzYvzZvz_vz`vzayzbyzcyz\
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  CAzC8zC7zE5zE3zE1zG0zG0zG
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  06-06-01  (Golden Chariot [8])
Date: 06 Jun 2001 08:38:24 -0400 (EDT)


Classic FOTD -- June 06, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

The formula -0.6(Z^(-1.3))-0.006(Z^(-3))+(1/C), when calculated
with an escape radius of 900, draws an hourglass-shaped figure
composed of almost total chaos.  Two out-zooms are needed to see
the entire figure, which is a Mandeloid sitting on its nose,
with the tiny hourglass lying in the center of the main bay.

The figure is unusual in that the filaments extending from the
buds end in rings instead of simply petering out in ever-smaller
details.  Today's midget lies deep within the end-ring of the
main southwest filament of the main bud, which in today's
fractal lies on the south shore of the main bay.

I named the picture "Golden Chariot" because when I saw it, I
had an immediate impression of a chariot wheel.  I briefly
considered a name such as "Chariot of the Gods", but a similar
name has already been used in a well-known book.

The image rates an 8.  The rating might be a bit liberal, but
it's a strange scene in a fractal with even stranger scenes.
I'll present some of these other scenes in the next few FOTD's,
the first of which will be tomorrow's.

A good feature of today's image is that it renders in only 3-1/2
minutes.  In an hour or so, the image may also be seen by
visiting the web sites of Paul and Scott.  The URL's of those
sites are:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather, which everyone is waiting for with bated
breath, was average today.  The partly cloudy skies were partly
sunny during the daylight hours and partly starry after dark.
The temperature of 80F (26.5C) was average, and the fractal cats
had an average day on the porch and in the yard.

And it's the start of another average day for me.  I've got
about the average amount of work to finish before I can relax
and turn to tomorrow's FOTD, which is all goes well, will be far
above average.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Golden_Chariot     { ; time=0:03:30.04--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+7.63095735774279/-41.9285774906314/3.1\
  96408e+008/1/162.5 params=-0.6/-1.3/-0.006/-3/0/800
  float=y maxiter=380 inside=0
  logmap=65 periodicity=10
  colors=000045D45I45N45Q49V6GYCLbHSgMYkRdpVks`pxevz\
  jzzozztzztzztzzpzwpmpjviepdZiYPb0PYlXTseOwjJzmEzr9\
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  wkzwkzwizwizwizwizwgzwgzwgzwgzwfzwfzwfzwfzwdzwdzwd\
  zwdzwbzwbzwbzwbzwazwazwazwazwkzwizwizwixwixwixwixw\
  iwwiwwiwwitwitwitwitwiR45
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Ricardo M. Forno" <[e-mail]>
Subject: (fractint) Algorithmic Composer
Date: 06 Jun 2001 11:49:39 -0300

There are some algorithmic composers over the Web. I think the one I wrote
compares favorably to most of them. You can download it from:
http://www.geocities.com/rmforno/index.html
It does not use a fractal algorithm, but anyway I think this mail is on
topic.
Hope you like the music.


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  07-06-01  (Charged Midget [8])
Date: 07 Jun 2001 10:23:24 -0400 (EDT)


Classic FOTD -- June 07, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

When a package or roll of photographic film is opened carelessly
in a darkroom in dry weather, black tree-like figures sometimes
appear on the film when it is developed.  The figures are caused
by sparks of static electricity that are created as the layers
are peeled apart too roughly.  These figures have a name, which
eludes me at the moment, though I think it begins with the
letter 'l'.

If I could remember that word, I would have the perfect title
for today's image, which reminds me of the sheets of ruined film
that I have thrown away over the years.  But, being unable to
remember, I have named the image "Charged Midget".

The scene of today's picture lies in the same fractal as
yesterday's, though in a totally different part.  Whereas
yesterday's scene was located at the end of a filament, today's
is located deep in an almost featureless valley on the WNW shore
of the main bay.

And speaking of fractal bays, this one has that strange
hourglass-shaped chunk of total chaos sitting in the middle of
it.  Usually, such totally chaotic areas hold nothing of
interest, but this one is worth at least a cursory
investigation.  If I find something, it will be tomorrow's FOTD;
if not, I'll turn somewhere else.

Today's image rates an 8, keeping the run of exceptional images
unbroken.  The total lack of reds is intentional.  Sometimes
fewer colors can have greater impact than more.

The image was rendered with the 'passes equal b' option, which I
rarely use, but which sometimes is the fastest of all.  With
today's 3-3/4 minute parameter file, the difference of a few
seconds is inconsequential however.

As always, the GIF image will soon be available on the web for
those who would rather not run the parameter file.  The URL's
are:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today featured a temperature of 81F (27C),
changeable skies, with nearly every cloud type imaginable, and a
light sprinkle at noon to wet those going to lunch.  It also wet
the fractal cats, who scowled as they retreated indoors until
the rain stopped.

And it's now time for me to retreat to the task of accomplishing
the day's work.  Until next time, take care, and will we ever
find out who is right?


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Charged_Midget     { ; time=0:03:42.60--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=b
  center-mag=-14.16793212758799/-11.36345363439138/2\
  6147.93/1/19.999 params=-0.6/-1.3/-0.006/-3/0/800
  float=y maxiter=1500 inside=255
  logmap=43 periodicity=0
  colors=0000Mp0Ho0Co09m09l69jD9iH9gM9jPElSJmXOo`Trc\
  Xsgaujgvmkyrqzuvzxyzrxzmsxinudhr`coWZlRVjMRgHNdDKa\
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  VzUXzUYzUYzU_zW`zW`zWbzWbzXdzXezXezXgzZizZizZjzZjz\
  cizgizlizpizuizygzzgzzgzzgzzgzzezzdzzdzzbzzbzz`zz_\
  zz_zzYzzYzzXzzVzzVzzUzzUzzSzzSzzQzzPzzNzzMzzKzzJzz\
  HzzFzzEzzCzzAzz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9z\
  z9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9zz9\
  zzAzzAzzAzzKzzSzz_zziz000
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Some intriguing stuff.
Date: 07 Jun 2001 22:16:27 -0400


------=_NextPart_001_0000_01C0EF9F.7F321100
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable



These formulas make it possible to investigate the escape behavior of the=
 Henon map:

x -> a - by + x^2
y -> x

both for the case where x and y are real, and the case where they may be =
complex.

The formulas whose names end in 'J' are Julia-like. Henon_J1 will vary y =
over the screen while fixing x. The parameters fix a,
b, and z. Henon-J2 will vary real x and real y over the screen; setting t=
heir imaginary parts to
zero is accomplished by setting p3 to zero. If p1 and p2 are real (e.g. t=
he classic 1.4 and -0.3) the basin of attraction of the familiar real Hen=
on map appears.

The formulas whose names end in 'M' are Mandelbrot-like. Henon-M3 is most=
 Mandelbrot-like; b varies over the screen while a and initial x and y (a=
ll complex) are set with parameters. No known choice of initial x and y a=
cts like the "critical" value 0
for the classic Mandelbrot set, so the result always seems to look pertur=
bed. (I looked long and hard with the evolver/explorer to find a good app=
roximation to a "critical" value; nothing seems to cut it, perhaps becaus=
e there is no
"critical" value for such multi-recurrence maps as this. The Jacobian has=
 nonzero determinant if b is not zero -- if b is zero,
both x and y do the usual Mandelbrot set with x =3D 0, y =3D anything "cr=
itical". However, the imaginary parts of initial x and y should be zero t=
o get "Mandelbrot-like" it seems.) Henon-M2 varies real a and real b over=
 the screen. The result resembles Lyaounov space! Henon-M4 is like Henon-=
M2, but it automatically composites the maps obtained for nine choices of=
 initial real x and y. These iterate the real Henon map -- imaginary x, y=
, a, and b are identically zero. Henon-M5 is complex instead of real, lik=
e Henon-M3, but is a composite like Henon-M4 using nine values of initial=
 real x and y. Henon-M2, M3, and M5 are best viewed with inside =3D per, =
outside =3D numb, outside =3D 0, maxiter > 255, and a color map that make=
s colors 0 and 255 different and varies a lot in the early colors (try th=
e default VGA palette modified to invert the last 32 colors or so). A zoo=
m down M5's seahorse valley is interesting. The "halo" of color 255 about=
 the Set in M5 and in the lower right quadrant of M4 represents the regim=
es where strange attractors can occur in the system. The set of points fo=
r which actual strange attractors occur is buried among "islands" of orde=
r and pockets of escape -- the former look like Lyapunov swallows in M4 a=
nd presumably would appear to be mini Mandelbrots in M5 if "critical" val=
ues for initial real x and y could be found.

WARNING: The below probably has the dreaded "3D" disease, no thanks to MS=
N Exploder. If it does, IIRC someone published a utility to strip the enc=
rufting^H^H^H^H^H^H^Hoding on here a year or so ago.

Henon_M2 { ; p1 is a point in the Henon map. Screen coordinates are param=
eters 'a' and 'b'.
           ; Escape pixels escaped radius 1000. Try non-standard inside o=
ptions with
           ; periodicity checking enabled.
  a =3D real(pixel), b =3D imag(pixel), z =3D p1:
  z =3D a - b*imag(z) - sqr(real(z)) + (0,1)*real(z),
  |z| < 1000000
}

Henon_M3 { ; Henon map on complex numbers.
           ; p1 and p2 are a point in the Henon map. Screen coordinates a=
re parameter 'b'.
           ; Escape pixels escaped radius 1000. Try non-standard inside o=
ptions with
           ; periodicity checking DISabled.
  a =3D 1.4, b =3D pixel, z =3D p1, w =3D p2:
  z1 =3D a - b*w - sqr(z)
  w =3D z
  z =3D z1,
  lastsqr+|w| < 1000000
}

Henon_M4 { ; Screen coordinates are parameters 'a' and 'b'.
           ; Escape pixels escaped radius 1000. Try non-standard inside o=
ptions with
           ; periodicity checking enabled. Composite view.
  a =3D real(pixel), b =3D imag(pixel), z =3D 0, r =3D 0, done =3D 0:
  z =3D a - b*imag(z) - sqr(real(z)) + (0,1)*real(z),
  IF (|z| > 1000000)
    IF (r =3D=3D 0)
      z =3D 1
      r =3D 1
    ELSEIF (r =3D=3D 1)
      z =3D (0,1)
      r =3D 2
    ELSEIF (r =3D=3D 2)
      z =3D -1
      r =3D 3
    ELSEIF (r =3D=3D 3)
      z =3D -(0,1)
      r =3D 4
    ELSEIF (r =3D=3D 4)
      z =3D 1+(0,1)
      r =3D 5
    ELSEIF (r =3D=3D 5)
      z =3D 1-(0,1)
      r =3D 6
    ELSEIF (r =3D=3D 6)
      z =3D -1+(0,1)
      r =3D 7
    ELSEIF (r =3D=3D 7)
      z =3D -1-(0,1)
      r =3D 8
    ELSE
      done =3D 1
    ENDIF
  ENDIF
  done =3D=3D 0
}

Henon_M5 { ; Henon map on complex numbers. Screen coordinates are paramet=
er 'b'.
           ; Escape pixels escaped radius 1000. Try non-standard inside o=
ptions with
           ; periodicity checking DISabled. Composite view.
  a =3D 1.4, b =3D pixel, z =3D 0, w =3D 0, r =3D 0, done =3D 0:
  z1 =3D a - b*w - sqr(z)
  w =3D z
  z =3D z1,
  IF (lastsqr+|w| > 1000000)
    IF (r =3D=3D 0)
      z =3D 1
      w =3D 0
      r =3D 1
    ELSEIF (r =3D=3D 1)
      z =3D 0
      w =3D 1
      r =3D 2
    ELSEIF (r =3D=3D 2)
      z =3D -1
      w =3D 0
      r =3D 3
    ELSEIF (r =3D=3D 3)
      z =3D 0
      w =3D -1
      r =3D 4
    ELSEIF (r =3D=3D 4)
      z =3D 1
      w =3D 1
      r =3D 5
    ELSEIF (r =3D=3D 5)
      z =3D 1
      w =3D -1
      r =3D 6
    ELSEIF (r =3D=3D 6)
      z =3D -1
      w =3D 1
      r =3D 7
    ELSEIF (r =3D=3D 7)
      z =3D -1
      w =3D -1
      r =3D 8
    ELSE
      done =3D 1
    ENDIF
  ENDIF
  done =3D=3D 0
}

Henon_J1 { ; Henon map on complex numbers.
           ; p1 and p2 are a and b. Screen coordinates are y. p3 is x.
           ; Escape pixels escaped radius 1000. Try non-standard inside o=
ptions with
           ; periodicity checking DISabled.
  a =3D p1, b =3D p2, z =3D p3, w =3D pixel:
  z1 =3D a - b*w - sqr(z)
  w =3D z
  z =3D z1,
  lastsqr+|w| < 1000000
}

Henon_J2 { ; Henon map on complex numbers.
           ; p1 and p2 are a and b. Screen coordinates are real(x), real(=
y). p3 is imag(x), imag(y).
           ; Escape pixels escaped radius 1000. Try non-standard inside o=
ptions with
           ; periodicity checking DISabled.
  a =3D p1, b =3D p2, z =3D real(pixel) + (0,1)*real(p3), w =3D imag(pixe=
l) + (0,1)*imag(p3):
  z1 =3D a - b*w - sqr(z)
  w =3D z
  z =3D z1,
  lastsqr+|w| < 1000000
}<br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <a=
 href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0000_01C0EF9F.7F321100
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV><BR><BR>These =
formulas make it possible to investigate the escape behavior of the Henon=
 map:</DIV> <DIV> </DIV> <DIV>x -> a - by + x^2</DIV> <DIV>y ->=
; x</DIV> <DIV> </DIV> <DIV>both for the case where x and y are real=
, and the case where they may be complex.</DIV> <DIV> </DIV> <DIV>Th=
e formulas whose names end in 'J' are Julia-like. Henon_J1 will vary =
;y over the screen while fixing x. The parameters fix a,</DIV> <DIV>b, an=
d z. Henon-J2 will vary real x and real y over the screen; sett=
ing their imaginary parts to</DIV> <DIV>zero is accomplished by setting p=
3 to zero. If p1 and p2 are real (e.g. the classic 1.4 and -0.3) the basi=
n of attraction of the familiar real Henon map appears.</DIV> <DIV> =
</DIV> <DIV>The formulas whose names end in 'M' are Mandelbrot-like. Heno=
n-M3 is most Mandelbrot-like; b varies over the screen while a and initia=
l x and y (all complex) are set with parameters. No known choice of initi=
al x and y acts like the "critical" value 0</DIV> <DIV>for the classic Ma=
ndelbrot set, so the result always seems to look perturbed. (I looked lon=
g and hard with the evolver/explorer to find a good approximation to a "c=
ritical" value; nothing seems to cut it, perhaps because there is no</DIV=
> <DIV>"critical" value for such multi-recurrence maps as this. The =
Jacobian has nonzero determinant if b is not zero -- if b is zero,</DIV> =
<DIV>both x and y do the usual Mandelbrot set with x =3D 0, y =3D anythin=
g "critical". However, the imaginary parts of initial x and y should=
 be zero to get "Mandelbrot-like" it seems.) Henon-M2 varies real a and r=
eal b over the screen. The result resembles Lyaounov space! Henon-M4 is l=
ike Henon-M2, but it automatically composites the maps obtained for nine =
choices of initial real x and y. These iterate the real Henon map -- imag=
inary x, y, a, and b are identically zero. Henon-M5 is complex instead of=
 real, like Henon-M3, but is a composite like Henon-M4 using nine values =
of initial real x and y. Henon-M2, M3, and M5 are best viewed with inside=
 =3D per, outside =3D numb, outside =3D 0, maxiter > 255, and a color =
map that makes colors 0 and 255 different and varies a lot in the ea=
rly colors (try the default VGA palette modified to invert the last 32 co=
lors or so). A zoom down M5's seahorse valley is interesting. The "halo" =
of color 255 about the Set in M5 and in the lower right quadrant of M4 re=
presents the regimes where strange attractors can occur in the system. Th=
e set of points for which actual strange attractors occur is buried among=
 "islands" of order and pockets of escape -- the former look like Lyapuno=
v swallows in M4 and presumably would appear to be mini Mandelbrots in M5=
 if "critical" values for initial real x and y could be found.</DIV> <DIV=
> </DIV> <DIV>WARNING: The below probably has the dreaded "3D" disea=
se, no thanks to MSN Exploder. If it does, IIRC someone published a utili=
ty to strip the encrufting^H^H^H^H^H^H^Hoding on here a year or so ago.</=
DIV> <DIV> </DIV> <DIV>Henon_M2 { ; p1 is a point in the Henon map. =
Screen coordinates are parameters 'a' and 'b'.<BR>    =
;       ; Escape pixels escaped radius 1000=
. Try non-standard inside options with<BR>     &=
nbsp;     ; periodicity checking enabled.<BR>  a=
 =3D real(pixel), b =3D imag(pixel), z =3D p1:<BR>  z =3D a - b*imag=
(z) - sqr(real(z)) + (0,1)*real(z),<BR>  |z| < 1000000<BR>}</DIV>=
 <DIV> </DIV> <DIV>Henon_M3 { ; Henon map on complex numbers.<BR>&nb=
sp;          ; p1 and p2 are=
 a point in the Henon map. Screen coordinates are parameter 'b'.<BR> =
;          ; Escape pixels e=
scaped radius 1000. Try non-standard inside options with<BR>  &=
nbsp;        ; periodicity checking DI=
Sabled.<BR>  a =3D 1.4, b =3D pixel, z =3D p1, w =3D p2:<BR>  z=
1 =3D a - b*w - sqr(z)<BR>  w =3D z<BR>  z =3D z1,<BR>  la=
stsqr+|w| < 1000000<BR>}</DIV> <DIV> </DIV> <DIV>Henon_M4 { ; Scr=
een coordinates are parameters 'a' and 'b'.<BR>    &n=
bsp;      ; Escape pixels escaped radius 1000. T=
ry non-standard inside options with<BR>     &nbs=
p;     ; periodicity checking enabled. Composite view=
.<BR>  a =3D real(pixel), b =3D imag(pixel), z =3D 0, r =3D 0, done =
=3D 0:<BR>  z =3D a - b*imag(z) - sqr(real(z)) + (0,1)*real(z),<BR>&=
nbsp; IF (|z| > 1000000)<BR>    IF (r =3D=3D 0)<BR>&nbs=
p;     z =3D 1<BR>      r =3D=
 1<BR>    ELSEIF (r =3D=3D 1)<BR>    &=
nbsp; z =3D (0,1)<BR>      r =3D 2<BR> &nbs=
p;  ELSEIF (r =3D=3D 2)<BR>      z =3D -1<B=
R>      r =3D 3<BR>    ELSEIF (r =
=3D=3D 3)<BR>      z =3D -(0,1)<BR>  &=
nbsp;   r =3D 4<BR>    ELSEIF (r =3D=3D 4)<BR>&n=
bsp;     z =3D 1+(0,1)<BR>    &nb=
sp; r =3D 5<BR>    ELSEIF (r =3D=3D 5)<BR>  &nbs=
p;   z =3D 1-(0,1)<BR>      r =3D 6<BR=
>    ELSEIF (r =3D=3D 6)<BR>     =
 z =3D -1+(0,1)<BR>      r =3D 7<BR>  =
  ELSEIF (r =3D=3D 7)<BR>      z =3D -1-(0,=
1)<BR>      r =3D 8<BR>    ELSE<B=
R>      done =3D 1<BR>    ENDIF<B=
R>  ENDIF<BR>  done =3D=3D 0<BR>}</DIV> <DIV> </DIV> <DIV>=
Henon_M5 { ; Henon map on complex numbers. Screen coordinates are paramet=
er 'b'.<BR>           ;=
 Escape pixels escaped radius 1000. Try non-standard inside options with<=
BR>           ; periodi=
city checking DISabled. Composite view.<BR>  a =3D 1.4, b =3D pixel,=
 z =3D 0, w =3D 0, r =3D 0, done =3D 0:<BR>  z1 =3D a - b*w - sqr(z)=
<BR>  w =3D z<BR>  z =3D z1,<BR>  IF (lastsqr+|w| > 100=
0000)<BR>    IF (r =3D=3D 0)<BR>    &n=
bsp; z =3D 1<BR>      w =3D 0<BR>  &nb=
sp;   r =3D 1<BR>    ELSEIF (r =3D=3D 1)<BR>&nbs=
p;     z =3D 0<BR>      w =3D=
 1<BR>      r =3D 2<BR>    ELSEIF=
 (r =3D=3D 2)<BR>      z =3D -1<BR>  &=
nbsp;   w =3D 0<BR>      r =3D 3<BR>&n=
bsp;   ELSEIF (r =3D=3D 3)<BR>      z =
=3D 0<BR>      w =3D -1<BR>   &nb=
sp;  r =3D 4<BR>    ELSEIF (r =3D=3D 4)<BR> &nbs=
p;    z =3D 1<BR>      w =3D 1<BR=
>      r =3D 5<BR>    ELSEIF (r =3D=
=3D 5)<BR>      z =3D 1<BR>   &nb=
sp;  w =3D -1<BR>      r =3D 6<BR> &nb=
sp;  ELSEIF (r =3D=3D 6)<BR>      z =3D -1<=
BR>      w =3D 1<BR>    &nbs=
p; r =3D 7<BR>    ELSEIF (r =3D=3D 7)<BR>   =
;   z =3D -1<BR>      w =3D -1<BR>&nbs=
p;     r =3D 8<BR>    ELSE<BR> &n=
bsp;    done =3D 1<BR>    ENDIF<BR>  E=
NDIF<BR>  done =3D=3D 0<BR>}</DIV> <DIV> </DIV> <DIV>Henon_J1 {=
 ; Henon map on complex numbers.<BR>      &=
nbsp;    ; p1 and p2 are a and b. Screen coordinates are y=
. p3 is x.<BR>          =
; ; Escape pixels escaped radius 1000. Try non-standard inside options wi=
th<BR>           ; peri=
odicity checking DISabled.<BR>  a =3D p1, b =3D p2, z =3D p3, w =3D =
pixel:<BR>  z1 =3D a - b*w - sqr(z)<BR>  w =3D z<BR>  z =3D=
 z1,<BR>  lastsqr+|w| < 1000000<BR>}</DIV> <DIV> </DIV> <DIV=
>Henon_J2 { ; Henon map on complex numbers.<BR>    &n=
bsp;      ; p1 and p2 are a and b. Screen coordi=
nates are real(x), real(y). p3 is imag(x), imag(y).<BR>   =
        ; Escape pixels escaped radius=
 1000. Try non-standard inside options with<BR>    &n=
bsp;      ; periodicity checking DISabled.<BR>&n=
bsp; a =3D p1, b =3D p2, z =3D real(pixel) + (0,1)*real(p3), w =3D imag(p=
ixel) + (0,1)*imag(p3):<BR>  z1 =3D a - b*w - sqr(z)<BR>  w =3D=
 z<BR>  z =3D z1,<BR>  lastsqr+|w| < 1000000<BR>}</DIV> <DIV=
> </DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private,=
 Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">http:=
//www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0000_01C0EF9F.7F321100--

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-------------------------------------------------------------------------------

From: "Thierry B." <[e-mail]>
Subject: Re: (fractint) Some intriguing stuff.
Date: 08 Jun 2001 07:25:49 +0000

> These formulas make it possible to investigate the escape behavior of t=
he Henon map:
=20
> x -> a - by + x^2
> y -> x

    I've also a few research on the mappin of H=E9non diagram.
    http://la.buvette.org/fractales/map_henon.euh
    Sorry, this is only a Fortran source, but I can write some
    explanation in english this weekend.

=20
--=20
Thierry, 42++

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-------------------------------------------------------------------------------

From: Guy Marson <[e-mail]>
Subject: Re: (fractint) Some intriguing stuff.
Date: 08 Jun 2001 09:57:44 +0200

At 07:25 08/06/01 +0000, you wrote:
>> These formulas make it possible to investigate the escape behavior of
the Henon map:
>=20
>> x -> a - by + x^2
>> y -> x
>
>    I've also a few research on the mappin of H=E9non diagram.
>    http://la.buvette.org/fractales/map_henon.euh
>    Sorry, this is only a Fortran source, but I can write some
>    explanation in english this weekend.


mais pas dans la buvette, avec des Jupiler s.v.p. (hickkk..)=20

>
>=20
>--=20
>Thierry, 42++
>

cheers,=20

guy 47+





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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  08-06-01  (Too Much Fractal [7])
Date: 08 Jun 2001 09:15:51 EDT


Classic FOTD -- June 08, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

It seems strange to denigrate a fractal with a rating two points
above average, but that's what I feel I must do with today's
image.

Sometimes, even in the world of fractals, it's possible to have
too much of a good thing.  Today's image is an example of such
fractal excess.  The image simply goes too far with too little.
The midget at the center is too small to act as a center of
attention, leaving the surrounding decorations with nothing to
decorate.  And the color is excessive.  Vibrant color can be
spectacular when it is done properly.  When it's not done right,
the result is boring gaudiness.  Today's image just doesn't give
me that "this color is right" feeling.

Oh, the scene has a surface glitter that brings its rating up to
a 7, but it lacks the depth that could bring a rating of 8 or 9.
I named the image "Too Much Fractal" in response to my feelings
about it.

Today's scene lies in another valley, directly across the bay
from yesterday's, though it is some distance back from the
shoreline, and at a considerable greater depth.  It is actually
located at the center of a figure-8 ring, which the area is
filled with.

The 4-1/2 minute render time is marginal, making it the viewers
choice whether to go online and download the GIF image from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today started with rain, but the rain ended
in mid-morning, and the sun returned in mid-afternoon, sending
the temperature up to 75F (24C).  The fractal cats celebrated by
venturing cautiously into the still-wet grass.

It's now time to get busy on other things, so until next time,
take care and check the fractal on the cover of the latest issue
of "Skeptic" magazine.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Too_Much_Fractal   { ; time=0:04:25.66--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=b
  center-mag=+10.09705566264443000/-15.5438271495980\
  4000/1.007928e+011/1/166.953/-0.502
  params=-0.6/-1.3/-0.006/-3/0/1000 float=y
  maxiter=1500 inside=255 logmap=133 periodicity=10
  colors=0800DL0DL0DO0DR0DU0DX0D_0Db0De0Dh0Dk0Dn0Dq6\
  FtGGwPDzZIzhQzrXzzdzzlzztzzwzwzwYjlnZrzQyzGzZIf0IN\
  0QW0V`0bf0hl0pt0vz0wz1wz1wz8wzGwzNrzWjzbbzjVzrOzzG\
  zzDzzDzzDzzDzzDzzDvzDnzDfyD`tDUpGLlIGhM8dO1`R0YT0W\
  V0ZX0bX0dX0hX0jX0nX1rX4tX8yXAzXEzXHzXJzwJzwPywUvwY\
  tw`vwYywWywRzwPzwLzwJzwGzwEzwCzwGzwHztJzpNzjPzdRz`\
  WzVYzQZzM`zOdzQfzRjzTlzVnzXrzZtz`yzbzzbzzfzzhzzlzz\
  nzzrzztzzwzzwzlnzWbnETZ0IL0D80F40I14M0EQ0LT0UX0bb0\
  jf0rj0zn0zr0zv0zt0zr0zp0zp0z`0jO0PD06D0ED0JD0RD2YG\
  6dMAjQErVHyZLzbNvfPphPhlRbnRYrRPtUJwUEwU6wW1wW0wW0\
  rN0bG0O80T00Z00d00j00n00r00v06w0Cw0Jw0Rw0Yw0dw0lw0\
  rw0fw4YwUNwrEwzCwzCwzCvzCtzArzApzAnzAlzAlzHvzNwzWw\
  z`wzfwzbwz`wzZwzWnzUdzRVzYRzbOzfKzlGzpDtvDpzDjzDdz\
  DZzDUzDNzDJzDLzDNrIPfTRWbULlWAvY0wZ0w`0wb0wb0wW2wN\
  JfH`OApD4rD4tD6vD6CwfGwdHwbLwZNwYRwWUwUZwWdwYhwZnw\
  `rwbywdzwflwnYwtHwz2wz0D0
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Hairy Newton
Date: 08 Jun 2001 21:29:56 -0400


------=_NextPart_001_0000_01C0F062.2AD5F4A0
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Yesterday evening I set out to find an interesting family of Newton-based=
 Mandelbrot mappings. The result was the collection of formulae below.

You'll note the lack of 3D disease -- false alarm. All my posts to anothe=
r listserv had it, but I now think it must be that listserv rather than M=
SN Exploder. Or rather, some interaction between the two (since some post=
s from that listserv don't have it), like the weird "email laser" that ha=
ppened with this listserv last week (lots of peoples' messages were being=
 duplicated, but for some reason mine were showing up in sets of five or =
six!)...Anyone who's an expert on listservs care to speculate further on =
what might be going on? One thing is clear: recent mail software and list=
servs have unnecessary complexity, and while we like complexity in our fr=
actals, we could do without chaos erupting in the mail system we depend o=
n to communicate here...

The hrynewt_j and hrynewt_m formulae iterate Newton's method for p(z) =3D=
 (z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is the toleranc=
e, an inverse bailout radius about the roots of p. The Mandelbrot variant=
 has a vary over the screen while initial z is zero; this is a critical p=
oint but not a root of p for n real and greater than 2. You can plug in o=
ther values of n -- arbitrary negative or even complex values -- but won'=
t generally be able to find minibrots unless n has a positive real part g=
reater than two. If n is not an integer, there will be branch cuts in bot=
h the Mandelbrot and the Julia variants.

The hrynewtnnn_j and _m formulae are optimized versions with specific val=
ues for n, mostly small positive integers. They avoid a slow arbitrary ex=
ponentiation, and for the smaller values of n re-use powers that are used=
 on both sides of the polynomial or its derivative. The hrynewt2_m formul=
a also has the feature of using a critical point for initial z, instead o=
f zero (which is *not* a critical point for n =3D 2). The result is a pro=
per Mandelbrot view, but it has a branch cut due to a square root in the =
calculation of the critical point, which is a-dependent. The branch cut h=
as been intentionally manipulated to put it in a fairly unobtrusive place=
, but can't be eliminated; the full Mandelbrot for this one lives on a tw=
o-layer Riemann sheet like that of the square root function.

The hrynewtnnn_m formulae also use an (XAXIS) symmetry declaration. (The =
generic hrynewt_m can't use this without trashing the output for non-real=
 values of n.)

Observations:
* Certain choices of n produce three-fold-symmetric Mandelbrot sets. Find=
 out which!
* Mangled and occasionally also intact Mandelbrots can be extracted when =
n is "strange" but has a real part greater than 2.
* You get radial petals with n real, concentric patterns with n imaginary=
, and logarithmic spirals with complex n; the ratio of
   real to imaginary parts determines whether the spiral is steep (n clos=
e to real) or shallow (n close to imaginary).
* The Mandelbrots are always quadratic -- for real n > 2, the critical po=
int at zero is nondegenerate, and the critical point
   pair for hrynewt2_m is degenerate only at one specific value of a.

The formula file begins with an extensive comment that details the mathem=
atical constructions that informed their design.

comment {
  We want a Newton's method with a large number of basins, most of which =
are fixed and predictable.
  This is accomplished by choosing a polynomial function to solve compose=
d of two factors, one with many fixed roots,
  the other with a few mobile ones:
  p(z) =3D (z^n-1)(z^3-az-1).
  The Newton iteration is:
  z -> r(z)
  where
  r(z) =3D z - p(z)/p'(z)
       =3D (zp'(z) - p(z))/p'(z)
  We easily discover p'(z) to be
  p'(z) =3D (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)
        =3D (3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a
  so
  (zp'(z) - p(z)) =3D (z^n-1)(3z^3-az)+(nz^n)(z^3-az-1) - (z^n-1)(z^3-az-=
1)
                  =3D (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)
                  =3D (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1
  and
  r(z) =3D ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)/((3+n)z^(n+2)=
 - a(n+1)z^n - nz^(n-1) - 3z^2 + a)
  Using the quotient rule the numerator of r'(z) is
  ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)((n+2)(n+3)z^(n+2) - an=
(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -
    ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+2)(n+3)z^(n+1) - =
an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
  which factors into
  ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
  and
  ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 + az) - ((2+n)z^(n+3) - anz=
^(n+1) - (n-1)z^n - 2z^3 - 1)
  which simplifies to
  z^(n+3) - az^(n+1) - z^n - z^3 + az + 1
  Note that p(z) =3D z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.
  Thus the critical points of r(z) are the roots of p(z) and the roots of
  q(z) :=3D ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
  These latter are the "interesting" critical points, as the other critic=
al points of r(z) are all superattracting.
  Note that q(z) is divisible by z, so 0 is an "interesting" critical poi=
nt of r(z), for n not one of 2, 1, or -1.
  This is the critical point used in the below hrynewt_m formulas except =
for hrynewt2_m. For n =3D 2,
  q(z)/2 =3D 10z^3 - 3(a+1)z - 1
  Put z =3D y + (a+1)/10y to get
  q(z)/2 =3D y^6 - y^3/10 + (a+1)^3/1000
  so
  2y^3 =3D 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),
  y =3D ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)
  and
  z =3D ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10 +/=
-sqrt(1/100 - 4(a+1)^3)/1000)/2)^(1/3)
}

hrynewt_j { ; p1 is Julia parameter, p2 is exponent n, p3 is tolerance (i=
f 0, will act like 0.001).
            ; SLOW. Use predefined hrynewtnnn_j where possible.
  z =3D pixel, a =3D p1, n =3D p2, n1 =3D n - 1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D z^n1
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + n*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt_m { ; p2 is exponent n, p3 is tolerance (if 0, will act like 0.00=
1).
            ; SLOW. Use predefined hrynewtnnn_m where possible.
  z =3D 0, a =3D pixel, n =3D p2, n1 =3D n - 1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D z^n1
  zn =3D z*zn1
  zno =3D (zn - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + n*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt2_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 2.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z2 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 2*z*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt2_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 2.
  a =3D pixel,
  ap1 =3D a + 1,
  IF((real(ap1) >=3D 0) || ((abs(real(ap1))*(3^(0.5))) < abs(imag(ap1))))
    t =3D ((0.1 + (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
  ELSE
    t =3D ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
  ENDIF
  z =3D t + 0.1*ap1/t, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z2 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 2*z*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt3_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 3.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z3 - 1)
  zzz =3D zno - a*z
  tz2 =3D 3*z2
  pz =3D zno*zzz
  ppz =3D zno*(tz2 - a) + tz2*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 3.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z3 - 1)
  zzz =3D zno - a*z
  tz2 =3D 3*z2
  pz =3D zno*zzz
  ppz =3D zno*(tz2 - a) + tz2*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt4_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 4.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z*z3 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 4*z3*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt4_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 4.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z*z3 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 4*z3*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 5.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(z2)
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 5.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(z2)
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt17_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act li=
ke 0.001).
              ; n =3D 17.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(z2)))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 17*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
              ; n =3D 17.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(z2)))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 17*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act li=
ke 0.001).
              ; n =3D 33.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(sqr(z2))))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 33*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt33_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
              ; n =3D 33.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(sqr(z2))))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 33*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}<br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <a=
 href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0000_01C0F062.2AD5F4A0
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>Yesterday even=
ing I set out to find an interesting family of Newton-based Mandelbrot ma=
ppings. The result was the collection of formulae below.</DIV> <DIV> =
;</DIV> <DIV>You'll note the lack of 3D disease -- false alarm. All my po=
sts to another listserv had it, but I now think it must be that listserv =
rather than MSN Exploder. Or rather, some interaction between the two (si=
nce some posts from that listserv don't have it), like the weird "em=
ail laser" that happened with this listserv last week (lots of peoples' m=
essages were being duplicated, but for some reason mine were showing up i=
n sets of five or six!)...Anyone who's an expert on listservs care to spe=
culate further on what might be going on? One thing is clear: recent mail=
 software and listservs have unnecessary complexity, and while we like co=
mplexity in our fractals, we could do without chaos erupting in the mail =
system we depend on to communicate here...</DIV> <DIV> </DIV> <DIV>T=
he hrynewt_j and hrynewt_m formulae iterate Newton's method for p(z) =3D =
(z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is the tolerance=
, an inverse bailout radius about the roots of p. The Mandelbrot variant =
has a vary over the screen while initial z is zero; this is a critical po=
int but not a root of p for n real and greater than 2. You can =
plug in other values of n -- arbitrary negative or even complex values --=
 but won't generally be able to find minibrots unless n has a positive re=
al part greater than two. If n is not an integer, there will be branch cu=
ts in both the Mandelbrot and the Julia variants.</DIV> <DIV> </DIV>=
 <DIV>The hrynewtnnn_j and _m formulae are optimized versions with specif=
ic values for n, mostly small positive integers. They avoid a slow arbitr=
ary exponentiation, and for the smaller values of n re-use powers that ar=
e used on both sides of the polynomial or its derivative. The hrynewt2_m =
formula also has the feature of using a critical point for initial z, ins=
tead of zero (which is *not* a critical point for n =3D 2). The result is=
 a proper Mandelbrot view, but it has a branch cut due to a square root i=
n the calculation of the critical point, which is a-dependent. The branch=
 cut has been intentionally manipulated to put it in a fairly unobtrusive=
 place, but can't be eliminated; the full Mandelbrot for this one lives o=
n a two-layer Riemann sheet like that of the square root function.</DIV> =
<DIV> </DIV> <DIV>The hrynewtnnn_m formulae also use an (XAXIS) symm=
etry declaration. (The generic hrynewt_m can't use this without trashing =
the output for non-real values of n.)</DIV> <DIV> </DIV> <DIV>Observ=
ations:</DIV> <DIV>* Certain choices of n produce three-fold-symmetric Ma=
ndelbrot sets. Find out which!</DIV> <DIV>* Mangled and occasionally also=
 intact Mandelbrots can be extracted when n is "strange" but has a real p=
art greater than 2.</DIV> <DIV>* You get radial petals with n real, conce=
ntric patterns with n imaginary, and logarithmic spirals with complex n; =
the ratio of</DIV> <DIV>   real to imaginary parts determines w=
hether the spiral is steep (n close to real) or shallow (n close to imagi=
nary).</DIV> <DIV>* The Mandelbrots are always quadratic -- for real n &g=
t; 2, the critical point at zero is nondegenerate, and the critical point=
</DIV> <DIV>   pair for hrynewt2_m is degenerate only at o=
ne specific value of a.</DIV> <DIV> </DIV> <DIV>The formula file beg=
ins with an extensive comment that details the mathematical constructions=
 that informed their design.</DIV> <DIV> </DIV> <DIV>comment {<BR>&n=
bsp; We want a Newton's method with a large number of basins, most of whi=
ch are fixed and predictable.<BR>  This is accomplished by choosing =
a polynomial function to solve composed of two factors, one with many fix=
ed roots,<BR>  the other with a few mobile ones:<BR>  p(z) =3D =
(z^n-1)(z^3-az-1).<BR>  The Newton iteration is:<BR>  z -> r=
(z)<BR>  where<BR>  r(z) =3D z - p(z)/p'(z)<BR>  &nbs=
p;    =3D (zp'(z) - p(z))/p'(z)<BR>  We easily discov=
er p'(z) to be<BR>  p'(z) =3D (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)=
<BR>        =3D (3+n)z^(n+2) - a(n+1)z=
^n - nz^(n-1) - 3z^2 + a<BR>  so<BR>  (zp'(z) - p(z)) =3D (z^n-=
1)(3z^3-az)+(nz^n)(z^3-az-1) - (z^n-1)(z^3-az-1)<BR>   &nb=
sp;           &nbs=
p;  =3D (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)<BR>    =
            &=
nbsp; =3D (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1<BR>  and<BR=
>  r(z) =3D ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)/((3+n)z=
^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)<BR>  Using the quotient ru=
le the numerator of r'(z) is<BR>  ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-=
1) - 3z^2 + a)((n+2)(n+3)z^(n+2) - an(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -<B=
R>    ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+=
2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)<BR>  which fac=
tors into<BR>  ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) -=
 6z)<BR>  and<BR>  ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 =
+ az) - ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)<BR>  which =
simplifies to<BR>  z^(n+3) - az^(n+1) - z^n - z^3 + az + 1<BR> =
 Note that p(z) =3D z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.<BR>  Th=
us the critical points of r(z) are the roots of p(z) and the roots of<BR>=
  q(z) :=3D ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z=
)<BR>  These latter are the "interesting" critical points, as the ot=
her critical points of r(z) are all superattracting.<BR>  Note that =
q(z) is divisible by z, so 0 is an "interesting" critical point of r(z), =
for n not one of 2, 1, or -1.<BR>  This is the critical point used i=
n the below hrynewt_m formulas except for hrynewt2_m. For n =3D 2,<BR>&nb=
sp; q(z)/2 =3D 10z^3 - 3(a+1)z - 1<BR>  Put z =3D y + (a+1)/10y to g=
et<BR>  q(z)/2 =3D y^6 - y^3/10 + (a+1)^3/1000<BR>  so<BR> =
; 2y^3 =3D 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),<BR>  y =3D ((1/10 +/=
-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)<BR>  and<BR>  z =3D ((1/=
10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10 +/-sqrt(1/100 =
- 4(a+1)^3)/1000)/2)^(1/3)<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt_j { =
; p1 is Julia parameter, p2 is exponent n, p3 is tolerance (if 0, will ac=
t like 0.001).<BR>         &=
nbsp;  ; SLOW. Use predefined hrynewtnnn_j where possible.<BR> =
 z =3D pixel, a =3D p1, n =3D p2, n1 =3D n - 1, r =3D p3<BR>  IF(r =3D=
=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>&=
nbsp; z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D z^n1<BR> =
; zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D z=
no*zzz<BR>  ppz =3D zno*(3*z2 - a) + n*zn1*zzz<BR>  z =3D z - p=
z/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt_m =
{ ; p2 is exponent n, p3 is tolerance (if 0, will act like 0.001).<BR>&nb=
sp;           ; SLOW. U=
se predefined hrynewtnnn_m where possible.<BR>  z =3D 0, a =3D pixel=
, n =3D p2, n1 =3D n - 1, r =3D p3<BR>  IF(r =3D=3D 0)<BR> &nbs=
p;  r =3D 0.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<=
BR>  z3 =3D z*z2<BR>  zn1 =3D z^n1<BR>  zn =3D z*zn1<BR>&n=
bsp; zno =3D (zn - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D z=
no*zzz<BR>  ppz =3D zno*(3*z2 - a) + n*zn1*zzz<BR>  z =3D z - p=
z/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt2_j=
 { ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.001).<=
BR>           &nbs=
p; ; n =3D 2.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  IF(r =3D=
=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>&=
nbsp; z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z2 - 1)<BR>&=
nbsp; zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D z=
no*(3*z2 - a) + 2*z*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r=
<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt2_m (XAXIS) { ; p3 is tolerance=
 (if 0, will act like 0.001).<BR>      &nbs=
p;      ; n =3D 2.<BR>  a =3D pixel,<BR>&nb=
sp; ap1 =3D a + 1,<BR>  IF((real(ap1) >=3D 0) || ((abs(real(ap1))=
*(3^(0.5))) < abs(imag(ap1))))<BR>    t =3D ((0.1 + (0.=
01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),<BR>  ELSE<BR>  &=
nbsp; t =3D ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),<BR> =
; ENDIF<BR>  z =3D t + 0.1*ap1/t, r =3D p3<BR>  IF(r =3D=3D 0)<=
BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>  z=
2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z2 - 1)<BR>  z=
zz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(3*z=
2 - a) + 2*z*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</=
DIV> <DIV> </DIV> <DIV>hrynewt3_j { ; p1 is Julia parameter, p3 is t=
olerance (if 0, will act like 0.001).<BR>     &n=
bsp;       ; n =3D 3.<BR>  z =3D pixel=
, a =3D p1, r =3D p3<BR>  IF(r =3D=3D 0)<BR>    r =3D=
 0.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D=
 z*z2<BR>  zno =3D (z3 - 1)<BR>  zzz =3D zno - a*z<BR>  tz=
2 =3D 3*z2<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(tz2 - a) + tz2=
*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV>&n=
bsp;</DIV> <DIV>hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act li=
ke 0.001).<BR>          =
;   ; n =3D 3.<BR>  z =3D 0, a =3D pixel, r =3D p3<BR>&nbs=
p; IF(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>&n=
bsp; :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z=
3 - 1)<BR>  zzz =3D zno - a*z<BR>  tz2 =3D 3*z2<BR>  pz =3D=
 zno*zzz<BR>  ppz =3D zno*(tz2 - a) + tz2*zzz<BR>  z =3D z - pz=
/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt4_j =
{ ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.001).<B=
R>            =
; ; n =3D 4.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  IF(r =3D=
=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>&=
nbsp; z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z*z3 - 1)<BR=
>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D=
 zno*(3*z2 - a) + 4*z3*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| >=
; r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt4_m (XAXIS) { ; p3 is tolera=
nce (if 0, will act like 0.001).<BR>      &=
nbsp;      ; n =3D 4.<BR>  z =3D 0, a =3D p=
ixel, r =3D p3<BR>  IF(r =3D=3D 0)<BR>    r =3D 0.001=
<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z=
2<BR>  zno =3D (z*z3 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR> =
 pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 4*z3*zzz<BR>  z =3D=
 z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hryn=
ewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.=
001).<BR>          &nbs=
p;  ; n =3D 5.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  I=
F(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR> =
 :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D sqr(z2=
)<BR>  zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR> =
; pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz<BR>  z=
 =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>=
hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).<BR>&n=
bsp;            ; =
n =3D 5.<BR>  z =3D 0, a =3D pixel, r =3D p3<BR>  IF(r =3D=3D 0=
)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR> =
 z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D sqr(z2)<BR>  =
zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno=
*zzz<BR>  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz<BR>  z =3D z - pz/=
ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt17_j =
{ ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.001).<B=
R>            =
;  ; n =3D 17.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  I=
F(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR> =
 :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D sqr(sq=
r(sqr(z2)))<BR>  zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1=
)<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 17*zn1*zzz<=
BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> <=
/DIV> <DIV>hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0=
.001).<BR>          &nb=
sp;   ; n =3D 17.<BR>  z =3D 0, a =3D pixel, r =3D p3<BR>&=
nbsp; IF(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR=
>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D=
 sqr(sqr(sqr(z2)))<BR>  zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - =
a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 17*z=
n1*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV>=
 </DIV> <DIV>hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance =
(if 0, will act like 0.001).<BR>       =
;       ; n =3D 33.<BR>  z =3D pixel, =
a =3D p1, r =3D p3<BR>  IF(r =3D=3D 0)<BR>    r =3D 0=
.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D=
 z*z2<BR>  zn1 =3D sqr(sqr(sqr(sqr(z2))))<BR>  zno =3D (z*zn1 -=
 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  p=
pz =3D zno*(3*z2 - a) + 33*zn1*zzz<BR>  z =3D z - pz/ppz,<BR>  =
|pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt33_m (XAXIS) { ; p3 =
is tolerance (if 0, will act like 0.001).<BR>    &nbs=
p;         ; n =3D 33.<BR>  =
z =3D 0, a =3D pixel, r =3D p3<BR>  IF(r =3D=3D 0)<BR>  &n=
bsp; r =3D 0.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>&=
nbsp; z3 =3D z*z2<BR>  zn1 =3D sqr(sqr(sqr(sqr(z2))))<BR>  zno =
=3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz=
<BR>  ppz =3D zno*(3*z2 - a) + 33*zn1*zzz<BR>  z =3D z - pz/ppz=
,<BR>  |pz| > r<BR>}<BR></DIV></BODY></HTML><DIV><BR><br clear=3D=
all><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http=
://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Hairy Newton
Date: 08 Jun 2001 21:29:56 -0400


------=_NextPart_001_0000_01C0F062.2AD5F4A0
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Yesterday evening I set out to find an interesting family of Newton-based=
 Mandelbrot mappings. The result was the collection of formulae below.

