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fractint-digest          Friday, July 7 2000          Volume 01 : Number 483




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

Date: Thu, 29 Jun 2000 23:39:30 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 30-06-00  (Un-named [5])

FOTD -- June 30, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

Today's fractal has no name.  It lacks a name because I lacked
the mood to invent one.  But the fractal does not lack merit.

The image shows a rather sinister little midget surrounded by
sharp, angular, knife-like elements such as might me used for
the cover of a horror novel.  The formula that created the image
is 2.45(Z^0.9-Z^1.1)+C -- nothing out of the ordinary, except in
the fractal it draws.

The parameter file takes 2-1/2 minutes to finish.  If that's too
long to wait to see the picture, the 640x480x256 GIF image file
can be downloaded from:

          <alt.binaries.pictures.fractals>

or from:

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

The day's fractal weather was partly cloudy and mild, with
thunder in the area this evening, but no rain.  The temperature
of 81F (27C) was perfect for the cats and the people as well.

The profound philosophy went nowhere today, though I posted a
little less-than-profound philosophy to the philofractal list
earlier this afternoon.  I'll try again tomorrow.  For now it's
time to shut down the fractal shoppe and call it an evening.
Until tomorrow, take care, and the fractals just keep coming.


Jim Muth
[e-mail]


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

Un-named           { ; time=0:02:23.30 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-5.16646549738710400/+1.58947089666920000\
  /5976.393/1/45 params=1/0.9/-1/1.1/1.45/0 float=y
  maxiter=1200 inside=0 logmap=34 periodicity=10
  colors=000r_B<3>vXcwWjwWq<2>BGHOHK_IMiJOzRQiOIXRA<3>\
  Bi66n51r53n65j6Ff6Kb6<4>UJ6WF6<6>ia8kd8mg8<2>tp8vs8x\
  tBzuD<3>nwLkxNhyP<2>hzV<3>XzjVznPyh<2>8wS<9>SnDUnBWm\
  A<3>bj4UiILiW<3>BaQ9`P7ZO<2>0UK<3>8VQAVRCVSEVT<9>QZM\
  R_MS_L<3>W`J<8>HXKFXKDWK<3>7VK<2>fa4g`6<3>hdBieDifEj\
  gGjhHjiI<6>bpEaqD`rD<3>XvB<3>2zB<7>HzbJzeLzi<3>Szv<3\
  >rzXxzRozV<3>Izi<4>UzmXzmZzn<3>gzp<5>_zjZziYzh<3>Tzd\
  <8>FzpEzqCzr<3>7zwDzUJz0<2>ezs<3>SzB<5>Pz7Pz6Oz6<3>N\
  z4<3>NzLNzPNzTszE5z5<2>IzBmzE
  }

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

Date: Sat, 1 Jul 2000 01:07:05 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 01-07-00  (A Midget in Lilac [3])

FOTD -- July 01, 2000  (Rating 3)

Fractal visionaries and enthusiasts:

Today's fractal is another quickie.  In fact it's the first
midget I came upon in my brief 5-minute exploration this
evening.  The image was found in such haste because I spent most
of my fractal-hunting time this afternoon thinking profound
philosophical thoughts and replying to the profound
philosophical thoughts of others.

The formula that drew the image is a whimsical one that was calc-
ulated by the M-Mix4 formula, Z^(-1.618)+1.618Z^(-16.*)+(1/C).
The midget in the picture is located toward the center of a
shallow valley that divides the main bud of the parent fractal.

I named the picture "A Midget in Lilac" because of the color
scheme, which features pastel green and lilac hues, arranged
around the central midget in an unusual pattern filled with
circular disks.

The parameter file renders in exactly 2 minutes on a P200, plus
2/100ths of an extra second, which will never be noticed.  The
GIF image file has been posted in all its meager glory to the
Usenet group

          <alt.binaries.pictures.fractals>

and to Paul's site on the W.W.W. at

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

The fractal weather today was perfect, with a deep blue sky,
cottonpuff clouds, gentle breeze, low humidity, and a
temperature of 80F (27C), which made the fractal cats
ecstatic.  Too bad it won't last.

