ftp.xmission.com/2014.06.ftp.xmission.com.tar/ftp.xmission.com/pub/lists/fractint/archive/fractint.200007

Internet Message Format | 2000-07-31 | 165KB

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


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

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

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

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

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

From: "John Wilson" <[e-mail]>
Subject: Re: (fractint) FOTD, 28-06-00 (Boo [3])
Date: 02 Jul 2000 11:10:32 -0700

> > >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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-------------------------------------------------------------------------------

From: "John Wilson" <[e-mail]>
Subject: (fractint) Fractal Animations
Date: 02 Jul 2000 13:14:53 -0700

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

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 03-07-00  (Galactic Minibrot [6])
Date: 02 Jul 2000 23:55:12 -0400 (EDT)


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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  MRPNNQNKQOGStg<4>RfVRcSQ`P<3>QQFfPD<3>YODWODUODSODIG\
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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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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD, 03-07-00  (Holiday Sparkler [6])
Date: 02 Jul 2000 23:57:51 -0400 (EDT)


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

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


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
  maxiter=1000 inside=0 logmap=94 periodicity=10
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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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-------------------------------------------------------------------------------

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


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

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 06-07-00  (A Deep-down Midget [6])
Date: 05 Jul 2000 23:04:51 -0400 (EDT)


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


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

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

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


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

From: Lee Skinner <[e-mail]>
Subject: (fractint) Galleries
Date: 08 Jul 2000 16:57:40 -0400

Hi all,

  Just a note to announce some newer galleries of some of my images.
Although the Fractal Dimensions web site is no longer available at Michae=
l
Taylor's website, a few representative images may now be found at:

  English version:
   <http://www.fractalus.com/sylvie/fracdime.htm>
  French version:
   <http://www.fractalus.com/sylvie/fracdimf.htm>

And a few much more recent "lake" images of the MandelbrotMix4 formula
may be found here:

  English version:
   <http://www.fractalus.com/sylvie/lslakese.htm>
  French version:
   <http://www.fractalus.com/sylvie/lslakesf.htm>

Some very high-res (1600x1200) true-color of the formula Carr2821-lake
images may be found at

http://members.xoom.com/ereckase/skinnermuseum.htm

Enjoy.

Lee

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

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 09-07-00  (Nothing Much [6])
Date: 08 Jul 2000 23:01:26 -0400 (EDT)


FOTD -- July 09, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

Today's FOTD is nothing much -- so that's what I named it.  How
can it be much, when it's nothing more than a scene deep in the
Seahorse Valley area of the classic Mandelbrot set.  The scene
is not even deep enough to require arbitrary precision math.
It's the kind of fractal we were impressed by 10 years ago, but
most of us have long since outgrown.

Oh, it's a little bit unusual.  At 3,000,000, the maxiter is
quite high, and most of the features in the picture are well
over the 100,000 iteration range, but with our modern high-speed
computers such an image can be calculated in an hour or less.
On an aging Pentium 200mhz it takes 1-1/2 hours to render.

I have rated the picture a somewhat above average 6 on my scale
of fractal worth.  I gave it this rating because of the
coloring, which in my opinion is just good enough to raise the
image the 1 point to a little above average.  Basically, the
picture features a lurid inner area, hinting at violence and
evil, surrounded by a celestial blue background, suggesting
peace and serenity.

The midget in the picture lies deep in one of those triple
spirals that are located at the mouths of the secondary buds
deep in Seahorse Valley.  The triple spiral effect is quite
noticeable at the edge of the dark red disk surrounding the
midget.

The hour or two render time is quite a long while to wait to see
such an unimportant fractal.  The far more efficient way to view
the scene is to download the pre-rendered image file in GIF
format from the Usenet binary group:

          <alt.binaries.pictures.fractals>

or from the web at:

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

The fractal weather today was once again perfect, with deep blue
skies streaked with angel-hair cirrus, and a temperature of 81F
(27C), which pleased the cats, who showed their pleasure by
sleeping most of the day.  I was not as pleased, since I had no
excuse to postpone trimming the fractal lawn.  But all was not
lost, for while pushing the mower, I pondered the mysteries of
the fourth dimension, which of course are not mysteries at all.