You'll note the lack of 3D disease -- false alarm. All my posts to anothe=
r listserv had it, but I now think it must be that listserv rather than M=
SN Exploder. Or rather, some interaction between the two (since some post=
s from that listserv don't have it), like the weird "email laser" that ha=
ppened with this listserv last week (lots of peoples' messages were being=
 duplicated, but for some reason mine were showing up in sets of five or =
six!)...Anyone who's an expert on listservs care to speculate further on =
what might be going on? One thing is clear: recent mail software and list=
servs have unnecessary complexity, and while we like complexity in our fr=
actals, we could do without chaos erupting in the mail system we depend o=
n to communicate here...

The hrynewt_j and hrynewt_m formulae iterate Newton's method for p(z) =3D=
 (z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is the toleranc=
e, an inverse bailout radius about the roots of p. The Mandelbrot variant=
 has a vary over the screen while initial z is zero; this is a critical p=
oint but not a root of p for n real and greater than 2. You can plug in o=
ther values of n -- arbitrary negative or even complex values -- but won'=
t generally be able to find minibrots unless n has a positive real part g=
reater than two. If n is not an integer, there will be branch cuts in bot=
h the Mandelbrot and the Julia variants.

The hrynewtnnn_j and _m formulae are optimized versions with specific val=
ues for n, mostly small positive integers. They avoid a slow arbitrary ex=
ponentiation, and for the smaller values of n re-use powers that are used=
 on both sides of the polynomial or its derivative. The hrynewt2_m formul=
a also has the feature of using a critical point for initial z, instead o=
f zero (which is *not* a critical point for n =3D 2). The result is a pro=
per Mandelbrot view, but it has a branch cut due to a square root in the =
calculation of the critical point, which is a-dependent. The branch cut h=
as been intentionally manipulated to put it in a fairly unobtrusive place=
, but can't be eliminated; the full Mandelbrot for this one lives on a tw=
o-layer Riemann sheet like that of the square root function.

The hrynewtnnn_m formulae also use an (XAXIS) symmetry declaration. (The =
generic hrynewt_m can't use this without trashing the output for non-real=
 values of n.)

Observations:
* Certain choices of n produce three-fold-symmetric Mandelbrot sets. Find=
 out which!
* Mangled and occasionally also intact Mandelbrots can be extracted when =
n is "strange" but has a real part greater than 2.
* You get radial petals with n real, concentric patterns with n imaginary=
, and logarithmic spirals with complex n; the ratio of
   real to imaginary parts determines whether the spiral is steep (n clos=
e to real) or shallow (n close to imaginary).
* The Mandelbrots are always quadratic -- for real n > 2, the critical po=
int at zero is nondegenerate, and the critical point
   pair for hrynewt2_m is degenerate only at one specific value of a.

The formula file begins with an extensive comment that details the mathem=
atical constructions that informed their design.

comment {
  We want a Newton's method with a large number of basins, most of which =
are fixed and predictable.
  This is accomplished by choosing a polynomial function to solve compose=
d of two factors, one with many fixed roots,
  the other with a few mobile ones:
  p(z) =3D (z^n-1)(z^3-az-1).
  The Newton iteration is:
  z -> r(z)
  where
  r(z) =3D z - p(z)/p'(z)
       =3D (zp'(z) - p(z))/p'(z)
  We easily discover p'(z) to be
  p'(z) =3D (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)
        =3D (3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a
  so
  (zp'(z) - p(z)) =3D (z^n-1)(3z^3-az)+(nz^n)(z^3-az-1) - (z^n-1)(z^3-az-=
1)
                  =3D (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)
                  =3D (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1
  and
  r(z) =3D ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)/((3+n)z^(n+2)=
 - a(n+1)z^n - nz^(n-1) - 3z^2 + a)
  Using the quotient rule the numerator of r'(z) is
  ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)((n+2)(n+3)z^(n+2) - an=
(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -
    ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+2)(n+3)z^(n+1) - =
an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
  which factors into
  ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
  and
  ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 + az) - ((2+n)z^(n+3) - anz=
^(n+1) - (n-1)z^n - 2z^3 - 1)
  which simplifies to
  z^(n+3) - az^(n+1) - z^n - z^3 + az + 1
  Note that p(z) =3D z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.
  Thus the critical points of r(z) are the roots of p(z) and the roots of
  q(z) :=3D ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
  These latter are the "interesting" critical points, as the other critic=
al points of r(z) are all superattracting.
  Note that q(z) is divisible by z, so 0 is an "interesting" critical poi=
nt of r(z), for n not one of 2, 1, or -1.
  This is the critical point used in the below hrynewt_m formulas except =
for hrynewt2_m. For n =3D 2,
  q(z)/2 =3D 10z^3 - 3(a+1)z - 1
  Put z =3D y + (a+1)/10y to get
  q(z)/2 =3D y^6 - y^3/10 + (a+1)^3/1000
  so
  2y^3 =3D 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),
  y =3D ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)
  and
  z =3D ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10 +/=
-sqrt(1/100 - 4(a+1)^3)/1000)/2)^(1/3)
}

hrynewt_j { ; p1 is Julia parameter, p2 is exponent n, p3 is tolerance (i=
f 0, will act like 0.001).
            ; SLOW. Use predefined hrynewtnnn_j where possible.
  z =3D pixel, a =3D p1, n =3D p2, n1 =3D n - 1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D z^n1
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + n*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt_m { ; p2 is exponent n, p3 is tolerance (if 0, will act like 0.00=
1).
            ; SLOW. Use predefined hrynewtnnn_m where possible.
  z =3D 0, a =3D pixel, n =3D p2, n1 =3D n - 1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D z^n1
  zn =3D z*zn1
  zno =3D (zn - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + n*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt2_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 2.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z2 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 2*z*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt2_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 2.
  a =3D pixel,
  ap1 =3D a + 1,
  IF((real(ap1) >=3D 0) || ((abs(real(ap1))*(3^(0.5))) < abs(imag(ap1))))
    t =3D ((0.1 + (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
  ELSE
    t =3D ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
  ENDIF
  z =3D t + 0.1*ap1/t, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z2 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 2*z*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt3_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 3.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z3 - 1)
  zzz =3D zno - a*z
  tz2 =3D 3*z2
  pz =3D zno*zzz
  ppz =3D zno*(tz2 - a) + tz2*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 3.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z3 - 1)
  zzz =3D zno - a*z
  tz2 =3D 3*z2
  pz =3D zno*zzz
  ppz =3D zno*(tz2 - a) + tz2*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt4_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 4.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z*z3 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 4*z3*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt4_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 4.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zno =3D (z*z3 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 4*z3*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act lik=
e 0.001).
             ; n =3D 5.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(z2)
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
             ; n =3D 5.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(z2)
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt17_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act li=
ke 0.001).
              ; n =3D 17.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(z2)))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 17*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
              ; n =3D 17.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(z2)))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 17*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act li=
ke 0.001).
              ; n =3D 33.
  z =3D pixel, a =3D p1, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(sqr(z2))))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 33*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}

hrynewt33_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
              ; n =3D 33.
  z =3D 0, a =3D pixel, r =3D p3
  IF(r =3D=3D 0)
    r =3D 0.001
  ENDIF
  :
  z2 =3D sqr(z)
  z3 =3D z*z2
  zn1 =3D sqr(sqr(sqr(sqr(z2))))
  zno =3D (z*zn1 - 1)
  zzz =3D (z3 - a*z - 1)
  pz =3D zno*zzz
  ppz =3D zno*(3*z2 - a) + 33*zn1*zzz
  z =3D z - pz/ppz,
  |pz| > r
}<br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <a=
 href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0000_01C0F062.2AD5F4A0
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>Yesterday even=
ing I set out to find an interesting family of Newton-based Mandelbrot ma=
ppings. The result was the collection of formulae below.</DIV> <DIV> =
;</DIV> <DIV>You'll note the lack of 3D disease -- false alarm. All my po=
sts to another listserv had it, but I now think it must be that listserv =
rather than MSN Exploder. Or rather, some interaction between the two (si=
nce some posts from that listserv don't have it), like the weird "em=
ail laser" that happened with this listserv last week (lots of peoples' m=
essages were being duplicated, but for some reason mine were showing up i=
n sets of five or six!)...Anyone who's an expert on listservs care to spe=
culate further on what might be going on? One thing is clear: recent mail=
 software and listservs have unnecessary complexity, and while we like co=
mplexity in our fractals, we could do without chaos erupting in the mail =
system we depend on to communicate here...</DIV> <DIV> </DIV> <DIV>T=
he hrynewt_j and hrynewt_m formulae iterate Newton's method for p(z) =3D =
(z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is the tolerance=
, an inverse bailout radius about the roots of p. The Mandelbrot variant =
has a vary over the screen while initial z is zero; this is a critical po=
int but not a root of p for n real and greater than 2. You can =
plug in other values of n -- arbitrary negative or even complex values --=
 but won't generally be able to find minibrots unless n has a positive re=
al part greater than two. If n is not an integer, there will be branch cu=
ts in both the Mandelbrot and the Julia variants.</DIV> <DIV> </DIV>=
 <DIV>The hrynewtnnn_j and _m formulae are optimized versions with specif=
ic values for n, mostly small positive integers. They avoid a slow arbitr=
ary exponentiation, and for the smaller values of n re-use powers that ar=
e used on both sides of the polynomial or its derivative. The hrynewt2_m =
formula also has the feature of using a critical point for initial z, ins=
tead of zero (which is *not* a critical point for n =3D 2). The result is=
 a proper Mandelbrot view, but it has a branch cut due to a square root i=
n the calculation of the critical point, which is a-dependent. The branch=
 cut has been intentionally manipulated to put it in a fairly unobtrusive=
 place, but can't be eliminated; the full Mandelbrot for this one lives o=
n a two-layer Riemann sheet like that of the square root function.</DIV> =
<DIV> </DIV> <DIV>The hrynewtnnn_m formulae also use an (XAXIS) symm=
etry declaration. (The generic hrynewt_m can't use this without trashing =
the output for non-real values of n.)</DIV> <DIV> </DIV> <DIV>Observ=
ations:</DIV> <DIV>* Certain choices of n produce three-fold-symmetric Ma=
ndelbrot sets. Find out which!</DIV> <DIV>* Mangled and occasionally also=
 intact Mandelbrots can be extracted when n is "strange" but has a real p=
art greater than 2.</DIV> <DIV>* You get radial petals with n real, conce=
ntric patterns with n imaginary, and logarithmic spirals with complex n; =
the ratio of</DIV> <DIV>   real to imaginary parts determines w=
hether the spiral is steep (n close to real) or shallow (n close to imagi=
nary).</DIV> <DIV>* The Mandelbrots are always quadratic -- for real n &g=
t; 2, the critical point at zero is nondegenerate, and the critical point=
</DIV> <DIV>   pair for hrynewt2_m is degenerate only at o=
ne specific value of a.</DIV> <DIV> </DIV> <DIV>The formula file beg=
ins with an extensive comment that details the mathematical constructions=
 that informed their design.</DIV> <DIV> </DIV> <DIV>comment {<BR>&n=
bsp; We want a Newton's method with a large number of basins, most of whi=
ch are fixed and predictable.<BR>  This is accomplished by choosing =
a polynomial function to solve composed of two factors, one with many fix=
ed roots,<BR>  the other with a few mobile ones:<BR>  p(z) =3D =
(z^n-1)(z^3-az-1).<BR>  The Newton iteration is:<BR>  z -> r=
(z)<BR>  where<BR>  r(z) =3D z - p(z)/p'(z)<BR>  &nbs=
p;    =3D (zp'(z) - p(z))/p'(z)<BR>  We easily discov=
er p'(z) to be<BR>  p'(z) =3D (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)=
<BR>        =3D (3+n)z^(n+2) - a(n+1)z=
^n - nz^(n-1) - 3z^2 + a<BR>  so<BR>  (zp'(z) - p(z)) =3D (z^n-=
1)(3z^3-az)+(nz^n)(z^3-az-1) - (z^n-1)(z^3-az-1)<BR>   &nb=
sp;           &nbs=
p;  =3D (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)<BR>    =
            &=
nbsp; =3D (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1<BR>  and<BR=
>  r(z) =3D ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)/((3+n)z=
^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)<BR>  Using the quotient ru=
le the numerator of r'(z) is<BR>  ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-=
1) - 3z^2 + a)((n+2)(n+3)z^(n+2) - an(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -<B=
R>    ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+=
2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)<BR>  which fac=
tors into<BR>  ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) -=
 6z)<BR>  and<BR>  ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 =
+ az) - ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)<BR>  which =
simplifies to<BR>  z^(n+3) - az^(n+1) - z^n - z^3 + az + 1<BR> =
 Note that p(z) =3D z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.<BR>  Th=
us the critical points of r(z) are the roots of p(z) and the roots of<BR>=
  q(z) :=3D ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z=
)<BR>  These latter are the "interesting" critical points, as the ot=
her critical points of r(z) are all superattracting.<BR>  Note that =
q(z) is divisible by z, so 0 is an "interesting" critical point of r(z), =
for n not one of 2, 1, or -1.<BR>  This is the critical point used i=
n the below hrynewt_m formulas except for hrynewt2_m. For n =3D 2,<BR>&nb=
sp; q(z)/2 =3D 10z^3 - 3(a+1)z - 1<BR>  Put z =3D y + (a+1)/10y to g=
et<BR>  q(z)/2 =3D y^6 - y^3/10 + (a+1)^3/1000<BR>  so<BR> =
; 2y^3 =3D 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),<BR>  y =3D ((1/10 +/=
-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)<BR>  and<BR>  z =3D ((1/=
10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10 +/-sqrt(1/100 =
- 4(a+1)^3)/1000)/2)^(1/3)<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt_j { =
; p1 is Julia parameter, p2 is exponent n, p3 is tolerance (if 0, will ac=
t like 0.001).<BR>         &=
nbsp;  ; SLOW. Use predefined hrynewtnnn_j where possible.<BR> =
 z =3D pixel, a =3D p1, n =3D p2, n1 =3D n - 1, r =3D p3<BR>  IF(r =3D=
=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>&=
nbsp; z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D z^n1<BR> =
; zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D z=
no*zzz<BR>  ppz =3D zno*(3*z2 - a) + n*zn1*zzz<BR>  z =3D z - p=
z/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt_m =
{ ; p2 is exponent n, p3 is tolerance (if 0, will act like 0.001).<BR>&nb=
sp;           ; SLOW. U=
se predefined hrynewtnnn_m where possible.<BR>  z =3D 0, a =3D pixel=
, n =3D p2, n1 =3D n - 1, r =3D p3<BR>  IF(r =3D=3D 0)<BR> &nbs=
p;  r =3D 0.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<=
BR>  z3 =3D z*z2<BR>  zn1 =3D z^n1<BR>  zn =3D z*zn1<BR>&n=
bsp; zno =3D (zn - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D z=
no*zzz<BR>  ppz =3D zno*(3*z2 - a) + n*zn1*zzz<BR>  z =3D z - p=
z/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt2_j=
 { ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.001).<=
BR>           &nbs=
p; ; n =3D 2.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  IF(r =3D=
=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>&=
nbsp; z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z2 - 1)<BR>&=
nbsp; zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D z=
no*(3*z2 - a) + 2*z*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r=
<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt2_m (XAXIS) { ; p3 is tolerance=
 (if 0, will act like 0.001).<BR>      &nbs=
p;      ; n =3D 2.<BR>  a =3D pixel,<BR>&nb=
sp; ap1 =3D a + 1,<BR>  IF((real(ap1) >=3D 0) || ((abs(real(ap1))=
*(3^(0.5))) < abs(imag(ap1))))<BR>    t =3D ((0.1 + (0.=
01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),<BR>  ELSE<BR>  &=
nbsp; t =3D ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),<BR> =
; ENDIF<BR>  z =3D t + 0.1*ap1/t, r =3D p3<BR>  IF(r =3D=3D 0)<=
BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>  z=
2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z2 - 1)<BR>  z=
zz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(3*z=
2 - a) + 2*z*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</=
DIV> <DIV> </DIV> <DIV>hrynewt3_j { ; p1 is Julia parameter, p3 is t=
olerance (if 0, will act like 0.001).<BR>     &n=
bsp;       ; n =3D 3.<BR>  z =3D pixel=
, a =3D p1, r =3D p3<BR>  IF(r =3D=3D 0)<BR>    r =3D=
 0.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D=
 z*z2<BR>  zno =3D (z3 - 1)<BR>  zzz =3D zno - a*z<BR>  tz=
2 =3D 3*z2<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(tz2 - a) + tz2=
*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV>&n=
bsp;</DIV> <DIV>hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act li=
ke 0.001).<BR>          =
;   ; n =3D 3.<BR>  z =3D 0, a =3D pixel, r =3D p3<BR>&nbs=
p; IF(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>&n=
bsp; :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z=
3 - 1)<BR>  zzz =3D zno - a*z<BR>  tz2 =3D 3*z2<BR>  pz =3D=
 zno*zzz<BR>  ppz =3D zno*(tz2 - a) + tz2*zzz<BR>  z =3D z - pz=
/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt4_j =
{ ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.001).<B=
R>            =
; ; n =3D 4.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  IF(r =3D=
=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR>&=
nbsp; z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zno =3D (z*z3 - 1)<BR=
>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D=
 zno*(3*z2 - a) + 4*z3*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| >=
; r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt4_m (XAXIS) { ; p3 is tolera=
nce (if 0, will act like 0.001).<BR>      &=
nbsp;      ; n =3D 4.<BR>  z =3D 0, a =3D p=
ixel, r =3D p3<BR>  IF(r =3D=3D 0)<BR>    r =3D 0.001=
<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z=
2<BR>  zno =3D (z*z3 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR> =
 pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 4*z3*zzz<BR>  z =3D=
 z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hryn=
ewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.=
001).<BR>          &nbs=
p;  ; n =3D 5.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  I=
F(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR> =
 :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D sqr(z2=
)<BR>  zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR> =
; pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz<BR>  z=
 =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>=
hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).<BR>&n=
bsp;            ; =
n =3D 5.<BR>  z =3D 0, a =3D pixel, r =3D p3<BR>  IF(r =3D=3D 0=
)<BR>    r =3D 0.001<BR>  ENDIF<BR>  :<BR> =
 z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D sqr(z2)<BR>  =
zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno=
*zzz<BR>  ppz =3D zno*(3*z2 - a) + 5*zn1*zzz<BR>  z =3D z - pz/=
ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt17_j =
{ ; p1 is Julia parameter, p3 is tolerance (if 0, will act like 0.001).<B=
R>            =
;  ; n =3D 17.<BR>  z =3D pixel, a =3D p1, r =3D p3<BR>  I=
F(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR> =
 :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D sqr(sq=
r(sqr(z2)))<BR>  zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1=
)<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 17*zn1*zzz<=
BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV> <=
/DIV> <DIV>hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0=
.001).<BR>          &nb=
sp;   ; n =3D 17.<BR>  z =3D 0, a =3D pixel, r =3D p3<BR>&=
nbsp; IF(r =3D=3D 0)<BR>    r =3D 0.001<BR>  ENDIF<BR=
>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D z*z2<BR>  zn1 =3D=
 sqr(sqr(sqr(z2)))<BR>  zno =3D (z*zn1 - 1)<BR>  zzz =3D (z3 - =
a*z - 1)<BR>  pz =3D zno*zzz<BR>  ppz =3D zno*(3*z2 - a) + 17*z=
n1*zzz<BR>  z =3D z - pz/ppz,<BR>  |pz| > r<BR>}</DIV> <DIV>=
 </DIV> <DIV>hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance =
(if 0, will act like 0.001).<BR>       =
;       ; n =3D 33.<BR>  z =3D pixel, =
a =3D p1, r =3D p3<BR>  IF(r =3D=3D 0)<BR>    r =3D 0=
.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>  z3 =3D=
 z*z2<BR>  zn1 =3D sqr(sqr(sqr(sqr(z2))))<BR>  zno =3D (z*zn1 -=
 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz<BR>  p=
pz =3D zno*(3*z2 - a) + 33*zn1*zzz<BR>  z =3D z - pz/ppz,<BR>  =
|pz| > r<BR>}</DIV> <DIV> </DIV> <DIV>hrynewt33_m (XAXIS) { ; p3 =
is tolerance (if 0, will act like 0.001).<BR>    &nbs=
p;         ; n =3D 33.<BR>  =
z =3D 0, a =3D pixel, r =3D p3<BR>  IF(r =3D=3D 0)<BR>  &n=
bsp; r =3D 0.001<BR>  ENDIF<BR>  :<BR>  z2 =3D sqr(z)<BR>&=
nbsp; z3 =3D z*z2<BR>  zn1 =3D sqr(sqr(sqr(sqr(z2))))<BR>  zno =
=3D (z*zn1 - 1)<BR>  zzz =3D (z3 - a*z - 1)<BR>  pz =3D zno*zzz=
<BR>  ppz =3D zno*(3*z2 - a) + 33*zn1*zzz<BR>  z =3D z - pz/ppz=
,<BR>  |pz| > r<BR>}<BR></DIV></BODY></HTML><DIV><BR><br clear=3D=
all><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http=
://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

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-------------------------------------------------------------------------------

From: harry <[e-mail]>
Subject: Re: (fractint) Hairy Newton
Date: 09 Jun 2001 00:27:37 -0400

Hairy Newton ???

Brother of "Fig" by any chance ???

BTW you are coming through in two's tonight....  Perhaps your
posts are bifurcating ???

H^) Harry (not Newton)

Multiple Bogeys wrote:

> Yesterday evening I set out to find an interesting family of
> Newton-based Mandelbrot mappings. The result was the collection of
> formulae below. You'll note the lack of 3D disease -- false alarm. All
> my posts to another listserv had it, but I now think it must be that
> listserv rather than MSN Exploder. Or rather, some interaction between
> the two (since some posts from that listserv don't have it), like the
> weird "email laser" that happened with this listserv last week (lots
> of peoples' messages were being duplicated, but for some reason mine
> were showing up in sets of five or six!)...Anyone who's an expert on
> listservs care to speculate further on what might be going on? One
> thing is clear: recent mail software and listservs have unnecessary
> complexity, and while we like complexity in our fractals, we could do
> without chaos erupting in the mail system we depend on to communicate
> here... The hrynewt_j and hrynewt_m formulae iterate Newton's method
> for p(z) = (z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is
> the tolerance, an inverse bailout radius about the roots of p. The
> Mandelbrot variant has a vary over the screen while initial z is zero;
> this is a critical point but not a root of p for n real and greater
> than 2. You can plug in other values of n -- arbitrary negative or
> even complex values -- but won't generally be able to find minibrots
> unless n has a positive real part greater than two. If n is not an
> integer, there will be branch cuts in both the Mandelbrot and the
> Julia variants. The hrynewtnnn_j and _m formulae are optimized
> versions with specific values for n, mostly small positive integers.
> They avoid a slow arbitrary exponentiation, and for the smaller values
> of n re-use powers that are used on both sides of the polynomial or
> its derivative. The hrynewt2_m formula also has the feature of using a
> critical point for initial z, instead of zero (which is *not* a
> critical point for n = 2). The result is a proper Mandelbrot view, but
> it has a branch cut due to a square root in the calculation of the
> critical point, which is a-dependent. The branch cut has been
> intentionally manipulated to put it in a fairly unobtrusive place, but
> can't be eliminated; the full Mandelbrot for this one lives on a
> two-layer Riemann sheet like that of the square root function. The
> hrynewtnnn_m formulae also use an (XAXIS) symmetry declaration. (The
> generic hrynewt_m can't use this without trashing the output for
> non-real values of n.) Observations:* Certain choices of n produce
> three-fold-symmetric Mandelbrot sets. Find out which!* Mangled and
> occasionally also intact Mandelbrots can be extracted when n is
> "strange" but has a real part greater than 2.* You get radial petals
> with n real, concentric patterns with n imaginary, and logarithmic
> spirals with complex n; the ratio of   real to imaginary parts
> determines whether the spiral is steep (n close to real) or shallow (n
> close to imaginary).* The Mandelbrots are always quadratic -- for real
> n > 2, the critical point at zero is nondegenerate, and the critical
> point   pair for hrynewt2_m is degenerate only at one specific value
> of a. The formula file begins with an extensive comment that details
> the mathematical constructions that informed their design. comment {
>   We want a Newton's method with a large number of basins, most of
> which are fixed and predictable.
>   This is accomplished by choosing a polynomial function to solve
> composed of two factors, one with many fixed roots,
>   the other with a few mobile ones:
>   p(z) = (z^n-1)(z^3-az-1).
>   The Newton iteration is:
>   z -> r(z)
>   where
>   r(z) = z - p(z)/p'(z)
>        = (zp'(z) - p(z))/p'(z)
>   We easily discover p'(z) to be
>   p'(z) = (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)
>         = (3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a
>   so
>   (zp'(z) - p(z)) = (z^n-1)(3z^3-az)+(nz^n)(z^3-az-1) -
> (z^n-1)(z^3-az-1)
>                   = (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)
>                   = (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1
>   and
>   r(z) = ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 -
> 1)/((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)
>   Using the quotient rule the numerator of r'(z) is
>   ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)((n+2)(n+3)z^(n+2) -
> an(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -
>     ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+2)(n+3)z^(n+1)
> - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
>   which factors into
>   ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
>   and
>   ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 + az) - ((2+n)z^(n+3) -
> anz^(n+1) - (n-1)z^n - 2z^3 - 1)
>   which simplifies to
>   z^(n+3) - az^(n+1) - z^n - z^3 + az + 1
>   Note that p(z) = z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.
>   Thus the critical points of r(z) are the roots of p(z) and the roots
> of
>   q(z) := ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
>   These latter are the "interesting" critical points, as the other
> critical points of r(z) are all superattracting.
>   Note that q(z) is divisible by z, so 0 is an "interesting" critical
> point of r(z), for n not one of 2, 1, or -1.
>   This is the critical point used in the below hrynewt_m formulas
> except for hrynewt2_m. For n = 2,
>   q(z)/2 = 10z^3 - 3(a+1)z - 1
>   Put z = y + (a+1)/10y to get
>   q(z)/2 = y^6 - y^3/10 + (a+1)^3/1000
>   so
>   2y^3 = 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),
>   y = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)
>   and
>   z = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10
> +/-sqrt(1/100 - 4(a+1)^3)/1000)/2)^(1/3)
> } hrynewt_j { ; p1 is Julia parameter, p2 is exponent n, p3 is
> tolerance (if 0, will act like 0.001).
>             ; SLOW. Use predefined hrynewtnnn_j where possible.
>   z = pixel, a = p1, n = p2, n1 = n - 1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = z^n1
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + n*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt_m { ; p2 is exponent n, p3 is tolerance (if 0, will act like
> 0.001).
>             ; SLOW. Use predefined hrynewtnnn_m where possible.
>   z = 0, a = pixel, n = p2, n1 = n - 1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = z^n1
>   zn = z*zn1
>   zno = (zn - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + n*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt2_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 2.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z2 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 2*z*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt2_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 2.
>   a = pixel,
>   ap1 = a + 1,
>   IF((real(ap1) >= 0) || ((abs(real(ap1))*(3^(0.5))) <
> abs(imag(ap1))))
>     t = ((0.1 + (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
>   ELSE
>     t = ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
>   ENDIF
>   z = t + 0.1*ap1/t, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z2 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 2*z*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt3_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 3.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z3 - 1)
>   zzz = zno - a*z
>   tz2 = 3*z2
>   pz = zno*zzz
>   ppz = zno*(tz2 - a) + tz2*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 3.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z3 - 1)
>   zzz = zno - a*z
>   tz2 = 3*z2
>   pz = zno*zzz
>   ppz = zno*(tz2 - a) + tz2*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt4_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 4.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z*z3 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 4*z3*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt4_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 4.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z*z3 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 4*z3*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 5.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(z2)
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 5*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 5.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(z2)
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 5*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt17_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>               ; n = 17.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(z2)))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 17*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>
>               ; n = 17.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(z2)))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 17*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>               ; n = 33.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(sqr(z2))))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 33*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt33_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>
>               ; n = 33.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(sqr(z2))))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 33*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> }
>
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-------------------------------------------------------------------------------

From: [e-mail]
Subject: Re: (fractint) Hairy Newton
Date: 09 Jun 2001 01:26:59 -0500

I'm getting Multiple Bogeys in Multiples tonight , too.

D. Freed

harry wrote:

> Hairy Newton ???
>
> Brother of "Fig" by any chance ???
>
> BTW you are coming through in two's tonight....  Perhaps your
> posts are bifurcating ???
>
> H^) Harry (not Newton)
>
> Multiple Bogeys wrote:
>
> > Yesterday evening I set out to find an interesting family of
> > Newton-based Mandelbrot mappings. The result was the collection of
> > formulae below. You'll note the lack of 3D disease -- false alarm. All
> > my posts to another listserv had it, but I now think it must be that
> > listserv rather than MSN Exploder. Or rather, some interaction between
> > the two (since some posts from that listserv don't have it), like the
> > weird "email laser" that happened with this listserv last week (lots
> > of peoples' messages were being duplicated, but for some reason mine
> > were showing up in sets of five or six!)...Anyone who's an expert on
> > listservs care to speculate further on what might be going on? One
> > thing is clear: recent mail software and listservs have unnecessary
> > complexity, and while we like complexity in our fractals, we could do
> > without chaos erupting in the mail system we depend on to communicate
> > here... The hrynewt_j and hrynewt_m formulae iterate Newton's method
> > for p(z) = (z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is
> > the tolerance, an inverse bailout radius about the roots of p. The
> > Mandelbrot variant has a vary over the screen while initial z is zero;
> > this is a critical point but not a root of p for n real and greater
> > than 2. You can plug in other values of n -- arbitrary negative or
> > even complex values -- but won't generally be able to find minibrots
> > unless n has a positive real part greater than two. If n is not an
> > integer, there will be branch cuts in both the Mandelbrot and the
> > Julia variants. The hrynewtnnn_j and _m formulae are optimized
> > versions with specific values for n, mostly small positive integers.
> > They avoid a slow arbitrary exponentiation, and for the smaller values
> > of n re-use powers that are used on both sides of the polynomial or
> > its derivative. The hrynewt2_m formula also has the feature of using a
> > critical point for initial z, instead of zero (which is *not* a
> > critical point for n = 2). The result is a proper Mandelbrot view, but
> > it has a branch cut due to a square root in the calculation of the
> > critical point, which is a-dependent. The branch cut has been
> > intentionally manipulated to put it in a fairly unobtrusive place, but
> > can't be eliminated; the full Mandelbrot for this one lives on a
> > two-layer Riemann sheet like that of the square root function. The
> > hrynewtnnn_m formulae also use an (XAXIS) symmetry declaration. (The
> > generic hrynewt_m can't use this without trashing the output for
> > non-real values of n.) Observations:* Certain choices of n produce
> > three-fold-symmetric Mandelbrot sets. Find out which!* Mangled and
> > occasionally also intact Mandelbrots can be extracted when n is
> > "strange" but has a real part greater than 2.* You get radial petals
> > with n real, concentric patterns with n imaginary, and logarithmic
> > spirals with complex n; the ratio of   real to imaginary parts
> > determines whether the spiral is steep (n close to real) or shallow (n
> > close to imaginary).* The Mandelbrots are always quadratic -- for real
> > n > 2, the critical point at zero is nondegenerate, and the critical
> > point   pair for hrynewt2_m is degenerate only at one specific value
> > of a. The formula file begins with an extensive comment that details
> > the mathematical constructions that informed their design. comment {
> >   We want a Newton's method with a large number of basins, most of
> > which are fixed and predictable.
> >   This is accomplished by choosing a polynomial function to solve
> > composed of two factors, one with many fixed roots,
> >   the other with a few mobile ones:
> >   p(z) = (z^n-1)(z^3-az-1).
> >   The Newton iteration is:
> >   z -> r(z)
> >   where
> >   r(z) = z - p(z)/p'(z)
> >        = (zp'(z) - p(z))/p'(z)
> >   We easily discover p'(z) to be
> >   p'(z) = (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)
> >         = (3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a
> >   so
> >   (zp'(z) - p(z)) = (z^n-1)(3z^3-az)+(nz^n)(z^3-az-1) -
> > (z^n-1)(z^3-az-1)
> >                   = (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)
> >                   = (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1
> >   and
> >   r(z) = ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 -
> > 1)/((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)
> >   Using the quotient rule the numerator of r'(z) is
> >   ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)((n+2)(n+3)z^(n+2) -
> > an(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -
> >     ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+2)(n+3)z^(n+1)
> > - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
> >   which factors into
> >   ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
> >   and
> >   ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 + az) - ((2+n)z^(n+3) -
> > anz^(n+1) - (n-1)z^n - 2z^3 - 1)
> >   which simplifies to
> >   z^(n+3) - az^(n+1) - z^n - z^3 + az + 1
> >   Note that p(z) = z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.
> >   Thus the critical points of r(z) are the roots of p(z) and the roots
> > of
> >   q(z) := ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
> >   These latter are the "interesting" critical points, as the other
> > critical points of r(z) are all superattracting.
> >   Note that q(z) is divisible by z, so 0 is an "interesting" critical
> > point of r(z), for n not one of 2, 1, or -1.
> >   This is the critical point used in the below hrynewt_m formulas
> > except for hrynewt2_m. For n = 2,
> >   q(z)/2 = 10z^3 - 3(a+1)z - 1
> >   Put z = y + (a+1)/10y to get
> >   q(z)/2 = y^6 - y^3/10 + (a+1)^3/1000
> >   so
> >   2y^3 = 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),
> >   y = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)
> >   and
> >   z = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10
> > +/-sqrt(1/100 - 4(a+1)^3)/1000)/2)^(1/3)
> > } hrynewt_j { ; p1 is Julia parameter, p2 is exponent n, p3 is
> > tolerance (if 0, will act like 0.001).
> >             ; SLOW. Use predefined hrynewtnnn_j where possible.
> >   z = pixel, a = p1, n = p2, n1 = n - 1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = z^n1
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + n*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt_m { ; p2 is exponent n, p3 is tolerance (if 0, will act like
> > 0.001).
> >             ; SLOW. Use predefined hrynewtnnn_m where possible.
> >   z = 0, a = pixel, n = p2, n1 = n - 1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = z^n1
> >   zn = z*zn1
> >   zno = (zn - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + n*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt2_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 2.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z2 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 2*z*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt2_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 2.
> >   a = pixel,
> >   ap1 = a + 1,
> >   IF((real(ap1) >= 0) || ((abs(real(ap1))*(3^(0.5))) <
> > abs(imag(ap1))))
> >     t = ((0.1 + (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
> >   ELSE
> >     t = ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
> >   ENDIF
> >   z = t + 0.1*ap1/t, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z2 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 2*z*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt3_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 3.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z3 - 1)
> >   zzz = zno - a*z
> >   tz2 = 3*z2
> >   pz = zno*zzz
> >   ppz = zno*(tz2 - a) + tz2*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 3.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z3 - 1)
> >   zzz = zno - a*z
> >   tz2 = 3*z2
> >   pz = zno*zzz
> >   ppz = zno*(tz2 - a) + tz2*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt4_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 4.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z*z3 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 4*z3*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt4_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 4.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z*z3 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 4*z3*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 5.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(z2)
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 5*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 5.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(z2)
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 5*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt17_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >               ; n = 17.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(z2)))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 17*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >
> >               ; n = 17.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(z2)))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 17*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >               ; n = 33.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(sqr(z2))))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 33*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt33_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >
> >               ; n = 33.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(sqr(z2))))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 33*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > }
> >
> > -----------------------------------------------------------------------
> > Get Your Private, Free E-mail from MSN Hotmail at
> > http://www.hotmail.com.
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"


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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Bug
Date: 09 Jun 2001 05:16:02 -0400


------=_NextPart_001_0000_01C0F0A3.46F0DE20
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Try this:

1. Display some fractal from a type that has parameters. Set passes=3Dt.
2. Ctrl-E -- evolver/explorer. Turn it on. Use F6 and set two parameters =
to x and y respectively, leave the rest normal.
    Accept the F6 screen and change "show parameter zoom box" to "yes".
3. Page-up to get zoom box, move it with a ctrl-arrow, enter.
4. Space, turn off evolver/explorer, enter.
5. Observe something the manufacturer definitely didn't intend.
6. Hit 'b' to save parameters.
7. Observe something else the manufacturer didn't intend.

Type: bug
Reported-against: 20.01.10
Severity: low
Workaround: yes


Incidentally, the latest developer patches act weird when AF7 is bound to=
 1024x768x256 disk-video. Hitting it produces an error message that seems=
 to say something about not enough memory (on a 64 meg box!) after which =
it works anyway(!) -- this never occurred with 20.0 or 19.x.<br clear=3Da=
ll><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http:=
//www.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0000_01C0F0A3.46F0DE20
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>Try this:</DIV=
> <DIV> </DIV> <DIV>1. Display some fractal from a type that has par=
ameters. Set passes=3Dt.</DIV> <DIV>2. Ctrl-E -- evolver/explorer. Turn i=
t on. Use F6 and set two parameters to x and y respectively, leave the re=
st normal.</DIV> <DIV>    Accept the F6 screen and change =
"show parameter zoom box" to "yes".</DIV> <DIV>3. Page-up to get zoom box=
, move it with a ctrl-arrow, enter.</DIV> <DIV>4. Space, turn off evolver=
/explorer, enter.</DIV> <DIV>5. Observe something the manufacturer defini=
tely didn't intend.</DIV> <DIV>6. Hit 'b' to save parameters.</DIV> <DIV>=
7. Observe something else the manufacturer didn't intend.</DIV> <DIV>&nbs=
p;</DIV> <DIV>Type: bug</DIV> <DIV>Reported-against: 20.01.10</DIV> <DIV>=
Severity: low</DIV> <DIV>Workaround: yes</DIV> <DIV> </DIV> <DIV>&nb=
sp;</DIV> <DIV>Incidentally, the latest developer patches act weird when =
AF7 is bound to 1024x768x256 disk-video. Hitting it produces an error mes=
sage that seems to say something about not enough memory (on a 64 meg box=
!) after which it works anyway(!) -- this never occurred with 20.0 or 19.=
x.<BR><BR></DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Priva=
te, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">ht=
tp://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0000_01C0F0A3.46F0DE20--

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Bug
Date: 09 Jun 2001 06:04:19 -0400


------=_NextPart_001_0000_01C0F0AA.05960C00
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> Try this:

> 1. Display some fractal from a type that has parameters. Set passes=3Dt=
.
> 2. Ctrl-E -- evolver/explorer. Turn it on. Use F6 and set two parameter=
s to x and y respectively, leave the rest normal.
>    Accept the F6 screen and change "show parameter zoom box" to "yes".
> 3. Page-up to get zoom box, move it with a ctrl-arrow, enter.
> 4. Space, turn off evolver/explorer, enter.
> 5. Observe something the manufacturer definitely didn't intend.
> 6. Hit 'b' to save parameters.
> 7. Observe something else the manufacturer didn't intend.