As for me, the day has ended, the cats are hungry, and I'm
growing tired.  That means it's time to shut down the shoppe and
call it an evening.  But I'll return tomorrow with fractal and
philosophy.  Until then, take care, and long live fractals.


Jim Muth
[e-mail]


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

A_Midget_in_Lilac  { ; time=0:02:00:02
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.92588928983815400/+0.00024206172436048\
  /1137618/1/124.999 params=1/-1.618/1.618/-16.8/0/0
  float=y maxiter=1200 inside=0 logmap=32 periodicity=9
  colors=000RSV<3>Zfd`ifbmidqkftm<3>Ij4qls<3>m`mlYlkVj\
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  iL<3>ciJehJghI<2>mhH<7>RONOLOMJP<3>B9R<3>ZTf<8>EQqCQ\
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  _HOYH<3>GSH`ALWEKx4W<3>`2JV1GP1DSQLVmSE3t<3>VDeZGabI\
  ZfLVjNSL7V<2>u6l<2>qcM<2>tqluuttoetiStcE<3>UWFNUFHTF\
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  RNhMLmIJrEI<3>eOObRQ_TR<2>R_V<3>`_cb_ed_g<2>k_m<8>QF\
  ROCPLAM<3>C1D<5>POS
  }

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

Date: Sun, 2 Jul 2000 00:22:49 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 02-07-00  (Galactic Minibrot [4])

FOTD -- July 02, 2000  (Rating 4)

Fractal visionaries and enthusiasts:

Between holiday weekend activities, writing my philosophy, and
completing a little leftover work, I had almost no time today to
search for a proper fractal.  In desperation I turned to the
MandelbrotMix4 formula, entered the parameters 1, -1.25, 1,
- -5.33, 1/C, and let her rip.

The parameters did produce a fractal, and the fractal does have
midgets in it.  The midget in today's picture is just one of an
infinity of midgets lurking in the parent fractal.  The image
can rate no more than a 4, and considering the lack of effort,
even that is a liberal rating.

I named the picture "Galactic Minibrot" because of the four
galaxy-like spirals that surround the midget.  The parameter
file renders in a little under 8 minutes -- far too slowly for
an image of below-average worth.  But the picture is worth at
least a trip to the Usenet group:

          <alt.binaries.pictures.fractals>

or Paul's web site at:

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

where the GIF image file is waiting to be downloaded.

The fractal weather today was a repeat of yesterday, except that
the temperature was a few degrees warmer at 83F (28C).  The
ideal conditions brought out the best, (or worst), in the
fractal cats.

The philosophy was also quite active today, and can be seen in
several other articles that I posted earlier to the philofractal
list.  As for my present condition -- it rates a 2 on the
0-to-10 energy scale.  The only cure is to settle in front of
the TV and watch an episode of Dr. Who.

Until next time, when the energies will hopefully be restored,
take care, and when tension strikes, take a fractal or two.


Jim Muth
[e-mail]


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

Galactic_Minibrot  { ; time=0:07:51.81 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.41583652310222700/-0.15553310911297980\
  /13842.18/1/27.499 params=1/-1.25/1/-5.33/0/0 float=y
  maxiter=1200 inside=0 logmap=54 periodicity=10
  colors=000<16>000000000000000<3>300400501<2>82493584\
  6<79>8Xu8Xv8Yv<2>8Zx8Zy7Yz<37>NksNlsOls<2>PmsPmsNnp<\
  8>CqVBqSArQ<2>6sI5sG2vD<3>9rEBqECpEEoEGnF<6>RmGTmGVm\
  GWmGYmG_mG_mI<5>cmAdm9em8em7fm6gm3<42>`mb
  }

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

Date: Sun, 02 Jul 2000 10:40:46 -0700
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) FOTD, 28-06-00 (Boo [3])

At 11:36 AM 6/29/00 GMT, you wrote:
>...
>Yep. That's definitely the one. The real reason I wanted it was for
>animation... Anyone know of some good utilities for chaining GIFs into an
>anim?