The metaphysical (Isn't the fourth dimension also metaphysical?)
philosophy didn't even stir today, which could be a good or bad
thing, depending on whether or not one agrees with the
philosophy.

There's no debate that the time has come to shut down the
fractal shoppe, feed the fractal cats, and settle into my
laziest chair to watch the usual Saturday evening junky movie
thriller.  Until next time, when some 4-D talk is a good bet,
take care, and mid-summer (or mid-winter) is but a few weeks
away.


Jim Muth
[e-mail]


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

Nothing_Much       { ; time=1:25:02.35 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=mandel passes=1
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  }

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


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

From: [e-mail]
Subject: (fractint) FOTD, 10-07-00  (A Midget for Sunday [5])
Date: 10 Jul 2000 00:44:20 EDT


FOTD -- July 10, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

Today brings another very slow midget from a very difficult high-
iteration part of the Mandelbrot set.  The midget in today's
picture lies in the north branch of the fifth valley of the
period-10 radical on the northeast shore of the main bay of the
M-set.

I named the picture "A Midget for Sunday" because that's the day
of the week on which I found it.  The image was given a small
but helpful contrast boost in a separate graphic program.  (I do
occasionally permit myself this one bit of fractal impurity.)

I thought I was being liberal when I set the maxiter to 360,000
for today's picture.  But it turns out that even this was too
conservative, for even at a maxiter of 360,000, the central
midget is not fully resolved.  A maxiter of 500,000 would be
more appropriate for this image.

The logmap of -55373 indicates that most of the image is
composed of fractal material in the 100,000-plus iteration
range.  It is this aspect of the picture that causes the
parameter file to render so slowly.  Any render time over one
hour demands a download of the image, which may be found on
Usenet at:

          <alt.binaries.pictures.fractals>

and on the WWW at:

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

The fractal weather today turned out to be just about average
for these parts in early July.  The temperature of 87F (30.5C)
and high humidity made things a but too sultry for heavy outdoor
work, but near perfect for light indoor work such as searching
for fractals.  The fractal cats slept through most of the midday
heat.

The fractosophy went nowhere today.  Not only is it hard to
concentrate in hot weather, it's even harder when one has
nothing to concentrate on.  Eventually I'll solve the mysteries
of existence, but not for quite some time yet.

For now, it's time to shut down the fractal shoppe and call it a
night.  Until next time, take care, and fractals will always be
a mystery to me.


Jim Muth
[e-mail]


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

A_Midget_forSunday { ; time=1:15:74.75 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=mandel passes=1
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  /3.64154e+012/1/20.001 params=0/0 float=y
  maxiter=360000 bailout=25 inside=0 logmap=-55373
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  SMXSMXSM<2>XSMXSMXUM<33>YVMYVMYUM<9>YUM
  }

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

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

From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) FOTD 08-07-00 (A Midget in Blue [7])
Date: 10 Jul 2000 13:19:31 GMT

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

Once again, you rock! What a stunner!!!

PS. Trouble with my 4D raytracer: ray tracing is heavily based on
calculating surface normals. But the surface normal of a 4D plane is another
plane... I can't even construct a fuction for deciding which points lie
inside and which are outside, never mind perform ray intersection tests on
it...

Further worries later (I'm shure!)...


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

From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) FOTD 08-07-00 (A Midget in Blue [7])
Date: 11 Jul 2000 03:34:27 +1200

At 13:19 10/07/2000 +0000, Andrew Coppin wrote:

>PS. Trouble with my 4D raytracer: ray tracing is heavily based on
>calculating surface normals. But the surface normal of a 4D plane is
>another plane... I can't even construct a fuction for deciding which
>points lie inside and which are outside, never mind perform ray
>intersection tests on it...