Argh. That should have been:

1. Display some fractal from a type that has parameters. Set passes=3Dt.
2. Ctrl-E -- evolver/explorer. Turn it on. Use F6 and set two parameters =
to x and y respectively, leave the rest normal.
   Accept the F6 screen and change "show parameter zoom box" to "yes".
3. Page-up to get zoom box, move it with a ctrl-arrow, enter.
4. Space, turn off evolver/explorer, enter.
5. Observe something the manufacturer definitely didn't intend.
6. Page up, page up, enter to zoom in slightly, and observe something els=
e the manufacturer didn't intend.
7. Hit 'b' to save parameters.
8. Observe yet another behavior the manufacturer didn't intend.<br clear=3D=
all><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http=
://www.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0000_01C0F0AA.05960C00
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Try this:=
</DIV> <DIV> </DIV> <DIV>> 1. Display some fractal from a type th=
at has parameters. Set passes=3Dt.</DIV> <DIV>> 2. Ctrl-E -- evolver/e=
xplorer. Turn it on. Use F6 and set two parameters to x and y respectivel=
y, leave the rest normal.</DIV> <DIV>>    Accept the F6=
 screen and change "show parameter zoom box" to "yes".</DIV> <DIV>> 3.=
 Page-up to get zoom box, move it with a ctrl-arrow, enter.</DIV> <DIV>&g=
t; 4. Space, turn off evolver/explorer, enter.</DIV> <DIV>> 5. Observe=
 something the manufacturer definitely didn't intend.</DIV> <DIV>> 6. =
Hit 'b' to save parameters.</DIV> <DIV>> 7. Observe something else the=
 manufacturer didn't intend.</DIV> <DIV> </DIV> <DIV>Argh. That shou=
ld have been:</DIV> <DIV> </DIV> <DIV> <DIV>1. Display some fractal =
from a type that has parameters. Set passes=3Dt.</DIV> <DIV>2. Ctrl-E -- =
evolver/explorer. Turn it on. Use F6 and set two parameters to x and y re=
spectively, leave the rest normal.</DIV> <DIV>   Accept the F6 =
screen and change "show parameter zoom box" to "yes".</DIV> <DIV>3. Page-=
up to get zoom box, move it with a ctrl-arrow, enter.</DIV> <DIV>4. Space=
, turn off evolver/explorer, enter.</DIV> <DIV>5. Observe something the m=
anufacturer definitely didn't intend.</DIV> <DIV>6. Page up, page up, ent=
er to zoom in slightly, and observe something else the manufacturer didn'=
t intend.</DIV> <DIV>7. Hit 'b' to save parameters.</DIV> <DIV>8. Observe=
 yet another behavior the manufacturer didn't intend.</DIV></DI=
V></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, Free E-mai=
l from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotma=
il.com</a>.<br></p></DIV>

------=_NextPart_001_0000_01C0F0AA.05960C00--

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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: (fractint) Fractint version 20.1.11
Date: 09 Jun 2001 07:32:46 -0500

Fractint version 20.1.11 is now available on the developer's web site:
www.fractint.org

What's new:
Fixed a bug that caused a panned image to miss part of a line when the
  image was panned while the first row was being generated.

  Adjusted the time for keyboard checks when the showdot feature is used.
Now
  the iterations stop much quicker when a key is pressed.

  Fixed a problem with the float-only version that appeared when an
incomplete
  image was saved and restarted in the standard version.

  Fixed a problem in Xfractint pointed out by Ken on the Fractint bug list.

Jonathan



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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  09-06-01  (Chrysanthemums [4])
Date: 09 Jun 2001 10:27:52 EDT


Classic FOTD -- June 09, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

The run of exceptional fractals had to eventually come to an end.

Due to another busy day, today's image is not only late, but it
rates only a slightly below average 4.  The scene is one of a
midget in the Z^1.741101127 Mandeloid, lying 11 rotations up (or
is it down?) the logarithmic spiral.  The exponent is not random
however.  I intentionally chose the 5th root of 16, just to see
what would happen.

What happened is today's area of interesting chaos, featuring a
large but harmless chrysanthemum, which is infested by a spiral
and surrounded by countless smaller mums.

I doubt that the image is worth the 25 minutes it takes to draw
it from the attached parameter file.  A trip to:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or to:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

to download the image is recommended

The fractal weather today was uneventful, with lots of sun and a
temperature of 81F (27C).  The cats enjoy uneventful weather, so
they were happy.

it's now already 10:20am of Saturday morning, and I've got
chores to do around Fractal Central.  Until next time, take
care, and what is the meaning of fractals?


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Chrysanthemums     { ; time=0:25:47.03--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-0.010176721962093/-0.348637919700844/2\
  682929/1/57.499 params=1.741101127/0/11/0 float=y
  maxiter=10000 inside=0 logmap=-686 periodicity=10
  colors=000FA0HD0IE0IF0JI0KJ0MK0MM0SK2ZJ2eI3kH3qF3n\
  J8kMDiOHfSKcVOaYUZaYXcaUfeRjiOmnMorJsvHvzEyzFvzFsz\
  HqyHnvHkuIjsIgqIeoJbnJ_kJZjKXiKUfMReMOcMMaNK_RIZNF\
  XO0POAUO8SZKUiXVsgXzrYzn_zkazibzfczcezafzZgzXizUjz\
  RkzOmzMnzGozYqzcrzmszmuzhvzcwzZyzUzzPvzKsyFoyAmwDi\
  wFfvIcvK_uNYuQUsSRsVOrYKr_IqbEqeBog8oj4nm2no0mr0mu\
  0nr0oo0om0qj3rg6re8sbBuaEuZHvXJwUMwROyORzMUzKXvMVr\
  NVoNVkOVgOVeQVaQVZRVVSVRSVOUVKUVHVVEVVAXV7XVBYSFZR\
  J_QNaORbNVbMZcKbeJffIjgHniFriEvjDzkBzmAzn8zn7oc3VV\
  0AK00B00I07O0FV0N_0Vf0bm3jr4ry7zz8zzAzz7zz4zz2zz0z\
  z0zz0zz0zy0zu0zr0yn0vk0ug0re0qa0nZ0mV0jS0iO0gM0ZaE\
  RqUJzgKzeMzcMzbNyaNw_OvZOuYQrXQqVRoURnSSmRSkQUjOUi\
  NSeJSaHSZESVARS7RO4RM0RI0RF0UI0XK4YMA_OEbRIcSNfVRi\
  YVjZ_macocgqemsgqvjuwkzznzzozzqzzrzzswzusyvoywmyyi\
  yzfwzbwzZwzXwzSvzOvzMvzIvzFwzIwzKwzNwzOwzRwzUwzVwz\
  Ywz_wzbwzcwzfyziyzjyzmyzo
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================

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-------------------------------------------------------------------------------

From: "Jean-Pierre SEIMAN" <[e-mail]>
Subject: (fractint) Fractint20 with Windows98
Date: 10 Jun 2001 03:19:13 +0200

C'est un message de format MIME en plusieurs parties.

------=_NextPart_000_000B_01C0F15C.1F933440
Content-Type: text/plain;
    charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable

Question from a new user of Fractint 20 (DOS)

How may Y use it with Windows?

Which are the settings?

Thank you in advance?

Jean-Pierre

------=_NextPart_000_000B_01C0F15C.1F933440
Content-Type: text/html;
    charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Dwindows-1252">
<META content=3D"MSHTML 5.50.4611.1300" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DTahoma color=3D#008000>Question from a new user of =
Fractint 20=20
(DOS)</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma color=3D#008000>How may Y use it with =
Windows?</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma color=3D#008000>Which are the =
settings?</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma color=3D#008000>Thank you in =
advance?</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma =
color=3D#008000>Jean-Pierre</FONT></DIV></BODY></HTML>

------=_NextPart_000_000B_01C0F15C.1F933440--


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-------------------------------------------------------------------------------

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Fractint20 with Windows98
Date: 10 Jun 2001 15:45:45 +1200

At 13:19 10/06/2001, you wrote:
>Question from a new user of Fractint 20 (DOS)
>
>How may Y use it with Windows?
>
>Which are the settings?
>
>Thank you in advance?
>
>Jean-Pierre

A page that covers this issue can be found at
http://spanky.triumf.ca/www/fractint/fracwin95.html.

Win98 isn't too different - it's just Win95 released three years after
deadline. Now, if you'd asked about Windows Millennium or Win2000 ...

You might want to run makefcfg.exe first, to get a customised video mode
config file.

Morgan L. Owens
"MS-DOS is a relicensing of something called 'Quick and Dirty Operating
System'. Says it all, really..."


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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  10-06-01  (Fractal Shortfall [6])
Date: 10 Jun 2001 00:25:15 EDT


Classic FOTD -- June 10, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

As I write this, I have on the desk beside me the most recent
issue of 'Skeptic' magazine, a publication that I often read,
which features articles about many strange and wonderfully
interesting paranormal things that do not happen.  On the cover
is a fractal created by a well-known fractal artist, and a well-
known fractal generating program other than Fractint.

As I study the image with its multiple layers and different
coloring methods, I remember the Mandelbrot set as it was in
1985, with its one layer and flat equal-iteration bands.
Fractals are (or were) graphs of the things iterated complex
numbers do.  When I see so-called fractals such as the one on
the magazine cover, I ask myself, "is this what the numbers have
done or what the artist has done?"

If this type of image is to be considered a fractal, so be it.
But then I must think of some new name to call the conservative
images that I produce, which emphasize the behavior of the
numbers rather than any possible artistic ability on my part.
(The word 'protofractals' comes to mind.)  I'll be pondering
this minor dilemma over the next few days.  I may invent a new
name; I may not.  But regardless, the images as well as the
blather will keep coming.

And speaking of images, with today's 6-rated image we begin a
slow climb back to the lofty heights of fractal excellence.  The
rating of 6 is only slightly above average, but it is 2 points
above yesterday's less-than-stellar effort.

I named the image, which was created by the iterated expression
-Z^(-1.3)-0.02Z^(-13)+(1/C), Fractal Shortfall.  I gave it this
name because the magnitude of the image falls short of revealing
the midget at the center.  In fact, the midget is so tiny that
not a trace of it is visible.

Instead of my normal inside=0 outside=iter coloring, I set the
inside to bof61 and the outside to tdis.  This is not too much
of a sacrilege, since the basic forms are still clearly visible.
Unfortunately, the parameter file takes well over 1/2 hour to
render.  Therefore, a download of the GIF image from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

is strongly recommended.

The fractal weather today was once again perfect, with blue
skies, puffy white cumulus clouds, a temperature of 83F (28C),
and happy cats.

As for me, I've about had it for the day.  It's already past
midnight and there's not much left to do but settle into my
favorite chair and grow sleepy watching an exciting old sci-fi
movie.  But I'll be back in 24 or 36 hours with the next fractal
image.  Until then, take care, and after 16 years of fascination
with fractals, I don't even know what a fractal is.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Fractal_Shortfall  { ; time=0:36:18.07--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-60.81552655003062/-416.9838484676321/8\
  .371123e+007/1/94.999 params=-1/-1.3/-0.02/-13/0/0
  float=y maxiter=6400 inside=atan
  outside=tdis periodicity=10
  colors=0001zW0od0_n0Lx0Ko0Ih0Hb0GX2ER4EL2HG2KB2N6L\
  XBggEzsIokObbTRWYGOb6Hh0Bn06s0Kh6Y_GoRRzITnUUYdWKo\
  RGhNDbK9XG7RC4L91H0v07q2KlDYgQoohzxzXQz40zC0zK0vT0\
  q`0lk0hb1eW1bO2`H2YB2W54U04R04Q07L59IBCEHECOI9WL6b\
  O4kR1lU7nWDoXKq_Rs`Ytbevdlq_kzXkgTkbQkYLkUIkQEkNCk\
  0UrLlWG`QBRL7HH29D01900600200806E5GL9RTEb_KogQzo2g\
  0C_6LTKXLYgEos8zqX`oxCqt7sq2zz0tl0tk0zX4zLIzBYzCbz\
  DgvDlsEqqEvb8qR4nE0h50e00b00Y40U70RQObRK_RGXRCUR8R\
  T5OT1LT0IT0H_0Qg5Yo9gxEqzIzzGttEnqCglB`h8Wd7Q`5KX4\
  GU1BQ06N01I00G00C00900I70RN0_e0hz2dv4_s5Wq5Rn6Ol6L\
  oWNqRNqOOqLOqHQqE0z12z5Dv80zz0zo4zdBxUItK00g02Y5HR\
  EYI00v00q10n20k51g65d89`9DYCIWDNTGRQHXNK`KLgHOlEt0\
  0h95YU84n8LsnNqkNqgNqdNq`OqYOqWOqTOqQQqNQqKQqHQqE5\
  B57E68H69L7CO7DT8EW8HY9Ib9KeBNkBOnC78X9DUBHTDLQEQO\
  GULIYKKbHNgGOlD02k07e2Bb5E_7KX9OUCTQEXNHbKKgHNlEWX\
  2CO4DR5ET6GW6HX7H_7I`8Kd8
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Fractint20 with Windows98
Date: 10 Jun 2001 01:56:49 -0500

Jean-Pierre SEIMAN wrote:
>
> Question from a new user of Fractint 20 (DOS)
> How may Y use it with Windows?
> Which are the settings?
> Thank you in advance?
>

If you are experiencing problems running FractInt under Windows, then
try reading some of this:

    http://spanky.triumf.ca/www/fractint/fracwin95.html

More information may be found here:

    http://home.san.rr.com/jayrhill/iFAQ/Resource.htm

If you have not created the FractInt Documentation yet, then try the
following from your command line:

      Fractint.exe makedoc

Also, you will need to setup your SSTOOLS.INI file with some options
that may make things a little easier for you.  Any problems in this
area, then just send another message to the Discussion List.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: [e-mail]
Subject: Re: (fractint) C-FOTD  10-06-01  (Fractal Shortfall [6])
Date: 10 Jun 2001 12:20:59 -0500

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Paul Lee-
<p>Could you assist?
<p>In reviewing my list of highly rated FOTD's, I find that Jim gave his
Oct 10, 2000 contribution entitled "The Perfect Fractal" a grade of "10".
<p>However, when I go to your page, scroll to October, 2000, and click
on the date October 10 - which in every other case produces a download
of the image and Jim's attached text, I instead get a variety of other
webpages with your name on them somwhere, but not the image I seek.
<p>I also <b>searched</b> on your page both the date October 10, 2000 and
the title "The Perfect Fractal", and get lists of other fractals in which
the word "perfect " is used by Jim in the text description, but not in
the Title of the image itself.
<p>What am I doing wrong??
<p>Thanks, Nice not to live in Houston this week, eh?
<br>
<p>DeBow Freed
<br>
<p>[e-mail] wrote:
<blockquote TYPE=CITE>Classic FOTD -- June 10, 2001 (Rating 6)
<p>Fractal visionaries and enthusiasts:
<p>As I write this, I have on the desk beside me the most recent
<br>issue of 'Skeptic' magazine, a publication that I often read,
<br>which features articles about many strange and wonderfully
<br>interesting paranormal things that do not happen.  On the cover
<br>is a fractal created by a well-known fractal artist, and a well-
<br>known fractal generating program other than Fractint.
<p>As I study the image with its multiple layers and different
<br>coloring methods, I remember the Mandelbrot set as it was in
<br>1985, with its one layer and flat equal-iteration bands.
<br>Fractals are (or were) graphs of the things iterated complex
<br>numbers do.  When I see so-called fractals such as the one on
<br>the magazine cover, I ask myself, "is this what the numbers have
<br>done or what the artist has done?"
<p>If this type of image is to be considered a fractal, so be it.
<br>But then I must think of some new name to call the conservative
<br>images that I produce, which emphasize the behavior of the
<br>numbers rather than any possible artistic ability on my part.
<br>(The word 'protofractals' comes to mind.)  I'll be pondering
<br>this minor dilemma over the next few days.  I may invent a new
<br>name; I may not.  But regardless, the images as well as the
<br>blather will keep coming.
<p>And speaking of images, with today's 6-rated image we begin a
<br>slow climb back to the lofty heights of fractal excellence.  The
<br>rating of 6 is only slightly above average, but it is 2 points
<br>above yesterday's less-than-stellar effort.
<p>I named the image, which was created by the iterated expression
<br>-Z^(-1.3)-0.02Z^(-13)+(1/C), Fractal Shortfall.  I gave it this
<br>name because the magnitude of the image falls short of revealing
<br>the midget at the center.  In fact, the midget is so tiny that
<br>not a trace of it is visible.
<p>Instead of my normal inside=0 outside=iter coloring, I set the
<br>inside to bof61 and the outside to tdis.  This is not too much
<br>of a sacrilege, since the basic forms are still clearly visible.
<br>Unfortunately, the parameter file takes well over 1/2 hour to
<br>render.  Therefore, a download of the GIF image from:
<p>          <<a href="http://home.att.net/~Paul.N.Lee/FotD/FotD.html">http://home.att.net/~Paul.N.Lee/FotD/FotD.html</a>>
<p>or from:
<p>          <<a href="http://sdboyd.dyndns.org/~sdboyd/fotd/index.html">http://sdboyd.dyndns.org/~sdboyd/fotd/index.html</a>>
<p>is strongly recommended.
<p>The fractal weather today was once again perfect, with blue
<br>skies, puffy white cumulus clouds, a temperature of 83F (28C),
<br>and happy cats.
<p>As for me, I've about had it for the day.  It's already past
<br>midnight and there's not much left to do but settle into my
<br>favorite chair and grow sleepy watching an exciting old sci-fi
<br>movie.  But I'll be back in 24 or 36 hours with the next fractal
<br>image.  Until then, take care, and after 16 years of fascination
<br>with fractals, I don't even know what a fractal is.
<p>Jim Muth
<br>[e-mail]
<p>START 20.0 PAR-FORMULA FILE================================
<p>Fractal_Shortfall  { ; time=0:36:18.07--SF5 on a P200
<br>  reset=2001 type=formula formulafile=allinone.frm
<br>  formulaname=MandelbrotMix4 function=recip passes=1
<br>  center-mag=-60.81552655003062/-416.9838484676321/8\
<br>  .371123e+007/1/94.999 params=-1/-1.3/-0.02/-13/0/0
<br>  float=y maxiter=6400 inside=atan
<br>  outside=tdis periodicity=10
<br>  colors=0001zW0od0_n0Lx0Ko0Ih0Hb0GX2ER4EL2HG2KB2N6L\
<br>  XBggEzsIokObbTRWYGOb6Hh0Bn06s0Kh6Y_GoRRzITnUUYdWKo\
<br>  RGhNDbK9XG7RC4L91H0v07q2KlDYgQoohzxzXQz40zC0zK0vT0\
<br>  q`0lk0hb1eW1bO2`H2YB2W54U04R04Q07L59IBCEHECOI9WL6b\
<br>  O4kR1lU7nWDoXKq_Rs`Ytbevdlq_kzXkgTkbQkYLkUIkQEkNCk\
<br>  0UrLlWG`QBRL7HH29D01900600200806E5GL9RTEb_KogQzo2g\
<br>  0C_6LTKXLYgEos8zqX`oxCqt7sq2zz0tl0tk0zX4zLIzBYzCbz\
<br>  DgvDlsEqqEvb8qR4nE0h50e00b00Y40U70RQObRK_RGXRCUR8R\
<br>  T5OT1LT0IT0H_0Qg5Yo9gxEqzIzzGttEnqCglB`h8Wd7Q`5KX4\
<br>  GU1BQ06N01I00G00C00900I70RN0_e0hz2dv4_s5Wq5Rn6Ol6L\
<br>  oWNqRNqOOqLOqHQqE0z12z5Dv80zz0zo4zdBxUItK00g02Y5HR\
<br>  EYI00v00q10n20k51g65d89`9DYCIWDNTGRQHXNK`KLgHOlEt0\
<br>  0h95YU84n8LsnNqkNqgNqdNq`OqYOqWOqTOqQQqNQqKQqHQqE5\
<br>  B57E68H69L7CO7DT8EW8HY9Ib9KeBNkBOnC78X9DUBHTDLQEQO\
<br>  GULIYKKbHNgGOlD02k07e2Bb5E_7KX9OUCTQEXNHbKKgHNlEWX\
<br>  2CO4DR5ET6GW6HX7H_7I`8Kd8
<br>  }
<p>frm:MandelbrotMix4 {; Jim Muth
<br>a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
<br>g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
<br>k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
<br>z=k*((a*(z^b))+(d*(z^f)))+c,
<br>|z| < l
<br>}
<p>END 20.0 PAR-FORMULA FILE==================================
<p>--------------------------------------------------------------
<br>Thanks for using Fractint, The Fractals and Fractint Discussion List
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fractint"</blockquote>
</html>


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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) C-FOTD  10-06-01  (Fractal Shortfall [6])
Date: 10 Jun 2001 14:14:25 -0500

[e-mail] wrote:
>
> Could you assist?

Hey there!!  Yes, I would be most glad to, if I am able to do so.   :-)

>
> ....Jim gave his Oct 10, 2000 contribution
> entitled "The Perfect Fractal" a grade of
> "10".
>
> However, when I go to your page.....instead
> get a variety of other webpages....

Apparently, AT&T was doing some maintenance and lost about 15 days worth
of web pages during this time period.  I have recently restored those
particular pages.  Thank you for letting me know that this had occurred.

>
> I also searched.......title "The Perfect Fractal",
> and get lists of other fractals in which the word
> "perfect " is used by Jim in the text description,
> but not in the Title of the image itself.

If you use the double quotes around strings of words, then AltaVista
considers everything within the quotes (exactly as it is written) to be
a single entity to search for.  Otherwise it uses each word separately
and finds all pages that may contain those words anywhere within the web
page.

I will most likely have to add these 15 pages back into the search
engine before they will be found again by using the search tool.  And
this usually takes AltaVista several days to update their databases.
Afterwards, everything should function again normally.

>
> Nice not to live in Houston this week, eh?

Though I wish the rains could have made it up to our area, we could use
some about now.  It has been way to dry lately, and those days of 90║
weather took it's toll on the grass and grounds.

Later,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: "Morgan L. Owens" <[e-mail]>
Subject: (fractint) Re: [philofractal] C-FOTD  10-06-01  (Fractal Shortfall [6])
Date: 11 Jun 2001 18:30:18 +1200

At 16:25 10/06/2001, [e-mail] wrote:

>When I see so-called fractals such as the one on
>the magazine cover, I ask myself, "is this what the numbers have
>done or what the artist has done?"

Let's generalise (mathematicians just loooooove to generalise things...).
Is this not merely a special case of the question as to whether mathematics
is discovered or invented?

Me, I still tend towards "discovered", though the Second Gratuitous Greg
Egan Excerpt tells me that it's more a matter of utility and some other
word that escapes me for the moment than some rigorously argued position.

Morgan L. Owens
"Ah! Expedience!"



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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  11-06-01  (Pentagonal Midget [6])
Date: 11 Jun 2001 10:02:28 -0400 (EDT)


Classic FOTD -- June 11, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

The reason I have named today's image "Pentagonal Midget" is
obvious.  The very obvious hole filling the center of the frame
is shaped like an irregular pentagon.  To be technically
accurate, I should not call the hole a midget, for it has no
relation whatever to a mini-M-set.  The image, with its rating
of 6, is not a great one, though the arms surrounding the hole
add just enough interest to get the image into the honor-legion
of FOTD's.

The parent fractal of today's scene was created by the formula
Z^(sqrt(2))+C.  The scene itself it located on the chaotic shore
of a midget sitting on a very prominent filament of the main bud
of the parent.  The filament cannot be called a negative stem
because it shoots out in a northerly direction, and due to the
fragmentary nature of the entire fractal, the filament is not
continuous.

The parameter file takes 1/4 hour to run.  The more efficient
choice is to download the GIF image from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather was once again perfect, with sunshine and a
temperature of 85F (29.5C).  These conditions kept the fractal
cats happy.

As for myself, I'll be happy when I finish the work now before
me.  And the only way to finish is to get started.  So until
next fractal, take care, and things are never so good that they
can't get better.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Pentagonal_Midget  { ; time=0:15:19.62--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=mandelbrotbc1 function=floor
  center-mag=-0.48705650547436810/+3.374397806780400\
  00/250175.2/1/-124.998 params=1.414213562373/0/0/0
  float=y maxiter=9000 inside=0
  logmap=230 periodicity=10
  colors=000kf7kg6mi4nj3ok2om0qn0ro0sq0sr0us0vu0wv0w\
  w0vv0uv0sv0rv0qu0ou0nu2mu3ks4ks6js7is8grAfrBerEcrF\
  bqHaqIaqJ_qKZoMYoNXoOVoQUnRSnSRnURnVQoYOo_OqbNqeMr\
  gMrjKsmJsoJurIuuHvwHvzFwzFwzIyzKyzNyzQyzSzzVzyXzwZ\
  zwazvczufzsizsjzrmzqozorzouznwzmzznyzmyzkywjyvjysi\
  wqgwnfwmfwjewgcvebvcbvaavZ_vXZvVZuSYuQXuNVuMVuJUsH\
  SsERsDRsAQs7Os6Oo8RkAUgDVeEYaFZYIaVLbRMeNPfKRiHTjD\
  VmBWpAXnAWkATg8Re8Oa8NZ7MV7KS7JO6IM6HI6FFGEBID8KB4\
  MB0OA2Q86R7BS6FT4KU3OV2UW2YY0b_0f`0kc0of0ud0yf0zg0\
  ze0zc0za0z_0zZ0zZ0zY0zY0yX0wV0vV2uU3sS3rS4qR6oR6oR\
  6oQ7qQ7qQ8qQ8rQ8rQArQAsQAsQBsQBsQDuQDuQDuQEvQEvOEv\
  OFwOFwOFwOHwOHyOIyOIyOIzOJzOJzOJzOKzOKzOKzQNwQOsQQ\
  oQSmQUiQVeRXaRZZR_VRaRRbNReKSfHSgDSi8Sk6Sm2Sn0Rq0S\
  o0Un0Vm0Xk2Yj4Yi6Zg8_fBaeDbcFcbIcaJe_MfZOgYQiXSjVV\
  jUXkSZmRanQboOeqNgqIgqMiqQjqUkqYmqanqeoqiqqmrqqsqu\
  uqyvcYHeZFf_EfaDgbBicAje8
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Interesting FOTD statistics...
Date: 11 Jun 2001 10:56:35 -0500

Greetings,

Just looked over some of the counters for the past couple of years and
noticed that the most viewed FOTD from Jim Muth's postings is the one
for August 30, 2000.  But that is most likely due to the title and the
words found within the text.  I am sure several search engines turn up
this page fairly regularly:

    Giant Flying Boobs ⌐
        http://home.att.net/~Paul.N.Lee/FotD/FotD_00-08-30.html

So for those that want to have their web pages and galleries viewed by a
wider audience, take heed on what really sells and creates "hits".


BTW, the five most viewed FOTD months have been the following, in this
order:
    May, 1999
    January, 2000
    July, 1999
    December, 1999
    August, 1999
And the five most viewed FOTD days (besides the one above) have been
these:
    December 17, 1999
    May 31, 1999
    February 04, 2000
    May 01, 1999
    November 10, 1999


Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  12-06-01  (Firecracker Fractal [7])
Date: 12 Jun 2001 10:30:53 -0400 (EDT)


Classic FOTD -- June 12, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

I am occasionally asked why I set the periodicity to 10 when I
use Fractint, when such a setting slows the calculation
noticeably.  Today's image shows the reason.  With periodicity
set to 10, as it is in the parameter file, the image renders in
4-1/2 minutes.  With periodicity turned off, the image takes 5
full minutes to render.  With maximum periodicity checking, (a
setting of 1), the image renders in only 4 minutes, but the
midget is distorted because the program thinks it sees periodic
behavior where none exists, and stops calculating.

Through trial and error I found that a periodicity setting of
10 gives the best compromise between time saved and correct
rendering.  Therefore, I use 10 as the default periodicity
setting.

Today's image is a dark somber thing with a ring of small and
brilliant but shattered cylinders surrounding the midget.  I
pondered the image a few minutes before noticing that the small
red cylinders resemble exploding firecrackers.  Once I noticed
this, I had my name -- "Firecracker Fractal".

Rating the image gave me more reason to ponder.  Several minutes
of doing other things passed, while the image sat idly on the
screen, before I decided that it was worth a 7, a rating that
might be a bit liberal.

The rather gloomy image was created by iterating the formula
-0.6(Z^(-1.3))-0.006(Z^(-3))+(1/Z).  The 4-1/2 minute render
time can be reduced to one minute or less by giving Paul and
Scott a chance to render the image and post it to their web
sites at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was partly sunny with a temperature of
86F (30C) and a few rumbles of thunder in the evening from a
small thunder-shower that passed just north of Fractal Central.
The fractal cats had an uneventful day, displaying moods of
neutrality as they slept peacefully.  I had a day of deeper than
usual meditation as I pondered the rightness or wrongness of
inflicting the death penalty.

It's now around 10:30am -- past the time to get busy.  So I'll
have to cut things short.  But I'll return within 24 hours with
the next in the unending series of fractals.  Until then, take
care, and keep those iterations up.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

FirecrackerFractal { ; time=0:04:33.04--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+9.688449083063871/-16.01010465889809/1\
  .588386e+008/1/40 params=-0.6/-1.3/-0.006/-3/0/1200
  float=y maxiter=1500 inside=0
  logmap=66 periodicity=10
  colors=000I0XI0bK0fM0iN0nP0sR0vSMtUftM9aXcsIMgN`qI\
  VqFShDIZAAP9EQ53M30020000F0Cd0Iz0Fy0Dv0Cq0An0Uz05f\
  03m02Z05UA6PK9KfAHdCCvO6zX3zcCzAKr3Sc0`D0h30p00x00\
  z00x09q0Im0Uf0d`2nW5yP9zIAzDFzAIq6Mc3PP0SA0W00U02U\
  06U0CU0IS0NS0SS0ZS0cS0hU5fW9dXDcZHbZM``PZbUXcXWdbU\
  ddSfiRhmPiqNktMkxMmyZmykmzxmzznyzpxzqvzstytsvvqtxp\
  qynpzmmzkkzihzhfzfczdbzcZzbXzXRqUKhPDZM9PH2FD05A0M\
  HzRMzURzXUz`Zzcczffzcnzbvp`zcZzPXzCfv6p`2yD0z00z00\
  z09z0Hz3Pz6XzAczDkzHszKzzNzzRzvSzsUzpWzkWzhXzdZzb`\
  zX`zUbzRczNdzIdyFfxChv9hvImySqzbvzizzkyzmxxmxtnvpp\
  vmptiqsdssbsqZtqUvpRvpNpnUin`dnfZmmSmsNmxRqzStzWyz\
  Xzz`zzbzz`zy`zmZz`ZzMXz9Xz0Xz0izN`z0bz0cz0dz0fz0hz\
  2iz5kz9mzCnzFpzIqzMszPtzSvzWczzdzzfzzhzzizzizzkzzm\
  zynzvnztpzqqznszkszhtzdvzbxzZkzzmzznzzpzzpzxqztszp\
  tzmtzhvzdxz`zzizzhzzfzzfzzdzzdzzczzczzbzz`zz`zzZyz\
  ZxzX0z0Cz0Pz5`zFzzPzzS0z0
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  13-06-01  (Cerberus [7])
Date: 13 Jun 2001 10:00:12 -0400 (EDT)


Classic FOTD -- June 13, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

I named today's FOTD "Cerberus" when, for some reason, I was
reminded of the gates of hades.  (I used the *good* word for
that place down there.)  In ancient mythology, Cerberus was the
watchdog of Hades, who treated the entering souls with kindness,
but ate any souls that tried to escape.  Descriptions of the
monstrous hound vary, but according to most reports it had at
least three heads with poisonous bites, and several snake-like
tails.

Today's fractal comes nowhere near being a hound of the
underworld, but with it's strings of bof60 bubbles and
mysterious glowing fiery pyramid in the background, it does have
just enough of a surrealistic quality to justify the name.

To create the image, I returned to number 4 in my series of 12
MandNewt formulae, a series I have been woefully ignoring
lately.  The formulae are variations of the Ikenaga function,
and I'm still not sure what the Ikenaga function is supposed to
accomplish, or why its creator seems to have disowned it.

I have rated the image a 7 -- a rating perhaps a bit liberal --
but the colors blend quite well, with the bands in the spheres
at the bottom being virtually invisible.  Perhaps I'll devote
more effort to images such as today's in the future.  One thing
for sure is that the midgets are starting to become a bit
routine.

The 8-1/2 minute render time can be avoided by giving Paul and
Scott a chance to post the GIF image to their web sites and
downloading it from there.  Paul's site is at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and Scott's can be found at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was typical of summer in this part of
the world, with hazy sun, 89F (31.5C) heat, humidity, and
evening thunder-showers in the area.  The fractal cats, who
enjoy such conditions, except for the thunder, enjoyed the day.

As for myself, I'll find my enjoyment when the day's work is
finished.  And the only way to finish is to start.  Until next
time, take care, and be careful to avoid the hound of Cerberus.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Cerberus           { ; time=0:08:28.77--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=mandnewt04 passes=1
  center-mag=0.221881/2.99156/2.308161/1/-82.5
  params=-2.7/0.32/-2.8/-2.21/0.35/-2.04 float=y
  maxiter=250 inside=bof60 logmap=yes periodicity=0
  colors=000_pz_pyZoyZoxZnxYnwWmwWmvVlvVluUkuUktSjtS\
  jsRisRirQhrQhqOgqOgpQfpOfoOeoOenOdnOdmNcmNclNblNbk\
  NakNajM`jM`iM_iM_hMZhLZgLYgLYfLXfLXeLWeJWdJVdJVcJU\
  cJUbJTbITaISaIS`IR`IR_HQ_HQZHPZHPYHOYHOXGNXGNWGMWG\
  MVGLVGLUEKUEKTEJTEJSEISDIRDHRDHQDGQDGPDFPCFOCEOCEN\
  CDNCDMDCMCCLCBLCBKCAKCAJC9JC9IC8IC8HC7HC7GC6GC6FC5\
  FA5EA4EA4DA3DA3CA2CA2BA4BA4AA4AA49A49A48A489479479\
  46946945945944944943943942C42E41H41J10M40O50R60U80\
  W95ZAAaAFcAKdANeANfAMgAMhALiALjAJkAJlAImAInAHoAHyc\
  8xb6wa5v`4u_2tZ1sY0rX0qW0pV0oU0nT0mS0lR0kQ0UWUSWUR\
  YUQZUO_UNaUMbUJcVIdVHfVGgVEhVDhVCjVAkV9lV8mV6oV5pV\
  4rV2sV1tV0uV0uS0uU0uV0uW1uW2uY4uZ5uZ8u_9uaAuaCubDu\
  cEudGudHufJugLugMuhNujOujQukRulUumVumWuoYupZup_ura\
  usaxtbwsbusbusctscsrcsrcrrdrrdppdopdopfmpfloflofko\
  gkogjmghmhhmhgmhflhfljdljdljckjbkkbkkakk_jk_jlZjlZ\
  jlYhmWhcLmcLmbMmbMoaNoaNo
  }

frm:MandNewt04 {; Jim Muth
z=c=pixel:
a=z^3+(c-1)*z-c
b=p1*z^2+c-1
z=z-p2*a/b
p3 <= |a|
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Copyright infringement
Date: 13 Jun 2001 14:28:47 -0400

Hi All,

  I've been contacted by the owner of this site:

    <http://www.geocities.com/tantrapages/>

  who is asking my permission to use some of my fractals on his site, and=

who also begs my pardon for having always posted some of them.  Although =
he
clearly says he is not the author of the images and mentions for most (bu=
t
not all) of them the author and the source of the image, I asked him to
remove my images from his site.

  He is probably in the process of contacting all the authors of the imag=
es
he's using, but if you haven't been contacted yet, you may be interested.=


  Cheers,

        - Sylvie

 E-mail:
   [e-mail]
 Web site:
   http://www.fractalus.com/sylvie/homepage.htm

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-------------------------------------------------------------------------------

From: caren <[e-mail]>
Subject: Re: (fractint) Copyright infringement
Date: 13 Jun 2001 11:44:19 -0700 (PDT)

there were a few there that looked like they could have been some of my
very early work, but had different names (and authors)...  i saw a few
by damien jones, too, attributed correctly...

while i generally like his taste/choices, i suppose someone will have
to go in there and explain to him what copyright infringement is all
about...

00 caren


--- Sylvie Gallet <[e-mail]> wrote:
> Hi All,
>
>   I've been contacted by the owner of this site:
>
>     <http://www.geocities.com/tantrapages/>
>
>   who is asking my permission to use some of my fractals on his site,
> and
> who also begs my pardon for having always posted some of them.
> Although he
> clearly says he is not the author of the images and mentions for most
> (but
> not all) of them the author and the source of the image, I asked him
> to
> remove my images from his site.
>
>   He is probably in the process of contacting all the authors of the
> images
> he's using, but if you haven't been contacted yet, you may be
> interested.
>
>   Cheers,
>
>         - Sylvie
>
> -----------------------------------------------
>  E-mail:
>    [e-mail]
>  Web site:
>    http://www.fractalus.com/sylvie/homepage.htm
> -----------------------------------------------
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"


__________________________________________________
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Get personalized email addresses from Yahoo! Mail - only $35
a year!  http://personal.mail.yahoo.com/

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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) tantrapages
Date: 13 Jun 2001 12:53:26 -0600

Sylvie,

I already sent Anatoly e-mail about his site, saying he should explicitly
state that he has permission from the artists to display the images, and
then make sure he really does have permission, by contacting the artists.
I offered to help him identify the remaining images in his collection so
that he can properly obtain permission; I expect he is contacting anyone
he doesn't have permission from yet. I did give him permission to use my
images, provided that the attributions are present. I would probably
withdraw that permission if he continued to post images for which he did
not have explicit permission.

--Damien

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Re: [fractal-art] Copyright infringement
Date: 13 Jun 2001 14:27:03 -0500

Sylvie Gallet wrote:
>
> I've been contacted by the owner of this site:
>     <http://www.geocities.com/tantrapages/>
>

Anatoly Goifman (a 28 year old Russian born Jew) states the following on
the About page:

     "I respect copyright of any web artist."

And then later states:

     "Most of fractal images with provided links are
      posted with the artist permission !  Otherwise
      I am waiting to receive it or I shall withdraw
      the pictures."

The site appears to have been recently established.  So that person may
truely be attempting to contact everyone.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: Bob Margolis <[e-mail]>
Subject: (fractint) Re: [fractal-art] Copyright infringement
Date: 13 Jun 2001 14:34:13 -0500

"Paul N. Lee" wrote:
>

>
> Anatoly Goifman (a 28 year old Russian born Jew) states the following on
> the About page:
>


Hi Paul;

What does his being 28 years old have to do with the issue at hand?

What does his being Russian have to do with the issue at hand?

What does his being Jewish have to do with the issue at hand?

Best regards,

Bob
--
************************************

  Alcohol and calculus don't mix -
  PLEASE don't drink and derive.

************************************

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Re: [fractal-art] Copyright infringement
Date: 13 Jun 2001 14:57:24 -0500

Bob Margolis wrote:
>
> What does his being 28 years old have
> to do with the issue at hand?
> What does his being Russian have
> to do with the issue at hand?
> What does his being Jewish have
> to do with the issue at hand?
>

Only that he is young, comes from one country and is living in another,
and may not be familiar with such things as copyright infringement.

Those that are older, and usually with more experience, most often know
about such things.  Also, that English is not his native tongue, which
is where most of the copyright information is obatined these days.  It
was only an extremely short summation of his About web page to possibly
explain his actions of not contacting artists initially.  Nothing more
or less.

Why, do you have some other reasoning behind my statements??

P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: Bob Margolis <[e-mail]>
Subject: (fractint) Re: [fractal-art] Copyright infringement
Date: 13 Jun 2001 15:17:27 -0500

"Paul N. Lee" wrote:
>
> Bob Margolis wrote:
> >
> > What does his being 28 years old have
> > to do with the issue at hand?
> > What does his being Russian have
> > to do with the issue at hand?
> > What does his being Jewish have
> > to do with the issue at hand?
> >
>
> Only that he is young, comes from one country and is living in another,
> and may not be familiar with such things as copyright infringement.
>
> Those that are older, and usually with more experience, most often know
> about such things.  Also, that English is not his native tongue, which
> is where most of the copyright information is obatined these days.  It
> was only an extremely short summation of his About web page to possibly
> explain his actions of not contacting artists initially.  Nothing more
> or less.
>
> Why, do you have some other reasoning behind my statements??
>

I was just curious as to why his age, country of origin and religion
were of importance to the discussion.

In your reply you say why you mentioned his age and his being Russian as
possibly having something to do with whether he is aware of and
understands what copyright is all about, but you did not say what
connection there is between his being Jewish and his alleged copyright
infringement. Would you kindly enlighten me? Thank you.

Respectfully,

Bob
--
************************************

  Alcohol and calculus don't mix -
  PLEASE don't drink and derive.

************************************

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Re: [ultrafractal] Re: [fractal-art] Copyright infringement
Date: 13 Jun 2001 16:12:50 -0500

Bob Margolis wrote:
>
> I was just curious as to why his age,
> country of origin and religion were
> of importance to the discussion.
>

If you are trying to read something into this that is not and was not
meant, then you should do so off-list privately where others will not be
bothered by an ongoing discussion.

And I wish to thank Daniel Kuzmenka and David E. Shanholtzer for
replying to the UF-List, and understanding that nothing negative was
meant.  Only a very short explanation about the person and his
statements.     :-)

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: Sylvie Gallet <[e-mail]>
Subject: (fractint) tantrapages
Date: 13 Jun 2001 17:19:44 -0400

Damien,

>> I offered to help him identify the remaining images in his collection =
so
>> that he can properly obtain permission; I expect he is contacting anyo=
ne
>> he doesn't have permission from yet.

  This is probably why he contacted me.  Thank you.

        - Sylvie

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-------------------------------------------------------------------------------

From: Sylvie Gallet <[e-mail]>
Subject: (fractint) Re: [fractal-art] Copyright infringement
Date: 13 Jun 2001 17:19:40 -0400

Hi Paul,

>> The site appears to have been recently established.  So that person ma=
y
>> truely be attempting to contact everyone.

  It has also been recently updated!  The About page I have in my cache
has:

"I respect copyright of any web artist. That is why I confirm that no one=

of the fractal images on these pages was created by me and I also provide=

links to pictures sources. Unfortunately I had not registered specific
artist for each image in due time, so sometimes it is quite difficult to
identify the specific picture. I plan to do this in the future."

  Cheers,

        - Sylvie

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-------------------------------------------------------------------------------

From: Sylvie Gallet <[e-mail]>
Subject: Re: (fractint) Copyright infringement
Date: 13 Jun 2001 17:19:47 -0400

Caren,

>> there were a few there that looked like they could have been some of m=
y
>> very early work, but had different names (and authors)...  i saw a few=

>> by damien jones, too, attributed correctly...

  There's also images that come form the fractal art contests, I don't kn=
ow
if they were attributed correctly because I didn't download the large
images.

>> while i generally like his taste/choices, i suppose someone will have =
to
>> go in there and explain to him what copyright infringement is all
>> about...

  It has probably been done.