GIF Construction Set, by Alchemy Mindworks Inc..
You can download their shareware at

http://www.mindworkshop.com

Good luck with your project.  I have only done one animation,
a little 18-frame number, but have other projects in mind.  Several
actually.  As always, it's a matter of finding the time...


Regards,
        Bud


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

Date: Sun, 02 Jul 2000 13:59:25 -0400
From: Mike Traynor <[e-mail]>
Subject: Re: (fractint) FOTD, 28-06-00 (Boo [3])

Mark Christenson wrote:
>
> At 11:36 AM 6/29/00 GMT, you wrote:
> >...
> >Yep. That's definitely the one. The real reason I wanted it was for
> >animation... Anyone know of some good utilities for chaining GIFs into an
> >anim?
>
> GIF Construction Set, by Alchemy Mindworks Inc..
> You can download their shareware at
>
> http://www.mindworkshop.com
>
> Good luck with your project.  I have only done one animation,
> a little 18-frame number, but have other projects in mind.  Several
> actually.  As always, it's a matter of finding the time...

I've found that on a fast machine you can actually do a reasonable animation
as large as 640x480x256 unsing the slideshow feature of LviewPro and bmp
format images (makes loading quicker).  Crude but then so are my animations.

Mike

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

Date: Sun, 2 Jul 2000 11:10:32 -0700
From: "John Wilson" <[e-mail]>
Subject: Re: (fractint) FOTD, 28-06-00 (Boo [3])

> > >Yep. That's definitely the one. The real reason I wanted it was for
> > >animation... Anyone know of some good utilities for chaining GIFs into
an
> > >anim?
> >
> > GIF Construction Set, by Alchemy Mindworks Inc..
> > You can download their shareware at
> >
> > http://www.mindworkshop.com
> >
> > Good luck with your project.  I have only done one animation,
> > a little 18-frame number, but have other projects in mind.  Several
> > actually.  As always, it's a matter of finding the time...
>
> I've found that on a fast machine you can actually do a reasonable
animation
> as large as 640x480x256 unsing the slideshow feature of LviewPro and bmp
> format images (makes loading quicker).  Crude but then so are my
animations.

What about Paint Shop Pro 6.0 from JASC?   You can do the whole job with the
built-in Animation Shop.

John W.


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

Date: Sun, 2 Jul 2000 13:14:53 -0700
From: "John Wilson" <[e-mail]>
Subject: (fractint) Fractal Animations

Inspired by the recent messages, I tried an animation using Paint Shop Pro
6.0's "Animation Shop".   It was a trivial task, taking about 10 minutes, to
form a 21-frame zoom into a part of the Mandelbrot set.  The results are
great, if a little jerky...I didn't zoom in equal increments.   PSP
assembled the whole thing into a 176 KB file, optimizing the whole mess
before saving it.   I'm impressed.

John W.


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

Date: Sun, 2 Jul 2000 23:55:12 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 03-07-00  (Galactic Minibrot [6])

FOTD -- July 03, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

It's a holiday week-end here in the USA -- the Fourth of July
week-end -- the time of year we celebrate with fireworks and
parades our country's independence from the British.

Most fireworks are now illegal, except at professionally
presented displays, but in some areas sparklers are still
permitted.  I would have preferred something more exciting in
today's fractal, such as a cherry bomb or hammerhead, but being
a law-abiding citizen, I settled for a relatively safe sparkler.
I wasn't too disappointed, for the sparkler rates a 6.

For today's image I took Z^32 and added its reciprocal,
Z^0.03125.  To complete the expression I added 1/C and let it
iterate.  When the iterating was done, I was left with today's
image.  I named the picture "Holiday Sparkler" because of the
sparkling effect of the many filaments radiating from the always-
present midget at the center.

The parameter file renders in just under 8 minutes on an aging
Pentium 200mhz.  The GIF image file downloads in less than 1/4
of that time.  For those who desire the download, the image may
be found posted to the Usenet binary group:

          <alt.binaries.pictures.fractals>

and to Paul Lee's web site at:

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

The fractal weather was another repeat today, though the
humidity was a bit higher, and the air a bit more hazy.  The
temperature of 84F (29C) was ideal for the two fractal cats, who
due to attacks of sleepiness, took almost no advantage of the
perfect conditions.