Ah, but you're using _rays_, aren't you? One-dimensional things? The
surface of a four-dimensional object is a _volume_!

Morgan L. Owens
"Rubik's Tesseract!"



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From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 11-07-00  (Infinite Diamonds [5])
Date: 10 Jul 2000 21:56:33 -0400 (EDT)


FOTD -- July 11, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

Converging strings of pearls.  Radiating strings of diamonds.
Diamonds without end.  An infinity of fractal diamonds -- all
this in a simple fractal.  That fractal is today's fractal, and
once again, the fractal comes from the unlimited reservoir of
the MandelbrotMix4 formula.

The parent fractal is an asymmetrical Mandeloid rotated 110
degrees CCW from the normal left-is-west position.  The midget
in today's image lies at the tip of the period-2 tail of the
parent fractal.

The expression that drew the image is Z^(-0.6)-1.2Z+1/C, a
mixture of positive and negative powers of Z.  Such a mixture
often draws fractals with eye-shaped features, or in the case of
today's image, perfectly symmetrical sharp-angled eye-shaped
features that resemble diamonds.

At first glance the picture appears to have X-axis symmetry.
This is an illusion.  Though it cannot be noticed in the image,
the scene is in no way symmetrical.

I named the picture "Infinite Diamonds" because the number of
diamonds in it is infinite.  Of course, infinity is not a
number, it is the condition of being without limit, which is
just another way of saying that the number of diamonds in the
picture is without limit.

The picture rates a perfectly average 5 on my 0-to-10 scale of
fractal value.  If I had more time, I could have worked out a
more suitable color scheme, and with more time, I also could
have found a midget with more diamonds.

As an extra bonus, the parameter file is the fastest in several
days.  On a tired old P200 machine, it runs in 36 seconds.  The
time spent copying the file to the Fractint directory will be
longer than this.

For those who wish to avoid the hassle of copying and naming a
file, 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 weather today here at Fractal Central was sultry.  The day
started with a thunder-shower at daybreak, and ended with
another thunder-shower just before sunset.  neither of the
showers amounted to much.  The temperature of 91F (33C) was a
bit too warm for the fractal cats, who preferred to pass the day
lounging in the air-cooled fractal room.

The fractal philosophy stirred only a tiny bit as I pondered the
mysteries of the fourth dimension with its metaphysical four-
dimensional objects composed of curved and flat three-
dimensional spaces.  The surfaces of these 4-D objects are 3-D
boundaries with 3-D volume.  The task of visualizing an object
with a 3-D boundary-surface is impossible, yet there appears to
be no reason why this must be so.  The math flows smoothly from
one dimension to the next, with nothing special about 3-space.
Perhaps it's all in our minds.  I'll ponder this aspect in far
more depth when the muse stirs.

Regardless of where the secret to the fourth dimension lies,
it's now time to shut down the fractal shoppe for another
evening, shoo the cats, and call it a day.  Until tomorrow, when
I'll return with more goodies, take care, and when good fractals
happen to good people, everyone is happiest.


Jim Muth
[e-mail]


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

Infinite_Diamonds  { ; time=0:00:36.26 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip
  center-mag=-0.03474520578034267/+0.08388234702240095\
  /9.91477e+010/1/-112.5 params=1/-0.6/-1.2/1/0/0
  float=y maxiter=1200 bailout=25 inside=0
  logmap=16 symmetry=none periodicity=10
  colors=000668064<3>6DG7FJ9HM<2>DMVENmGPmrRzrSzGcYFc_\
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  6>`zd`ze`zg<2>`zj`zkZzf<3>TzQSzMRzI<5>JzhQzKJzGDzC
  }

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) FOTD 12-07-00  (An Alien Minibrot [6])
Date: 11 Jul 2000 23:10:27 -0400 (EDT)


FOTD -- July 12, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

I named today's fractal picture "An Alien Minibrot".  This name
seemed appropriate when I noticed that the irregular debris
surrounding the central midget is unlike anything I have
previously come upon.  The fractal expression that drew the
image is -24Z^(-1.2)-24Z^(-2.25)+(1/C).  The image was
calculated by the MandelbrotMix4 formula, which automatically
initializes Z to a critical point of the expression being
calculated.