  Cheers,

        - Sylvie

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-------------------------------------------------------------------------------

From: Tim Lavoie <[e-mail]>
Subject: (fractint) XFractint, disk video, true color, shell
Date: 14 Jun 2001 01:21:57 -0500

Hello,

I'm recently starting to use XFractint under Linux, Version 20.01.11. I'm
new at using the program, but am trying to RTFM and so on, and I realize
that the DOS heritage changes some things for me.

I've heard of the program for years, but never tinkered too far with it.
Still, I start drooling over the goodies, and have decided to go at it
again.

That said, there are some quirks that I've run into so far. If they're mere
ignorance, that's OK too.  <grin>

 - The docs say to press <del> to use disk video mode, but this does nothing
 for me other than re-drawing the image. The man page that I've got claims
 that DELETE and D are Dos <--> Unix equivalent key mappings, but they don't
 appear to be. 'D' redraws, and 'd' goes into shell mode. I also tried the
 -disk command-line flag, and the program died immediately with a seg fault
 and core dump.

 - How do I get true-color to work? Should it appear in my View Window
 Options screen? I see nothing there for either image size or true-color
 options.

 - While I don't need the 'd' shell command, I do whack it by accident.
Typing "exit" as usual to get out of the shell also causes a
segfault/coredump.

 - I get some strange rendering artifacts in some fractals, and weird stuff
that ends up in saved images as well. The rendering-time one is a grid
pattern of dots on the left-hand side, say with the default mandel as an
example. I can avoid this if I switch from "guess" to another pass type in
the 'x' option panel, so no big deal there. The other appears as a vertical
line travelling down the display window when I save to a .gif, and it
appears in the saved image as well. Along with that, the sides of the image
look like they're out of sync with the middle, with the left one bordering
on that vertical line I mentioned. I can also see this weird look if I
switch to a different virtual desk top and back again, without saving.

       So, any suggestions out there? I'm itching to play!

  Thanks,
  Tim

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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  14-06-01  (Cerberus [4])
Date: 14 Jun 2001 10:39:47 -0400 (EDT)


Classic FOTD -- June 14, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

Today's FOTD is named "The New Thing".  This name could possibly
lead to questions such as: 'what is the *Old* Thing?', or 'where
is the Old Thing?'.  The answer is there never was an *old*
thing.  I gave today's image its name when I could think of
nothing better.

The image is another venture into the world of bof60 bubbles,
this one created by number 5 in my series of MandNewt formulae.
We'll be seeing more of this type of image in the future, since
I feel that the string of images with midgets is growing a
little too routine.

Due to too little time to work on it and too much other stuff to
do, today's image rates only a 4.  But better things are to
come.  The parameter file renders in 5 minutes; the GIF image
downloads in 1/4 of the time.  The GIF file is available at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather was typical of summer -- hazy, hot and
humid.  The temperature of 92F (33C) caused the fractal cats to
slip into their lazy mode, though it would take a careful
observer to notice the difference.

I'll return in the allotted time.  Until that time comes, take
care, and be of good cheer.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

The_New_Thing      { ; time=0:05:02.25--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandNewt05 function=acos passes=1
  center-mag=-2.19269720346380100/+1.019368761059859\
  00/3732.62/1/17.499
  params=-3.983/2.042/-3.399/-4.9415/-1.464/0.326
  float=y maxiter=255 inside=bof60 logmap=yes
  symmetry=none periodicity=10
  colors=000ljojhnhflgdkfbje`id_hcZgbYfaXeaWd`Wc`Vb_\
  Va_U`ZU_ZTZYTYYSXXSWXRVWRUWQTVQSVPRUPQUOPTOOTNNSNM\
  SMLRMKRLJQLIQKHzzczzZyzUxzPwzKvzFuzCtzBszArzAqzBpz\
  CozDnzEmzElzFkzGjzHiyIhxIgwJfvKeuLdtMcsMbrNdqOfpPh\
  oQgnPfmOelNekMdjPciLbhKbgJafI`eH_dG_cGZbFYaEX`DX_C\
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  qKGpKGoKGoKGnKGmKGlKGkKGkKGjKGiKFhKFgKFgKFfKFeKFdK\
  FcKFcKFbKFaKF`LE_LE_LEZLEYLEXLEWLEWLEVLEULETLESLDS\
  LDRLDQLDPLDOLDOLDNLDMLDLLDKLDLMCKLDKLEKKFKKGKJHKJI\
  KIJKIJKHKKHLKGMKGNKFOKFPKEPJEQJDRJDSJCTJCUJBVJBWJA\
  WJAXJ9YJ9ZJ8_J8`J7aJ7aI6bI6cI5dI5eI4fI4gI3hI3hI2iI\
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  HXCIY6HZ9H_CH`FG`IGaLGbOFbRFcUFdXFe_EebEfeEghDgkDh\
  nDiqDisEhrFhrGhrHgrIgrJgr
  }

frm:MandNewt05 {; Jim Muth
z=c=fn1(pixel):
a=z^2+(c-p1)*z-c
b=p2*z^2+c-1
z=z-1*a/b
p3 <= |a|
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  14-06-01  (The New Thing [4])
Date: 14 Jun 2001 10:41:23 -0400 (EDT)


Classic FOTD -- June 14, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

Today's FOTD is named "The New Thing".  This name could possibly
lead to questions such as: 'what is the *Old* Thing?', or 'where
is the Old Thing?'.  The answer is there never was an *old*
thing.  I gave today's image its name when I could think of
nothing better.

The image is another venture into the world of bof60 bubbles,
this one created by number 5 in my series of MandNewt formulae.
We'll be seeing more of this type of image in the future, since
I feel that the string of images with midgets is growing a
little too routine.

Due to too little time to work on it and too much other stuff to
do, today's image rates only a 4.  But better things are to
come.  The parameter file renders in 5 minutes; the GIF image
downloads in 1/4 of the time.  The GIF file is available at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather was typical of summer -- hazy, hot and
humid.  The temperature of 92F (33C) caused the fractal cats to
slip into their lazy mode, though it would take a careful
observer to notice the difference.

I'll return in the allotted time.  Until that time comes, take
care, and be of good cheer.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

The_New_Thing      { ; time=0:05:02.25--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandNewt05 function=acos passes=1
  center-mag=-2.19269720346380100/+1.019368761059859\
  00/3732.62/1/17.499
  params=-3.983/2.042/-3.399/-4.9415/-1.464/0.326
  float=y maxiter=255 inside=bof60 logmap=yes
  symmetry=none periodicity=10
  colors=000ljojhnhflgdkfbje`id_hcZgbYfaXeaWd`Wc`Vb_\
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  MEjMEkMEkLFlLFmLFmLFnKGoKGoKGpKGqJHqJHrJHsJHsJHrKG\
  qKGpKGoKGoKGnKGmKGlKGkKGkKGjKGiKFhKFgKFgKFfKFeKFdK\
  FcKFcKFbKFaKF`LE_LE_LEZLEYLEXLEWLEWLEVLEULETLESLDS\
  LDRLDQLDPLDOLDOLDNLDMLDLLDKLDLMCKLDKLEKKFKKGKJHKJI\
  KIJKIJKHKKHLKGMKGNKFOKFPKEPJEQJDRJDSJCTJCUJBVJBWJA\
  WJAXJ9YJ9ZJ8_J8`J7aJ7aI6bI6cI5dI5eI4fI4gI3hI3hI2iI\
  2jI1kI1lI0mI0nI0nH3jH6gH9dHBaHEYHHVHJSHMPHPLHRIHUF\
  HXCIY6HZ9H_CH`FG`IGaLGbOFbRFcUFdXFe_EebEfeEghDgkDh\
  nDiqDisEhrFhrGhrHgrIgrJgr
  }

frm:MandNewt05 {; Jim Muth
z=c=fn1(pixel):
a=z^2+(c-p1)*z-c
b=p2*z^2+c-1
z=z-1*a/b
p3 <= |a|
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) XFractint, disk video, true color, shell
Date: 14 Jun 2001 19:26:58 -0500

Tim,

> - The docs say to press <del> to use disk video mode, but this does
nothing
> for me other than re-drawing the image. The man page that I've got claims
> that DELETE and D are Dos <--> Unix equivalent key mappings, but they
don't
> appear to be. 'D' redraws, and 'd' goes into shell mode. I also tried the
> -disk command-line flag, and the program died immediately with a seg fault
> and core dump.

I haven't tried the <del> key to use disk mode, but I knew that -disk was
broken.  I'm looking at it now.

> - How do I get true-color to work? Should it appear in my View Window
> Options screen? I see nothing there for either image size or true-color
> options.

If you are running Linux in a true-color mode, then Xfractint will run in
the same mode.  There are some issues with this.  Like people expecting the
colors to be saved in a PAR even though they are in a true-color mode and
this doesn't necessarily make any sense.

> - While I don't need the 'd' shell command, I do whack it by accident.
> Typing "exit" as usual to get out of the shell also causes a
> segfault/coredump.

I'll have to look into this one.  Thanks.

>  - I get some strange rendering artifacts in some fractals, and weird
stuff
> that ends up in saved images as well. The rendering-time one is a grid
> pattern of dots on the left-hand side, say with the default mandel as an
> example. I can avoid this if I switch from "guess" to another pass type in
> the 'x' option panel, so no big deal there. The other appears as a
vertical
> line travelling down the display window when I save to a .gif, and it
> appears in the saved image as well. Along with that, the sides of the
image
> look like they're out of sync with the middle, with the left one bordering
> on that vertical line I mentioned. I can also see this weird look if I
> switch to a different virtual desk top and back again, without saving.

I'll have a look at this.  If I can't reproduce it, I'll get back with you.

Jonathan



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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  15-06-01  (The Unseen Midget [6])
Date: 14 Jun 2001 22:40:02 -0400 (EDT)


Classic FOTD -- June 15, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

I have decided that the month of July will me a midgetless
month.  I need a break from the unending string of midgets.  But
July is still 2 weeks away, and there's lots of time for midgets
before then.  And don't worry all you fans of the mighty
midgets, the midgets will return in August, when they will
appear much fresher due to the month's absence.

I sometimes hear it said that nothing of interest remains to be
discovered in the classic Mandelbrot set.  I find this statement
to be rather puzzling in view of the fact that the set is
infinite, and Fractint can enlarge it to a size nearly one
googol times that of the visible universe.  (If not larger!)

Today's image pictures a midget in the classic Mandelbrot set,
which holds more midgets than one can shake anything at.  This
midget is located in the northwest suburbs of a larger midget in
a high-iteration area of a second-order valley of a small bud on
the west-northwest shore of the main bud of the M-set.  The
scene is actually in double-scepter valley.

I named the picture "The Unseen Midget".  Almost certainly, this
particular midget has never before been seen, a fact that
inspired the name.  The scene proved to be a particularly
difficult one to color.  Nothing worked until I tried the -nnn
logmap option, which causes a quadratic compression of the
iteration values.  This particular compression reveals the
unusual pattern of twisting, folding arms surrounding the midget.

Considering the fact that the image is part of the warhorse
M-set, and not part of some exotic formula, I could rate it no
higher than a 6, which is still above average.  The render time
is a short 5 minutes; the download time of the GIF image file is
even shorter.  And in an hour or so, that image file will be
available on Paul Lee's web site at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and on Scott Boyd's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was near perfect, with blue skies and
a temperature of 86F (30C).  Only the unusually high humidity
kept it from being absolutely perfect.  The cats showed their
approval by resting in the yard for a good part of the afternoon.

My urge to philosophize is once again rising.  This time I'm
thinking of my favorite form of mental exercise -- the fourth
dimension.  About 10 years ago I wrote a novelette about a man
who got snatched into hyperspace, and was lost there until he
found his way back into his home space.  Unfortunately, he
returned as his mirror image.  I ignored the fact that his body
would have appeared as anti-matter and the resulting explosion
would have wiped out half the state, but this did not mean that
all was well for him, because his reversed body could not digest
the normal unreversed food, and he nearly starved.  I think the
story, which after much struggling turns out well, is still on a
disk somewhere in my vast archives.  Maybe I'll dig it out and
re-write it one of these days.

But for this evening, I'll do nothing but take it easy and
supply the pesky fractal cats with a bedtime snack.  Until next
time, which will arrive sooner than suspected, take care and see
you then.


Jim Muth
[e-mail]


START PARAMETER FILE=======================================

The_Unseen_Midget  { ; time=0:04:51.00--SF5 on a P200
  reset=2001 type=mandel passes=1
  center-mag=-1.23484961150443600/+0.113183231817535\
  00/1.823247e+012/1/-104.803/-0.327 params=0/0
  float=y maxiter=24000 inside=0 logmap=-4680
  colors=0009KPAJRBJSCITCHVDGWEGYFFZFE`GEaHDcICdIBfJ\
  BgKAiL9jL9kPFgTLdXR``XYdbUhhRknOilNgkMejLchKagK_fJ\
  YeIWcHUbGTaGR`FPZENYDLXCJWCHUBFTADS9CR9HV8LZ8Pa8Te\
  7Xh7al7ep6is6mw6qz6ov8nrAmnCkjDjfFibHhZIiXHjWGkVFl\
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  0_60Z60Y50X50W50X70X90XB0XC0XE0XG0XI0XJ0XL0XN0XP0X\
  Q0XS0YU0YW0YX0YZ0Y`0Yb0Yc0Ye0Yg0Yi0Yj0Yl0Yn0Yo0Wn3\
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  qbvrbwrbxqcvpcwocxncumczmczlczkczjczicziczhczgczfc\
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  pgzqgzrgzsgzsgzqfzpezodzmdzlczkbzjazhazg`zf_zeZzcZ\
  zbYzaXz`Xz_Zz``zaazbbzccz
  }

END PARAMETER FILE=========================================


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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 15-06-01 (The Unseen Midget [6])
Date: 15 Jun 2001 09:07:08 -0000

>From: Jim Muth <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  15-06-01  (The Unseen Midget [6])
>Date: Thu, 14 Jun 2001 22:40:02 -0400 (EDT)
>
>
>Classic FOTD -- June 15, 2001 (Rating 6)
>
>Fractal visionaries and enthusiasts:
>
>Considering the fact that the image is part of the warhorse
>M-set, and not part of some exotic formula, I could rate it no
>higher than a 6, which is still above average

I don't follow that logic; for me, I rate an image by how good it looks,
not how it was made (or how hard it was to make!)

>My urge to philosophize is once again rising.  This time I'm
>thinking of my favorite form of mental exercise -- the fourth
>dimension.  About 10 years ago I wrote a novelette about a man
>who got snatched into hyperspace, and was lost there until he
>found his way back into his home space.  Unfortunately, he
>returned as his mirror image.  I ignored the fact that his body
>would have appeared as anti-matter and the resulting explosion
>would have wiped out half the state, but this did not mean that
>all was well for him, because his reversed body could not digest
>the normal unreversed food, and he nearly starved.  I think the
>story, which after much struggling turns out well, is still on a
>disk somewhere in my vast archives.  Maybe I'll dig it out and
>re-write it one of these days.

Erm... wouldn't this poor sod also be unable to breathe unreversed air and
thus instantly sufforcate?!?!

Thanks.
Andrew.

"Life is only hopeless if you stop hoping" - My new slogan. Like it?

_________________________________________________________________________
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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) XFractint, disk video, true color, shell
Date: 15 Jun 2001 09:09:42 -0000

>From: "Jonathan Osuch" <[e-mail]>
>Reply-To: [e-mail]
>To: <[e-mail]>
>Subject: Re: (fractint) XFractint, disk video, true color, shell
>Date: Thu, 14 Jun 2001 19:26:58 -0500
>
>Tim,
> >  - I get some strange rendering artifacts in some fractals, and weird
>stuff
> > that ends up in saved images as well. The rendering-time one is a grid
> > pattern of dots on the left-hand side, say with the default mandel as an
> > example. I can avoid this if I switch from "guess" to another pass type
>in
> > the 'x' option panel, so no big deal there.

I've seen this one too. It didn't happen under RadHat 6 / GNOME, but it did
show up with SuSE 7.1 / KDE.

Thanks.
Andrew.

_________________________________________________________________________
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-------------------------------------------------------------------------------

From: Guy Marson <[e-mail]>
Subject: (fractint) evolver
Date: 15 Jun 2001 11:49:06 +0200

Hi Fractint developers,

Since a few weeks I am playing around with Fractints Evolver. That's the
most powerful tool I ever found to demonstrate Evolution and Darwinism.
Ideal to show Kids what 'Selection' in Nature (etc..) is.

It'll be the moment to kindly ask the insertion of p4 and p5 into the Evolver?

Thanks for the good work to all of you!!


Cheers,

Guy


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-------------------------------------------------------------------------------

From: Ralph Feltens <[e-mail]>
Subject: Re: (fractint) C-FOTD 15-06-01 (The Unseen Midget [6])
Date: 15 Jun 2001 12:22:15 +0200

Hi there!

(lurk mode off)

Andrew Coppin wrote:

> >My urge to philosophize is once again rising.  This time I'm
> >thinking of my favorite form of mental exercise -- the fourth
> >dimension.  About 10 years ago I wrote a novelette about a man
> >who got snatched into hyperspace, and was lost there until he
> >found his way back into his home space.  Unfortunately, he
> >returned as his mirror image.  I ignored the fact that his body
> >would have appeared as anti-matter and the resulting explosion
> >would have wiped out half the state, but this did not mean that
> >all was well for him, because his reversed body could not digest
> >the normal unreversed food, and he nearly starved.  I think the
> >story, which after much struggling turns out well, is still on a
> >disk somewhere in my vast archives.  Maybe I'll dig it out and
> >re-write it one of these days.
>
> Erm... wouldn't this poor sod also be unable to breathe unreversed air and
> thus instantly sufforcate?!?!

No, all the gases (O2, CO2, N2) and other small molecules such as H2O would
pose no problems, since they possess no chirality. So breathing or drinking
water would be okay for a mirror-image person. Food, of course, would be a
different matter altogether (but one would be warned by a strange smell or
taste of an apparently normal looking beefsteak - it will taste only as sour
or salty as it used to be). And you would probably never be able to appreciate
the smell of a flower again ...

The advantage of beeing a mirror-man would be that no human pathogen will be
able to cause you any harm (no viruses, no bacteria), so you will never become
ill again. And you will be rid of your allergies (of course, you can start to
acquire new ones immediately).

Funny that a lot of other people are doing these mind-experiments.

>
> Thanks.
> Andrew.
>
> "Life is only hopeless if you stop hoping" - My new slogan. Like it?

Sounds nice!

Regards

            Ralph


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-------------------------------------------------------------------------------

From: Guy Marson <[e-mail]>
Subject: Re: (fractint) C-FOTD 15-06-01 (The Unseen Midget [6])
Date: 15 Jun 2001 13:57:01 +0200

At 09:07 15/06/01 -0000, you wrote:
>"Life is only hopeless if you stop hoping" - My new slogan. Like it?


not bad..




life_is1           { ; Version 2001 Patchlevel 10
                     ;  Version 2001 Patchlevel 10
  reset=3D2001 type=3Dformula formulafile=3Dla-life2.frm
  formulaname=3Dla-life2 function=3Dtanh/cabs/tan/sinh passes=3D1
  center-mag=3D-0.172865/-0.23958/1.349211
  params=3D4.517972350230415/-2.57126682332835/-1.829798272652363/-3.2219519=
\
  63866085/-0.1/-0.1/16/3/0.1/1 float=3Dy maxiter=3D200 inside=3Datan
  outside=3Dfmod decomp=3D64 symmetry=3Dnone periodicity=3D0
  colors=3D000yqQ<3>xmNxlMwkM<3>ueJudItbI<3>pVGoTGnRF<7>TD7QB6OA5<3>D21A00B0=
\
  0<3>F00G00I00J00K00M30P60R90<14>lgfmiiokl<3>uuxstx<24>clqblqalq<3>_jo_io\
  Zio<3>Wgm<3>bkodlpemp<3>lqsnrtpst<3>www<4>gindfladk<3>QUcNRaKO_<2>AFU<15\
  >`bibdjcek<3>jlolnpnoq<3>uvv<5>kloijnghm<5>Z_gXYfWWe<3>PP`NNZLLY<5>BBS99\
  R77Q<3>00L<3>66P88Q99R<2>FFUGGVIIWJJXLLY<15>llonnpooq<2>uutwwvwwt<11>xub\
  xuayu_<2>ytWytUyrRyqQ
  }

frm:la-life2   { ; lake-transformation =3D Sylvie Gallet, Jan 16, 2000
; requires: float=3Don, Fractint 20.0.6, periodicity=3D0' and 'passes=3D1'
; real part of p1: merging/position of text (x and y)
; imag part of p1: merging/position of text (x and y)
; real part of p2: merging/position of text (x and y)
; imag part of p2: merging/position of text (x and y)
; real part of p3: x-position of text bailout versus background fractal
; imag part of p3: y-position of text bailout versus background fractal
; real part of p4: 0 =3D lake transform disabled
;                  any value between 0 and 100: water level in % of
;                  the screen height (0 =3D bottom, 100 =3D top)
; If (B=3DA*C) then text=3Dinvisible, else=3Dvisible!
; imag part of p4: A (diameter of picture bailout)=20
; real part of p5: B (diameter of text bailout)=20
; imag part of p5: C (position of picture bailout -try '1'-)=20

pp_p3 =3D (0.2,300) ;  0.2=3Damplitude  and  300=3Dfrequency of the lake

; Lake transformation
; -------------------

if (real(p4) > 0 && real(p4) <=3D 100)
  level =3D real(p4) / 100            ; water level
  ampl =3D real(pp_p3)                ; amplitude of the wave
  freq =3D imag(pp_p3)                ; frequency
  angle =3D real(rotskew * pi / 180)
  exp_irot =3D exp(-flip(angle))
  h =3D 1 / real(magxmag)
  w =3D h / 0.75 * imag(magxmag)
  tanskew =3D tan(imag(rotskew * pi / 180))
  u =3D 2 * w * exp_irot
  v =3D 2 * h * (tanskew + flip(1)) * exp_irot
  z3rd =3D center + (-w-h*tanskew - flip(h)) * exp_irot
  z =3D pixel - z3rd
  b =3D imag(conj(u)*z) / imag(conj(u)*v)
  if (b <=3D level)
    dy =3D level - b
    z =3D z + 2*dy * (1+ampl*sin(freq*dy^0.2)) * v=20
  endif

 pixel =3D z + z3rd

endif

;hei kennt d'Formel hin.. an vergiess n=EBt, den Numm ze aenneren.(GM)
;life-is1 { ; using a standard Mandelbrot formula..
; text generated with FRACTEXT.EXE (by J.M.v.d.Walk & Sylvie Gallet

  z=3Dfn1(fn2(pixel-p3))*fn3(fn4(pixel-p3))-p2/p1

    x=3Dreal(z), y=3Dimag(z)
  chrL1 =3D x<-0.33362||y<0.5565&&x>-0.34012&&x<-0.31362
  chri2 =3D x>-0.30612&&x<-0.29962&&(y<0.587||y>0.5935)
  chrf3 =3D abs(cabs(z+(0.27373,-0.58353))-0.01009)<0.00325&&y>0.58353|\
  |(x>-0.28707&&x<-0.28057&&y<0.58353)||(x>-0.29212&&x<-0.27048&&y>0.\
  57175&&y<0.57825)
  chre4 =3D abs(cabs(z+(0.23413,-0.56875))-0.0155)<0.00325&&(x<-0.23413\
  ||y>0.56767||y<0.56442)||(y>0.56767&&y<0.57417&&x>-0.24963&&x<-0.21\
  863)
  chri6 =3D x>-0.18288&&x<-0.17638&&(y<0.587||y>0.5935)
  chrs7 =3D abs(cabs(z+(0.15788,-0.5765))-0.00775)<0.00325&&x<-0.15788|\
  |(abs(cabs(z+(0.15288,-0.5765))-0.00775)<0.00325&&x>-0.15288)&&(x<-\
  0.15788||y>0.5765)||((abs(cabs(z+(0.15788,-0.561))-0.00775)<0.00325\
  &&x<-0.15788)||(abs(cabs(z+(0.15288,-0.561))-0.00775)<0.00325&&x>-0\
  .15288)&&(x>-0.15288||y<0.561))||(x>-0.15788&&x<-0.15288&&(y<0.5565\
  ||(y>0.581&&y<0.5875)||(y>0.5655&&y<0.572)))
  chro9 =3D abs(cabs(z+(0.09063,-0.56875))-0.0155)<0.00325
  chrn10 =3D x>-0.06438&&x<-0.05788&&y<0.5875||(abs(cabs(z+(0.05104,-0.\
  57416))-0.01009)<0.00325&&y>0.57416)||(x>-0.0442&&x<-0.0377&&y<0.57\
  416)
  chrl11 =3D x<-0.0237&&x>-0.0302
  xy=3D2.5*x
  chry12 =3D y<xy+0.55299&&y>xy+0.53549||(y>-xy+0.54701&&y<-xy+0.56451)\
  &&y>xy+0.53549&&y<0.5875&&y>0.525
  chrh14 =3D x>0.05331&&x<0.05981||(abs(cabs(z+(-0.06665,-0.56875))-0.0\
  1009)<0.00325&&y>0.56875)||(x>0.07349&&x<0.07999&&y<0.56875)
  chro15 =3D abs(cabs(z+(-0.10624,-0.56875))-0.0155)<0.00325
  chrp16 =3D x>0.13249&&x<0.13899&&y<0.5875&&y>0.53125||(abs(cabs(z+(-0\
  .14837,-0.56875))-0.0155)<0.00325&&x>0.13899)
  chre17 =3D abs(cabs(z+(-0.19337,-0.56875))-0.0155)<0.00325&&(x<0.1933\
  7||y>0.56767||y<0.56442)||(y>0.56767&&y<0.57417&&x>0.17787&&x<0.208\
  87)
  chrl18 =3D x<0.22612&&x>0.21962
  chre19 =3D abs(cabs(z+(-0.25237,-0.56875))-0.0155)<0.00325&&(x<0.2523\
  7||y>0.56767||y<0.56442)||(y>0.56767&&y<0.57417&&x>0.23687&&x<0.267\
  87)
  chrs20 =3D abs(cabs(z+(-0.28962,-0.5765))-0.00775)<0.00325&&x<0.28962\
  ||(abs(cabs(z+(-0.29462,-0.5765))-0.00775)<0.00325&&x>0.29462)&&(x<\
  0.28962||y>0.5765)||((abs(cabs(z+(-0.28962,-0.561))-0.00775)<0.0032\
  5&&x<0.28962)||(abs(cabs(z+(-0.29462,-0.561))-0.00775)<0.00325&&x>0\
  .29462)&&(x>0.29462||y<0.561))||(x>0.28962&&x<0.29462&&(y<0.5565||(\
  y>0.581&&y<0.5875)||(y>0.5655&&y<0.572)))
  chrs21 =3D abs(cabs(z+(-0.32412,-0.5765))-0.00775)<0.00325&&x<0.32412\
  ||(abs(cabs(z+(-0.32912,-0.5765))-0.00775)<0.00325&&x>0.32912)&&(x<\
  0.32412||y>0.5765)||((abs(cabs(z+(-0.32412,-0.561))-0.00775)<0.0032\
  5&&x<0.32412)||(abs(cabs(z+(-0.32912,-0.561))-0.00775)<0.00325&&x>0\
  .32912)&&(x>0.32912||y<0.561))||(x>0.32412&&x<0.32912&&(y<0.5565||(\
  y>0.581&&y<0.5875)||(y>0.5655&&y<0.572)))
  test1 =3D chrL1||chri2||chrf3||chre4||chri6||chrs7||chro9||chrn10||ch\
  rl11||chrh14||chro15||chre17||chrl18||chre19||chrs20||chrs21&&y>0.5\
  5||chry12||chrp16&&y<0.6
  chri22 =3D x>-0.37014&&x<-0.36234&&(y<0.4644||y>0.4722)
  chrf23 =3D abs(cabs(z+(0.33128,-0.46024))-0.01211)<0.0039&&y>0.46024|\
  |(x>-0.34729&&x<-0.33949&&y<0.46024)||(x>-0.35334&&x<-0.32738&&y>0.\
  4461&&y<0.4539)
  chry25 =3D y<xy+1.06566&&y>xy+1.04466||(y>-xy-0.22566&&y<-xy-0.20466)\
  &&y>xy+1.04466&&y<0.465&&y>0.39
  chro26 =3D abs(cabs(z+(0.20036,-0.4425))-0.0186)<0.0039
  chru27 =3D x>-0.16886&&x<-0.16106&&y>0.43601&&y<0.465||(abs(cabs(z+(0\
  .15285,-0.43601))-0.01211)<0.0039&&y<0.43601)||(x>-0.14464&&x<-0.13\
  684&&y<0.465)
  chrs29 =3D abs(cabs(z+(0.08464,-0.4518))-0.0093)<0.0039&&x<-0.08464||\
  (abs(cabs(z+(0.07864,-0.4518))-0.0093)<0.0039&&x>-0.07864)&&(x<-0.0\
  8464||y>0.4518)||((abs(cabs(z+(0.08464,-0.4332))-0.0093)<0.0039&&x<\
  -0.08464)||(abs(cabs(z+(0.07864,-0.4332))-0.0093)<0.0039&&x>-0.0786\
  4)&&(x>-0.07864||y<0.4332))||(x>-0.08464&&x<-0.07864&&(y<0.4278||(y\
  >0.4572&&y<0.465)||(y>0.4386&&y<0.4464)))
  xt=3D1*x
  chrt30 =3D abs(cabs(z+(0.03437,-0.43601))-0.01211)<0.0039&&y<0.43601|\
  |(x>-0.05038&&x<-0.04258&&y>0.43601)||(x>-0.05644&&x<-0.03047&&y>0.\
  4572&&y<0.465)
  chro31 =3D abs(cabs(z+(-0.01314,-0.4425))-0.0186)<0.0039
  chrp32 =3D x>0.04464&&x<0.05244&&y<0.465&&y>0.3975||(abs(cabs(z+(-0.0\
  6369,-0.4425))-0.0186)<0.0039&&x>0.05244)
  chrh34 =3D x>0.12519&&x<0.13299||(abs(cabs(z+(-0.14121,-0.4425))-0.01\
  211)<0.0039&&y>0.4425)||(x>0.14942&&x<0.15722&&y<0.4425)
  chro35 =3D abs(cabs(z+(-0.18872,-0.4425))-0.0186)<0.0039
  chrp36 =3D x>0.22022&&x<0.22802&&y<0.465&&y>0.3975||(abs(cabs(z+(-0.2\
  3927,-0.4425))-0.0186)<0.0039&&x>0.22802)
  chri37 =3D x>0.27077&&x<0.27857&&(y<0.4644||y>0.4722)
  chrn38 =3D x>0.28757&&x<0.29537&&y<0.465||(abs(cabs(z+(-0.30358,-0.44\
  899))-0.01211)<0.0039&&y>0.44899)||(x>0.31179&&x<0.31959&&y<0.44899\
  )
  chrg39 =3D x>0.36234&&x<0.37014&&y<0.465||(abs(cabs(z+(-0.35109,-0.44\
  25))-0.0186)<0.0039&&x<0.36234)&&y>0.41092||(abs(cabs(z+(-0.34937,-\
  0.41092))-0.01687)<0.0039&&y<=3D0.41092)
  test2 =3D chri22||chrf23||chro26||chru27||chrs29||chrt30||chro31||chr\
  h34||chro35||chri37||chrn38&&y>0.42||chry25||chrp32||chrp36||chrg39\
  &&y<0.48
  test=3Dtest1||test2
  test0=3Dtest0&&whitesq
  test0=3D((test0||test)=3D=3D0)
  f1=3Dconj(imag(p5))*conj(imag(p4))*pixel
  f2=3Dreal(p5)*pixel
  pixel=3D(test=3D=3D0)*f1+test*f2
  z=3Dc=3Dpixel:
  z=3Dz*z+c
  |z| <=3D4
  }


cheers,


Guy

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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  16-06-01  (Midget [5])
Date: 16 Jun 2001 10:51:02 EDT


Classic FOTD -- June 16, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Today's midget lies in the classic Mandelbrot set, way out at
the tip of the long filament extending northwest from the
prominent midget on the negative stem.  It lies in the East
Valley area of a larger midget, which accounts for the East
Valley type features that appear at the break about halfway in
toward the center.

The scene is located quite deep in the M-set, causing the
relatively simple image to be burdened with a render time of
almost 20 minutes.  This is because of the need to shift to
arbitrary precision math.

Being unable to think of a better name, I gave the picture the
most simple and straightforward name possible.  I named it
"Midget".  Since it's pretty much an average image, I rated it
at an average 5.

The download will be available in an hour or so at the URL's:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was cloudy and very humid with
occasional showers.  The fractal cats, who dislike wet grass,
got grumpy.  And I've got some unexpected work to do, so until
next time, take care, and pray for science.


Jim Muth
[e-mail]


START 20.0 PARAMETER FILE==================================

Midget             { ; time=0:19:45.52--SF5 on a P200
  reset=2001 type=mandel passes=b
  center-mag=-1.7712568057684093329443456495111/0.06\
  616083696778904824193039979249/3.414565e+027/1/-57\
  .482/0.004 params=0/0 float=y maxiter=3200
  inside=255 periodicity=0
  colors=000jjSjoTlsXlxYlz_jrYiiYg`YfTXdLXcCXc4Xa3Ya\
  3_a1`a1aa0ca0ca0da0fa0ga0ia0ja0ja0la0ma0oa0pa0ra0r\
  i0ao3Ou77zC0uF0pG0lI0gL0cM3_O4VQ6QS7MT9OP7rS1pX6o`\
  AmdFmiLlmPjrTivYizadycaxcYvdVudSsfOsfLrgIpgDoiAmi7\
  miAofDocGoaJo_LoYOoVQoTToQXoPYoM`oLcoIfoGioDjoCgjA\
  df9ac9__7XV7TS6QO6OJ4LG4IC3F73CA11B10C04D03E41G71I\
  A0KF0MI0OL0QP0SS0XV0`_0da0id0mi0pl0so0qi0jc3_Y7PSC\
  HMFHICJJANL9RM7VO6ZP4bQ7fSFiTMlVToX`rYgu_gs``saTra\
  MrcFrc7pd0pd0pf0og0og0mi0mi0mj0lj0ll0ll3jiDigOgfYg\
  dgfcrdazd`y`YvYXuVVrSTpOSmLPlIOiFMfALd7Ja4G`1FY0DX\
  0CT0AS09V0AY0C`0Da0Fd1Gg4Ii6Jl9LoCMrFOsGPvJQyMSzOS\
  vSTsVVoYXlaYgd_dg``jaYocTrdQufMygJziFzjCzlFymGpoIi\
  pJ`rLTsMLuODuQCvSCxVCxXAy_Ay`Azc9zd9zf9zdCycFvaIsG\
  y4Jx6Mv7OsAQrCVoFXlI_jJaiLcgMfdPgcQjaSl`TgcQcdO`gL\
  XiISjFPmCLo9Gp6Ds39u06v0Dr0Jm3Pi4Vd7``9fXClTDvcTzm\
  izvxzxszxpzxmiYLiaOjfP000
  }

END 20.0 PARAMETER FILE====================================

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-------------------------------------------------------------------------------

From: Tim Lavoie <[e-mail]>
Subject: (fractint) Re: fractint-digest V1 #573
Date: 17 Jun 2001 00:39:10 -0500

Jonathan wrote:

> I haven't tried the <del> key to use disk mode, but I knew that -disk was
> broken.  I'm looking at it now.

OK, great. I started poking through the source a little, so I see where it
dies, but haven't gotten all the way back to the real cause. Short answer,
it tries to clear Ximage stuff, which it shouldn't have any of.
(and doesn't -  *BOOM*)
Here's the stack trace running it under gdb:

Program received signal SIGSEGV, Segmentation fault.
0x80f86e2 in clearXwindow () at unixscr.c:768
768         bzero(Ximage->data, Ximage->bytes_per_line*Ximage->height);
(gdb) bt
#0  0x80f86e2 in clearXwindow () at unixscr.c:768
#1  0x80f8a07 in startvideo () at unixscr.c:840
#2  0x80fc9bc in setvideomode (ax=0, bx=0, cx=0, dx=0) at video.c:186
#3  0x8084256 in big_while_loop (kbdmore=0xbffff920, stacked=0xbffff91f "",
    resumeflag=0) at framain2.c:106
#4  0x8083ce1 in main (argc=2, argv=0xbffff994) at fractint.c:515
#5  0x4017b2eb in __libc_start_main () from /lib/libc.so.6

I was stepping through the code for a while, and dotmode got bumped from 0
to 19. Unfortunately, I had stepped through too far at a time, and missed
the exact point. I think it was during the check_video_mode() call called
from line 426 of fractint.c Maybe I'll poke at it tomorrow...


> > - How do I get true-color to work? Should it appear in my View Window
> > Options screen? I see nothing there for either image size or true-color
> > options.
>
> If you are running Linux in a true-color mode, then Xfractint will run in
> the same mode.  There are some issues with this.  Like people expecting the
> colors to be saved in a PAR even though they are in a true-color mode and
> this doesn't necessarily make any sense.

Hm. OK, I wondered why it never showed me the option. I pretty much run in
high-color mode (16- or 24-bit) most of the time. When I check the image
info with the <tab> key, it says stuff like:
     Video: 640x480x256 xfractint mode

Naturally, I wonder how to get beyond that.


> > - While I don't need the 'd' shell command, I do whack it by accident.
> > Typing "exit" as usual to get out of the shell also causes a
> > segfault/coredump.
>
> I'll have to look into this one.  Thanks.

OK, sounds great.

> >  - I get some strange rendering artifacts in some fractals, and weird
> stuff
> > that ends up in saved images as well. The rendering-time one is a grid
> > pattern of dots on the left-hand side, say with the default mandel as an
> > example. I can avoid this if I switch from "guess" to another pass type in
> > the 'x' option panel, so no big deal there. The other appears as a
> vertical
> > line travelling down the display window when I save to a .gif, and it
> > appears in the saved image as well. Along with that, the sides of the
> image
> > look like they're out of sync with the middle, with the left one bordering
> > on that vertical line I mentioned. I can also see this weird look if I
> > switch to a different virtual desk top and back again, without saving.
>
> I'll have a look at this.  If I can't reproduce it, I'll get back with you.

Well, I can (unfortunately?) reproduce both glitches every time, but they
appears not to affect xfractint on my work PC. Both are x86 PCs running
Debian Linux, though perhaps not the same versions of all packages and
libraries. Both have Matrox G400 video (should it matter?). The work one has
an Intel PIII, versus an AMD K6-2 at home. Since the weird wrap-around and
line are visible in saved images, I'll mail a copy of one to you, off the
list. The little left-hand dots aren't visible in the saved image, but
they're in one part of the image which is already trashed anyway.

    Cheers (and thanks!)
    Tim

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-------------------------------------------------------------------------------

From: "Scott D. Boyd" <[e-mail]>
Subject: Re: (fractint) Re: fractint-digest V1 #573
Date: 17 Jun 2001 05:39:41 -0500

On Sunday 17 June 2001 00:39, Tim Lavoie wrote:
> >
> > If you are running Linux in a true-color mode, then Xfractint will run
> > in the same mode.  There are some issues with this.  Like people
> > expecting the colors to be saved in a PAR even though they are in a
> > true-color mode and this doesn't necessarily make any sense.
>
> Hm. OK, I wondered why it never showed me the option. I pretty much run
> in high-color mode (16- or 24-bit) most of the time. When I check the
> image info with the <tab> key, it says stuff like:
>      Video: 640x480x256 xfractint mode
>
> Naturally, I wonder how to get beyond that.
>
Actually, "Xfractint running in true-color mode" is kind of confusing.
Xfractint (and Fractint) have always created 256-color gif images. Before
version 20.1.07 or so, Xfractint would only work correctly if your X
server was running in 8-bit color mode. Some modifications were made to
the source, and now Xfractint works correctly whether you are in 8-bit
color mode, or 16-bit color mode. But it still only displays and saves the
images with 256 colors, as that's all the gif format allows. During the
"true-color fix", other features were broken, and I believe Jonathan is
currently working on some of them.
>
> > vertical line travelling down the display window when I save to a
> >.gif, and it appears in the saved image as well. Along with that, the
> > sides of the image

Fractint and Xfractint have always had a multi-colored line going down the
left side of the image window while saving. But I've never experienced or
heard of that line ending up in the saved image!
>
Just my 2-cents (USD) worth...
Scott Boyd
--
[e-mail]
http://sdboyd.dyndns.org/~sdboyd/
I always wanted to be a procrastinator,
but I never got around to it.
                            -- Unknown

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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Re: fractint-digest V1 #573
Date: 17 Jun 2001 07:34:23 -0500

Tim,

> I was stepping through the code for a while, and dotmode got bumped from 0
> to 19. Unfortunately, I had stepped through too far at a time, and missed
> the exact point.

Yes, I found why it was doing that.  There is a right brace that got placed
in the wrong place in the initunixwindow() routine in unixscr.c.  Part of
the reason that happened is that there are about 30 lines of duplicate code
in that routine.  This fixes the initial segment fault, but there is still
one that occurs just prior to the completion of the disk-video image.

I have the Shell to Linux/Unix problem fixed.

Jonathan



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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Re: fractint-digest V1 #573
Date: 17 Jun 2001 09:31:44 -0500

> but there is still
> one that occurs just prior to the completion of the disk-video image.

Got it.  The disk video mode now works as before.  It will be in my next
patch.

Jonathan



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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  17-06-01  (Midget-Two [6])
Date: 17 Jun 2001 11:07:35 EDT


Classic FOTD -- June 17, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

A glance at the center coordinates will show that today's midget
is located deep in the East Valley area of the Mandelbrot
fractal.  I use the term "Mandelbrot Fractal" because the
Mandelbrot Set consists only of the interior of the lake and the
buds.  (I'm not sure whether the interiors of the midgets, which
are connected by infinitely thin filaments, are considered to be
parts of the main set, or to be separate sets.)  All the fancy
colored bands that surround the lake are not part of the set
itself, but are a fractal whose appearance is determined by
parameters set by humans.  Thus we can make the outside (and
inside also) appear most any way we wish, but unless the basic
formula is changed, the border between inside and outside will
remain unchanged.

As I stated above, today's fractal is located deep in East
Valley.  In this area, the elements become pinched off, making
it a difficult area to color.  When I went to color the FOTD for
today, I tried all the variations of my usual equal iteration
band method without success.  Then I tried the outside=tdis
option.  This option has potential, but it slows down the
rendering by a factor of 10, and time was short.  I finally
decided on the outside=summ option, which adds together the
iteration count, real and imaginary values, and sets the bands
according to the value of the sum.

The summ option reveals a pattern in the image, which at this
extreme depth in East Valley is almost lost in the sand.  The
pinched-off elements are clearly visible, and even have some
detail.  After my effort, I rated the work a 6, and gave it the
name "Midget-Two".

The 25-minute render time may be avoided by giving Paul and
Scott a chance to render and post the image to their respective
web sites at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today featured (if one can call it a
feature) heavy rain and thunder-storms.  It's actually the
remnants of the storm that flooded Houston, Texas about a week
ago.  The storm just doesn't know when to quit.  The temperature
of 77F (25C) was irrelevant, since the fractal cats spent the
day crouched down, sulking because of the wetness and hissing
sound of heavy rain.  The fractal basement survived with only a
couple puddles.