It's now 11;30pm and I'd like to write at least one
philosophical reply to the philofractal list before the day
ends.  So until next time, take care, and always wax
philosophical.


Jim Muth
[e-mail]


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

Holiday_Sparkler   { ; time=0:07:56.10 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-4.0775785029129250/-8.163508424429640/2.\
  394443e+007/1/-172.499 params=1/32/1/0.03125/0.05/0
  float=y maxiter=3000 inside=0 logmap=152
  symmetry=none periodicity=10
  colors=0000EE0EE0GG2II5KK<2>DQSGSVJTYMU_<3>XXj<3>ejp\
  gnqiqskutmxu<9>QeZOdXMbV<3>DWM<3>TdEXfC`hAdj8hl6a_BW\
  OGKCKJ0KN0T<3>`0dd0gh0jk0m<3>d1ec1da1b`1`<3>R1QP1NM1\
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  m<8>zUuzUvzUwzUxzUy<21>zUz
  }

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

Date: Sun, 2 Jul 2000 23:57:51 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 03-07-00  (Holiday Sparkler [6])

FOTD -- July 03, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

It's a holiday week-end here in the USA -- the Fourth of July
week-end -- the time of year we celebrate with fireworks and
parades our country's independence from the British.

Most fireworks are now illegal, except at professionally
presented displays, but in some areas sparklers are still
permitted.  I would have preferred something more exciting in
today's fractal, such as a cherry bomb or hammerhead, but being
a law-abiding citizen, I settled for a relatively safe sparkler.
I wasn't too disappointed, for the sparkler rates a 6.

For today's image I took Z^32 and added its reciprocal,
Z^0.03125.  To complete the expression I added 1/C and let it
iterate.  When the iterating was done, I was left with today's
image.  I named the picture "Holiday Sparkler" because of the
sparkling effect of the many filaments radiating from the always-
present midget at the center.

The parameter file renders in just under 8 minutes on an aging
Pentium 200mhz.  The GIF image file downloads in less than 1/4
of that time.  For those who desire the download, the image may
be found posted to the Usenet binary group:

          <alt.binaries.pictures.fractals>

and to Paul Lee's web site at:

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

The fractal weather was another repeat today, though the
humidity was a bit higher, and the air a bit more hazy.  The
temperature of 84F (29C) was ideal for the two fractal cats, who
due to attacks of sleepiness, took almost no advantage of the
perfect conditions.

It's now 11;30pm and I'd like to write at least one
philosophical reply to the philofractal list before the day
ends.  So until next time, take care, and always wax
philosophical.


Jim Muth
[e-mail]


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

Holiday_Sparkler   { ; time=0:07:56.10 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-4.0775785029129250/-8.163508424429640/2.\
  394443e+007/1/-172.499 params=1/32/1/0.03125/0.05/0
  float=y maxiter=3000 inside=0 logmap=152
  symmetry=none periodicity=10
  colors=0000EE0EE0GG2II5KK<2>DQSGSVJTYMU_<3>XXj<3>ejp\
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  S<3>LJMMKLPJYeXN<3>VZ_TZcQZf<2>J_o<3>c_r<3>fLWgHQgEL\
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  m<8>zUuzUvzUwzUxzUy<21>zUz
  }

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

Date: Tue, 4 Jul 2000 01:18:33 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 04-07-00  (More than a Midget [4])

FOTD -- July 04, 2000  (Rating 4)

Fractal visionaries and enthusiasts:

What could be better for the fourth of July than a fractal that
rates a 4?  Well, perhaps a fractal that rates a 6 or 8 would be
better, but we'll ignore those technical details and consider
today's image just the thing for our national Independence Day
holiday here in the USA.

The image was created by Andrew's MandelbrotBC (Branch Cuts)
formula, which draws the more remote parts of the fractals with
fractional exponents.  I wandered a rather considerable distance
away from ground level in the Z^2.006+C Mandeloid to find
today's midget, which is close to a larger midget.