Due to an unexpected rush of work this afternoon, I lacked the
time to give the picture the coloring it deserves, but the
present palette serves rather well to illustrate the strange
features of this image, which I rate as a slightly optimistic 6.

At 8 minutes, the parameter file is a bit too slow to be
efficient.  Downloading the GIF image from:

          <alt.binaries.pictures.fractals>

or from:

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

is a far more efficient way of viewing the alien vista.

The fractal weather today was partly cloudy, with a temperature
of 80F (26.5C), which was perfect for the cats, who spent
several hours on the porch, watching the squirrels climbing and
leaping through the trees.

Due to all the work, the philosophy suffered a setback today,
but it is once again beginning to stir, and in a week or so will
be ready for presentation to the eagerly waiting world.

For now however it's time to shut down the fractal shoppe, shut
my mouth, make the cats happy (if possible), and call it a
night.  Until next time, take care, and a fractal snack twice a
day is a great way to lose weight.


Jim Muth
[e-mail]


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

An_Alien_Minibrot  { ; time=0:08:21.12 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
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  zo<3>dzt<3>HzdAz_Bz`<9>Kzg
  }

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: "Fernando Bresslau" <[e-mail]>
Subject: (fractint) surfaces
Date: 12 Jul 2000 20:53:19 -0300

Hi, all! I┤m having lot┤s of ideas, but I need some help. Can anyone show me
the path I┤ll have to follow?
I want to put fractals into a CAD/CAM system. That is, I want to make a
surface out of a height field. I┤ve done this (the height field) in POV, but
I really want to export this surface info to a CAD prog. Has anyone already
done that? Does anyone know which progs to use? I could learn a lot myself,
but I don┤t even know how to begin. If I could work the gif info into a file
containing the pixels coordinates and the color number (height), I think I
could gon on myself. So, suggestions most welcome!
Fernando Bresslau
http://www.fractal.art.br - my modest site, in portuguese, sorry.


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From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 13-07-00  (This is not a Midget [3])
Date: 12 Jul 2000 23:58:24 -0400 (EDT)


FOTD -- July 13, 2000  (Rating 3)

Fractal visionaries and enthusiasts:

The formula Z^2+C draws Mandelbrot sets or Julia sets, depending
on the way it is iterated.  If both parts of Z are fixed, the
formula draws Mandelbrot sets; if both parts of C are fixed, it
draws Julia sets.  But what if different parts of both Z and C
are fixed?

This can be done in four different ways.  And in these cases the
formula draws four entirely new types of fractals, which I have
named Oblate sets, Rectangular sets, Parabolic sets and Elliptic
sets.  These four new groups of sets, along with the familiar
Mandelbrot and Julia sets, mark the six perpendicular
orientations through the four-dimensional Julibrot figure.

Just as Mandelbrot and Julia sets have their distinguishing
characteristics, so do these four new families of sets.  In the
new sets we find few Mandelbrot features, but many of the
familiar features of the Julia sets are there, and also many new
features, such as stretching, and the narrow, straight-edged
bands I call bridges.  Two of these bridges are visible near the
top and bottom edges of the midget in today's picture.

Just as it is possible to draw perpendicular slices through the
Julibrot figure, so is it possible to draw slices oriented
obliquely.  Today's picture is one of these oblique slices.

The hole at the center is actually a midget in the Scepter
Valley area of the M-set.  It also appears as a fancy hole in
many Julia sets.  But this midget, which in its fullness is
actually a four-dimensional hole in a 4-D object, has been
sliced in an unfamiliar direction.

At this angle we do not see a Mandelbrot midget, nor do we see a
fancy hole in a Julia set.  We see an entirely new type of hole,
a roughly rectangular thing with those filamentary bridges at
the top and bottom.