As for me, I've got to get back to that M-set.  The next FOTD is
due in only 12 hours and I've nothing yet to show.  Until then,
take care, and walk with fractals in mind.


Jim Muth
[e-mail]


START PARAMETER FILE=======================================

Midget-Two         { ; time=0:24:49.52--SF5 on a P200
  reset=2001 type=mandel passes=1
  center-mag=+0.25061098021060020/-0.000027092113537\
  83/4.38592e+011/1/-155.001/0.001 params=0/0 float=y
  maxiter=250000 inside=0 outside=summ periodicity=10
  colors=000zg0zj0zn0zl0zl0zj1zj6ziAziEzgJzgNzfRzfXz\
  d`zddzcjzcozaszdzzczzaxz`zzZszYrzXpzVnzUlzSjzRizPf\
  zOdzNczL`zKZzJYzHVzGUzFSzCRzCSzBSzASz9Sz7Sz6Sv5Ss5\
  Sp3Sl3Si3Sd3SZ3SV3SO5OJ5HH5BH5BF5BG5BO5BL6HK9HHBGG\
  CFEEGCFJ9FKAGOBJPCNSEPUESVFXVGZXHaXJfYJiYKlZLpZNs`\
  Nv`KuZJuZGsYFsYCrYBrX9pX7pV5oV6uP5rS3oV2nY1jZ0ia0f\
  d0cg0ai0Zl0Yo0Vr0Vu0Us0Us0Ur0Sr0Sp0Sp0Sp0Ro0Ro0Rn0\
  Rn1Pn2Pl2Pl3Pj5Oj5Oj6Oi7Oi9Ng9NgANgBNfBLfCLdELd7Kj\
  BLgELdGLcJL`LLZPLXSLVVLSYLR`LOdLNgLKjLJnLGnJHoKGpL\
  FrLEr0Es5CuOBvOBvPAxP9zR9zB7zS6zS6zU5zU3zV3zV2zX1z\
  Z0za1za2za3za3za5za6za6za7zZ9zU9zOAzKBzGBzCCz1Ev0E\
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  UP0VR0XR0YS0ZS0`S0aU0cU0dV0fV0gO0aS0dV0gY0ia1ld5oi\
  0zg3ug7pgBlfFifJdfN`dSYdXUd`PcdNciJcnFdsAcrCcrEcrF\
  crGcrHcrKcrLcpNcpOcpPcpRcpUcpVcpXcoYcoZco`coccodco\
  fcogcnicnjcnncnocnpcnrzd0
  }

END PARAMETER FILE=========================================

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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  18-06-01  (The Brink of Oblivion [9])
Date: 18 Jun 2001 01:03:28 -0400 (EDT)


Classic FOTD -- June 18, 2001 (Rating 9)

Fractal visionaries and enthusiasts:

Today's fractal rates a most exceptional 9.  This is not due to
its artistic merit, which is mediocre at best, but to its
mathematical merits, which are unlike anything I have yet come
upon.  The name I gave to the image tells it all -- it is a
picture of a midget on "The Brink of Oblivion.  Oblivion in this
case means an existence only as a vague outline in the random
dots that fill the lower left half of the image.

The imag(p3) parameter tells the entire story.  The slightest
change makes the greatest difference.  If the value is reduced
to 26.6, the midget is all there; if it is increased to 29.7,
the midget totally evaporates.  A midget that had no reality to
start becomes even less real.  The actual value of 29.647, which
equals a bailout of 129.647, catches the midget half there and
half gone.

However, the midget never totally vanishes, for even when the
screen becomes a total blank, the midget's ghost remains in
position, and can be revealed by rendering the scene with an
inside setting of something like bof60.

Since so much of the scene consists of inside area, and the
single-pass algorithm must be used to pick up all the bits and
pieces, the image is a slow one, requiring 25 minutes on a slow
old Pentium 200mhz.  But relief is at hand on the internet at
the web sites of Paul and Scott, where the image will soon be
posted.

Paul's site can be found at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and Scott's is at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather was near perfect today, with brilliant blue
skies and a temperature of 88F (31C).  The fractal cats made up
for the time they lost yesterday by spending most of the
afternoon in the yard, watching for the cat that lives across
the street.  But luckily for someone, the other cat never showed
up.

That's it for now fractal fiends.  Until next fractal, take
care, and always be all there.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

TheBrinkOfOblivion { ; time=0:24:11.35--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-1.789309750688749/-0.9580640953043432/\
  8290.843/1/39.999 params=1/-1.2/-1.2/1/-1.8/29.647
  float=y maxiter=1000 inside=0
  logmap=306 periodicity=10
  colors=000wDkwCmvAov8qv7sv5uv4vpBtjIsdPrZWpTboNhnK\
  QfI7_K9YMBXODVQFUSHSUIRWKQYMO_ONaQLcSKeTJgVHiXGkZE\
  m`DnaCocDpdDqfDrgDsiDsjDtlEumEvoEwpExrExsEsrDoqCkq\
  BfpAbp9Zo8Vo8Qn7Mm6Im5Dl49l35k21k24h37e4Ab4D_5GX5J\
  V6MS7PP7SM8VJ8YG9_E9XI8VL8SO8QR8NU7LX7I_7Gb7De6Bh6\
  8k66n64q69k6Ef6Ia6NW6RR6WM6_G6dB6h66i95iB5iD5iF5iH\
  5iJ5iL5iN5iP5fQ4cR4`R4ZS4WS4TT4RT4OU4LV4JV4GW4DW4B\
  X48X45Y43Y42V82TB2RE2PI2NL2KO2IS2GV2EY2C`5EY7FWAHT\
  CIREKOHLMJNJLOHJNFINEGMDFMCDLBCLABL99K88K76J65J54J\
  47L5AN6DO7FQ8IR9LTANUBQWCTXDVZEY_F`aGbbHacLacOacRa\
  cUacXac_acb`ce`ch`ck`cn`cq`ct`cw`czbVfdMNfE42C64F8\
  6IA8KCANECPGESIGVKIXMK_OMaQOdSQgUSiWUlYVnZXYcZIh`2\
  ma5nb8nbAncDndFndIneLnfNnfQogSohVohYoi_ojbojdokgok\
  ioihnhhmghmehldhlcgkagk`gj_giYgiXghWfhVfgTfgSffRfe\
  PfeOedNedLecKecJebIebKgcMhdNiePjfQkgSlhTmiVnjWokYq\
  kZrl`smatncuodvpfwqgxriys
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: jerome schatten <[e-mail]>
Subject: Re: (fractint) C-FOTD  18-06-01  (The Brink of Oblivion [9])
Date: 17 Jun 2001 23:38:08 -0700

Outstanding!! It has become my wallpaper.
jerome


Jim Muth wrote:
>
> Classic FOTD -- June 18, 2001 (Rating 9)
>
> Fractal visionaries and enthusiasts:
>
> Today's fractal rates a most exceptional 9.  This is not due to
> its artistic merit, which is mediocre at best, but to its
> mathematical merits, which are unlike anything I have yet come
> upon.  The name I gave to the image tells it all -- it is a
> picture of a midget on "The Brink of Oblivion.  Oblivion in this
> case means an existence only as a vague outline in the random
> dots that fill the lower left half of the image.
>

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-------------------------------------------------------------------------------

From: harry <[e-mail]>
Subject: Re: (fractint) C-FOTD  18-06-01  (The Brink of Oblivion [9])
Date: 18 Jun 2001 23:38:05 -0400

Artistic Merit (mediocre) my @ss !!!

This is a great one. I love it. thanks for posting it. I'd give it a 9.2
!!!

H^) harry

resume lurk mode

Jim Muth wrote:

> Classic FOTD -- June 18, 2001 (Rating 9)
>
> Fractal visionaries and enthusiasts:
>
> Today's fractal rates a most exceptional 9.  This is not due to
> its artistic merit, which is mediocre at best, but to its
> mathematical merits, which are unlike anything I have yet come
> upon.  The name I gave to the image tells it all -- it is a
> picture of a midget on "The Brink of Oblivion.  Oblivion in this
> case means an existence only as a vague outline in the random
> dots that fill the lower left half of the image.
>
> The imag(p3) parameter tells the entire story.  The slightest
> change makes the greatest difference.  If the value is reduced
> to 26.6, the midget is all there; if it is increased to 29.7,
> the midget totally evaporates.  A midget that had no reality to
> start becomes even less real.  The actual value of 29.647, which
> equals a bailout of 129.647, catches the midget half there and
> half gone.
>
> However, the midget never totally vanishes, for even when the
> screen becomes a total blank, the midget's ghost remains in
> position, and can be revealed by rendering the scene with an
> inside setting of something like bof60.
>
> Since so much of the scene consists of inside area, and the
> single-pass algorithm must be used to pick up all the bits and
> pieces, the image is a slow one, requiring 25 minutes on a slow
> old Pentium 200mhz.  But relief is at hand on the internet at
> the web sites of Paul and Scott, where the image will soon be
> posted.
>
> Paul's site can be found at:
>
>           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
>
> and Scott's is at:
>
>           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
>
> The fractal weather was near perfect today, with brilliant blue
> skies and a temperature of 88F (31C).  The fractal cats made up
> for the time they lost yesterday by spending most of the
> afternoon in the yard, watching for the cat that lives across
> the street.  But luckily for someone, the other cat never showed
> up.
>
> That's it for now fractal fiends.  Until next fractal, take
> care, and always be all there.
>
> Jim Muth
> [e-mail]
>
> START 20.0 PAR-FORMULA FILE================================
>
> TheBrinkOfOblivion { ; time=0:24:11.35--SF5 on a P200
>   reset=2001 type=formula formulafile=allinone.frm
>   formulaname=MandelbrotMix4 function=recip passes=1
>   center-mag=-1.789309750688749/-0.9580640953043432/\
>   8290.843/1/39.999 params=1/-1.2/-1.2/1/-1.8/29.647
>   float=y maxiter=1000 inside=0
>   logmap=306 periodicity=10
>   colors=000wDkwCmvAov8qv7sv5uv4vpBtjIsdPrZWpTboNhnK\
>   QfI7_K9YMBXODVQFUSHSUIRWKQYMO_ONaQLcSKeTJgVHiXGkZE\
>   m`DnaCocDpdDqfDrgDsiDsjDtlEumEvoEwpExrExsEsrDoqCkq\
>   BfpAbp9Zo8Vo8Qn7Mm6Im5Dl49l35k21k24h37e4Ab4D_5GX5J\
>   V6MS7PP7SM8VJ8YG9_E9XI8VL8SO8QR8NU7LX7I_7Gb7De6Bh6\
>   8k66n64q69k6Ef6Ia6NW6RR6WM6_G6dB6h66i95iB5iD5iF5iH\
>   5iJ5iL5iN5iP5fQ4cR4`R4ZS4WS4TT4RT4OU4LV4JV4GW4DW4B\
>   X48X45Y43Y42V82TB2RE2PI2NL2KO2IS2GV2EY2C`5EY7FWAHT\
>   CIREKOHLMJNJLOHJNFINEGMDFMCDLBCLABL99K88K76J65J54J\
>   47L5AN6DO7FQ8IR9LTANUBQWCTXDVZEY_F`aGbbHacLacOacRa\
>   cUacXac_acb`ce`ch`ck`cn`cq`ct`cw`czbVfdMNfE42C64F8\
>   6IA8KCANECPGESIGVKIXMK_OMaQOdSQgUSiWUlYVnZXYcZIh`2\
>   ma5nb8nbAncDndFndIneLnfNnfQogSohVohYoi_ojbojdokgok\
>   ioihnhhmghmehldhlcgkagk`gj_giYgiXghWfhVfgTfgSffRfe\
>   PfeOedNedLecKecJebIebKgcMhdNiePjfQkgSlhTmiVnjWokYq\
>   kZrl`smatncuodvpfwqgxriys
>   }
>
> frm:MandelbrotMix4 {; Jim Muth
> a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
> g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
> k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
> z=k*((a*(z^b))+(d*(z^f)))+c,
> |z| < l
> }
>
> END 20.0 PAR-FORMULA FILE==================================
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
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> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"


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-------------------------------------------------------------------------------

From: "Tony (Anthony) Hanmer" <[e-mail]>
Subject: Re: (fractint) C-FOTD 18-06-01 (The Brink of Oblivion [9])
Date: 19 Jun 2001 09:25:26 +0500

I agree with the previous comments - this one's a great example that the
Fractiverse, or Fractality, or whatever one wants to call it, is a good deal
stranger and more beautiful than we could imagine.  Fantastic work, Jim.
I'm amazed at the sheer number (well, it's infinite) of variations on a
theme that midgets offer.  Much earlier I was wishing for other types from
you to break the "monotony", but then the pleasure of seeing what can
surround a midget set in, of waiting for what you'll find for the day, and
now I'm hooked.  (Though whatever you choose to depict for us is usually a
wonder.)
Thank you.

Tony Hanmer
_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Midgets...
Date: 19 Jun 2001 04:54:20 -0400


------=_NextPart_001_0001_01C0F87B.E70C9040
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Over the past couple of days I cobbled together a small C program that is=
 possibly the first Mandelbrot autoexplorer designed specifically to home=
 in on midgets -- and if not, then probably the first one that actually w=
orks.

I'd post the source code here, but there're about two thousand lines of i=
t. I'd stick it on the Web but my pages are in a shambles. Besides, the i=
nterface sucks -- it's noninteractive with no parameters, you have to act=
ually edit the source and recompile it to change any of the parameters, a=
nd without varying the parameters it has a limited repertoire. It produce=
s a short zoom sequence (as many as 20 images) of grey-scaled distance es=
timator images that look very nice and tend to close in on a midget (occa=
sionally a bud instead). Occasionally it "backs up" a bit and zooms back =
in in a slightly different spot.<br clear=3Dall><hr>Get Your Private, Fre=
e E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://ww=
w.hotmail.com</a>.<br></p>

------=_NextPart_001_0001_01C0F87B.E70C9040
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>Over the past =
couple of days I cobbled together a small C program that is possibly the =
first Mandelbrot autoexplorer designed specifically to home in on midgets=
 -- and if not, then probably the first one that actually works.</DIV> <D=
IV> </DIV> <DIV>I'd post the source code here, but there're about tw=
o thousand lines of it. I'd stick it on the Web but my pages are in a sha=
mbles. Besides, the interface sucks -- it's noninteractive with no parame=
ters, you have to actually edit the source and recompile it to chang=
e any of the parameters, and without varying the parameters it has a limi=
ted repertoire. It produces a short zoom sequence (as many as 20 images) =
of grey-scaled distance estimator images that look very nice and tend to =
close in on a midget (occasionally a bud instead). Occasionally it "backs=
 up" a bit and zooms back in in a slightly different spot.<BR><BR></DIV><=
/BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, Free E-mail f=
rom MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.=
com</a>.<br></p></DIV>

------=_NextPart_001_0001_01C0F87B.E70C9040--

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-------------------------------------------------------------------------------

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Midgets...
Date: 19 Jun 2001 00:43:13 -1000

Hmm, could you make a command line version that could
take parameters from the command line or via a batch
file, then display the results? Is there some way to
save the results? It sounds like fun!

David
[e-mail]

On 19 Jun 01 at 4:54, Multiple Bogeys wrote:

> Over the past couple of days I cobbled together a small
> C program that is possibly the first Mandelbrot
> autoexplorer designed specifically to home in on midgets
> -- and if not, then probably the first one that actually
> works.
>
> I'd post the source code here, but there're about two
> thousand lines of it. I'd stick it on the Web but my
> pages are in a shambles. Besides, the interface sucks --
> it's noninteractive with no parameters, you have to
> actually edit the source and recompile it to change any
> of the parameters, and without varying the parameters it
> has a limited repertoire. It produces a short zoom
> sequence (as many as 20 images) of grey-scaled distance
> estimator images that look very nice and tend to close
> in on a midget (occasionally a bud instead).
> Occasionally it "backs up" a bit and zooms back in in a
> slightly different spot.


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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 16-06-01 (Midget [5])
Date: 19 Jun 2001 12:58:48 -0000

>From: [e-mail]
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  16-06-01  (Midget [5])
>Date: Sat, 16 Jun 2001 10:51:02 EDT
>
>
>Classic FOTD -- June 16, 2001 (Rating 5)
>
>Fractal visionaries and enthusiasts:

I'd rate this one higher if only for the groovy colouring.

Thanks.
Andrew.

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  19-06-01  (Quantum Hysteria [8])
Date: 19 Jun 2001 11:17:20 EDT


Classic FOTD -- June 19, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

Sometimes I just don't know how I find the time to keep the FOTD
going.  Here it is 10:50am of the day of the FOTD, and I'm just
starting to write.  Well, late though it may be, the image is
worth waiting for.

Since one picture is worth a thousand words, I'll save the
thousand words and offer the picture.  The image, which
resembles a universe of bubbles, consists of almost all inside
stuff, made visible by the inside fill of bof60.  While studying
it, trying to find a name, I had a fleeting impression of a
scene in the sub-atomic world of forces and energies.  I named
the image "Quantum Hysteria".

Since the image consists of all inside and the periodicity is
turned off, the parameter file needs almost 1/2 hour to render.
The more efficient way of viewing the image is to go to Paul's
web site at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or to Scott's site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

and download the finished GIF file from there.

The fractal weather, the least important part of the FOTD, was
perfect today, with sunny skies and a temperature of 88F (31C)
to keep the cats happy.

I'll be happy when I get this work beside me out of the way.
Until next time and next FOTD, take care, and be a friend of
fractals.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Quantum_Hysteria   { ; time=0:26:56.29--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.18005066951765600/-0.181874553498594\
  20/1282.051 params=-1/-1.25/1.25/1/-1.8/1e+150
  float=y maxiter=600 inside=bof60 periodicity=0
  colors=000zzzyyzxxzwwzvvzuuzttzsszrrzqqzppzpoypnxp\
  mwplvpkuojtnismhrlgqkfojemidkhcigbgfaed_caX_YTWUPS\
  PKPKGHGBNC9TD6ZC6`D6bD6dF5fF5hG5jH3lH3nH3pJ3rJ3tL1\
  vJ3xH6zG9wFCvDFsCHrAKo9Nm7Pl6Si5Vh3Ye2`d1ba0e`0fZ6\
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  R`5Oa5Ld3Je3Gh2Di1Ak17m05o02r00s00z00t20p52l93hD6d\
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  V6VX5ZY3bZ9VL5XJ2eZ0zm0to1mo6foAaoFVoKOpOJpUCpY5pZ\
  1sa0pd0oe0mh0lk0il0ho0fr0es0bv0ay0`z0fz0Zv0Sr0Lm0D\
  i06e00b00d00e10f32h75iC9kFClJFmLHoPLpUOrXRs`UtdYvf\
  `wkbymezrizvlzyozzrzztzzrwwpttopplmmkkiifefdbeaZdz\
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  Yb``dZbeYdhXfiUikSkmRmoPppNrsLttKzzKHzKGzLAzHFzLJz\
  ONzRRzVVzYZz`bzdfzfkziozm
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================

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-------------------------------------------------------------------------------

From: [e-mail]
Subject: (fractint) C-FOTD  20-06-01  (A Midget at Midnight [7])
Date: 20 Jun 2001 08:22:37 EDT


Classic FOTD -- June 20, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Though the render time of today's FOTD is over 2 hours on a
Pentium 200mhz machine, this is at the SF7 resolution.  At the
normal SF5 resolution the image renders in 49 minutes.  I
entered the time comment in the parameter file at the SF7
resolution because today's image is one of those that needs the
highest resolution possible to prevent features that should
appear as tiny filaments from appearing as dots.

The unusually long render time is due to the extreme maxiter of
the image as well as to the fact that the short-cut passes
algorithms are useless.  When I studied the image, I was
impressed by the deep midnight blue surrounding the central
midget.  I named the picture "A Midget at Midnight", a name that
is not only descriptive, but poetic as well.  I rated it at a 7,
a rating that may be a bit liberal.

The scene is one in the classic Mandelbrot set, in a valley of a
tiny bud on the northwest shore of the main bay.  In this area
the scene is close to total chaos.  The points don't know what
to do.  One point may escape after 3000 iterations; it's
neighbor may be still trapped after 1-million.

The overall effect is one of lightning-like filaments or a
network of veins before a background of sandy grit.  But a very
broad color palette does reveal a rudimentary underlying
pattern, as today's image demonstrates.

The passes options other than 1, 2, or 3 are useless in an image
such as this, because so much detail exists that the time the
algorithm spends figuring what to do next is longer than the
time a straight single pass takes.

Although I'm not going to demonstrate the images the Julia
aspects of areas such as today's produce, they are well worth
the time spent in having a look.  The four remaining aspects of
the four-dimensional Julibrot figure are also worth seeing.
Perhaps I'll have time to investigate such things when things
slow down next month.

As I stated earlier, today's image is the slowest in quite some
time.  The most efficient way of viewing the scene is to give
Paul and Scott a chance to render and post the GIF images, and
then go to the web sites where the images will be waiting.

Paul's site is at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

Scott's is at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was uneventful, with hot sun and a
temperature of 89F (31.5C) to keep the cats happy.

As for me, I've got things that need to be done, and limited
time in which to do them.  So the rational thing is to get busy.
Until next FOTD, take care, and where are those Herman Rings?


Jim Muth
[e-mail]


START PARAMETER FILE=======================================

A_MidgetAtMidnight { ; time=2:05:12.08--SF7 on a P200
  reset=2001 type=mandel passes=1
  center-mag=-0.41357633605202350/+0.574830605134010\
  40/1.332446e+007/1/157.499 params=0/0 float=y
  maxiter=1200000 inside=0 logmap=3000 periodicity=10
  colors=000zG0zG0zG0zI0zI0zI0zK0zK0zK0zM0zM0zM0zM0z\
  O0zO0zO0zP0zQ0zP0zR0zR0zR0zT0zT0zT0zT0zV0zV0zV0zX0\
  yX2yX2yZ2wZ2wZ2w`2v`3v`3va3ta3ta3ta3rb6rb6rc6qd6qd\
  6qc6oc7ob7oc7md7me7mf7lg0oh2oi6mj7mkCmlElmIloMlqOj\
  rRjtTjvXiwZiyaizdgzggzjdzldzodzrbztbzwbzyazzazzazz\
  `zz`zz`zzZzzZzzZzz`zz`zz`zz`zz`zz`zz`zz`zy`zv`zt`y\
  q`wmavlatiatdatbat`atXatVatRatOatMatIatERt0Vt0Zt3a\
  tCdtIitOltVot`rtdvtlytqzyvyvtwtrvqqroqqloojmlimjdl\
  ibjd`jbZiaVgZTgXRdVObXMbZIaXG`VC`TAZP7XC3XA2V70T30\
  T20R00P00P00R00R00R00R00R00T00T00T00T00T00T00V00V0\
  0V00V00V00X00X00X00X00X00Z00Z00Z00Z00Z00`00`00`00`\
  00`00`00a00a00a00a00a00b00b00b02b02b02d02d02d02d03\
  d03g03g03g03g03g06b03d03d03g03g23i23i32i62j62j72l7\
  2lA2lC2mC0mE0oG0oG0oI0qI0qK0rM0rM0rO0tP0tP0vR0vR0v\
  T0wV0wV0yX0yZ0zZ0z`0za0za0zb0zb0zd0zg0zg2zg2zg2zg2\
  zg2zg2zg2zg2zg2zg2zg2zg2z
  }

END PARAMETER FILE=========================================

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-------------------------------------------------------------------------------

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) C-FOTD  20-06-01  (A Midget at Midnight [7])
Date: 20 Jun 2001 08:59:01 -1000

On 20 Jun 01 at 8:22, [e-mail] wrote:

> Classic FOTD -- June 20, 2001 (Rating 7)
>
> Fractal visionaries and enthusiasts:
>
> Though the render time of today's FOTD is over 2 hours
> on a Pentium 200mhz machine, this is at the SF7
> resolution.

First time I ever actually ran the PAR, rather than go
look att he picture on the web. 27 minutes on a Duron
700, running Fractint under OS/2 with an MP3 player
running simultaneously. Now lets try it at 2048x2048!
;-)

Well worth it for such a delightful picture - I think
I'll do it more often! Thanks, Jim!

David
[e-mail]


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-------------------------------------------------------------------------------

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD  20-06-01  (A Midget at Midnight [7])
Date: 20 Jun 2001 14:06:03 -0500

David Jones wrote:

> Now lets try it at 2048x2048!

And maybe make this hi-rez version available to the rest of us?....

FWIW, I'd be willing to put hi-rez versions of Jim's great images on my
website for a brief while (brief while per image)....  I just don't have
the time to actually *make* the images...

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) C-FOTD  20-06-01  (A Midget at Midnight [7])
Date: 20 Jun 2001 18:18:47 -0500

[e-mail] wrote:
>
> Though the render time of today's FOTD is
> over 2 hours on a Pentium 200mhz machine,
> this is at the SF7 resolution.  At the
> normal SF5 resolution the image renders in
> 49 minutes.

Since Jim mentioned the various times, I noticed something different
with today's image....

My P-III 700 usually can do each FOTD in slightly half the time of what
Jim's 200 MMX at the same SF5 resolution.  But today's image was
finished in 15-min. and 18-sec., which is about a third of the time.  I
was using the Developer's 20.01.11 version (non float-only).

I believe Jim said at one time that he used the FO version, and wondered
if that might have anything to do with the considerable time
difference.  Any thoughts ??

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: "David Jones" <[e-mail]>
Subject: (fractint) Re: C-FOTD  20-06-01  (A Midget at Midnight [7])
Date: 20 Jun 2001 18:54:25 -1000

On 20 Jun 01 at 14:06, Programmer Dude wrote:

> David Jones wrote:
>
> > Now lets try it at 2048x2048!
>
> And maybe make this hi-rez version available to the rest
> of us?....
>
> FWIW, I'd be willing to put hi-rez versions of Jim's
> great images on my website for a brief while (brief
> while per image)....  I just don't have the time to
> actually *make* the images...

OK, although I had to stop it before it finished. It was
about 3/4 of the way through after 1:46 hours of
calculation when it seemed to go into some kind of loop -
at least the calculation time on the Info screen seemed
to stop updating. Will see how this shot goes - I'm going
to be at the other computer most of the evening, anyway.

Maybe I should also put Fractint on my wife's 650MHz P3
notebook and see how fast it can calculate it, too. ;-)

David
[e-mail]


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-------------------------------------------------------------------------------

From: Tim Lavoie <[e-mail]>
Subject: (fractint) Yay!  XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 00:53:44 -0500

Hi all,

Further to the wierd image corruption that I'd had, as well as left-over
dots in "guess" mode: It seems to have gone away by avoiding 24-bpp X. I was
tinkering with a variety of software updates, which included some X
reconfiguration. While I still got the results that I'd had before when
using 24-bit color, it goes away when I use 16-bit instead.

The line on the side that Scott mentioned is not the same as what I'd had,
where an even amount was munged on each side of the frame, with a narrow
stripe being the part on the left that stayed. In this case, it looked more
like the edges wrapped around to the opposite side, for every other line or
so. Anyway, switching out of 24-bit mode did the trick, so I must say that
I'm happily trying out the recent FOTD examples plus anything else that I can.

    Thanks!
    Tim

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-------------------------------------------------------------------------------

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) C-FOTD  20-06-01  (A Midget at Midnight [7])
Date: 20 Jun 2001 21:28:57 -1000

On 20 Jun 01 at 8:22, [e-mail] wrote:

> Classic FOTD -- June 20, 2001 (Rating 7)
>
> Fractal visionaries and enthusiasts:
>
> Though the render time of today's FOTD is over 2 hours
> on a Pentium 200mhz machine, this is at the SF7
> resolution.

Someone on the list - sorry, can't find the original msg,
thought I'd saved it - expressed interest in the
2048x2048 rendering I was running. Just letting you know
that two hours and 29 minutes later, I have a 4225KB GIF
Because of the aspect ratio, it looks weird on screen.

Only way I could get it to anyone is to FTP it to someone
else ... our web site here doesn't have enough space
available.

David
[e-mail]


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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 08:13:29 -0000

Hmm... must try that!

(BTW, in what language is "munged" a word?!?!)

>From: Tim Lavoie <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: (fractint) Yay!  XFractint working - Just not in 24-bpp X?
>Date: Thu, 21 Jun 2001 00:53:44 -0500
>
>Hi all,
>
>Further to the wierd image corruption that I'd had, as well as left-over
>dots in "guess" mode: It seems to have gone away by avoiding 24-bpp X. I
>was
>tinkering with a variety of software updates, which included some X
>reconfiguration. While I still got the results that I'd had before when
>using 24-bit color, it goes away when I use 16-bit instead.
>
>The line on the side that Scott mentioned is not the same as what I'd had,
>where an even amount was munged on each side of the frame, with a narrow
>stripe being the part on the left that stayed. In this case, it looked more
>like the edges wrapped around to the opposite side, for every other line or
>so. Anyway, switching out of 24-bit mode did the trick, so I must say that
>I'm happily trying out the recent FOTD examples plus anything else that I
>can.
>
>     Thanks!
>     Tim
>
>--------------------------------------------------------------
>Thanks for using Fractint, The Fractals and Fractint Discussion List
>Post Message:   [e-mail]
>Get Commands:   [e-mail] "help"
>Administrator:  [e-mail]
>Unsubscribe:    [e-mail] "unsubscribe fractint"

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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-------------------------------------------------------------------------------

From: "Scott D. Boyd" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 03:22:43 +0000

On Thursday 21 June 2001 05:53, Tim Lavoie wrote:
> Hi all,
>
> Further to the wierd image corruption that I'd had, as well as left-over
> dots in "guess" mode: It seems to have gone away by avoiding 24-bpp X. I
> was tinkering with a variety of software updates, which included some X
> reconfiguration. While I still got the results that I'd had before when
> using 24-bit color, it goes away when I use 16-bit instead.
>
Looks like it might be a bug specific to 24-bit color mode and above. I've
never been able to use 24-bit color, because I only have 4 Meg of video
RAM on my (somewhat older) video board. I always run in 16-bit color mode,
at 1024 x 768 resolution. Not sure what  color depth Jonathan Osuch uses
when testing/running Xfractint on his machine. But... I would guess it's
only 16-bit at best, or he probably would've found the problem earlier.
8-)

Until later,
Scott
--
[e-mail]
http://sdboyd.dyndns.org/~sdboyd/



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-------------------------------------------------------------------------------

From: "Scott D. Boyd" <[e-mail]>
Subject: Re: (fractint) C-FOTD 20-06-01 (A Midget at Midnight [7])
Date: 21 Jun 2001 03:29:25 +0000

On Thursday 21 June 2001 07:28, David Jones wrote:

> Someone on the list - sorry, can't find the original msg,
> thought I'd saved it - expressed interest in the
> 2048x2048 rendering I was running. Just letting you know
> that two hours and 29 minutes later, I have a 4225KB GIF
> Because of the aspect ratio, it looks weird on screen.
>
> Only way I could get it to anyone is to FTP it to someone
> else ... our web site here doesn't have enough space
> available.
>
David,

It was Programmer Dude that said he could briefly store it on his Website.
I'd be willing to store it for you on my Web server, and I can keep it
there for a long time. (No space restrictions on my Web server.) Email me
directly for details.

Later,
Scott Boyd
--
[e-mail]
http://sdboyd.dyndns.org/~sdboyd/



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-------------------------------------------------------------------------------

From: "Scott D. Boyd" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 03:42:35 +0000

On Thursday 21 June 2001 08:13, Andrew Coppin wrote:
> Hmm... must try that!
>
> (BTW, in what language is "munged" a word?!?!)
>
Ummm.... English?  Maybe also the Scots dialect...
Please see the Jargon File at:
http://www.tuxedo.org/~esr/jargon/html/entry/mung.html
for more info. (see also 'munge', which has a link from the above page.)

Later,
Scott
--
[e-mail]
http://sdboyd.dyndns.org/~sdboyd/

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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  21-06-01  (Fractal Caterpillars [6])
Date: 21 Jun 2001 09:36:10 -0400 (EDT)


Classic FOTD -- June 21, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Yesterday's FOTD showed a midget deep in a tiny valley on the NW
shore of the main lake.  It was an interesting display of life
in a zone where chaos is becoming rampant, but has not yet
completely taken over.  The image took 49 minutes to render at
SF5 on my P200 machine.

Today's FOTD moves us deep into another tiny valley, this one
very deep in on the south shore of East Valley, where the
elements are pinched off.  I started the rendering out of
curiosity; by the time the image had finished, I was sorry I had
started it.  Demanding a maxiter of 12-million, the image took
4 hours and 48 minutes to complete on my tired old fractal
machine, even at the basic resolution of SF5, which is 640x480,
with 256-colors.

When the image finally finished, I found myself faced with a
different kind of quasi-chaos.  Instead of lightning-like arms
and filaments, I found rows of roughly circular elements strung
together in string-of-pearl-like spirals.  I used the same color
map that I had used on yesterday's 'midnight' image, so that a
better comparison of the two scenes could be made.

To name the image, I studied it a few minutes.  At first I saw
the strings of pearls, then the pearls became segments of
caterpillars, and I had found my name.  "Fractal Caterpillars"
serves quite well as a descriptive name for today's image.  I
could rate the effort at only a 6, since it's a little too much
of a good thing.

I'm thinking of purchasing another fractal computer, a state-of-
the-art machine, so I would be interested in hearing reports of
the time required to render today's particularly difficult scene
on different machines with different CPU's.  If I do make the
purchase, I want to be sure I'm getting the fastest fractal
rendering machine possible.

Because the rendering time of today's image is so long, I sent
the parameter file to Paul a few hours ago so that he can have
the image already rendered and ready to post when this
discussion arrives.  Paul's FOTD web site is at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

Unfortunately, the hour was late and I didn't have Scott's
e-mail address handy, so it will be a few hours before the image
is available on his web site at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But normally both sites are updated at approximately the same
time.

The fractal weather today was muggy and 91F (33C), climaxed by a
heavy thunder-storm in the evening, and followed by a cool
night.  The fractal cats were too busy sleeping all day to give
much response.

And it's now time to start another day.  I wonder whether the
cats will again sleep away most of the day.  I'll let you know
next time.  Until then, take care, and I'd bet that tomorrow's
FOTD will be faster than today's.


Jim Muth
[e-mail]


START 20.0 PARAMETER=FILE==================================

FractalCaterpilars { ; time=4:47:53.56--SF5 on a P200
  reset=2001 type=mandel passes=1
  center-mag=+0.25121832191078580/-0.000085296453604\
  55/7.897297e+010/1/-17.499 params=0/0 float=y
  maxiter=12000000 inside=0 logmap=15000 periodicity=9
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  rRjtTjvXiwZiyaizdgzggzjdzldzodzrbztbzwbzyazzazzazz\
  `zz`zz`zzZzzZzzZzz`zz`zz`zz`zz`zz`zz`zz`zy`zv`zt`y\
  q`wmavlatiatdatbat`atXatVatRatOatMatIatERt0Vt0Zt3a\
  tCdtIitOltVot`rtdvtlytqzuvyvtwtrvqqroqqloojmlimjdl\
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  zg2zg2zg2zg2zg2zg2zg2zg2z
  }

END 20.0 PARAMETER FILE====================================


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-------------------------------------------------------------------------------

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) C-FOTD  20-06-01  (A Midget at Midnight [7])
Date: 20 Jun 2001 21:28:57 -1000

On 20 Jun 01 at 8:22, [e-mail] wrote:

> Classic FOTD -- June 20, 2001 (Rating 7)
>
> Fractal visionaries and enthusiasts:
>
> Though the render time of today's FOTD is over 2 hours
> on a Pentium 200mhz machine, this is at the SF7
> resolution.

Someone on the list - sorry, can't find the original msg,
thought I'd saved it - expressed interest in the
2048x2048 rendering I was running. Just letting you know
that two hours and 29 minutes later, I have a 4225KB GIF
Because of the aspect ratio, it looks weird on screen.

Only way I could get it to anyone is to FTP it to someone
else ... our web site here doesn't have enough space
available.

David
[e-mail]


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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 14:27:55 -0000

Well I'll be damed...

>From: "Scott D. Boyd" <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
>Date: Thu, 21 Jun 2001 03:42:35 +0000
>
>On Thursday 21 June 2001 08:13, Andrew Coppin wrote:
> > Hmm... must try that!
> >
> > (BTW, in what language is "munged" a word?!?!)
> >
>Ummm.... English?  Maybe also the Scots dialect...
>Please see the Jargon File at:
>http://www.tuxedo.org/~esr/jargon/html/entry/mung.html
>for more info. (see also 'munge', which has a link from the above page.)
>
>Later,
>Scott
>--
>[e-mail]
>http://sdboyd.dyndns.org/~sdboyd/
>
>--------------------------------------------------------------
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-------------------------------------------------------------------------------

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD 20-06-01 (A Midget at Midnight [7])
Date: 21 Jun 2001 09:40:44 -0500

"Scott D. Boyd" wrote:

>> Someone on the list - sorry, can't find the original msg,
>> thought I'd saved it - expressed interest in the
>> 2048x2048 rendering I was running.

[raises hand]
That was me....

>> Only way I could get it to anyone is to FTP it to someone
>> else ... our web site here doesn't have enough space available.

Looks like Scott might have more space available, but I'm still
interested in the hi-rez image, and I'll still offer some space
if anyone wants to collaborate on offering Jim's images in hi-rez
form.

Whatever.  If you want to ftp the image, it's:

    ftp://ftp.visi.com/users/cjsonnack/incoming/

There isn't a ton of email space on the ftp machine, so if you do
upload, please email me so I can move the file.  (P.S. The way the
directory permissions are set, you won't see the file in the directory
once you upload it, but it will be there.)

thanks,
-Chris "wantin' some new wallpaper" Sonnack

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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-------------------------------------------------------------------------------

From: [e-mail]
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 11:52:25 -0500

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
<u>Is anyone other than me getting multiple copies of the Lavoie, Jone,
and Coppin Posts?</u>
<p>This time, I received:
<p>1) the first cluster (w/ Coppin in duplicates) at 12:48am, Thurs, 6/21/01
<br>2) the second (w/ Jones in duplicates) starting at 2:28am, Thurs, 6/21/01,
and
<br>3) the latest, consisting of a complete set (w/ all three posts in
duplicate, and ending w/ a single copy of PDude's Post) at 9:27-->9:48
this morning (Thurs, 6/21/01).
<p>My ISP, of course claims the replication is not arising in their servers.
<p>Any body else? Any comments?
<p>D. Freed
<br>
<br>
<p>Andrew Coppin wrote:
<blockquote TYPE=CITE>Well I'll be damed...
<p>>From: "Scott D. Boyd" <[e-mail]>
<br>>Reply-To: [e-mail]
<br>>To: [e-mail]
<br>>Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp
X?
<br>>Date: Thu, 21 Jun 2001 03:42:35 +0000
<br>>
<br>>On Thursday 21 June 2001 08:13, Andrew Coppin wrote:
<br>> > Hmm... must try that!
<br>> >
<br>> > (BTW, in what language is "munged" a word?!?!)
<br>> >
<br>>Ummm.... English?  Maybe also the Scots dialect...
<br>>Please see the Jargon File at:
<br>><a href="http://www.tuxedo.org/~esr/jargon/html/entry/mung.html">http://www.tuxedo.org/~esr/jargon/html/entry/mung.html</a>
<br>>for more info. (see also 'munge', which has a link from the above
page.)
<br>>
<br>>Later,
<br>>Scott
<br>>--
<br>>[e-mail]
<br>><a href="http://sdboyd.dyndns.org/~sdboyd/">http://sdboyd.dyndns.org/~sdboyd/</a>
<br>>
<br>>--------------------------------------------------------------
<br>>Thanks for using Fractint, The Fractals and Fractint Discussion List
<br>>Post Message:   [e-mail]
<br>>Get Commands:   [e-mail] "help"
<br>>Administrator:  [e-mail]
<br>>Unsubscribe:    [e-mail] "unsubscribe
fractint"
<p>_________________________________________________________________________
<br>Get Your Private, Free E-mail from MSN Hotmail at <a href="http://www.hotmail.com">http://www.hotmail.com</a>.
<p>--------------------------------------------------------------
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fractint"</blockquote>
</html>


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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) C-FOTD  21-06-01  (Fractal Caterpillars [6])
Date: 21 Jun 2001 11:50:24 -0500

Jim Muth wrote:
>
> Demanding a maxiter of 12-million, the
> image took 4 hours and 48 minutes to
> complete on my tired old fractal machine.....

And it only took 58-min. and 47-sec. on my somewhat old P-III 700.  This
is one-fifth the time of Jim's image, and yesterday's took me one-third
the time.  As I stated in yesterday's reply, the FOTD images I usually
generate have been one-half the time of what Jim's Pentium 200 MMX
machine, which it has been for over a year now.

So I am assuming at some point, the calculation times done on Jim's
machine stops being twice the amount, and then starts increasing
exponentially for some unknown reason.  I find this behavior rather
interesting.

>
> I'm thinking of purchasing another
> fractal computer....

Since there have been a lot of "PC Price Wars" going on for the past
several weeks, many exceptional deals may be found.  And a lot of the
online companies and major PC makers now offer good systems with decent
warranties and technical support, most with various incentives and
add-ons to entice the purchaser.

For example DELL's Dimension 8100 series, with a 400MHz system bus, the
Pentium 4 based system delivers three times the peak bandwidth of
today's P-III based systems.

    http://www.dell.com/us/en/dhs/products/series_dimen_desktops.htm

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: Tim Lavoie <[e-mail]>
Subject: (fractint) Re: duplicate posts
Date: 21 Jun 2001 12:25:16 -0500

I'm not getting duplicates, including my own posts. However, I was tempted
to post this message two or three times.  <grin>

   Cheers,
   Tim

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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 21:02:29 -0500

> Not sure what  color depth Jonathan Osuch uses
> when testing/running Xfractint on his machine. But... I would guess it's
> only 16-bit at best, or he probably would've found the problem earlier.

Not necessarily, I don't normally use Xfractint.  I'm running 24-bit color
at 1024x768.  I do see some minor artifacts at the edges when an image is
saved.  The colors saved to the image were completely different (without the
artifacts).  But, I have a bunch more changes in my source.

I have found that occasionally the xterm you are using will make a
difference.  At least it affects which key strokes get recognized.

Insert your 3 favorite rants here.  They'll make more sense.

Jonathan



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From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 22 Jun 2001 00:02:45 -0500

[e-mail] wrote:
>
> Is anyone other than me getting multiple
> copies of the Lavoie, Jones, and Coppin Posts?
>

The only duplicates I received were two from David Jones with the DATE
of Wed, 20 Jun 2001 21:28:57.  But I suspect that was because of
something at his end.

I have noticed that when the FractInt mail server has problems, then
there will be multiple copies of the "Thanks for using Fractint" message
at the end of each email.  I usually delete all those with more than one
of these additions.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From:     John Lewis <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 18:18:33 +0100

On Thu, 21 Jun 2001 11:52:25 -0500, [e-mail] wrote:
>Is anyone other than me getting multiple copies of the Lavoie,
>Jone, and Coppin Posts?


I have just received two David Jones posts, but only one each of=

three from Mr Coppin.

John

[e-mail]


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From:     John Lewis <[e-mail]>
Subject: (fractint) Formulae
Date: 21 Jun 2001 20:04:42 +0100

I am sure I should know the answer to this one, but can anyone=
 please
tell me how I could use the formulae kindly provided by Jim Muth=
 with
his excellent fractals - can I copy them into Fractint, or do I=
 have
to retype them?