I named today's picture "More than a Midget" because the midget
at the center is just a bit more complex than the standard Z^2+C
midget.  It is quite a bit more complex in fact, for it is split
right down the negative tail by one of those branch cuts, as
well as surrounded by cut-off bits of filament.

A close examination will reveal 8 plus a fraction elements
around the midget.  This is only to be expected in a fractal
with an exponent of 2.006.  In fact there are 8.072 (2.006^3)
elements circling the midget.

The parameter file renders in a relatively fast 3 minutes on a
Pentium 200 machine.  If this is too slow, the GIF image file
may be found ready for downloading at:

          <alt.binaries.pictures.fractals>

and at:

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

The day's fractal weather was partly cloudy and humid, with a
temperature of 88F (31C) that was perfect for the fractal cats,
who enjoyed the afternoon on the porch.  After dark a mild
thunder-shower passed over, which cooled things down for the
night.

Until tomorrow, take care, and see you in 22 hours.


Jim Muth
[e-mail]


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

More_than_a_Midget { ; time=0:02:50.98 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-1.05309114080759600/-0.00068667328146814\
  /3.069438e+008/1/-92.5 params=2.006/0/233/0 float=y
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  1<3>zwZ<5>zw`zwQzwOzwg
  }

frm:MandelbrotBC = { ; by Andrew Coppin
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(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|<100
}

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


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Date: Wed, 5 Jul 2000 00:24:00 EDT
From: [e-mail]
Subject: (fractint) FOTD 05-07-00  (Skewed Sweethearts [7])

FOTD -- July 05, 2000  (Rating 7)

Fractal visionaries and enthusiasts:

After an active day celebrating and philosophizing, I found
little time for fractaling.  But in that short time I managed to
find a fractal that rates a 7, a rating that has been notably
absent lately.

The expression (1/Z)-Z+(1/C) wouldn't be expected to create much
of a fractal, but fractals rarely do what's expected of them,
and today's fractal is a prime example of this fractal
stubbornness.

I named the picture "Skewed Sweethearts" because the midget's
pattern is a bit askew, and the sweethearts part of the name
will pique the curiosity of the ladies.  The parameter file
takes 6-1/2 minutes to render, making the download from:

          <alt.binaries.pictures.fractals>

or from:

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

the better choice.

The fractal weather today was partly cloudy and warm, with a
temperature of 86F (30C), which was perfect for the cats.  But
due to the fireworks going off in the neighborhood, the cats
stayed indoors, hiding most of the day in the hall closet.

I reached philosophical exhaustion this afternoon, so there will
be a rather lengthy break before the next outburst.  But the
break before I return with the next fractal will be only 24
hours.  Until then, take care, and be serene.


Jim Muth
[e-mail]


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

Skewed_Sweethearts { ; time=0:06:31.89 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.00005213775768595/+0.35587124080399530\
  /2.951152e+007/1/5 params=1/-1/-1/1/0/0 float=y
  maxiter=1400 inside=0 logmap=92 periodicity=10
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  scKscMsb<6>NsaNsaNsaOs_Os_Os_Os_QsZ<11>SsXSsXSsXUsV<\
  2>UsVYsYVs_UsVSsQSsHssX
  }

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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Date: Wed, 5 Jul 2000 23:04:51 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 06-07-00  (A Deep-down Midget [6])

FOTD -- July 06, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

The magnitude of today's fractal is 2e+14, making it most likely
the deepest I have yet gone with the MandelbrotMix4 formula.
True, the image is a bit past Fractint's limit of resolution,
but UltraFractal's more precise math routine should resolve it.
I had to set the math tolerance to /1 to reach such a magnitude
in Fractint, but the little midget is unusual enough to be worth
the effort.  The breakdown of resolution actually adds a rather
artistic effect to the picture.

I named the picture "A Deep-down Midget" because the central
midget lies so deep down in its parent fractal.