Thanks.


-- John Lewis, [e-mail] on 06/21/2001



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From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Formulae
Date: 22 Jun 2001 01:35:06 -0500

John Lewis wrote:
>
> .....can anyone please tell me how I could
> use the formulae kindly provided by Jim Muth
> with his excellent fractals - can I copy them
> into Fractint, or do I have to retype them?
>

If you are trying to run the FOTD image yourself, then you can either
save the whole email as a text file within the FractInt directory path
(or sub-directory), or save just the PAR and FRM portions as a text file
in the same area.  Then use the "run saved command set" function (the
'@' sign) and select the save text file.

If you just wish to explore your own parameters using one of Jim's
formulas, then basically do the same thing as above, but use the "select
fractal type" function (the 't' character).  Then choose the "formula"
option and find the saved text file.  Now enter your own parameter
values.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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From: "Scott D. Boyd" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 22 Jun 2001 01:38:20 +0000

On Friday 22 June 2001 02:02, Jonathan Osuch wrote:

> I have found that occasionally the xterm you are using will make a
> difference.  At least it affects which key strokes get recognized.
>
> Insert your 3 favorite rants here.  They'll make more sense.
>
Not necessarily rants - just observations.... I learned a long time ago
that I couldn't use the "konsole" app that comes with KDE.  The arrow keys
are interpreted as the "Esc" key, and takes me to the exit prompt. So I
always use just the regular xterm for running Xfractint. rxvt seems to
work OK also. (At least on my Linux box - your milage may vary....  8-)

Until later,
Scott
--
[e-mail]
http://sdboyd.dyndns.org/~sdboyd/


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From: "David Jones" <[e-mail]>
Subject: (fractint) Re: Yay! XFractint working - Just not in 24-bpp X?
Date: 21 Jun 2001 20:54:17 -1000

Duplicates? I don't recall sending any duplicates.
Although I think I did reply twice (different contents),
to the same note ... Oh, well, haven't seen any
duplicates here, but my two brain cells might actually be
talking to each other right now ... ;-)

David
[e-mail]

On 22 Jun 01 at 0:02, Paul N. Lee wrote:

> [e-mail] wrote:
> >
> > Is anyone other than me getting multiple
> > copies of the Lavoie, Jones, and Coppin Posts?
>
> The only duplicates I received were two from David Jones
> with the DATE of Wed, 20 Jun 2001 21:28:57.  But I
> suspect that was because of something at his end.
>
> I have noticed that when the FractInt mail server has
> problems, then there will be multiple copies of the
> "Thanks for using Fractint" message at the end of each
> email.  I usually delete all those with more than one of
> these additions.
>
> Sincerely,
> P.N.L.
> --------------------------------------------------------
> ------
> http://www.fractalus.com/cgi-bin/theway?ring=fractals&id
> =43&go
>
> --------------------------------------------------------
> ------ Thanks for using Fractint, The Fractals and
> Fractint Discussion List Post Message:
> [e-mail] Get Commands:
> [e-mail] "help" Administrator:
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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  22-06-01  (An Unfolding Midget [6])
Date: 22 Jun 2001 08:34:58 -0400 (EDT)


Classic FOTD -- June 22, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

The render-time difference between my machine and Paul's is
curious.  I would have expected his machine to finish the
rendering in perhaps half the time, but 1/4 and 1/5 the time
just doesn't make sense.  To account for the discrepancy, I have
checked and found that a clean boot into DOS almost doubles the
speed of my machine, thereby eliminating much of the difference,
but only when I am using type=mandel.  The clean boot makes no
difference when I am using type=formula.  There must be speed-up
code in type=mandel, which is effective only with no remnants of
windows running in the background.  To eliminate the problem,
I'll run Fractint from a clean boot when I use the built-in
mandel formula.

For today, the first full day of summer in all but the western-
most time zones of the northern hemisphere, where yesterday was
the first full day, we have a fractal midget caught in the act
of unfolding.  I naturally named the image "An Unfolding
Midget".  The image is a little above average, qualifying it for
a rating of 6.

The the formula 3.15(Z^(-0.5))+315(Z^(-5))+(1/C) created the
parent fractal, which consists of an ocean with numerous bays.
Today's midget lies on the eastern shore of the eastern-most bay.

Unlike the recent images, which required much patience, today's
image renders in under 9 minutes, even on my tired old machine.
And if 9 minutes still calls for too much patience, the GIF
image will soon be available on the internet at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was typically hot and sultry, with the
typical haze and evening thunder-shower.  The rain and
temperature of 87F (30.5C) were accepted by the cats, mostly
because they had no choice.

I've got to get busy now, so I guess it's time to shut down the
fractal stuff and power up the other stuff.  Until next FOTD,
take care, and keep a fractal as a pet.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

An_UnfoldingMidget { ; time=0:08:56.46--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.911162072257/+0.0710155030211/46512.\
  3/1/177.5 params=0.05/-0.5/5/-5/63/800 float=y
  maxiter=1200 inside=0 logmap=80 periodicity=10
  colors=000kdzWdzWdzWczWczWbzWbzWazWazW`zW`zW_zW_zW\
  ZzWZyV_xTZwSXvQZsPXrOXpMWoLVrJWtHSwGPyFPzBJz7Oz59z\
  3Mz10z0Kz00z0Jzo3z0Ixe3z0Hv00z0Dv00w0Gs00s00r00o00\
  n00l00j00i00f00e00d00a00_00Z01X01W01W01V13T33T53S5\
  3S75Q95PB5PA5OA7MA7MA7LA7LA9JA9HA9HAAGABFAEFABCAGC\
  AFGHIJLHMJLPHMQGOTFPWCSZBT_9Vb7We5Zg3_j1ak0dn0ep0f\
  s0gt0jw0ky0lz0nz0iv0eo0ai0Xb0TW0PO0LG0G70B00503J5B\
  TJHbVOkeTtoZzybywevtisrkopolnrikveixbgzZezWbzS_zPZ\
  zQXzQXzSXzSWzTWzTWxTVwVVvVVsWVrWTpWTnXTlXSkZSiZSg_\
  Sf_Qd_QbaQaaPZbPXbPWbPVeSTgTTjVSlXSoZQr_QtbPwdPxeS\
  tdTrdVobXkbZib_faadad__eX_fV_iQZjOZkLXlHXoCXp9Wr5W\
  s1Wv1Xw1Zx1_z1az1bz1dz1ez1fz1gz1iz1iz5jz9jzCjzGjxJ\
  kvMksPkpSknVlkXlj_lgbleenbgn_jnXlnVooSroPtoMwoLyoO\
  znPznSznTzlWzlXzl_zkazkdzkezjfzjgzjizijzikzilzgnzg\
  ozgpzfrzfszftzfvzewzexzdyzdzzCzzJzzOzzTzzXzz_zzazz\
  bzzdzzfzzgzzizzjzzlzznzzo
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Programmer Dude <[e-mail]>
Subject: (fractint) Jim Muth FOTD 2001-06-20
Date: 22 Jun 2001 12:00:22 -0500

If you've been following along, you know David Jones re-rendered Jim's
FOTD from 6/20 (in 2048x2048) and sent it to me.  I've made it available
to the rest of you (and the world).

See:
     http://www.Sonnack.com/Computers/Fractals/FOTD.html

I also did a resample down to 1024x768 for my own desktop, and that
is also available.  Hope to post some more of Jim's work soon...

P.S.
Please don't pay much attention to my Fractal pages.  What's there now
is more of a placeholder and statement of direction until I have some
time to do it up right...

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  23-06-01  (Super-Nova [5])
Date: 23 Jun 2001 10:54:47 -0400 (EDT)


Classic FOTD -- June 23, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

The learned Astronomers often wonder what it would be like to
actually see with X-ray vision the birth of a supernova.  They
wonder what they would observe if they could park their well-
insulated space craft nearby and watch as the oversize star's
core collapsed into a black hole and the resulting shock wave
blew the star apart.  They could see the rush of neutrinos that
herald the imminent explosion blast into space at (nearly?) the
speed of light.  They could watch as any nearby planets were
turned to ash and vaporized.

The astronomers cannot do this, learned as they may be, but they
can view today's FOTD image and see a slice through the center
of an exploding supernova.

I named the image "Super-Nova" because I decided that it looks
like one.  I rated it a 5 because of it's average quality.
Also, I'm not sure that the name I chose is the best one
possible.

I had to add a 'mathtolerance=' entry to the parameter file
because the magnitude of the image is so large that it may not
render correctly at the higher resolutions.  Actually, the scene
is not fully resolved even at the relatively low SF5 resolution.
The non-zero X-mag and skew factors are also due to exceeding
the precision of the math.  I tried changing these values in the
parameter file to zero, but this caused the image to shrink.

A good feature is the short rendering time -- 5 minutes on my
200mhz machine, only a minute or two on a state-of-the-art
fireball.  (Yesterday's fireball is today's turtle.)

The file of the GIF image will soon be available on the W.W.W.
at Paul's site at the URL:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at Scott's site at the URL:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today (June 22) was cloudy.  The fractal
cats approved of the temperature of 86F (30C), but disapproved
of the thunder, which rumbled for 6 hours before the downpour
finally arrived after sunset.

Today is Saturday, and it's 10:38am, and I've got a few tasks
such as lawn trimming to do.  (If it doesn't rain.) This is a
good enough reason to end the latest FOTD and start thinking
of the next one, which will appear in 12 or 24 hours.  Until
then, take care, and be neutral in all appropriate things.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Super-Nova         { ; time=0:05:03.58--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.39460847258706470/+0.043277920232490\
  68/7.833013e+013/0.9999/-132.58/0.058
  params=1/-1.8/-0.03/2.5/-7/0 float=y maxiter=800
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  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  24-06-01  (Super-Nova [6])
Date: 24 Jun 2001 10:43:47 -0400 (EDT)


Classic FOTD -- June 24, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

I seem to have just invented, or at least discovered, the wheel.
Today's image certainly does resemble a chariot wheel, with its
8 spokes and various decorations.  But actually, it's a midget
in the fractal that is created by the iterated formula:
-0.6(Z^(-1.3))-0.006(Z^(-3))+(1/C).  Regardless of what it is,
the name "The Wheel" serves well as a description of the picture.

The parent fractal is a routine shape created by combining
negative portions of Z^(-1.3) and Z^(-3).  Today's scene is
located very deep in a tiny valley, just inland of the
conventional buds, near to a larger midget.  I rated it at a 6
because of the unusually brilliant colors, though at times I
think that the colors are a bit too brilliant.

The magnitude of the image is so great that I needed to include
an entry in the parameter file telling the program to render the
scene at the correct magnitude regardless of whether it is fully
resolved.  I do not intentionally go beyond the limits of the
math routine as I did today, but sometimes the midget that I am
chasing doesn't appear until the resolution limit has been
reached.

The parameter file of the scene requires almost one hour to
render on my 200MHZ once-a-fireball-but-now-a-clunker computer.
A hasty trip to one of the two web sites where the image is
posted will be well worth the effort.  But give Paul and Scott a
chance to render and post the image before visiting.  The URL's
of those sites are:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was cloudy with light rain and a
temperature of 75F (24C).  Later in the afternoon however, the
rain stopped, the clouds blew away and the fractal cats ventured
out of doors.  When they returned to the house, I found a
freshly-killed and half-eaten sparrow on the pathway.  I have no
way of knowing for sure who did it, though Tippy had the more
satisfied attitude after the event.

It's now time to get on to other things.  So until next time,
which will be here before you know it, take care, and why do
fractals exist in a world where so much does not exist?


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

The_Wheel          { ; time=0:56:22.09--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-14.27546797101664000/-10.1681352980652\
  0000/5.003527e+011/1/-98.994/1 mathtolerance=/1
  params=-0.6/-1.3/-0.006/-3/0/800 float=y
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  UzKUzMUzNVzPVzRVzUFzSFzQF
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  24-06-01  (The Wheel [6])
Date: 24 Jun 2001 15:12:26 -0400 (EDT)


Classic FOTD -- June 24, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

I seem to have just invented, or at least discovered, the wheel.
Today's image certainly does resemble a chariot wheel, with its
8 spokes and various decorations.  But actually, it's a midget
in the fractal that is created by the iterated formula:
-0.6(Z^(-1.3))-0.006(Z^(-3))+(1/C).  Regardless of what it is,
the name "The Wheel" serves well as a description of the picture.

The parent fractal is a routine shape created by combining
negative portions of Z^(-1.3) and Z^(-3).  Today's scene is
located very deep in a tiny valley, just inland of the
conventional buds, near to a larger midget.  I rated it at a 6
because of the unusually brilliant colors, though at times I
think that the colors are a bit too brilliant.

The magnitude of the image is so great that I needed to include
an entry in the parameter file telling the program to render the
scene at the correct magnitude regardless of whether it is fully
resolved.  I do not intentionally go beyond the limits of the
math routine as I did today, but sometimes the midget that I am
chasing doesn't appear until the resolution limit has been
reached.

The parameter file of the scene requires almost one hour to
render on my 200MHZ once-a-fireball-but-now-a-clunker computer.
A hasty trip to one of the two web sites where the image is
posted will be well worth the effort.  But give Paul and Scott a
chance to render and post the image before visiting.  The URL's
of those sites are:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was cloudy with light rain and a
temperature of 75F (24C).  Later in the afternoon however, the
rain stopped, the clouds blew away and the fractal cats ventured
out of doors.  When they returned to the house, I found a
freshly-killed and half-eaten sparrow on the pathway.  I have no
way of knowing for sure who did it, though Tippy had the more
satisfied attitude after the event.

It's now time to get on to other things.  So until next time,
which will be here before you know it, take care, and why do
fractals exist in a world where so much does not exist?


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

The_Wheel          { ; time=0:56:22.09--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-14.27546797101664000/-10.1681352980652\
  0000/5.003527e+011/1/-98.994/1 mathtolerance=/1
  params=-0.6/-1.3/-0.006/-3/0/800 float=y
  maxiter=6000 inside=0 logmap=1000 periodicity=10
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  UzKUzMUzNVzPVzRVzUFzSFzQF
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: [e-mail]
Subject: Earlier Semi-Off-Topic Discussions of Dark Matter/Energy Re: (fractint)
Date: 24 Jun 2001 19:10:13 -0500

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Fellow Fractaliers:
<p>Jim's latest FotD ("Supernova") mentioned a link which led to <u>another</u>
link which discusses - in terms comprehensible even to me - the current
"state of the art" (and Federally-funded research) both observational and
otherwise - into the whole "dark matter/dark energy" issue: what is it
/ where is it?, etc.
<p>See the documents listed at the Homepage for Lawrence Berkeley National
Laboratory's (LBL's) Supernova Acceleration Project (SNAP):
<p>            <<A HREF="http://snap.lnl.gov">http://snap.lnl.gov</A>><b><font size=+1></font></b>
<p>(Also lots of examples multifractal data sets of all sorts (interstellar
particulates, star & galaxy mass/velocity distributions, etc.) for
those who are interested.
<p>Once again,thans to Jim and PNL for the annotation.
<p>D. Freed
<br><b><font size=+1></font></b>
<br>
<p>Jim Muth wrote:
<blockquote TYPE=CITE>Classic FOTD -- June 24, 2001 (Rating 6)
<p>Fractal visionaries and enthusiasts:
<p>I seem to have just invented, or at least discovered, the wheel.
<br>Today's image certainly does resemble a chariot wheel, with its
<br>8 spokes and various decorations.  But actually, it's a midget
<br>in the fractal that is created by the iterated formula:
<br>-0.6(Z^(-1.3))-0.006(Z^(-3))+(1/C).  Regardless of what it is,
<br>the name "The Wheel" serves well as a description of the picture.
<p>The parent fractal is a routine shape created by combining
<br>negative portions of Z^(-1.3) and Z^(-3).  Today's scene is
<br>located very deep in a tiny valley, just inland of the
<br>conventional buds, near to a larger midget.  I rated it at a 6
<br>because of the unusually brilliant colors, though at times I
<br>think that the colors are a bit too brilliant.
<p>The magnitude of the image is so great that I needed to include
<br>an entry in the parameter file telling the program to render the
<br>scene at the correct magnitude regardless of whether it is fully
<br>resolved.  I do not intentionally go beyond the limits of the
<br>math routine as I did today, but sometimes the midget that I am
<br>chasing doesn't appear until the resolution limit has been
<br>reached.
<p>The parameter file of the scene requires almost one hour to
<br>render on my 200MHZ once-a-fireball-but-now-a-clunker computer.
<br>A hasty trip to one of the two web sites where the image is
<br>posted will be well worth the effort.  But give Paul and Scott
a
<br>chance to render and post the image before visiting.  The URL's
<br>of those sites are:
<p>          <<a href="http://home.att.net/~Paul.N.Lee/FotD/FotD.html">http://home.att.net/~Paul.N.Lee/FotD/FotD.html</a>>
<p>and:
<p>          <<a href="http://sdboyd.dyndns.org/~sdboyd/fotd/index.html">http://sdboyd.dyndns.org/~sdboyd/fotd/index.html</a>>
<p>The fractal weather today was cloudy with light rain and a
<br>temperature of 75F (24C).  Later in the afternoon however, the
<br>rain stopped, the clouds blew away and the fractal cats ventured
<br>out of doors.  When they returned to the house, I found a
<br>freshly-killed and half-eaten sparrow on the pathway.  I have
no
<br>way of knowing for sure who did it, though Tippy had the more
<br>satisfied attitude after the event.
<p>It's now time to get on to other things.  So until next time,
<br>which will be here before you know it, take care, and why do
<br>fractals exist in a world where so much does not exist?
<p>Jim Muth
<br>[e-mail]
<p>START 20.0 PAR-FORMULA FILE================================
<p>The_Wheel          { ;
time=0:56:22.09--SF5 on a P200
<br>  reset=2001 type=formula formulafile=allinone.frm
<br>  formulaname=MandelbrotMix4 function=recip passes=1
<br>  center-mag=-14.27546797101664000/-10.1681352980652\
<br>  0000/5.003527e+011/1/-98.994/1 mathtolerance=/1
<br>  params=-0.6/-1.3/-0.006/-3/0/800 float=y
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<br>  _iCdhChgBmfAreAvgEpiHkkKflNanRXpUSrXNs_InYJjWJfVKb\
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<br>  UzKUzMUzNVzPVzRVzUFzSFzQF
<br>  }
<p>frm:MandelbrotMix4 {; Jim Muth
<br>a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
<br>g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
<br>k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
<br>z=k*((a*(z^b))+(d*(z^f)))+c,
<br>|z| < l
<br>}
<p>END 20.0 PAR-FORMULA FILE==================================
<p>--------------------------------------------------------------
<br>Thanks for using Fractint, The Fractals and Fractint Discussion List
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fractint"</blockquote>
</html>


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  25-06-01  (Hanging by a Thread [7])
Date: 25 Jun 2001 10:32:05 -0400 (EDT)


Classic FOTD -- June 25, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Today's fractal is a quickie.  I found it in less that 10
minutes, and rendered it in less than 8.  I rated it a 7, though
I harbor a feeling that anything including fractals that comes
so quickly cannot be worth much.

In coloring today's image, I set the background to a sky blue,
so that the effect is one of looking through the fractal toward
the brightness beyond, rather than looking into a bottomless pit.

I named the picture "Hanging by a Thread" because of the thread-
like filaments that seem to be holding the midget in place.

The parent fractal is a huge, grossly bloated, oversized thing
that needs several full outzooms before it is revealed in its
entirety.  Today's scene is located in a thread that spans a
hole in this oversized object.

With a run-time of a little over 7 minutes, the parameter file
is marginal.  The GIF image will soon be available on the
W.W.Web at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was perfect, with blue skies, warm
sun, puffy white clouds, and a cat-pleasing temperature of 82F
(28C).

The time being late, and having lazed away all of Sunday, I now
must turn my attention to non-fractal things.  But the next FOTD
will appear complete with fractal within 24 hours, if not
sooner.  Until then, take care, and have patience with your
fractals.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

HangingBy_a_Thread { ; time=0:07:15.72--SF5 on a p200
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  0zz2vzCrzKnwUisbeokalleinhhokgooeprdrubsy`szZuzXvz\
  WwzUwzTpzXkzaeze`yhUvlNrpHouCkw5hz0dz0az0Zz2Wz6TzC\
  SzGPzKMzPKzTHzXEzaDzZGzWHvTKnQMeNNZKQQHSHEU8CW08X0\
  dywbssaooakk`gg`bbZZ`ZUWXQSXMNWHJWDGWACW58W25Z5D08\
  z08z0Dz1Gz6KzDNvJSrPUoHNuAGy48zA6zE6zJ6zN6zS6yW6y`\
  6wd6wh6vl6vp6uu6uy6uuCorEkoJgkMbhPZeTUaWQZ`MWbHTeD\
  A0KE0PJ0TN2XQ4aU6dZ8haCleDpiGslHwpKzuMzwNziQwWSlHU\
  b55r21r10r20l40g41a52XPpz
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD  24-06-01  (Super-Nova [6])
Date: 25 Jun 2001 09:39:52 -0500

Jim Muth wrote:

> ...and why do fractals exist in a world where so much does not exist?

A1. Why not?

A2. Who says 'so much does not exist?'  Maybe it all exists....elsewhere!

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: (fractint) Fractint version 20.1.12
Date: 25 Jun 2001 21:07:58 -0500

The diff and executable for Fractint version 20.1.12 are now available at:
www.fractint.org

What's new:

Fixed a problem with a finished image not redrawing if the maxiter was
  increased and another parameter was changed.

  Added checks for p3, p4, and p5 to the browser for determining similar
  images.

  Updated Scott Boyd's email address.

Xfractint fixes:
  Fixed the command line -disk segmentation fault.

  Fixed the Shell to Linux/Unix segmentation fault and the displayed prompt.

  Fixed the bug causing colors= data to be incorrect when in a truecolor
mode.

  Removed or commented out extra lines of code and some experimental
  routines.  Some of this code was stealing key strokes.

  Changed the prompt for getting to the second <TAB> screen.

The Xfractint source hasn't been updated yet.  I should get to it tomorrow.

Jonathan



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-------------------------------------------------------------------------------

From: "nltnme" <[e-mail]>
Subject: (fractint) would like some help, please
Date: 25 Jun 2001 21:42:14 -0500

This is a multi-part message in MIME format.

------=_NextPart_000_0015_01C0FDBF.B2FA41A0
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

I've played around with fractint for a number of years... on and off.

I'm not really a programmer type.  I would like to set up the printer to =
print a ps file... i believe I did it once in an older version of =
fractint, running on a DOS machine.

but with windowsME, i'm not quite sure how to set things up.  maybe =
someone can walk me thru that.

Next.  I'd like to know if there is a formula that with do a Mandelbrott =
in reverse... that is.. fill the blue lake areas with the colors of the =
shore line.

Next.  There is a formula I use at work... would be lengthy to explain =
here... but involves some basic variable which are multiplied, results =
multiplied by other varialble, result divided.. I would like to.. for =
the fun of it... see what kind of factal the results would generate.  Is =
there anyone out there that might be able to assist me?

Thanks in advance to all

nltnme

------=_NextPart_000_0015_01C0FDBF.B2FA41A0
Content-Type: text/html;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4207.2601" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>
<DIV><FONT face=3DArial size=3D2>I've played around with fractint for a =
number of=20
years... on and off.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>I'm not really a programmer type.  =
I would=20
like to set up the printer to print a ps file... i believe I did it once =
in an=20
older version of fractint, running on a DOS machine.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>but with windowsME, i'm not quite sure =
how to set=20
things up.  maybe someone can walk me thru that.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Next.  I'd like to know if there =
is a formula=20
that with do a Mandelbrott in reverse... that is.. fill the blue lake =
areas with=20
the colors of the shore line.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Next.  There is a formula I use at =
work...=20
would be lengthy to explain here... but involves some basic variable =
which are=20
multiplied, results multiplied by other varialble, result divided.. I =
would like=20
to.. for the fun of it... see what kind of factal the results would=20
generate.  Is there anyone out there that might be able to assist=20
me?</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Thanks in advance to all</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial =
size=3D2>nltnme</FONT></DIV></FONT></DIV></BODY></HTML>

------=_NextPart_000_0015_01C0FDBF.B2FA41A0--


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  26-06-01  (Quadrilateral [6])
Date: 25 Jun 2001 23:02:02 -0400 (EDT)


Classic FOTD -- June 26, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Start with a bit of 1/Z, add a lot of Z^100, then add 1/C and
iterate a few thousand times.  What do you get? -- a fractal of
course.  The fractal, which is not visible in its entirety
unless an out-zoom is done, consists of a central Mandel-like
figure, with two vaguely Mandel-shaped satellite objects located
symmetrically north and south of it.  Today's little midget is
located in what passes for an East Valley of the north satellite.

Actually, today's midget is in the northeast suburbs of a larger
midget in the pseudo-East Valley of the north satellite.  I
named the picture "Quadrilateral" when I noticed that most of
the elements seem to be in the shape of four-sided geometrical
figures.  The rating of 6, which is a bit above average, seems
an honest assessment of this unassuming image.

I was surprised when I saw the difference made by adding such a
small portion of 1/Z to the Z^100 fractal, which is basically a
circle.  But the most unlikely things seem to happen in the
world of fractals.  If the portions of 1/Z and Z^100 are
reversed, real(p3) needs to be reset to -0.99, but when this is
done, another interesting fractal results.  Tomorrow's FOTD will
be a scene in the fractal that is the reciprocal of today's.

With a render time of just under 20 minutes, the slow parameter
file demands a trip to one of the FOTD web sites for a download
of the GIF image file.  Those sites are found at the URL's:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was once again perfect.  The
temperature of 86F (30C) and clear skies kept the cats happy.
And in addition to fractals, happy cats are one of life's
greatest enjoyments.

It's now getting late and near the time to shut down the fractal
shoppe and call it a night.  OK, it's a night!  Until tomorrow,
take care, and never forget that it's easier to think of
questions than to give answers.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Quadrilateral      { ; time=0:19:18.54--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-8.6414574311906/+4.74639557029845/4.67\
  691e+008/1/-82.503/0.001 params=1/-1/100/100/-0.1/0
  float=y maxiter=3300 inside=0
  logmap=393 periodicity=10
  colors=000MLOMLOGOP9SJ3YE0b80h30m00n00n00n01p04p09\
  p0Cq0Hq0Kq0Ns0Ss0Vs0Yu0bu0eu0iv0mv0pv0ux0xx0zu0zx0\
  uy1nz4hz6bz9XzCQzGKzHEzK8zN3zP4zN6zM6zM8zK8zK9yJ9v\
  JBuHBqHCnGCkGEiEEfEGcCG`CH_BHXBJT9JQ9KP8KM8MJ6NE3M\
  H6KK8JM9JPBHSEGTGEXHE_JC`KBcNBfP9hQ8kS6nV6pX4sY3v_\
  0zb3x`8v`Cs`Hq`Mn`Qm`Vk`_h`cf`hc`mb`n``q``fcfeTfeJ\
  fc8fc3fc0fe0hf1hf4ih6ii8iiBkkCkmEmmHmnJmpKnpNnqPps\
  QpsTpuVqvXqv_sx`sybsyeuzfuzhvzhuyhsxhsvhquhpshpqhn\
  phmnhmnhkmhikhiihhhhffhfehechcbhc`hbeiY`hbYfeTdhQa\
  mN`pJZpGWrBUr8Rq1Np4Rq6Ut8Yv9_xCczEfyGhyKmxUnvcqum\
  ssrvqzxpwyprzvrzzpzzmyzcxzUvzHszEqzCpz9nz6kz4iz1hz\
  0az6XzBPzGPzMKzQKzVKz`AzeKziUzpczumzymzzmzzmzzmzqc\
  zXhzBbz0fz0ez0ez0ez0ez0ez0ez0ez0ez1fz1hz9iuGk_MmEN\
  nBNp9Nq8Ns4Nu3Pv1Px0Px0Px0Px0bx6pxJzxVzxfzxezxczxb\
  zx`zx_yxYvxXsxXpxVmxTixSfxQcxP`xNYxMVxMTxNTxNTxNYx\
  SbxXex`ixemxiqxnixncxiYxc
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) C-FOTD 26-06-01 (Quadrilateral [6])
Date: 26 Jun 2001 09:31:37 -0000

>From: Jim Muth <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>CC: [e-mail]
>Subject: (fractint) C-FOTD  26-06-01  (Quadrilateral [6])
>Date: Mon, 25 Jun 2001 23:02:02 -0400 (EDT)
>
>
>Classic FOTD -- June 26, 2001 (Rating 6)
>
>Fractal visionaries and enthusiasts:
>The rating of 6, which is a bit above average, seems
>an honest assessment of this unassuming image.

Unassuming??? Jim, that is a LUSH colour scheme. I *love* it!

Thanks.
Andrew.

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.


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-------------------------------------------------------------------------------

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD  26-06-01  (Quadrilateral [6])
Date: 26 Jun 2001 12:38:07 -0500

Jim Muth wrote:

> ...and never forget that it's easier to think of questions than to give
> answers.

Prolly 'cause there's so gosh-darned many questions,...

And so gosh-darned few answers!

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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-------------------------------------------------------------------------------

From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) C-FOTD 26-06-01 (Quadrilateral [6])
Date: 26 Jun 2001 12:42:18 -0500

Andrew Coppin wrote:

>>an honest assessment of this unassuming image.
>
> Unassuming??? Jim, that is a LUSH colour scheme. I *love* it!

I agree!  Looks ... edible ... tasty even!!

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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-------------------------------------------------------------------------------

From: [e-mail]
Subject: Re: (fractint) C-FOTD  26-06-01  (Quadrilateral [6])
Date: 26 Jun 2001 15:12:15 -0500

Happy cats and happy people, too.

Must agree w/ Coppin, PDudely, et al that this is one of your best,
precisely because of the coloring scheme. Maybe not much to you, Jim,
but everyone I had look at it now wants a large format copy to put on
her desk.

June has been a good month for you - and for us as a result. Also have
really enjoyed the last week's worth of >5-rated images across the
board.

m Muth wrote:

> Classic FOTD -- June 26, 2001 (Rating 6)
>
> Fractal visionaries and enthusiasts:
>
> Start with a bit of 1/Z, add a lot of Z^100, then add 1/C and
> iterate a few thousand times.  What do you get? -- a fractal of
> course.  The fractal, which is not visible in its entirety
> unless an out-zoom is done, consists of a central Mandel-like
> figure, with two vaguely Mandel-shaped satellite objects located
> symmetrically north and south of it.  Today's little midget is
> located in what passes for an East Valley of the north satellite.
>
> Actually, today's midget is in the northeast suburbs of a larger
> midget in the pseudo-East Valley of the north satellite.  I
> named the picture "Quadrilateral" when I noticed that most of
> the elements seem to be in the shape of four-sided geometrical
> figures.  The rating of 6, which is a bit above average, seems
> an honest assessment of this unassuming image.
>
> I was surprised when I saw the difference made by adding such a
> small portion of 1/Z to the Z^100 fractal, which is basically a
> circle.  But the most unlikely things seem to happen in the
> world of fractals.  If the portions of 1/Z and Z^100 are
> reversed, real(p3) needs to be reset to -0.99, but when this is
> done, another interesting fractal results.  Tomorrow's FOTD will
> be a scene in the fractal that is the reciprocal of today's.
>
> With a render time of just under 20 minutes, the slow parameter
> file demands a trip to one of the FOTD web sites for a download
> of the GIF image file.  Those sites are found at the URL's:
>
>           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
>
> and:
>
>           <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
>
> The fractal weather today was once again perfect.  The
> temperature of 86F (30C) and clear skies kept the cats happy.
> And in addition to fractals, happy cats are one of life's
> greatest enjoyments.
>
> It's now getting late and near the time to shut down the fractal
> shoppe and call it a night.  OK, it's a night!  Until tomorrow,
> take care, and never forget that it's easier to think of
> questions than to give answers.
>
> Jim Muth
> [e-mail]
>
> START 20.0 PAR-FORMULA FILE================================
>
> Quadrilateral      { ; time=0:19:18.54--SF5 on a P200
>   reset=2001 type=formula formulafile=allinone.frm
>   formulaname=MandelbrotMix4 function=recip passes=1
>   center-mag=-8.6414574311906/+4.74639557029845/4.67\
>   691e+008/1/-82.503/0.001 params=1/-1/100/100/-0.1/0
>   float=y maxiter=3300 inside=0
>   logmap=393 periodicity=10
>   colors=000MLOMLOGOP9SJ3YE0b80h30m00n00n00n01p04p09\
>   p0Cq0Hq0Kq0Ns0Ss0Vs0Yu0bu0eu0iv0mv0pv0ux0xx0zu0zx0\
>   uy1nz4hz6bz9XzCQzGKzHEzK8zN3zP4zN6zM6zM8zK8zK9yJ9v\
>   JBuHBqHCnGCkGEiEEfEGcCG`CH_BHXBJT9JQ9KP8KM8MJ6NE3M\
>   H6KK8JM9JPBHSEGTGEXHE_JC`KBcNBfP9hQ8kS6nV6pX4sY3v_\
>   0zb3x`8v`Cs`Hq`Mn`Qm`Vk`_h`cf`hc`mb`n``q``fcfeTfeJ\
>   fc8fc3fc0fe0hf1hf4ih6ii8iiBkkCkmEmmHmnJmpKnpNnqPps\
>   QpsTpuVqvXqv_sx`sybsyeuzfuzhvzhuyhsxhsvhquhpshpqhn\
>   phmnhmnhkmhikhiihhhhffhfehechcbhc`hbeiY`hbYfeTdhQa\
>   mN`pJZpGWrBUr8Rq1Np4Rq6Ut8Yv9_xCczEfyGhyKmxUnvcqum\
>   ssrvqzxpwyprzvrzzpzzmyzcxzUvzHszEqzCpz9nz6kz4iz1hz\
>   0az6XzBPzGPzMKzQKzVKz`AzeKziUzpczumzymzzmzzmzzmzqc\
>   zXhzBbz0fz0ez0ez0ez0ez0ez0ez0ez0ez1fz1hz9iuGk_MmEN\
>   nBNp9Nq8Ns4Nu3Pv1Px0Px0Px0Px0bx6pxJzxVzxfzxezxczxb\
>   zx`zx_yxYvxXsxXpxVmxTixSfxQcxP`xNYxMVxMTxNTxNTxNYx\
>   SbxXex`ixemxiqxnixncxiYxc
>   }
>
> frm:MandelbrotMix4 {; Jim Muth
> a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
> g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
> k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
> z=k*((a*(z^b))+(d*(z^f)))+c,
> |z| < l
> }
>
> END 20.0 PAR-FORMULA FILE==================================
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
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> Unsubscribe:    [e-mail] "unsubscribe fractint"


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-------------------------------------------------------------------------------

From: "Jonathan Osuch" <[e-mail]>
Subject: (fractint) Xfractint version 20.1.12
Date: 26 Jun 2001 20:23:23 -0500

The source for Xfractint version 20.1.12 is now available at the developer's
web site:
www.fractint.org

The patch doesn't go in cleanly.  I was expecting this to happen because of
the nature of the changes.

Jonathan



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-------------------------------------------------------------------------------

From: "Osher Doctorow" <[e-mail]>
Subject: (fractint) Where the Big Bang Came From According to Memory (M) Theory With Chaos
Date: 26 Jun 2001 23:19:57 -0700


I have been generalizing my paper in B. N. Kursunuglu et al Editors Quantum
Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based
Unification, Kluwer Academic/Plenum: N.Y. 2000 89-97, into Memory (M)
Theory.  To make this introduction more rapid, I will just mention a few
points.

1. The universe is divided into events which depend on 2 or more past times
(Memory (M) events), events which depend on only one past time (Semi-Memory
(S) events), and events which depend on no past time (Non-Memory (N)
events).
2. I proved an inequality yesterday on anzap-l (Australian-New Zealand
Applied Probability) which in English translation approximately states that
when two random variables tend to increase together (technically they are
positively quadrant dependent according to the statistical dependence
literature - see Harry Joe's (University of British Columbia) recent volume
by Chapman Hall/Longmans on statistical dependence (you can reference it on
the internet under Professor Harry Joe or one of the publishers - I think
the internet hasn't gotten to categorizing dependence yet as a keyword),
then events associated with them are of M type if they have low probability,
S type if they have medium or fair probability, and N type if they have high
probability.   However, if the two random variables are negatively
statistically dependent (one tends to increase while the other tends to
decrease), then chaos is generated at the boundary or transition between
fair/medium and high probability events associated with these random
variables.  It is not generated anywhere else.
3.  For those who are interested in actually using the inequality, for the
case of positive quadrant dependent events it states that for positively
quadrant dependence, which is to say P(AB) > = P(A) times P(B)  where P(A)
is the probability of set/event A, P(AB) is the probability of the
intersection of set/events A and B, then the probable influences of A on B
or the probability of B given A (the first applies to M and N events, the
second to S events) are related by in the relative order from left (M) to
center (S) to right (N): 1 + y - x > = y/x > = z   where x = P(A) is assumed
non-zero in the middle expression, y = P(AB), z = P(B).   For negative
quadrant dependence, only y/x > = z fails, which is the boundary between M
and N events.   Notice that S events are usually described as Bayesian or
involving Bayesian conditional probability (BCP).

There is no question about the above results.  However, there is a bit more
theorizing and conjecture involved in applying them to the Big Bang.  The
most plausible present conjectured scenario that I have based partly on the
above is as follows, numbered starting with 4.

4. The universe at the exact time of the Big Bang was either in a state of
*tired radiation* or a combined matter-radiation state (a phase which no
longer exists except perhaps in quantum entanglement, although it may be
remotely related to Memory (M)).  If it was in a state of *tired radiation*,
I am referring to radiation which has travelled a very long distance and is
at an extreme boundary of an earlier universe - for example, a prior
expanding-accelerating universe which may still exist *outside* ours.   I
will refer to this universe as the Proto Object or PO.
5. The PO was in a combined S and N state, which means the following in
practice.  It was in an analogue of a type of equilibrium between a tendency
to depend on no past time (time independence or N state, similar to
radiation in the case of light in some respects) and a tendency to depend on
one past time (S state).  Markov chains and Markov processes exemplify S
states in the present time universe, as do differential and partial
differential equation models which only have one explicit time variable t
and one implicit future time variable t + h or rather its limit as h
approaches 0 contained in the (partial) derivative(s), so that the event at
time t + h may be considered to depend on the one previous time t.  This is
not true of delay/retarded or advanced (functional) differential equations
or Volterra integral or integrodifferential equations, which depend on 2 or
more times.
6.  The tension between the tendency of the PO to depend on no or one
previous time is reflected in the present tension between matter which tends
to resist change of position (inertia) and radiation which tends to move or
resist *stopping at one position*.   However, present day radiation seems to
also have a time independence of a sort - a ray of light is well known to
*see* its entire past and future simultaneously, and the Penrose Diagram
separates light, space, and time into adjacent but different regions.  The
nature of radiation may have already changed from the PO till now.
7.  The Big Bang was triggered when the tension between radiation and matter
broke chaotically, and the radiation-dominated early era of the universe
began.   Later on, a matter-dominated era took over, in which however much
radiation still existed and exists.  In this scenario, some matter still
probably survived during the early radiation-dominated era.  What triggered
the breaking of the tension was a change from positive to negative
dependence of matter and radiation due to the increase of time as measured
positively from 0 at the Big Bang forward.  Early radiation was time
dependent, also reflected in present day radiation in its tendency to move
or resist stopping.  As time increased, it interacted with radiation more
than with matter.  Radiation became dominant and the radiation-dominated era
began.  However, as time went on, the universe began occupying such a large
volume that its spatial influence became dominant over its time influence,
and this interacted with matter which tends to preserve position in space.
The matter-dominated era took over.
8.  In both the rise of the radiation-dominated era and the matter-dominated
era, there is indication concerning the *resetting* of both internal clocks
in time and internal *spatial clocks* or spatial measurement in space by
what we call the universe from a zero point at the Big Bang.  Since it seems
plausible that a universe (or two) existed prior to the Big Bang, the
resetting of the time clock may be a characteristic of *tired radiation* as
well as the onset of chaos.  The clock jumped from its previous reading to
some unknown chaotic time value which the *reborn* universe labelled as
zero.  When it was relabelled, radiation had taken over and the Big Bang had
begun.  Later, expanding space exerted an increasing influence on the
universe in the direction of matter and a boundary was reached at which a
similar chaotic jump occurred in space, and the universe reset its *spatial
clock* or spatial measurement and matter had taken over mostly.
9.  The above theory may enable deciding between inflation, quintessence,
dark energy, the cosmological constant, and so on as to what force drives
the expanding/accelerating universe.  If inflation occurred as a sudden jump
twice, as the latest theory claims, then it may have jumped either at one or
both chaotic points indicated above or as a small chaotic transition
somewhere between them.  It is of course possible that all of the above have
some role.
10.  The recent claimed finding of a new form of *early universe* matter in
quasars may, if confirmed, help decide between the various alternatives in
9.

Osher Doctorow Ph.D.
Doctorow Consultants
Formerly (and still intermittently in parts) California State Universities
and Community Colleges, U.S. Defense Department, etc.




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-------------------------------------------------------------------------------

From: "Scott D. Boyd" <[e-mail]>
Subject: Re: (fractint) Xfractint version 20.1.12
Date: 27 Jun 2001 01:33:18 +0000

On Wednesday 27 June 2001 01:23, Jonathan Osuch wrote:
> The source for Xfractint version 20.1.12 is now available at the
> developer's web site:
> www.fractint.org
>
> The patch doesn't go in cleanly.  I was expecting this to happen because
> of the nature of the changes.
>
You were right about that! I found that out Tuesday morning when I tried
to apply the patch to v20.1.11 - no go.... I knew I would just have to
wait until you uploaded the full source. I'm anxious to try out your
fixes, so I'll compile it Wednesday night.

Until later,
Scott Boyd
--
[e-mail]
http://sdboyd.dyndns.org/~sdboyd/



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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  27-06-01  (Quadrilateral [6])
Date: 27 Jun 2001 10:27:34 -0400 (EDT)


Classic FOTD -- June 27, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

The parent fractal of today's image must be seen to believed.
One outzoom is needed before the entire thing will fit on the
screen, but once this is done, a fractal with more convolutions
than a junkyard dog has fleas appears.  This parent is one of
the most enigmatic figures I have yet stumbled upon.  It has
narrow valleys, broad valleys, mandel-buds, near-mandel buds,
plus an unlimited number of holes and indents of various and
assorted sizes and shapes.

The broad features are those of a high-order Mandeloid or Julia
set, but these features do not make up the entire fractal.
Rather, they form a kind of pattern theme around the smaller,
more irregular features.

Today's scene lies in one of the broader valleys.  I named it
"Mathematical Scythes" when the reddish crescent-shaped features
impressed me as blades of scythes.  Actually, with its strong
reds and greens, the scene has a rather Christmasy look about
it, but since we are about as far from Christmas as it is
possible to be, I decided against the Christmas theme.  I rated
the image a 6, since it is a bit above my long-term average.

The simple formula (1/Z)-Z^(300)+(1/C) created the parent
fractal.  Taken by itself (1/Z)+C does little, and Z^300+C does
little more.  But when combined, and when 1/C instead of C is
added, these two expressions work wonders.