The formula that created the image is (-1/Z)-(Z^1.1)+(1/C) --
another formula that does more than it's appearance would
suggest.  The render time is a nominal 6 minutes on a P200; the
download time is an even more nominal 1 minute or so.  That
download may be found on the Usenet network at:

          <alt.binaries.pictures.fractals>

and on the Worldwide Web at:

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

The fractal weather today was perfect, with blue skies, a few
clouds, and no noisy fireworks.  The temperature of 86F (30C)
lured the fractal cats into the yard, where they enjoyed as nice
a romp as nine-year-old cats can manage.

The philosophy sleeps while I recharge my philosophical
energies.  The charge cycle might be a lengthy one, so be
patient fans of wisdom, and eventually your patience will be
rewarded.

That's it for today, but tomorrow is near, and it will bring a
new and greater fractal.  And it's also about time I returned to
one of my favorite diversions -- higher dimensions.  So tomorrow
could be interesting.  Check then to find out.

Until next time, take care, and stay solidly grounded in the
third dimension.


Jim Muth
[e-mail]


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

A_Deep-down_Midget { ; time=0:06:01.96 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.12844758295825350/+0.02991434375250009\
  /1.993294e+014 params=-1/-1/-1/1.1/0/0 float=y
  maxiter=300 bailout=25 inside=0 logmap=123
  symmetry=none periodicity=10 mathtolerance=/1
  colors=000bWn<3>j_ol`pnapobp<4>M9SG3O<3>CPdBUhAZl<2>\
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  fhAnoQuud<10>eVU
  }

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

Date: Fri, 7 Jul 2000 00:35:31 EDT
From: [e-mail]
Subject: (fractint) FOTD, 07-07-00  (Ferndale [6])

FOTD -- July 07, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

I named today's fractal "Ferndale".  I gave it that name not
because the image contains anything like a fern, and not in
honor of any town of that name, but because the word just came
to mind while I was studying the image trying to decide what to
name it.

The iterated formula is 10Z^(-10)+Z+(1/C).  Such a formula would
not be expected to make much of a fractal . . . well, maybe
that's no longer true, since I've been making quite a few
interesting fractal images with such formulae lately.

The image, which rates a 6, features the standard midget at the
center, surrounded by a pink and turquoise pattern of dark and
light spots arranged in inwardly spiralling arms.

The GIF image was souped up in a graphic program to give it a
little added zip before I posted it to:

          <alt.binaries.pictures.fractals>

The image is also available on the web at:

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

The parameter file renders in 2 minutes or so, making it a
toss-up as to which way of viewing the image is the more
efficient.

The fractal weather was once again perfect, with deep blue
skies, low humidity, and a temperature of 82F (28C), which was
perfect for cats.  Unfortunately, when the fractal cats went
outdoors, they were harassed most of the afternoon by a blue
jay, who must have thought they were after its babies.  But
those angel cats would never harm the bird -- they just want to
eat the birds.

My philosophical musing returned to my old favorite, the
abstraction of the fourth dimension, this afternoon.  I tried
for a few minutes to visualize double revolution and a surface
of double revolution.  I failed miserably.  But even though I
failed to visualize this four-dimensional object, that does not
stop me from thinking about it.  I may ponder the imponderable
again tomorrow, but regardless of the outcome, I'll have the
next fractal ready.

Until then, take care, and the formula for the hypervolume of a
five-dimensional hypersphere is 8/15*PI^2*r^5.


Jim Muth
[e-mail]


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

Ferndale           { ; time=0:02:12.42 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip
  passes=1
  center-mag=-3.15202487684002900/+1.00536788746322700\
  /6611.272/1/-25 params=1/1/10/-10/0.15/0 float=y
  maxiter=1200 inside=0 logmap=27 periodicity=10
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  Vzj<3>gzpjzrmzspzsszuxzvzzxzzy<2>zzzzzzzzyzzvzzu<2>x\
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  7Fz6Cz39z00z07z0<2>Yz1fz1oz3xz3CzQ7zO4zM1zJ0zI0zF
  }

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

Date: Fri, 07 Jul 2000 14:16:33 GMT
From: "Andrew Coppin" <[e-mail]>
Subject: (fractint) FotD's

Hi Jim.

Just wanted to say: Ferndale (and the one 2 days before that...) rate about
8 on my fractal scale!

PS. Edge-and-corner construction of a hypercube is beyond my intelligence
quotiant. I am now attempting to construct one from the intersection of
planes instead. Basically I will re-write my raytracer to work with 4D
vectors and points and see what (if anything) comes out. Will let you
know...

PPS. Never mind the hypervolume of a hypersphere... what's the formula for a
double rotation?!?! 8-])

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


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Date: Fri, 7 Jul 2000 22:54:04 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 08-07-00  (A Midget in Blue [7])

FOTD -- July 08, 2000  (Rating 7)

Fractal enthusiasts and visionaries:

Today's fractal rates a 7 -- the second above average fractal
with such a rating in a week.  But before getting to the image,
I must finish what I started yesterday.

In yesterday's FOTD I mentioned the surface of double
revolution, while neglecting to tell what it is.  That oversight
will now be corrected.  A surface of double revolution is a
curved two-dimensional surface, which exists in the three-
dimensional boundary of a four-dimensional hypersphere.   It
consists of the points lying at a given distance from a given
great circle of the hypersphere, and so at the complementary
distance from the polar, or completely perpendicular, great
circle.  A surface of double revolution is also the path traced
by points of the hypersphere when it is subjected to a double
revolution.

A double revolution is a type of motion possible only in spaces
of four or more dimensions.  It is comprised of two simple but
completely perpendicular rotations applied simultaneously to a
single object, each rotation taking place in two separate
dimensions.  The surface of double revolution is of importance
in the theory of functions with two complex variables.

Nested surfaces of double revolution could serve to measure the
latitude of a four-dimensional hyperplanet.  In this case, they
would start at the equatorial great circle of the planet, where
they would resemble the torus or doughnut-shape of three-
dimensional space.  But they would undergo an impossible-to-
visualise transformation before they converged, as inside-out
doughnuts, on the polar great circle of the planet.  It is the
shape of this surface of double revolution when it measures 45
degrees of latitude that has me puzzled.

But there is no puzzle about today's FOTD, which turned out
unexpectedly good.  The formula behind the image is
0.3Z^(-1.05)+Z^(1.05)+(1/C).  The parent fractal is another of
those strange figures that appear when Z and 1/Z, or values
close to this are combined in various ways.  Adding 1/C instead
of C merely adds to the interest.

I named the picture "A Midget in Blue" when I noticed the deep
blue haze surrounding the central midget.  The colors of today's
picture blend together unusually smoothly.  In fact, the image
must be examined closely to be sure that it is not in true-color.

The parameter file is unusually slow, taking almost 1/2 hour to
render on an average Pentium.  But as always, the GIF image has
been posted to the Usenet binary group:

          <alt.binaries.pictures.fractals>

and to Paul Lee's web site at:

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

The fractal weather today was absolutely perfect, with deep blue
skies, puffy clouds, low humidity, a gentle north wind, and a
temperature of 80F (26.5C).  The cats must have approved, as
they spent the better part of the day sleeping on the porch and
keeping out of the blue jay's way.

The fractal philosophy is still on hold, and likely will remain
so for several weeks yet.  But fear not, for the four-
dimensional muse is once again stirring, giving me much to think
and write about.  And the impossible things that are possible in
four dimensions make the illusions of the world's greatest
magicians look like nothing.

For now, the time to shut down the fractal shoppe has arrived.
The cats need to be evicted and fed, and I need to settle in
front of the TV to doze off trying to watch a junky old movie.
But I'll be back in 24 hours, so until then, take care, and
don't let those higher dimensions make you hyper.


Jim Muth
[e-mail]


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

A Midget_in_Blue   { ; time=0:27:15.63 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-4.919970039353122/+1.649879877881105/1.8\
  42739e+010/1/-34.997 params=0.3/-1.05/1/1.05/0/0
  float=y maxiter=3600 inside=0 logmap=511
  colors=000P9T<3>SAQTBPUBO<19>mL_nM`oMa<3>rOcrPdsPdsQ\
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  20>hqBirBjsB<3>mxAkxBjyB<3>ezBdzBczB<3>ZzBQz`<11>bzT
  }

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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End of fractint-digest V1 #483
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