One of the wonders, which is today's FOTD, can be seen by
running the Fractint parameter file attached to the bottom of
this letter.  The parameter file renders in only 5-1/2 minutes
on my tired old Pentium 200mhz machine, but notably faster on
one of the current screaming fireballs.

The alternate way of viewing the scene is to go to one of the
internet web sites where the GIF file of the image will soon be
posted.  Paul's site can be found at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and Scott's is at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was the image of a lazy summer day,
with sunny but hazy skies, unhealthy air, and a temperature of
90F (32C) that kept Thomas happy.  Tippy however was not happy,
since it was the day for his annual visit to the doctor.  He
cried all the way there and back.  After being pronounced
healthy, he cried all the way back, and then sulked for several
hours before becoming his normal self.  Thomas was glad it was
not his time to go to the doctor, but his time is not far off.

And my time to do some useful work has arrived.  In fact, it
arrived an hour ago, and I've yet to get started.  So until next
time, take care, and regardless of how many fractals we find,
the number of fractals yet to be found will never be reduced.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Mathematic_Scythes { ; time=0:05:28.34--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-19.25482682013031000/-0.26917358759950\
  070/6407.871/1/52.5 params=1/-1/-1/300/0/0 float=y
  maxiter=4000 inside=0 logmap=91 periodicity=10
  colors=0007ma7mb6nc6nd6oe5pf5pg5qh5qi6oh7mg7kf8ie9\
  he9fdAdcBbbB`aC_aDY`DW_EUZFSYFRYGQUGQRHQOHQKIPHIPE\
  JPAJP7JP4NR5QT6TU7WW8_X9bZAe`BhaClcDodErfFugFqeImc\
  LiaOe_RaYUYWXUU_QSbVQYZPUbNQfMMjLHnJDrI9vH5uG5tG5s\
  G5rG5qF5qF5pF5oF5nE5mE5mE5lE5kD5jD5iD5iD5dG9_IDVKH\
  QMLLOPHQTLSVOUWSWYVYZZ_`aaaecchedVWkINr5EyBAlG7`L4\
  PQ1DR3GS5JT7LT9OUBQVDTWFVWGYXI_YKbZMdZOg_Qi`Sl`Tn9\
  1wB2pD2jF2cH3YJ3RL3LM3FJBMGJTDQZAYe8dkC`gGXcKT_OPW\
  SLSWHOZELXJHVODTTARY6Qa3QXBQSIQNQQIXQEcVGbZHabIagK\
  `kL_oM_mTSkZKieChk4_m7SnAJoCBpF3qH7rNArTDrZGrcKsiN\
  soQsuTszWrwYru_qsaqqcqoeplgpjiohkofmodonaqn_smYumW\
  wmUulTtlSskRrkQpkPojOnjNmiMkiLjiKihJhiIgjHdkGalFZm\
  EWnDToCQpBNqAKr9Hs8Et7Cu7EvDGwJIxOKyUMz_OzdQzjBzcC\
  zdDzeEzeFzfFzfGzgHzgIzh_zqezpkznqzlwzkmzBsz_yzwZzu\
  9zsQziez`uzSmzXez`ZzdRziJzmCzqDzoEznFzlGzkHzjIzjIz\
  iCzECz9Cz4BzCAzK9zS8zZ7z`
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  27-06-01  (Mathematical Scythes [6])
Date: 27 Jun 2001 14:25:25 -0400 (EDT)


Classic FOTD -- June 27, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

This version of the FOTD has the correct name in the subject
line.

The parent fractal of today's image must be seen to believed.
One outzoom is needed before the entire thing will fit on the
screen, but once this is done, a fractal with more convolutions
than a junkyard dog has fleas appears.  This parent is one of
the most enigmatic figures I have yet stumbled upon.  It has
narrow valleys, broad valleys, mandel-buds, near-mandel buds,
plus an unlimited number of holes and indents of various and
assorted sizes and shapes.

The broad features are those of a high-order Mandeloid or Julia
set, but these features do not make up the entire fractal.
Rather, they form a kind of pattern theme around the smaller,
more irregular features.

Today's scene lies in one of the broader valleys.  I named it
"Mathematical Scythes" when the reddish crescent-shaped features
impressed me as blades of scythes.  Actually, with its strong
reds and greens, the scene has a rather Christmasy look about
it, but since we are about as far from Christmas as it is
possible to be, I decided against the Christmas theme.  I rated
the image a 6, since it is a bit above my long-term average.

The simple formula (1/Z)-Z^(300)+(1/C) created the parent
fractal.  Taken by itself (1/Z)+C does little, and Z^300+C does
little more.  But when combined, and when 1/C instead of C is
added, these two expressions work wonders.

One of the wonders, which is today's FOTD, can be seen by
running the Fractint parameter file attached to the bottom of
this letter.  The parameter file renders in only 5-1/2 minutes
on my tired old Pentium 200mhz machine, but notably faster on
one of the current screaming fireballs.

The alternate way of viewing the scene is to go to one of the
internet web sites where the GIF file of the image will soon be
posted.  Paul's site can be found at:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and Scott's is at:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

The fractal weather today was the image of a lazy summer day,
with sunny but hazy skies, unhealthy air, and a temperature of
90F (32C) that kept Thomas happy.  Tippy however was not happy,
since it was the day for his annual visit to the doctor.  He
cried all the way there and back.  After being pronounced
healthy, he cried all the way back, and then sulked for several
hours before becoming his normal self.  Thomas was glad it was
not his time to go to the doctor, but his time is not far off.

And my time to do some useful work has arrived.  In fact, it
arrived an hour ago, and I've yet to get started.  So until next
time, take care, and regardless of how many fractals we find,
the number of fractals yet to be found will never be reduced.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Mathematic_Scythes { ; time=0:05:28.34--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-19.25482682013031000/-0.26917358759950\
  070/6407.871/1/52.5 params=1/-1/-1/300/0/0 float=y
  maxiter=4000 inside=0 logmap=91 periodicity=10
  colors=0007ma7mb6nc6nd6oe5pf5pg5qh5qi6oh7mg7kf8ie9\
  he9fdAdcBbbB`aC_aDY`DW_EUZFSYFRYGQUGQRHQOHQKIPHIPE\
  JPAJP7JP4NR5QT6TU7WW8_X9bZAe`BhaClcDodErfFugFqeImc\
  LiaOe_RaYUYWXUU_QSbVQYZPUbNQfMMjLHnJDrI9vH5uG5tG5s\
  G5rG5qF5qF5pF5oF5nE5mE5mE5lE5kD5jD5iD5iD5dG9_IDVKH\
  QMLLOPHQTLSVOUWSWYVYZZ_`aaaecchedVWkINr5EyBAlG7`L4\
  PQ1DR3GS5JT7LT9OUBQVDTWFVWGYXI_YKbZMdZOg_Qi`Sl`Tn9\
  1wB2pD2jF2cH3YJ3RL3LM3FJBMGJTDQZAYe8dkC`gGXcKT_OPW\
  SLSWHOZELXJHVODTTARY6Qa3QXBQSIQNQQIXQEcVGbZHabIagK\
  `kL_oM_mTSkZKieChk4_m7SnAJoCBpF3qH7rNArTDrZGrcKsiN\
  soQsuTszWrwYru_qsaqqcqoeplgpjiohkofmodonaqn_smYumW\
  wmUulTtlSskRrkQpkPojOnjNmiMkiLjiKihJhiIgjHdkGalFZm\
  EWnDToCQpBNqAKr9Hs8Et7Cu7EvDGwJIxOKyUMz_OzdQzjBzcC\
  zdDzeEzeFzfFzfGzgHzgIzh_zqezpkznqzlwzkmzBsz_yzwZzu\
  9zsQziez`uzSmzXez`ZzdRziJzmCzqDzoEznFzlGzkHzjIzjIz\
  iCzECz9Cz4BzCAzK9zS8zZ7z`
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "nltnme" <[e-mail]>
Subject: (fractint) need some assistance... third attempt to post
Date: 27 Jun 2001 20:34:17 -0500

This is a multi-part message in MIME format.

------=_NextPart_000_000D_01C0FF48.89B76680
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

I've played around with fractint for a number of years... on and off.

I'm not really a programmer type.  I would like to set up the printer to =
print a ps file... i believe I did it once in an older version of =
fractint, running on a DOS machine.

but with windowsME, i'm not quite sure how to set things up.  maybe =
someone can walk me thru that.

Next.  I'd like to know if there is a formula that with do a Mandelbrott =
in reverse... that is.. fill the blue lake areas with the colors of the =
shore line.

Next.  There is a formula I use at work... would be lengthy to explain =
here... but involves some basic variable which are multiplied, results =
multiplied by other varialble, result divided.. I would like to.. for =
the fun of it... see what kind of factal the results would generate.  Is =
there anyone out there that might be able to assist me?

Thanks in advance to all

nltnme

------=_NextPart_000_000D_01C0FF48.89B76680
Content-Type: text/html;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4207.2601" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>
<DIV><FONT face=3DArial size=3D2>
<DIV><FONT face=3DArial size=3D2>I've played around with fractint for a =
number of=20
years... on and off.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>I'm not really a programmer type.  =
I would=20
like to set up the printer to print a ps file... i believe I did it once =
in an=20
older version of fractint, running on a DOS machine.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>but with windowsME, i'm not quite sure =
how to set=20
things up.  maybe someone can walk me thru that.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Next.  I'd like to know if there =
is a formula=20
that with do a Mandelbrott in reverse... that is.. fill the blue lake =
areas with=20
the colors of the shore line.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Next.  There is a formula I use at =
work...=20
would be lengthy to explain here... but involves some basic variable =
which are=20
multiplied, results multiplied by other varialble, result divided.. I =
would like=20
to.. for the fun of it... see what kind of factal the results would=20
generate.  Is there anyone out there that might be able to assist=20
me?</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>Thanks in advance to all</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial=20
size=3D2>nltnme</FONT></DIV></FONT></DIV></FONT></DIV></BODY></HTML>

------=_NextPart_000_000D_01C0FF48.89B76680--


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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 20-06-01 (A Midget at Midnight [7])
Date: 28 Jun 2001 03:20:00 -0400


------=_NextPart_001_0003_01C0FF81.37110420
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> As for me, I've got things that need to be done, and limited
> time in which to do them.  So the rational thing is to get busy.
> Until next FOTD, take care, and where are those Herman Rings?

More to the point: What the hell are Herman Rings? :-)<br clear=3Dall><hr=
>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://www.=
hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0003_01C0FF81.37110420
Content-Type: text/html; charset="iso-8859-1"
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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> As for me=
, I've got things that need to be done, and limited<BR>> time in which=
 to do them.  So the rational thing is to get busy.<BR>> Until ne=
xt FOTD, take care, and where are those Herman Rings?<BR></DIV> <DIV>More=
 to the point: What the hell are Herman Rings? :-)</DIV></BODY></HTML><DI=
V><BR><br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail =
at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p>=
</DIV>

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 20-06-01 (A Midget at Midnight [7])
Date: 28 Jun 2001 03:21:11 -0400


------=_NextPart_001_0004_01C0FF81.613C9C00
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> First time I ever actually ran the PAR, rather than go
> look att he picture on the web. 27 minutes on a Duron
> 700, running Fractint under OS/2...

You mean, someone out there actually still uses OS/2? :-)<br clear=3Dall>=
<hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://w=
ww.hotmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0004_01C0FF81.613C9C00
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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> First tim=
e I ever actually ran the PAR, rather than go<BR>> look att he picture=
 on the web. 27 minutes on a Duron<BR>> 700, running Fractint under OS=
/2...</DIV> <DIV> </DIV> <DIV>You mean, someone out there actually s=
till uses OS/2? :-)</DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Y=
our Private, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmai=
l.com">http://www.hotmail.com</a>.<br></p></DIV>

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 28 Jun 2001 03:25:37 -0400


------=_NextPart_001_0005_01C0FF82.002DB240
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> Hmm... must try that!

> (BTW, in what language is "munged" a word?!?!)

Hackish.

http://www.tuxedo.org<br clear=3Dall><hr>Get Your Private, Free E-mail fr=
om MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.c=
om</a>.<br></p>

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Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Hmm... mu=
st try that!<BR><BR>> (BTW, in what language is "munged" a word?!?!)<B=
R></DIV> <DIV>Hackish.</DIV> <DIV> </DIV> <DIV><A href=3D"http://www=
.tuxedo.org">http://www.tuxedo.org</A></DIV> <DIV><BR> </DIV></BODY>=
</HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, Free E-mail from MS=
N Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</a=
>.<br></p></DIV>

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From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 21-06-01 (Fractal Caterpillars [6])
Date: 28 Jun 2001 03:37:30 -0400


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> I'm thinking of purchasing another fractal computer, a state-of-
> the-art machine, so I would be interested in hearing reports of
> the time required to render today's particularly difficult scene
> on different machines with different CPU's.  If I do make the
> purchase, I want to be sure I'm getting the fastest fractal
> rendering machine possible.

Unfortunately, there's no one answer to this question, and never will be.=
 There's always a cost-speed curve of available computers. If you can spa=
re a billion or so, you might want a Cray YMP or even a Connection Machin=
e. The latter could simultaneously devote a CPU to each pixel. For a hund=
red K or so, you could have an SGI workstation, with *really* impressive =
graphics and good numeric speed. In the same range, you could get a batch=
 of PCs and link them up into a Beowulf cluster, and probably achieve the=
 same capabilities as the Connection Machine for a fraction the cost. Jus=
t watch the electric bill. If you have a few thousand dollars, for the pr=
ice of a slightly used sedan you can get a Mac G4, which won't run Fracti=
nt, but will run fast enough that it is officially classed as a supercomp=
uter and cannot be exported to Tier 7 nations like Libya. (I think the go=
vernment's concern is that they'll use supercomputing to design nuclear w=
eapons -- unfortunately, these restrictions are pointless, since they'll =
just co-opt an American scientist for nuclear secrets like China did, or =
if worse comes to worst, buy some cheap IBMs from BuckADay.com and cobble=
 up a Beowulf cluster. Maybe the way to peace in those areas is to quit t=
he export laws and start weaving these countries into the global economy =
to such an extent that they can't possibly nuke anyone without killing of=
f one of their economy's important suppliers or consumers?)
A lower-end RISC chip like the Alpha is another option. If you have a mer=
ely mortal ability to take financial punishment, then a recent Athlon, Du=
ron, or Pentium III or IV CPU is your choice. There are price lists with =
comparisons of FPU performance, integer performance, and other characteri=
stics out there on the net for these Intel-family CPUs. Even among these,=
 a curve of available power is apparent, with generally more money needed=
 to get a faster box.<br clear=3Dall><hr>Get Your Private, Free E-mail fr=
om MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.c=
om</a>.<br></p>

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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> I'm think=
ing of purchasing another fractal computer, a state-of-<BR>> the-art m=
achine, so I would be interested in hearing reports of<BR>> the time r=
equired to render today's particularly difficult scene<BR>> on differe=
nt machines with different CPU's.  If I do make the<BR>> purchase=
, I want to be sure I'm getting the fastest fractal<BR>> renderin=
g machine possible.</DIV> <DIV> </DIV> <DIV>Unfortunately, there's n=
o one answer to this question, and never will be. There's always a cost-s=
peed curve of available computers. If you can spare a billion or so, you =
might want a Cray YMP or even a Connection Machine. The latter could simu=
ltaneously devote a CPU to each pixel. For a hundred K or so, you could h=
ave an SGI workstation, with *really* impressive graphics and good numeri=
c speed. In the same range, you could get a batch of PCs and link them up=
 into a Beowulf cluster, and probably achieve the same capabilities as th=
e Connection Machine for a fraction the cost. Just watch the electri=
c bill. If you have a few thousand dollars, for the price of a slightly u=
sed sedan you can get a Mac G4, which won't run Fractint, but will run fa=
st enough that it is officially classed as a supercomputer and cannot be =
exported to Tier 7 nations like Libya. (I think the government's concern =
is that they'll use supercomputing to design nuclear weapons -- unfortuna=
tely, these restrictions are pointless, since they'll just co-opt an Amer=
ican scientist for nuclear secrets like China did, or if worse comes to w=
orst, buy some cheap IBMs from BuckADay.com and cobble up a Beowulf clust=
er. Maybe the way to peace in those areas is to quit the export laws and =
start weaving these countries into the global economy to such an ext=
ent that they can't possibly nuke anyone without killing off one of their=
 economy's important suppliers or consumers?)<BR>A lower-end RISC chip li=
ke the Alpha is another option. If you have a merely mortal ability to ta=
ke financial punishment, then a recent Athlon, Duron, or Pentium III or I=
V CPU is your choice. There are price lists with comparisons of FPU perfo=
rmance, integer performance, and other characteristics out there on the n=
et for these Intel-family CPUs. Even among these, a curve of available po=
wer is apparent, with generally more money needed to get a faster box.</D=
IV> <DIV> </DIV> <DIV></DIV></BODY></HTML><DIV><BR><br clear=3Dall><=
hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://ww=
w.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0006_01C0FF83.A9CDA840--

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Yay! XFractint working - Just not in 24-bpp X?
Date: 28 Jun 2001 03:41:00 -0400


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> Is anyone other than me getting multiple copies of the Lavoie, Jone, an=
d Coppin Posts? =20

It's gotta be the xmission listserv. A while back it was duplicating mine=
; then for a day or so it was spitting out three, four, even five copies =
of mine, before it suddenly started behaving normally. Now it seems to be=
 happening again to other posters... Weird.<br clear=3Dall><hr>Get Your P=
rivate, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com=
">http://www.hotmail.com</a>.<br></p>

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<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Is anyone=
 other than me getting multiple copies of the Lavoie, Jone, and Coppin Po=
sts? </DIV> <DIV> </DIV> <DIV>It's gotta be the xmission listserv. A=
 while back it was duplicating mine; then for a day or so it was spitting=
 out three, four, even five copies of mine, before it suddenly started be=
having normally. Now it seems to be happening again to other posters... W=
eird.</DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, F=
ree E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://=
www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0007_01C0FF84.2678F0C0--

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Midgets...
Date: 28 Jun 2001 04:11:31 -0400


------=_NextPart_001_0008_01C0FF88.69F6F000
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> Hmm, could you make a command line version that could
> take parameters from the command line or via a batch
> file, then display the results? Is there some way to
> save the results? It sounds like fun!

Mine already does save the results. OTOH it needs to be recompiled to cha=
nge its settings.<br clear=3Dall><hr>Get Your Private, Free E-mail from M=
SN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotmail.com</=
a>.<br></p>

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Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Hmm, coul=
d you make a command line version that could<BR>> take parameters from=
 the command line or via a batch<BR>> file, then display the results? =
Is there some way to<BR>> save the results? It sounds like fun!<BR></D=
IV> <DIV>Mine already does save the results. OTOH it needs to be recompil=
ed to change its settings.</DIV></BODY></HTML><DIV><BR><br clear=3Dall><h=
r>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://www=
.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0008_01C0FF88.69F6F000--

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-------------------------------------------------------------------------------

From: "David Jones" <[e-mail]>
Subject: Re: (fractint) C-FOTD 20-06-01 (A Midget at Midnight [7])
Date: 27 Jun 2001 22:58:45 -1000

On 28 Jun 01 at 3:21, Multiple Bogeys wrote:

> > First time I ever actually ran the PAR, rather than go
> > look att he picture on the web. 27 minutes on a Duron
> > 700, running Fractint under OS/2...
>
> You mean, someone out there actually still uses OS/2?
> :-)

Yup, quite a goodly number of us. Fractint runs happily
on my Tower box (AMD 350MHz K6-2, 128MB PC100 RAM, 12GB
total of disk space, Elsa GLoria Synergy adaptor) under
OS/2. Under W9x on the same box, it hangs the system,
fighting over the display adaptor with Windows.

I also run OS/2 on the Duron box, a 700MHz Duron
processor with 256MB of PC133 memory and 30GB of disk
space, and a Voodoo3-based video card. Fractint runs
happily on it, and the change in video cards restored
Fractint's ability to run high display resolutions (the
Elsa card doesn't support any VESA modes except
640*480*256).

I'm still trying to get Windows to install on the Duron
box. But then, it took four tries to get Windows to
install on the Tower.

With disk video modes, I can run Fractint under either OS
at higher resolutions in the background, but doing so
under W9x makes everything else too jerky to use. OS/2
multitasks *much* better than W9x - no jerkiness in other
programs while Fractint is rendering something.

I also run Linux, too. I'd love to see Fractint's
capabilities available as a GIMP plug-in ... ;-)

David
[e-mail]


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-------------------------------------------------------------------------------

From: Pedro Lopes <[e-mail]>
Subject: Re: (fractint) C-FOTD 21-06-01 (Fractal Caterpillars [6])
Date: 28 Jun 2001 02:06:05 -0700 (PDT)


--- Multiple Bogeys <[e-mail]> wrote:
> > I'm thinking of purchasing another fractal
computer, a state-of-
> > the-art machine, so I would be interested in
hearing reports of
> > the time required to render today's particularly
difficult scene
> > on different machines with different CPU's.  If I
do make the
> > purchase, I want to be sure I'm getting the
fastest fractal
> > rendering machine possible.
>
(snip)
> If you have a merely mortal ability to take
> financial punishment, then a recent Athlon, Duron,
> or Pentium III or IV CPU is your choice. There are
> price lists with comparisons of FPU performance,
> integer performance, and other characteristics out
> there on the net for these Intel-family CPUs. Even
> among these, a curve of available power is apparent,
> with generally more money needed to get a faster
> box.

I would recommend staying well away from Pentium 4,
unless you really don't care about how much you spend.
Among these I would go for the AMD Athlon. The
floating point performance of these chips is very
strong... in fact the overall price/performance ratio
of the Athlons is *much* better than anything intel
has to offer right now.
Of course CPU prices change every week, so I don't
know
how much longer this will hold true...
Cheers,Pedro Lopes


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  28-06-01  (Fringed Minibrot [8])
Date: 28 Jun 2001 09:25:10 -0400 (EDT)


Classic FOTD -- June 28, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

I consider myself a fractal purist -- that is I see fractals as
the same things they were considered to be when they were
originally discovered.  I do not see fractals as a means of
expressing one's latent artistic talent.  There are countless
other ways to do this.

When they were discovered 20 or so years ago, fractals were seen
as a means of visualizing the things numbers do when taken far
beyond the limit of human calculating ability.  The most common
means of coloring those early images was to leave the area of
trapped points black and color the outside area according to how
many iterations were needed for the points to pass beyond a
certain escape radius.  We realized even then that other
coloring methods were possible, but this equal-iteration-band
method became the unofficial fractal reference standard.

This is the method I still use for nearly all my images.  I use
it because it eliminates much of what I have done and shows more
of what the numbers are doing.  True, even I am not perfect, so
I express a little of my creativeness when I color the images.
I do the FOTD for fun, not profit, though if profit came along,
I would not turn it down.

I mention fractal purity because today's image digresses a bit
from my ideals.  In today's image, the outside area has been set
to <summ> rather than <iter>.  I did this because the <summ>
outside option in this case makes the better picture -- an image
filled with delicate detail compared to the flat areas created
by the traditional equal-iteration-bands rendering method.

The formula behind the image, (1/Z)-Z^300+(1/C), is a
surprisingly simple formula for such a detailed image.  But
that's the way it is when chaos raises its head.  I named the
image "Fringed Minibrot" as a description, and rated it at an 8
because I like it.

The parameter file takes 20 minutes to render.  The GIF-format
image takes only one minute to download from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But give Paul and Scott a chance to render and post the image
before attempting the download.

The fractal weather today was the typical stagnant summer
pattern, with hazy sunshine and lots of ozone.  The fractal cats
didn't worry about the ozone, but the temperature of 93F (34C)
was a bit too warm for their delicate constitutions.

As for myself, it's time to get busy and make some money.  But
I'll return within 24 hours with another fractal to go 'WOW!'
at.  Until then, take care, and I'm still searching for one of
those elusive Herman Rings.  I went to the jewelers, but they
had never heard of them.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Fringed_Minibrot   { ; time=0:20:31.10--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-13.06399625631058/+10.40371429338124/1\
  91811.7/1/-172.499 params=1/-1/-1/300/0/0 float=y
  maxiter=2400 inside=0 outside=summ periodicity=10
  colors=000EXUDWTCVRBUQBTPAURAVT9WV9XX8YZ8Z`7_b7`d6\
  af6bg9ecCg_FjWIlSLoOOqKRsGUoEXkD_gCbcAe_9hW8kS6nO5\
  qK4sH3pGBmFIjFPgEWdEbaDi_DpaEocEneEmgEliFlkFkmFjoF\
  iqGisGhuGgwGfyGfvKdsNbpQ`mUZjXYg_WebUbfS_iQXlPUpNR\
  sLOvJMyIKxOJxUIx_GxdFxjExpDxuHrsLlqPgoSanWWl_RjcLh\
  fGghJciM`kPYlRVnUSoXPpZMmXPjVShTUeRXcPZ`NaYLcWJfTH\
  hRFkODmLBpJ9rG7uE6wSRpdjiSchGYg4SgBUeHWcNYaUZ__`Ye\
  bWkcVlgZlkamoensinwlnwlmvkmvklvjlujkujktijtijthjsh\
  isgirghrghrfgqfgqefqefpeepdeodeocdocdnbcnbcmbbmabm\
  aal`al`MTgNVfOWfPXeQYeR_dS`dTacUbcVdcWebXfbYgafhti\
  jtfelc`e`XYYSRVNJSJCTMFUPHVSKWVMXYPY`RZcUal__fW`iZ\
  BwjItgPqeWnbdBLcJPbRSbYVaeYRJUTOVVSWWWXY`YZdZ`h_Fq\
  AGpCHpDIpEaRm`PmZNmYLmWJmVImYJo`KpbLqeMrhNsjOtlSon\
  VkpYgr`ctdZvgVxjRzmNxlQvlTtlVrlYpk_nkblkejkghjjfjl\
  djobjqjfcrcQz`CrWDkSEcOFXKGQFHIBIB7J43J7CS9L`BTiDU\
  hEUhFUhGUhHUhIUhJUhKUhLUh
  }

frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: [e-mail]
Subject: Re: (fractint) need some assistance... third attempt to post
Date: 28 Jun 2001 11:16:45 -0400



Dear nltnme:

Since nobody has helped you so far, I will respond, although I won't be able to
be very helpful.

>>>  I would like to set up the printer to print a ps file... i believe I did it
once in an older version of fractint, running on a DOS machine.<<<

What is a ps file?? If you want to print a fractal generated by fractint, save
it as a gif and use a 3rd party Windows program.

>>>  I'd like to know if there is a formula that with do a Mandelbrott in
reverse... that is.. fill the blue lake areas with the colors of the shore
line.<<<

You can get colors in the 'lake' by choosing Inside options on the Basic Options
screen (hit X while the fractal is on the screen). I'm not exactly sure what you
mean by 'colors of the shore line'.

>>> There is a formula I use at work... would be lengthy to explain here... but
involves some basic variable which are multiplied, results multiplied by other
varialble, result divided.. I would like to.. for the fun of it... see what kind
of factal the results would generate.  Is there anyone out there that might be
able to assist me? <<<

I can't help you here. Maybe somebody else will jump in. Bradley Beacham wrote a
tutorial on how to use the formula editor. See:
http://spanky.triumf.ca/www/fractint/frm-tut/frm-tutor.html

Nick



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-------------------------------------------------------------------------------

From: "O Bd" <[e-mail]>
Subject: Re: (fractint) need some assistance... third attempt to post
Date: 28 Jun 2001 23:37:32 +0800

Just a quick tip...

Often, when attempting to print from a DOS application running in Windows, it doesn't work. This is due to the printer driver not being set up for printing from DOS.

A quick test can be done like so...

COPY CONFIG.SYS LPT1:

If nothing prints, this confirms the printer problem.

Solution!!!

Reinstall the printer in Windows. During the installation a prompt asking if you wish to print from DOS based applications appears (usually bottom left of window so you ignore it). Select YES

Then try to print from DOS again, like the example above.

VOILA!!!!

Well, it's always worked for me anyway. I work for a company who still sell DOS applications to thousands of clients. They often have this problem.

Also, another idea is to save the fractal as a GIF file and then print from Windows. There's a pretty neat program that comes with MS Office which handles images in various formats quite well.

My two pence...

<going back to hiding under that stone>



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-------------------------------------------------------------------------------

From: "O Bd" <[e-mail]>
Subject: Re: (fractint) need some assistance... third attempt to post
Date: 28 Jun 2001 23:37:56 +0800

Just a quick tip...

Often, when attempting to print from a DOS application running in Windows, it doesn't work. This is due to the printer driver not being set up for printing from DOS.

A quick test can be done like so...

COPY CONFIG.SYS LPT1:

If nothing prints, this confirms the printer problem.

Solution!!!

Reinstall the printer in Windows. During the installation a prompt asking if you wish to print from DOS based applications appears (usually bottom left of window so you ignore it). Select YES

Then try to print from DOS again, like the example above.

VOILA!!!!

Well, it's always worked for me anyway. I work for a company who still sell DOS applications to thousands of clients. They often have this problem.

Also, another idea is to save the fractal as a GIF file and then print from Windows. There's a pretty neat program that comes with MS Office which handles images in various formats quite well.

My two pence...

<going back to hiding under that stone>



--

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-------------------------------------------------------------------------------

From: "O Bd" <[e-mail]>
Subject: Re: (fractint) need some assistance... third attempt to post
Date: 28 Jun 2001 23:37:59 +0800

Just a quick tip...

Often, when attempting to print from a DOS application running in Windows, it doesn't work. This is due to the printer driver not being set up for printing from DOS.

A quick test can be done like so...

COPY CONFIG.SYS LPT1:

If nothing prints, this confirms the printer problem.

Solution!!!

Reinstall the printer in Windows. During the installation a prompt asking if you wish to print from DOS based applications appears (usually bottom left of window so you ignore it). Select YES

Then try to print from DOS again, like the example above.

VOILA!!!!

Well, it's always worked for me anyway. I work for a company who still sell DOS applications to thousands of clients. They often have this problem.

Also, another idea is to save the fractal as a GIF file and then print from Windows. There's a pretty neat program that comes with MS Office which handles images in various formats quite well.

My two pence...

<going back to hiding under that stone>



--

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-------------------------------------------------------------------------------

From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) Fractal God
Date: 28 Jun 2001 16:55:39 -0000

The immortal book "The Beauty of Fractals" rants on at length about
"critical points". IIRC, a critical point is a solution to the derrivative
of the formula drawing the fractal, and further, I believe it says somewhere
that every basin of attraction must contain at least one critical point. (I
think there was some restriction on the kind of formula for which this is
true...)

Clearly critical points are important. So I decided to create a formula
where *I* control the critical points.

I began with
  (Z-S)(Z-T)(Z-U)=0,
who's solutions (I hope) are S, T and U. If you open the brackets, I think
you get
  Z^3 + (S+T+U)Z^2 + (ST+TU+SU)Z + (STU) = 0.
If my sister's integral calculus is correct, then the integral of the above
is
  (1/4)Z^4 + ((S+T+U)/3)Z^3 + ((ST+TU+SU)/2)Z^2 + (STU)Z + C.
In other words, this formula creates a fractal with critical points S, T and
U.

The results of this experiment were interesting. (I shall have to download
that developer patch that gives you extra FRM paramerets though!) By
choosing the right figures (S=1, T=-1, U=i or something I think it was) I
can get a quadratic Julia surrounded by mini Julias (of the same type). It's
difficult to controll though...

Does any one here know the conditions required for a minibrot to form? I
know it has something to do with critical points, but can't remember the
details...

If anyone has anything else to say about this mumbo, then let's hear it!

Thanks.
Andrew.

PS. Quartics are slow to render...

_________________________________________________________________________
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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) need some assistance... third attempt to post
Date: 28 Jun 2001 13:50:36 -0500

[e-mail] wrote:
>
> "nltnme" wrote:
> >
> > I would like to set up the printer to
> > print a ps file... i believe I did it
> > once in an older version of fractint,
> > running on a DOS machine.
>
> What is a ps file??  If you want to print a fractal
> generated by fractint, save it as a gif and use a
> 3rd party Windows program.
>

The "PS" refers to PostScript.

Nick and "O Bd" have given you some very useful information to get you
started.  Another item is the FractInt Documentation, which may be
created by running the following from the command line:

     Fractint.exe makedoc

The FractInt Documentation has several references within the 226 pages
concerning PostScript printers.  In fact, under Section 5, sub-section
15, it discusses "PostScript Parameters".  The problems you may
encounter is that a lot of the printer support within FractInt has not
been kept up-to-date.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) need some assistance... third attempt to post
Date: 28 Jun 2001 14:03:43 -0500

nltnme wrote:
>
> I would like to set up the printer to
> print a ps file... i believe I did it
> once in an older version of fractint,
> running on a DOS machine.

What is the printer brand and model??
What version of FractInt are you running??

Have you considered running another Windows OS besides ME??    ;-}

>
> There is a formula I use at work...
> I would like to ..... see what kind of
> factal the results would generate.

Post the formula here so that others may be able to assist you with
possible solutions.

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: [e-mail]
Subject: Re: (fractint) need some assistance... third attempt to post
Date: 28 Jun 2001 15:09:03 -0400



I wrote:

>> What is a ps file??  If you want to print a fractal
>> generated by fractint, save it as a gif and use a
>> 3rd party Windows program.

Paul N. Lee wrote:

>The "PS" refers to PostScript.

Good grief! I thought he might have meant PostScript, but I had no idea fractint
supported PostScript printing. I guess I should read the docs myself. Anyway,
nltnme, if you would tell us exactly what you are trying to do perhaps we could
be more helpful. Does it have to be PostScript?

Nick



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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) C-FOTD 21-06-01 (Fractal Caterpillars [6])
Date: 28 Jun 2001 14:57:18 -0500

Pedro Lopes wrote:
>
> I would recommend staying well away from
> Pentium 4, unless you really don't care
> about how much you spend.  Among these I
> would go for the AMD Athlon.

Strong competition between AMD and Intel has pushed processor prices to
surprisingly low levels in recent months, especially for the faster
high-end CPUs.  Prices on the Pentium 4 and III recently dropped
dramatically while AMD's high-end chips continue a slower decline and
will likely drop more with the release of their new 1.4 GHz chip.  Here
are some of the best price cuts early this month on high-end processors:

   Intel Pentium 4, 1.7 GHz                    -- $49 Drop to $386
   Intel Pentium 4, 1.5 GHz                    -- $40 Drop to $266 (OEM)
   Intel Pentium 3, 1 GHz FC-PGA 133 MHz FSB   -- $36 Drop to $194
   Intel Pentium 3, 600 MHz FC-PGA 100 MHz FSB -- $10 Drop to $99
   AMD Athlon 1.33 GHz, 266 MHz FSB            -- $10 Drop to $190 (OEM)
   AMD Athlon 1.0 GHz 266 MHz FSB              -- $16 Drop to $134
   AMD Athlon 1.2 GHz 200 MHz FSB              -- $10 Drop to $156 (OEM)

And the continuing saga of the PC price wars is making it easy for one
to purchase a dependable PC without spending more than a $1,000.  Many
of the major PC makers now offer good systems in this lower price range
with decent warranties and technical support.  Here is what could be
found two weeks ago (the specs are for the lowest priced model listed):

   Compaq iPAQ Desktop with Legacy Ports Celeron 700 MHz
   --64MB, 10GB hard drive
   --Lowest price is $586

   HP Pavilion 8860 1 GHz
   --128MB, 60GB hard drive, CD-RW, DVD-ROM
   --Lowest price is $899

   Dell Dimension 4100 Pentium III 1 GHz
   --128MB, 17 inch monitor, 20GB hard drive, CD-RW or DVD-ROM
   --Lowest price is $949

   Cyberpower AMD Athlon Special CPU 800 MHz
   --256MB, 17 inch monitor, 40GB hard drive, CD-ROM
   --Lowest price is $978

   --ABS AMD Web Special Athlon 900 MHz
   --128 MB, 17 inch monitor, 30GB hard drive, DVD-ROM
   --Lowest price is $979

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) Fractal God
Date: 28 Jun 2001 16:06:35 -0400

You probably know this but I will state it anyway.
When you iterate a formula (poly nomial) you end up with a higher order
poly.
If you iterate a quadratic 100 times then you end up with a 200dth order
poly and
the roots of this poly are found in the bays (basins of attractions).
The more times you iterate it the more bays you make. So the S T U of your
eq. only define 3 roots (main roots?) and each time it is iterated you get 3
more roots.

The minibrots are formed at these extra roots.

If this is worth while I can go on on.....

Doug Stewart


----- Original Message -----
Sent: Thursday, June 28, 2001 12:55 PM


> The immortal book "The Beauty of Fractals" rants on at length about
> "critical points". IIRC, a critical point is a solution to the derrivative
> of the formula drawing the fractal, and further, I believe it says
somewhere
> that every basin of attraction must contain at least one critical point.
(I
> think there was some restriction on the kind of formula for which this is
> true...)
>
> Clearly critical points are important. So I decided to create a formula
> where *I* control the critical points.
>
> I began with
>   (Z-S)(Z-T)(Z-U)=0,
> who's solutions (I hope) are S, T and U. If you open the brackets, I think
> you get
>   Z^3 + (S+T+U)Z^2 + (ST+TU+SU)Z + (STU) = 0.
> If my sister's integral calculus is correct, then the integral of the
above
> is
>   (1/4)Z^4 + ((S+T+U)/3)Z^3 + ((ST+TU+SU)/2)Z^2 + (STU)Z + C.
> In other words, this formula creates a fractal with critical points S, T
and
> U.
>
> The results of this experiment were interesting. (I shall have to download
> that developer patch that gives you extra FRM paramerets though!) By
> choosing the right figures (S=1, T=-1, U=i or something I think it was) I
> can get a quadratic Julia surrounded by mini Julias (of the same type).
It's
> difficult to controll though...
>
> Does any one here know the conditions required for a minibrot to form? I
> know it has something to do with critical points, but can't remember the
> details...
>
> If anyone has anything else to say about this mumbo, then let's hear it!
>
> Thanks.
> Andrew.
>
> PS. Quartics are slow to render...
>
> _________________________________________________________________________
> Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.
>
>
> --------------------------------------------------------------
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-------------------------------------------------------------------------------

From: Kathy Roth <[e-mail]>
Subject: Re: (fractint) Fractal God
Date: 28 Jun 2001 15:11:09 -0700

Hi
Do go on with this-
Kathy

Doug Stewart wrote:
>
> You probably know this but I will state it anyway.
> When you iterate a formula (poly nomial) you end up with a higher order
> poly.
> If you iterate a quadratic 100 times then you end up with a 200dth order
> p

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-------------------------------------------------------------------------------

From: "nltnme" <[e-mail]>
Subject: (fractint) need assistance part 2
Date: 28 Jun 2001 20:42:56 -0500

This is a multi-part message in MIME format.

------=_NextPart_000_0017_01C10012.E9033F40
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Ok... I guess I need to go a little slower.

The documentation states the following:
"5.14 Printer Parameters

PRINTER=3Dtype[/resolution[/port#]]

Defines your printer setup. The SSTOOLS.INI file... "

NOW....

years ago, I had a programmer person who understood some things assist =
me in setting up the "sstools.ini" file.

I downloaded the most recent version of Fractint 20 for dos and =
installed on my me computer with WindowsME.  If I recall, when I had a =
purely DOS machine, the SSTOOLS.INI file was located in the same =
directory (maybe the root) as the command.com and autoexec.bat files.

I don't know where to create, find, or edit the SSTOOLS.INI file.

example of what I would do if I knew where:

PRINTER =3D PS/600/0

TYPE  would be PS

/600 would be resolution

/0 would equal "to file"

is that right?

Second, as I recall, I was able to set the PS printer parameters to =
print to ".ps" file, and not a "printer" specifically... this allowed me =
to send the ".ps" file to any ps printer and/or open the file as an eps =
as in PhotoShop.  In anycase.. .I was able to achieve a 300 dpi full =
color ps printout or the fractals... but that was like 7 years ago, and =
I've had lots of changes in my life... (without going into that... it's =
hard to believe that 8 years ago, I was exploring Fractint on a 25Mhz =
PC:)))) now I have a 733 celceron..

Anyway...=20

second, is there a way to generate bands of color ranging from the =
"shore" of the mandelbrot to the center of the lake... NOT inside =
color.... but FILLED WITH COLORS... plural?

THANKS ALL... It's been "enlighting!"

nltnme


------=_NextPart_000_0017_01C10012.E9033F40
Content-Type: text/html;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4207.2601" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2>Ok... I guess I need to go a little=20
slower.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT> </DIV>
<DIV><FONT face=3DArial size=3D2>The documentation states the=20
following:</FONT></DIV>
<DIV>
<DIV>
<DIV>
<P><FONT face=3DArial size=3D2>"5.14 Printer Parameters</FONT></P>
<P><FONT face=3DArial =
size=3D2>PRINTER=3Dtype[/resolution[/port#]]</FONT></P>
<P><FONT face=3DArial size=3D2>Defines your printer setup. The =
SSTOOLS.INI file...=20
"</FONT></P>
<P><FONT face=3DArial size=3D2>NOW....</FONT></P>
<P><FONT face=3DArial size=3D2>years ago, I had a programmer person who =
understood=20
some things assist me in setting up the "sstools.ini" file.</FONT></P>
<P><FONT face=3DArial size=3D2>I downloaded the most recent version of =
Fractint 20=20
for dos and installed on my me computer with WindowsME.  If I =
recall, when=20
I had a purely DOS machine, the SSTOOLS.INI file was located in the same =

directory (maybe the root) as the command.com and autoexec.bat =
files.</FONT></P>
<P><FONT face=3DArial size=3D2>I don't know where to create, find, or =
edit the=20
SSTOOLS.INI file.</FONT></P>
<P><FONT face=3DArial size=3D2>example of what I would do if I knew=20
where:</FONT></P>
<P><FONT face=3DArial size=3D2>PRINTER =3D PS/600/0</FONT></P>
<P><FONT face=3DArial size=3D2>TYPE  would be PS</FONT></P>
<P><FONT face=3DArial size=3D2>/600 would be resolution</FONT></P>
<P><FONT face=3DArial size=3D2>/0 would equal "to file"</FONT></P>
<P><FONT face=3DArial size=3D2>is that right?</FONT></P>
<P><FONT face=3DArial size=3D2>Second, as I recall, I was able to set =
the PS printer=20
parameters to print to ".ps" file, and not a "printer" specifically... =
this=20
allowed me to send the ".ps" file to any ps printer and/or open the file =
as an=20
eps as in PhotoShop.  In anycase.. .I was able to achieve a 300 dpi =
full=20
color ps printout or the fractals... but that was like 7 years ago, and =
I've had=20
lots of changes in my life... (without going into that... it's hard to =
believe=20
that 8 years ago, I was exploring Fractint on a 25Mhz PC:)))) now I have =
a 733=20
celceron..</FONT></P>
<P><FONT face=3DArial size=3D2>Anyway... </FONT></P>
<P><FONT face=3DArial size=3D2>second, is there a way to generate bands =
of color=20
ranging from the "shore" of the mandelbrot to the center of the lake... =
NOT=20
inside color.... but FILLED WITH COLORS... plural?</FONT></P>
<P><FONT face=3DArial size=3D2>THANKS ALL... It's been =
"enlighting!"</FONT></P>
<P><FONT face=3DArial =
size=3D2>nltnme</FONT></P></DIV></DIV></DIV></BODY></HTML>

------=_NextPart_000_0017_01C10012.E9033F40--


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-------------------------------------------------------------------------------

From: Thaddaeus Parker <[e-mail]>
Subject: RE: (fractint) need assistance part 2
Date: 28 Jun 2001 19:25:58 -0700

>I don't know where to create, find, or edit the SSTOOLS.INI file.
>example of what I would do if I knew where:
>
I think that was question asked not too long ago, concerning the sstools.ini
file.   There is a portion of the fractint documentation that deals with
creating and setting up an sstools.ini file.
I have a template that George martin made back in 1999. Here is a snippet to
give you an idea of what to do:  Make sure that you go to the docs to find
exactly what everything does and where it goes.
--sstools.ini--
[Fractint]
parmfile=c:\fractint\parfiles
filename=c:\fractint\pics
map=c:\fractint\maps
.
.
.
video=sf7
comment=t=$calctime$

thanks to George for giving this out earlier.

Thaddaeus Parker
San Diego CA
ICQ# 3304633



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-------------------------------------------------------------------------------

From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) Fractal  math
Date: 28 Jun 2001 23:09:47 -0400

To expand on my first message I will do a short example.

z1=z0^2+c

z2=z1^2+c but  z1=z0^2+c
so
z2=(z0^2+c)^2+c
now remove the brackets
z2=z0^4+2*c*z0^2+c^2 +c

and
z3=z2^2+c but z2=z0^4+2*c*z0^2+c^2 +c
and if you do the math you will get a z0^8 term etc

This shows that iterating a poly produces a higher order poly.

If you start with z0=0 you get:
z1=c
z2=z1^2+c  =c^2+c
z3=z2^2+c=  (c^2+c)+c  = c^4 + 2*c*c^2+c^2+c = c^4+2*c^3+c^2+c
etc.
Now we can ask, "what values of c will give z3=0 =z0", these values of c are
the
roots of
c^4+2*c^3+c^2+c=0

If you ask this after each iteration you will get a set of numbers that when
they are plotted on the mandelbrot picture they will be found in each "bay".
Obviously after an infinite number of iterations you will have an infinite
number of roots and an infinite number of bays.

I hope that this is clearer than mud :-).
Doug Stewart




----- Original Message -----
Sent: Thursday, June 28, 2001 6:11 PM


> Hi
> Do go on with this-
> Kathy
>
> Doug Stewart wrote:
> >
> > You probably know this but I will state it anyway.
> > When you iterate a formula (poly nomial) you end up with a higher order
> > poly.
> > If you iterate a quadratic 100 times then you end up with a 200dth order
> > p
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"
>


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-------------------------------------------------------------------------------

From: "Morgan L. Owens" <[e-mail]>
Subject: (fractint) Re: [philofractal] C-FOTD  28-06-01  (Fringed Minibrot [8])
Date: 29 Jun 2001 21:41:56 +1200

At 01:25 29/06/2001, Jim Muth wrote:

>I consider myself a fractal purist -- that is I see fractals as
>the same things they were considered to be when they were
>originally discovered.  I do not see fractals as a means of
>expressing one's latent artistic talent.  There are countless
>other ways to do this.
>
>When they were discovered 20 or so years ago,

...closer to 120 years ago - 20 years ago computing technology caught up
with the maths.

Morgan L. Owens
"So now they _can_ be rendered."


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-------------------------------------------------------------------------------

From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  28-06-01  (Fringed Minibrot [8])
Date: 29 Jun 2001 06:07:38 -0400


----- Original Message -----
Cc: <[e-mail]>
Sent: Friday, June 29, 2001 5:41 AM
[8])


> At 01:25 29/06/2001, Jim Muth wrote:
>
> >I consider myself a fractal purist -- that is I see fractals as
> >the same things they were considered to be when they were
> >originally discovered.  I do not see fractals as a means of
> >expressing one's latent artistic talent.  There are countless
> >other ways to do this.
> >
> >When they were discovered 20 or so years ago,
>
> ...closer to 120 years ago - 20 years ago computing technology caught up
> with the maths.
>
> Morgan L. Owens
> "So now they _can_ be rendered."

Truly the math has been known for a long time, but it was the ability to
"render" the math, that has accelerated out understanding of chaos and
fractals. If the computer could only show us lists of numbers, would we be
as far as we are now?
Though for tomorrow:
How else should we present the information so that we can understand math
more?

Doug Stewart




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-------------------------------------------------------------------------------

From: Jim Shaffer Jr. <[e-mail]>
Subject: Re: (fractint) need assistance part 2
Date: 29 Jun 2001 09:50:14 -0400

On Thursday 28 June 2001 21:42, nltnme wrote:

> I don't know where to create, find, or edit the SSTOOLS.INI file.

Mine is in C:\Windows, and it seems to work.  I think you can also have it in
your Fractint directory, or maybe in the root directory.  But why the
problem?  Just try it and if it doesn't work, move it somewhere else.


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From: Programmer Dude <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  28-06-01  (Fringed Minibrot
Date: 29 Jun 2001 09:15:34 -0500

Doug Stewart wrote:

> How else should we present the information so that we can understand
> math more?

Intravenously?  FPU implants?...   ;-|

--
|_ CJSonnack <[e-mail]> _____________| How's my programming? |
|_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL  |
|_____________________________________________|_______________________|

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From: [e-mail]
Subject: (fractint) C-FOTD  29-06-01  (A New Seahorse [7])
Date: 29 Jun 2001 10:42:37 EDT


Classic FOTD -- June 29, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Midgets are found everywhere around the border and along the
filaments of the Mandelbrot set.  Some of the best midgets are
found in East Valley, sometimes known as Elephant Valley, and in
the two symmetrical valleys on the west side of the lake, known
together as Seahorse Valley.  Today's image pictures a typical
though rather deep midget lying in Seahorse Valley.

So far, so good.  The image is filled with the seahorse tails
typical of this area, and all the expected features surround the
midget in the 2,4,8... series, without being cut off, just as
they would be expected to do.  But things go awry as we approach
the actual midget at the center.

Where there should be a minibrot, we find a roughly triangular
hole, which has little resemblance to either a midget M-set or
to a hole in a Julia set.  Something strange indeed is going on.

At first glance, one might suspect that the image is part of a
perturbed Mandelbrot set, and that the fully-formed midget will
appear if only Z (p3) were initialized to 0,0.  Unfortunately,
doing this results in a screen filled with diagonal lines, with
no midget anywhere in sight.  So what is going on?

True, the image is perturbed, but it is not a Mandelbrot set.
The answer lies elsewhere.

The Mandelbrot sets and Julia sets are perpendicularly oriented
slices of an abstract four-dimensional figure known as the
Julibrot, only parts of which can be seen in our three-
dimensional space.  And four-dimensional objects can be sliced
by two-dimensional planes in six mutually perpendicular
directions.  Today's picture shows a midget sliced in one of the
odd perpendicular directions.

Mandelbrot sets display the C plane, Julia sets display the Z
plane.  Today's image displays the plane determined by imag(C)
and imag(Z).  I have named this orientation 'Rectangular',
because the slice in this direction through the origin of the
Julibrot shows a roughly rectangular lake.

If one wishes to call these slices 'Rectangular sets', very
well.  Though don't expect the midgets to be shaped like
rectangles unless the slice cuts them exactly through the point
that corresponds to the origin of the Mandelbrot set, and they
happen to lie in the same orientation.

In addition to the Rectangular direction, there are three other
new directions, as well as an unlimited number of oblique
directions in which to slice the Julibrot.  And every new
direction shows a new and unique aspect of the Julibrot.  During
the upcoming month of July, I'll be exploring these new
directions.

I named today's image "A New Seahorse" because though it is a
scene in Seahorse Valley and is filled with sea horses, the
midget at the center is unlike anything seen in the standard
Mandelbrot or Julia views of this area.  I rated the image at a
7, mostly because of the striking coloring.

The parameter file takes only 3-3/4 minutes to render on a
Pentium 200mhz machine.  The already-rendered GIF image
downloads in even less time.  That GIF image may be found posted
to:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

and to:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

But give Paul and Scott a chance to post it before visiting
their sites.

The fractal weather today (June 28) brought the first really hot
day of the season, with a temperature of 95F (35C), and all the
haze and humidity that goes with such heat.  The fractal cats
had no complaints, though they showed little activity in the
sweltering conditions.

Tomorrow (today, June 29) promises to be just as hot, so I'm
going to take it easy and let the CPU do all the work.  Until
next time, take care, and when the going gets hot, get going on
a hot fractal.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

A_New_Seahorse     { ; time=0:03:42.07--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=multirot-XY-ZW-new function=flip/ident
  passes=1 center-mag=+0.00000000006028511/-0.000000\
  00000678208/1.223635e+009/0.2406/6.418/71.294
  params=0/90/2/0/-0.7692602987818452/0.109559945816\
  0586/-0.7692602987818452/0.1095599458160586 float=y
  maxiter=2000 inside=0 logmap=388 periodicity=10
  colors=000VzeYzfZzf_zfazfczfezffzfgzfizgkzgmzgnzgo\
  zgqzgszguzgvziwziyzizzizzizzizzizzizzjzzkzzmzznzzo\
  zzqzzrzzrzzszyuzwvzvwzuyzszzrzzrzzqzzozznzzmzzkzzj\
  zzjzvizrgyogskfnifieecbeZZcUXcOSbJQbEMa8J_3FY0DW0E\
  T0EO2FL6F7AH0EH0HM0JR0KX0Na0Of0Rk0Sq2Vv3Xz4Zz4_s6a\
  m6af7b_8cU0aN0bH0c00g00e00b44_AAYEEVIISMMQRRNVVKZZ\
  IbbH_eIZfJYiKXjMVmMUnNRqOQrQOuQNvRMySKzUIzRJzUKyVK\
  uYMrZNo_NkbOicQefQbgR_iSXkSUmUQoVNqVKrXHuYEvYAyZ7z\
  _4z_0za0za0zc0ze3yf6ugAqiEmjHikKemOaoRYqVUrZQsaMue\
  IviEwkAyo6zs0zr2yq7yoBwnHvmMvkQujVzkbujZqiXkiSggQc\
  fMZfJVeFQeDMc8Ib6Db28a04a0D_0K_0SZ0ZZ0fY0nY0vX0w_0\
  yc6ujJrrXnyimzpkzvkzukvskrrkmqjinjcmhZkfPjcKffNihR\
  jgUkfZnfdoekqcqsbwubtvcosejrfeqg`ogXniSmhOkgKjgJie\
  IgdHigHjkFknHmoInqJotKqvMrwNswOuyQvzRwzSyzUzzVzzXz\
  zYzzZzz_zyazybzyczyezyfzwfzwfzwfzwfzwfzvfzvfzvfzvf\
  zvfzvfzvfzvfzvfzvfzvfzvfz
  }

frm:multirot-XY-ZW-new {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=z^(p2)+c,
|z| <= 36  }

END 20.0 PAR-FORMULA FILE==================================

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) need assistance part 2
Date: 29 Jun 2001 11:26:55 -0500

nltnme wrote:
>
> I downloaded the most recent version of
> Fractint 20 for dos....

Is that the 20.0 version from the Spanky Database at:
    http://spanky.triumf.ca/www/fractint/fractint.html
Or the 20.1.12 version from the Development Team's site at:
    http://www.fractint.org/

>
> If I recall, when I had a purely DOS machine,
> the SSTOOLS.INI file was located in the same
> directory (maybe the root) as the command.com
> and autoexec.bat files.

Personally, I would keep it within the same directory path as the
executable module.

>
> I don't know where to create, find, or edit
> the SSTOOLS.INI file.

Here is a "generic" one that I use, and you may wish to copy it, but
make the modifications to any field that contains directory path
information:


[fractint]
;
;------------Startup Parameters----------------
;
TEMPDIR=C:\Temp\
WORKDIR=F:\Fracta~1\FractInt\Work\
; FILENAME=G:\Artwork\GIF_s\Fractals\Ooooo\*.gif
; CURDIR=yes
; MAKEPAR=parfile/entryname
COMMENT=_(c)_Paul_N._Lee_--_$date$_-_$time$/time=$calctime$_on_a_PIII-700_at_$xdots$x$ydots$/using_FractInt_$version$.$patch$/__
; BATCH=yes
; AUTOKEY=play|record
AUTOKEYNAME=F:\Fracta~1\FractInt\KEY_s\auto.key
; MAKEDOC=Fractint.doc
MAXHISTORY=20
; FPU=387|iit|noiit
;
;
;------------Calculation Mode Parameters-------
;
PASSES=t   ; 1|2|3|g|g1|g2|g3|g4|g5|g6|b|t
; FILLCOLOR=normal|<nnn>
; FLOAT=yes
; SYMMETRY=xxx   ; Forces symmetry to None, Xaxis, Yaxis, XYaxis,
;                  Origin, or Pi symmetry.
;
;
;------------Fractal Type Parameters-----------
;
TYPE=mandel    ; formula, julia, etc....
; PARAMS=n/n/n/n...
; FUNCTION=[fn1[/fn2[/fn3[/fn4]]]]
; FORMULANAME=[formulaname]
; LNAME=[lsystemname]
; IFS=[ifsname]
;
;
;------------Image Calculation Parameters------
;
MAXITER=150    ; Values range from 2 to 2147483647, default is 150.
; CORNERS=[xmin/xmax/ymin/ymax[/x3rd/y3rd]]
; CENTER-MAG=[Xctr/Yctr/Mag[/Xmagfactor/Rotation/Skew]]
; BAILOUT=nnn
; BAILOUTEST=mod|real|imag|or|and|manh|manr
; RESET
; INITORBIT=pixel|nnn/nnn
; ORBITDELAY=<nn>
; SHOWORBIT=yes|no
; PERIODICITY=no|show|nnn
; RSEED=nnnn
; SHOWDOT=[auto|bright|medium|dark|<nnn>[/<size>]]
; ASPECTDRIFT=<nn>
;
;
;------------Color Parameters------------------
;
; INSIDE=nnn|bof60|bof61|zmag|attractor|epscross|startrail|period
; OUTSIDE=nnn|iter|real|imag|summ|mult|atan
MAP=F:\Fracta~1\FractInt\MAP_s\
; COLORS=@filename|colorspecification
RECORDCOLORS=comment    ; auto|comment|yes
; CYCLERANGE=nnn/nnn
CYCLELIMIT=55    ; values are 1 - 256, default is 55.
TEXTCOLORS=1F/1A/2E/70/28/71/31/78/70/17/1F/1E/2F/3F/5F/07/0D/71/70/78/0F/70/0E/0F/4F/20/17/20/28/0F/07
; mono | 31 seperate values.
; OLDDEMMCOLORS=yes|no
; TRUECOLOR=yes
;
;
;------------Doodad Parameters-----------------
;
; LOGMAP=yes|old|n
; LOGMODE=fly/table
; RANGES=nn/nn/nn/...
; DISTEST=nnn/nnn
; DECOMP=2|4|8|16|32|64|128|256
; BIOMORPH=nnn
; POTENTIAL=maxcolor[/slope[/modulus[/16bit]]]
; INVERT=nn/nn/nn
; FINATTRACT=no|yes
; EXITNOASK=yes
;
;
;------------File Parameters-------------------
;
SAVENAME=F:\Fracta~1\FractInt\GIF_s\fract001.gif
OVERWRITE=no    ; no|yes
; SAVETIME=nnn|-nnn
; GIF87a=yes
; DITHER=yes
PARMFILE=F:\Fracta~1\FractInt\PAR_s\*.par
FORMULAFILE=F:\Fracta~1\FractInt\FRM_s\*.frm
LFILE=F:\Fracta~1\FractInt\L_s\*.l
IFSFILE=F:\Fracta~1\FractInt\IFS_s\*.ifs
; FILENAME=[.suffix]
; ORBITSAVE=yes
;
;
;------------Video Parameters------------------
;
VIDEO=SF5      ;640x480 @ 256
; VIDEO=SF6    ;800x600 @ 256
; VIDEO=SF7   ;1024x768 @ 256
; VIDEO=SF8  ;1280x1024 @ 16
; VIDEO=SF9  ;1280x1024 @ 256
; ASKVIDEO=yes|no
;
ADAPTER=hgc|cga|ega|egamono|mcga|vga|ATI|Everex|Trident|NCR|Video7|Genoa|Paradise|Chipstech|Tseng3000|Tseng4000|AheadA|AheadB|Oaktech
; VESADETECT=yes|no
; AFI=yes|8514|no
TEXTSAFE=save    ; yes|no|bios|save
; EXITMODE=nn
; TPLUS=yes|no
; NONINTERLACED=yes|no
; MAXCOLORRES=8|16|24
; PIXELZOOM=0|1|2|3
; VIEWWINDOWS=xx[/xx[/yes|no[/nn[/nn]]]]
; FASTRESTORE=yes|no    ;Default is NO.  If YES, resets VIEWWINDOWS to
;                        "no" prior to restoring a gif file.
;
;------------Sound Parameters------------------
;
; SOUND=off|x|y|z
; HERTZ=nnn
; ORBITSAVE=sound
;
;
;------------Printer Parameters----------------
;
; PRINTER=type[/resolution[/port#]]
; COMPORT=port/baud/options
; LINEFEED=crlf|lf|cr
; TITLE=yes
; PRINTFILE=filename
;
;
;------------PostScript Parameters-------------
;
; EPSF=1|2|3
; COLORPS=yes|no
; RLEPS=yes|no
; TRANSLATE=yes|-n|n
; HALFTONE=frq/ang/sty[/f/a/s/f/a/s/f/a/s]
;
;
;------------PaintJet Parameters---------------
;
; HALFTONE=r/g/b
;
;
;------------Plotter Parameters----------------
;
; PLOTSTYLE=0|1|2
;
;
;------------3D Parameters---------------------
;
; 3D=Yes|Overlay
; RANDOMIZE=nnn    ; (0 - 100)
; AMBIENT=nnn    ; (0 - 100)
; FULLCOLOR=yes
; HAZE=nnn    ; (0 - 100)
; LIGHTNAME=<filename>
; MONITORWIDTH=<nnn>
; PREVIEW=yes                Turns on 3D 'preview' default mode
; SHOWBOX=yes                Turns on 3D 'showbox' default mode
; COARSE=nn                  Sets Preview 'coarseness' default value
; SPHERE=yes                 Turns on spherical projection mode
; STEREO=n                   Selects the type of stereo image creation
; RAY=nnn                    selects raytrace output file format
; BRIEF=yes                  selects brief/verbose file for DKB output
; USEGRAYSCALE=yes           use grayscale as depth instead of color #
; INTEROCULAR=nn             Sets the interocular distance for stereo
; CONVERGE=nn                Determines the overall image separation
; CROP=nn/nn/nn/nn           Trims the edges off stereo pairs
; BRIGHT=nn/nn               Compensates funny glasses filter parameters
; LONGITUDE=nn/nn            Longitude minimum and maximum
; LATITUDE=nn/nn             Latitude minimum and maximum
; RADIUS=nn                  Radius scale factor
; ROTATION=nn[/nn[/nn]]      Rotation about x,y, and z axes
; SCALEZYZ=nn/nn/nn          X,y,and z scale factors
; ROUGHNESS=nn               Same as z scale factor
; WATERLINE=nn               Colors nn and below will be "inside" color
; FILLTYPE=nn                3D filltype
; PERSPECTIVE=nn             Perspective distance
; XYSHIFT=nn/nn              Shift image in x and y directions with
;                            perspective
; LIGHTSOURCE=nn/nn/nn       Coordinates for light-source vector
; SMOOTHING=nn               Smooths images in light-source fill modes
; TRANSPARENT=min/max        Defines a range of colors to be treated as
;                            "transparent" when <#>Overlaying 3D images.
; XYADJUST=nn/nn             This shifts the image in the x/y dir
;                            without perspective
;
;
;-------------Batch Mode-----------------------
;


Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) need assistance part 2
Date: 29 Jun 2001 11:34:55 -0500

nltnme wrote:
>
> second, is there a way to generate bands
> of color ranging from the "shore" of the
> mandelbrot to the center of the lake...
> NOT inside color.... but FILLED WITH COLORS...
> plural?
>

After you get the initial default image upon starting FractInt, use the
"x" option to take you to the "Basic Options" screen.  Amongst the may
values that may be set, you will see these four with their values:

    Inside Color      1
    Inside            numb
    Outside Color     0
    Outside           iter

Try modifying the above to the following values:

    Inside Color      1
    Inside            bof60
    Outside Color     0
    Outside           numb

Sincerely,
P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: Kathy Roth <[e-mail]>
Subject: Re: (fractint) Fractal  math
Date: 29 Jun 2001 15:34:27 -0700

Thanks!

Doug Stewart wrote:
>
> To expand on my first message I will do a short example.
>
> z1=z0^2+c
>
> z2=z1^2+c but  z1=z0^2+c
> so
> z2=(z0^2+c)^2+c
>

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-------------------------------------------------------------------------------

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Re: [philofractal] C-FOTD  28-06-01  (Fringed
Date: 30 Jun 2001 14:58:53 +1200

At 22:07 29/06/2001, Doug Stewart wrote:

> > At 01:25 29/06/2001, Jim Muth wrote:
> >
> > >
> > >When they were discovered 20 or so years ago,
> >
> > ...closer to 120 years ago - 20 years ago computing technology caught up
> > with the maths.
> >
> > Morgan L. Owens
> > "So now they _can_ be rendered."
>
>Truly the math has been known for a long time, but it was the ability to
>"render" the math, that has accelerated out understanding of chaos and
>fractals.

None of which has to do with their "discovery", but drawings (by hand) of
fractal structures were being published a century ago, as well.


>  If the computer could only show us lists of numbers, would we be
>as far as we are now?

No, because "lists of numbers" would be irrelevant to understanding the
maths; although they were enough for Edward Lorenz to see something was up
in his weather modelling, they couldn't tell him what.

Morgan L. Owens
"Abram Besicovitch - d.1970; Felix Hausdorff - d.1942; Gaston Julia -
d.1978; Georg Cantor - d.1918; Niels von Koch - d.1924; Aleksandr Lyapunov
- d.1918; Henri Poincare - d.1912; Karl Weierstrass - d.1897; Waclaw
Sierpinski - d.1969; Gieseppe Peano - d.1932"



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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) C-FOTD 21-06-01 (Fractal Caterpillars [6])
Date: 30 Jun 2001 02:51:32 -0400


------=_NextPart_001_0001_01C1010F.92759080
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

[Some damn Celery or another]

Celeron sucks for FP math.

>   HP Pavilion 8860 1 GHz
>   --128MB, 60GB hard drive, CD-RW, DVD-ROM
>   --Lowest price is $899

*drool*

But what's the CPU vendor? AMD? Intel? Please tell me it wasn't Cyrix. (C=
yrix sucks for FP math.)

Woah -- I don't see anything about video cards here.<br clear=3Dall><hr>G=
et Your Private, Free E-mail from MSN Hotmail at <a href=3D"http://www.ho=
tmail.com">http://www.hotmail.com</a>.<br></p>

------=_NextPart_001_0001_01C1010F.92759080
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>[Some damn Cel=
ery or another]</DIV> <DIV> </DIV> <DIV>Celeron sucks for FP math.</=
DIV> <DIV> </DIV> <DIV>>   HP Pavilion 8860 1 GHz<BR>&g=
t;   --128MB, 60GB hard drive, CD-RW, DVD-ROM<BR>> &nbs=
p; --Lowest price is $899<BR></DIV> <DIV>*drool*</DIV> <DIV> </DIV> =
<DIV>But what's the CPU vendor? AMD? Intel? Please tell me it wasn't Cyri=
x. (Cyrix sucks for FP math.)</DIV> <DIV> </DIV> <DIV>Woah -- I don'=
t see anything about video cards here.</DIV></BODY></HTML><DIV><BR><br cl=
ear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D=
"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV>

------=_NextPart_001_0001_01C1010F.92759080--

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-------------------------------------------------------------------------------

From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Fractal math
Date: 30 Jun 2001 02:56:34 -0400


------=_NextPart_001_0002_01C10110.4616FA20
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> If you ask this after each iteration you will get a set of numbers that=
 when
> they are plotted on the mandelbrot picture they will be found in each "=
bay".
> Obviously after an infinite number of iterations you will have an infin=
ite
> number of roots and an infinite number of bays.

Just to clarify, the union of all these sets isn't M, but it does accumul=
ate on the boundary of M.<br clear=3Dall><hr>Get Your Private, Free E-mai=
l from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotma=
il.com</a>.<br></p>

------=_NextPart_001_0002_01C10110.4616FA20
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> If you as=
k this after each iteration you will get a set of numbers that when<BR>&g=
t; they are plotted on the mandelbrot picture they will be found in each =
"bay".<BR>> Obviously after an infinite number of iterations you will =
have an infinite<BR>> number of roots and an infinite number of bays.<=
BR></DIV> <DIV>Just to clarify, the union of all these sets isn't M,=
 but it does accumulate on the boundary of M.</DIV></BODY></HTML><DIV><BR=
><br clear=3Dall><hr>Get Your Private, Free E-mail from MSN Hotmail at <a=
 href=3D"http://www.hotmail.com">http://www.hotmail.com</a>.<br></p></DIV=
>

------=_NextPart_001_0002_01C10110.4616FA20--

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-------------------------------------------------------------------------------

From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) Fractal math
Date: 30 Jun 2001 09:59:38 -0400

This is a multi-part message in MIME format.

------=_NextPart_000_00D0_01C1014B.60004550
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

If you start with z0=3D0 you get:
z1=3Dc
z2=3Dz1^2+c  =3Dc^2+c
z3=3Dz2^2+c=3D  (c^2+c)^2+c  =3D c^4 + 2*c*c^2+c^2+c =3D c^4+2*c^3+c^2+c
etc.
Now we can ask, "what values of c will give z3=3D0 =3Dz0", these values =
of c are
the
roots of
c^4+2*c^3+c^2+c=3D0

The root for z1 is 0+j0 this is approximately in the center of the =
biggest "bay".

The roots for z2 are
                 -1
                  0

The roots for z3 are
 -1.75488 + 0.00000i this is approximately in the center of period 3 =
minibrot's biggest "bay".
  -0.12256 + 0.74486i The bays above and below the main bay
  -0.12256 - 0.74486i
   0


The roots for z4 are

 -1.94080 + 0.00000i this is approximately in the center of a minibrot's =
biggest "bay".
  -1.31070 + 0.00000i 3rd bay on main part
  -1.00000 + 0.00000i 2nd bay on main part
  -0.15652 + 1.03225i biggest minibrot at top and bottom
  -0.15652 - 1.03225i
   0.28227 + 0.53006i biggest bud top right
   0.28227 - 0.53006i
   0

The roots for z5 are


  -1.98542 + 0.00000i
  -1.86078 + 0.00000i
  -1.62541 + 0.00000i
  -1.25637 + 0.38032i
  -1.25637 - 0.38032i
  -0.19804 + 1.10027i
  -0.19804 - 1.10027i
  -0.04421 + 0.98658i
  -0.04421 - 0.98658i
  -0.50434 + 0.56277i
  -0.50434 - 0.56277i
   0.35926 + 0.64251i
   0.35926 - 0.64251i
   0.37951 + 0.33493i
   0.37951 - 0.33493i
   0

You can look at these locations using Fractint or Ultra Fractal.

z6

  -1.99638 + 0.00000i
  -1.96677 + 0.00000i
  -1.90728 + 0.00000i
  -1.77289 + 0.00000i
  -1.75488 + 0.00000i
  -1.47601 + 0.00000i
  -1.28408 + 0.42727i
  -1.28408 - 0.42727i
  -1.13800 + 0.24033i
  -1.13800 - 0.24033i
  -1.00000 + 0.00000i
  -0.59689 + 0.66298i
  -0.59689 - 0.66298i
  -0.21753 + 1.11445i
  -0.21753 - 1.11445i
  -0.16360 + 1.09778i
  -0.16360 - 1.09778i
  -0.01557 + 1.02050i
  -0.01557 - 1.02050i
  -0.11342 + 0.86057i
  -0.11342 - 0.86057i
  -0.12256 + 0.74486i
  -0.12256 - 0.74486i
   0.35989 + 0.68476i
   0.35989 - 0.68476i
   0.39653 + 0.60418i
   0.39653 - 0.60418i
   0.44333 + 0.37296i
   0.44333 - 0.37296i
   0.38901 + 0.21585i
   0.38901 - 0.21585i
   0.00000 + 0.00000i



All of these roots are in "bays" and not on the boundary.

I did the math and roots  in Octave. I hope I haven't made any mistakes =
but if I did someone will help.
Respectfully
Doug Stewart

  ----- Original Message -----=20
  From: Multiple Bogeys=20
  To: [e-mail]=20
  Sent: Saturday, June 30, 2001 2:56 AM
  Subject: Re: (fractint) Fractal math


  > If you ask this after each iteration you will get a set of numbers =
that when
  > they are plotted on the mandelbrot picture they will be found in =
each "bay".
  > Obviously after an infinite number of iterations you will have an =
infinite
  > number of roots and an infinite number of bays.

  Just to clarify, the union of all these sets isn't M, but it does =
accumulate on the boundary of M.



-----
  Get Your Private, Free E-mail from MSN Hotmail at =
http://www.hotmail.com.



------=_NextPart_000_00D0_01C1014B.60004550
Content-Type: text/html;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"MSHTML 5.50.4522.1800" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY=20
style=3D"BORDER-RIGHT: medium none; BORDER-TOP: medium none; FONT: 10pt =
verdana; BORDER-LEFT: medium none; BORDER-BOTTOM: medium none"=20
bgColor=3D#ffffff>
<DIV>If you start with z0=3D0 you get:<BR>z1=3Dc<BR>z2=3Dz1^2+c =20
=3Dc^2+c<BR>z3=3Dz2^2+c=3D  (c^2+c)^2+c  =3D c^4 + =
2*c*c^2+c^2+c =3D=20
c^4+2*c^3+c^2+c<BR>etc.<BR>Now we can ask, "what values of c will give =
z3=3D0=20
=3Dz0", these values of c are<BR>the<BR>roots =
of<BR>c^4+2*c^3+c^2+c=3D0<BR></DIV>
<DIV><FONT face=3DArial>The root for z1 is 0+j0 this is approximately in =
the=20
center of the biggest "bay".</FONT></DIV>
<DIV><FONT face=3DArial></FONT> </DIV>
<DIV><FONT face=3DArial>
<DIV><FONT face=3DArial>The roots for z2 are</FONT></DIV>
<DIV><FONT=20
face=3DArial>          =
       -1</FONT></DIV>
<DIV>           &n=
bsp;      0</DIV>
<DIV></FONT> </DIV></DIV>
<DIV><FONT face=3DArial>
<DIV><FONT face=3DArial>The roots for z3 are</FONT></DIV>
<DIV> -1.75488 + 0.00000i this is approximately in the center of =
period 3=20
minibrot's biggest "bay".<BR>  -0.12256 + 0.74486i The bays above =
and below=20
the main bay<BR>  -0.12256 - 0.74486i<BR>   0</DIV>
<DIV><BR> </DIV></FONT><FONT face=3DArial></FONT></DIV>
<DIV><FONT face=3DArial>
<DIV><FONT face=3DArial>The roots for z4 are</FONT></DIV>
<DIV><BR> -1.94080 + 0.00000i this is approximately in the center =
of a=20
minibrot's biggest "bay".<BR>  -1.31070 + 0.00000i 3rd bay on main=20
part<BR>  -1.00000 + 0.00000i 2nd bay on main part<BR>  =
-0.15652 +=20
1.03225i biggest minibrot at top and bottom<BR>  -0.15652 -=20
1.03225i<BR>   0.28227 + 0.53006i biggest bud top=20
right<BR>   0.28227 - 0.53006i<BR>   0</DIV>
<DIV> </DIV>
<DIV>
<DIV><FONT face=3DArial>The roots for z5 are</FONT></DIV></DIV>
<DIV> </DIV>
<DIV><BR>  -1.98542 + 0.00000i<BR>  -1.86078 + =
0.00000i<BR> =20
-1.62541 + 0.00000i<BR>  -1.25637 + 0.38032i<BR>  -1.25637 -=20
0.38032i<BR>  -0.19804 + 1.10027i<BR>  -0.19804 - =
1.10027i<BR> =20
-0.04421 + 0.98658i<BR>  -0.04421 - 0.98658i<BR>  -0.50434 +=20
0.56277i<BR>  -0.50434 - 0.56277i<BR>   0.35926 +=20
0.64251i<BR>   0.35926 - 0.64251i<BR>   0.37951 +=20
0.33493i<BR>   0.37951 - 0.33493i</DIV>
<DIV>   0</DIV>
<DIV> </DIV>
<DIV>You can look at these locations using Fractint or Ultra =
Fractal.</DIV>
<DIV> </DIV>
<DIV>z6</DIV>
<DIV><BR>  -1.99638 + 0.00000i<BR>  -1.96677 + =
0.00000i<BR> =20
-1.90728 + 0.00000i<BR>  -1.77289 + 0.00000i<BR>  -1.75488 +=20
0.00000i<BR>  -1.47601 + 0.00000i<BR>  -1.28408 + =
0.42727i<BR> =20
-1.28408 - 0.42727i<BR>  -1.13800 + 0.24033i<BR>  -1.13800 -=20
0.24033i<BR>  -1.00000 + 0.00000i<BR>  -0.59689 + =
0.66298i<BR> =20
-0.59689 - 0.66298i<BR>  -0.21753 + 1.11445i<BR>  -0.21753 -=20
1.11445i<BR>  -0.16360 + 1.09778i<BR>  -0.16360 - =
1.09778i<BR> =20
-0.01557 + 1.02050i<BR>  -0.01557 - 1.02050i<BR>  -0.11342 +=20
0.86057i<BR>  -0.11342 - 0.86057i<BR>  -0.12256 + =
0.74486i<BR> =20
-0.12256 - 0.74486i<BR>   0.35989 + 0.68476i<BR>   =
0.35989 -=20
0.68476i<BR>   0.39653 + 0.60418i<BR>   0.39653 -=20
0.60418i<BR>   0.44333 + 0.37296i<BR>   0.44333 -=20
0.37296i<BR>   0.38901 + 0.21585i<BR>   0.38901 -=20
0.21585i<BR>   0.00000 + 0.00000i</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV>All of these roots are in "bays" and not on the boundary.<BR></DIV>
<DIV>I did the math and roots  in Octave. I hope I haven't made any =

mistakes but if I did someone will help.</DIV>
<DIV>Respectfully</DIV>
<DIV>Doug Stewart</DIV>
<DIV> </DIV></FONT></DIV>
<BLOCKQUOTE dir=3Dltr=20
style=3D"PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
  <DIV style=3D"FONT: 10pt arial">----- Original Message ----- </DIV>
  <DIV=20
  style=3D"BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>=20
  <A title=[e-mail] =
href=3D"mailto:[e-mail]">Multiple=20
  Bogeys</A> </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>To:</B> <A =
title=[e-mail]=20
  =
href=3D"mailto:[e-mail]">[e-mail]</=
A>=20
  </DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Sent:</B> Saturday, June 30, 2001 =
2:56=20
  AM</DIV>
  <DIV style=3D"FONT: 10pt arial"><B>Subject:</B> Re: (fractint) Fractal =

math</DIV>
  <DIV><BR></DIV>
  <DIV>> If you ask this after each iteration you will get a set of =
numbers=20
  that when<BR>> they are plotted on the mandelbrot picture they will =
be=20
  found in each "bay".<BR>> Obviously after an infinite number of =
iterations=20
  you will have an infinite<BR>> number of roots and an infinite =
number of=20
  bays.<BR></DIV>
  <DIV>Just to clarify, the union of all these sets isn't M, but it =
does=20
  accumulate on the boundary of M.</DIV>
  <DIV><BR><BR clear=3Dall>
  <HR>
  Get Your Private, Free E-mail from MSN Hotmail at <A=20
  href=3D"http://www.hotmail.com">http://www.hotmail.com</A>.<BR>
  <P></P></DIV></BLOCKQUOTE></BODY></HTML>

------=_NextPart_000_00D0_01C1014B.60004550--


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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  30-06-01  (Head of Zardoz [4])
Date: 30 Jun 2001 10:15:03 -0400 (EDT)


Classic FOTD -- June 30, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

Today's image is another view of yesterday's midget.  Of course,
yesterday's image was not a picture of a midget, it was a slice
through a hole in a four-dimensional object known as the
Julibrot.  Such slices are known as midgets only when the slices
are oriented in the direction determined by real C and imaginary
C, and the starting point of Z is 0,0.  Under these conditions
the holes appear as miniature versions of the entire Mandelbrot
set.

When the orientation of a slice is changed, or the starting
point of Z is set to a value other than 0,0, a slice will not
cut a hole in a miniature M-set.  The slice of the hole will
appear as a Julia set or as an irregular open area.  True, some
of these slices come very close to being intact mini-M-sets, but
there is always some tiny imperfection when one searches deeply
enough.

When cut in an odd direction, (other than Mandelbrot or Julia),
a hole often presents an irregular triangular shape, as did the
hole in yesterday's image.  But in yesterday's image the pattern
around the hole was intact.  In today's slice of the same hole,
the pattern has been distorted and stretched in three directions
until it is barely recognizable.  It is apparently the same
three-way distortion that shaped yesterday's hole, but this time
it affects the entire surrounding area.

This three-way stretching appears quite often around holes when
they are sliced in odd directions.  There must be some geometric
feature of the Julibrot causing the effect, which would be quite
apparent if we could visualize four-dimensional forms.  In
today's scene the hole itself has been reduced to a narrow slit.
This also happens quite often in the odd slices, and is due to
the unusual shape of the actual hole, which has two extended Z
dimensions and two much smaller C dimensions.

I named today's image "Head of Zardoz".  Anyone who knows the
movie, which features a flying head, knows why I chose the name.
I rated the picture at only a 4.  The twisting, stretching
effect is really rather unattractive, and I chose it only to
show what could be done by rotating the direction of the slice,
while keeping it centered in the hole.  I also kept the same
palette of colors as an aid in identifying the same features.

Taking an even 4 minutes to render, the image is mercifully
convenient to render from the parameter file.  Downloading the
GIF image from:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or from:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

is equally convenient.  But give Paul and Scott a chance to post
the image before trying.

The fractal weather today continued sultry.  The temperature of
90F (32C) and occasional distant thunder kept the cats alert.
But all went well.  No storm broke and the cats finally relaxed.

And it's about time for me to relax.  It's 10am on a Saturday
morning, with other stuff to do.  But I'll be here again, right
on time with the next FOTD.  Until then, take care, and though
we can speak the words about the fourth dimension, we cannot
picture what we are speaking of.


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Head_of_Zardoz     { ; time=0:04:00.58--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=multirot-XZ-YW-new passes=1
  center-mag=-0.00000000262628144/-0.000000000366346\
  96/1.493935e+009/0.02482/-8.307/87.302 params=91/1\
  74/2/0/-0.7692602987818452/0.1095599458160586/-0.7\
  692602987818452/0.1095599458160586 float=y
  maxiter=2000 inside=0 logmap=389 periodicity=10
  colors=000VzeYzfZzf_zfazfczfezffzfgzfizgkzgmzgnzgo\
  zgqzgszguzgvziwziyzizzizzizzizzizzizzjzzkzzmzznzzo\
  zzqzzrzzrzzszyuzwvzvwzuyzszzrzzrzzqzzozznzzmzzkzzj\
  zzjzvizrgyogskfnifieecbeZZcUXcOSbJQbEMa8J_3FY0DW0F\
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  IbbH_eIZfJYiKXjMVmMUnNRqOQrQOuQNvRMySKzUIzRJzUKyVK\
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  zYzzZzz_zyazybzyczyezyfzwfzwfzwfzwfzwfzvfzvfzvfzvf\
  zvfzvfzvfzvfzvfzvfzvfzvfz
  }

frm:multirot-XZ-YW-new {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36  }

END 20.0 PAR-FORMULA FILE==================================


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-------------------------------------------------------------------------------

From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) C-FOTD 21-06-01 (Fractal Caterpillars [6])
Date: 30 Jun 2001 15:32:40 -0500

Multiple Bogeys wrote:
>
> >   HP Pavilion 8860 1 GHz
> >   --128MB, 60GB hard drive, CD-RW, DVD-ROM
> >   --Lowest price is $899
> *drool*
>
> But what's the CPU vendor?  AMD?  Intel?
> I don't see anything about video cards here.
>

Here is one of the locations to read further:

http://www.computers4sure.com/product.asp?productid=117383&affid=933&adid=933

P.N.L.
http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go

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-------------------------------------------------------------------------------

From: Ralph Feltens <[e-mail]>
Subject: Re: (fractint) Fractal math
Date: 30 Jun 2001 23:58:03 +0200

But if you just plot all the points in all those infinitesimal bays,
together they will appear like an outline of the Mandelbrot set (a kind
of dust that grows ever denser near the "shoreline", similar to the
inverse (?) M-set in Fractint).

Ralph

Doug Stewart wrote:

>   All of these roots are in "bays" and not on the boundary.I did the
> math and roots  in Octave. I hope I haven't made any mistakes but if I
> did someone will help.RespectfullyDoug Stewart
>
>      ----- Original Message -----
>      From: Multiple Bogeys
>      To: [e-mail]
>      Sent: Saturday, June 30, 2001 2:56 AM
>      Subject: Re: (fractint) Fractal math
>       > If you ask this after each iteration you will get a set
>      of numbers that when
>      > they are plotted on the mandelbrot picture they will be
>      found in each "bay".
>      > Obviously after an infinite number of iterations you will
>      have an infinite
>      > number of roots and an infinite number of bays.Just to
>      clarify, the union of all these sets isn't M, but it does
>      accumulate on the boundary of M.
>
>      -------------------------------------------------------------
>      Get Your Private, Free E-mail from MSN Hotmail at
>      http://www.hotmail.com.
>


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-------------------------------------------------------------------------------

From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) Fractal math
Date: 30 Jun 2001 20:52:42 -0400

But there is only one root per bay so you will see an outline of the
manelbrot set but the shore line will not be defined, only a dot for each
small bay and there are many small bays on the shore line.
Doug Stewart

Ralph wrote:

> But if you just plot all the points in all those infinitesimal bays,
> together they will appear like an outline of the Mandelbrot set (a kind
> of dust that grows ever denser near the "shoreline", similar to the
> inverse (?) M-set in Fractint).
>
> Ralph
>
> Doug Stewart wrote:
>
> >   All of these roots are in "bays" and not on the boundary.I did the
> > math and roots  in Octave. I hope I haven't made any mistakes but if I
> > did someone will help.RespectfullyDoug Stewart
> >
> >      ----- Original Message -----
> >      From: Multiple Bogeys
> >      To: [e-mail]
> >      Sent: Saturday, June 30, 2001 2:56 AM
> >      Subject: Re: (fractint) Fractal math
> >       > If you ask this after each iteration you will get a set
> >      of numbers that when
> >      > they are plotted on the mandelbrot picture they will be
> >      found in each "bay".
> >      > Obviously after an infinite number of iterations you will
> >      have an infinite
> >      > number of roots and an infinite number of bays.Just to
> >      clarify, the union of all these sets isn't M, but it does
> >      accumulate on the boundary of M.
> >
> >      -------------------------------------------------------------
> >      Get Your Private, Free E-mail from MSN Hotmail at
> >      http://www.hotmail.com.
> >
>
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"


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