The orientation of this slice is within 6 degrees of the oblate
direction.  Many of the familiar features of Scepter Valley are
visible in the picture, but in places they are stretched beyond
recognition.

I named the picture "This is not a Midget" after Magritte's
famous painting of a pipe, which he named "This is not a Pipe",
implying that it is only a picture of a pipe.  The hole in
today's picture is not a midget because only holes sliced in the
Mandelbrot direction can be called midgets.  The artistic value
of the picture is below average, permitting a rating of only a 3.

Don't let the render time of 1 hour panic you.  This time is on
an ancient 486-66mhz machine, which was the only machine
available today, my Pentium being tied up with a very slow
fractal.  On a Pentium 200mhz the parameter file will finish in
around 8 minutes.  As always, the GIF image has been posted in
its full glory to:

          <alt.binaries.pictures.fractals>

and to:

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

The fractal weather was once again perfect, with crystal blue
skies and a temperature of 84F (29C).  The fractal cats approved
of the perfection by catching a cicada.

The fractal philosophy is still slumbering, but before long it
will awaken with a mighty roar, enlightening all who read it.
However today is not the day on which that will happen, so until
next time, take care, and happy fractaling.


Jim Muth
[e-mail]


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

ThisIsNot_A_Midget {;time=1:01:39.95--SF5 on a 486-66mhz
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=multirot.frm
  formulaname=multirot-XZ-YW passes=1
  center-mag=+0.00000014017740139/+0.00000000818683823\
  /91390.37/0.9263/-169.71/82.281
  params=84.124/-1.342/-1.2510561243/0.0133126434/-1.2\
  510561243/0.0133126434 float=y maxiter=15000
  inside=0 logmap=478 periodicity=10
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  3>zyizzjzzkzzl<6>zzm
  }

frm:multirot-XZ-YW {; 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)+p2, c=e*imag(pixel)+p3:
z=sqr(z)+c,
|z| <= 36  }

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


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

From: [e-mail]
Subject: (fractint) FOTD, 14-07-00  (One Wooly Minibrot [6])
Date: 14 Jul 2000 00:26:17 EDT


FOTD -- July 14, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

I've seen wooly-bears -- caterpillars that is.  But wooly
Minibrots?  Now that's something new.  However the elements
surrounding the Minibrot in today's FOTD certainly do look like
those wooly caterpillars that appear in the autumn and
supposedly can foretell the weather of the coming winter.  I'm
not convinced that the real caterpillars can actually foretell
weather, much less that the fractal look-alikes can do it,
though the fractal woolies do make an unusual picture.

The unusually simple fractal formula responsible for today's
image is 1.4(Z^1.5+Z^15)+1/C.  But don't be deceived by the
simplicity.  As is the case with nearly all fractals, the total
is greater than the sum of its parts.

The parent fractal consists of one Mandeloid and several
featureless holes, all these features lying beyond the southwest
edge of the default screen.  The Mandeloid is oriented East
Valley up, with excess detail radiating from the valley itself.
Knowing that where excess detail is found, interesting midgets
are also usually found, I explored these East Valley features.

The midgets eluded me at first, but soon I noticed the tell-tale
symmetrical features which indicate midgets.  Today's midget
soon followed.

The coloring was done a bit hastily, but it is still adequate.
The parameter file renders in a little under 3 minutes, making a
download of the GIF image the more efficient choice.  That image
may be found on Usenet at:

          <alt.binaries.pictures.fractals>

and on the Web at:

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

The fractal weather today was cloudy with occasional heavy
showers that kept the cats indoors.  The afternoon temperature
of 65F (18C) was about as cool as it ever gets in the afternoon
in mid-July.

The philosophy simmered most of the day, but failed to reach a
full boil.  We may have better luck tomorrow, when I'll return
with another fractal specially designed to amaze and delight.
Until then, take care, and be amazed and delighted.


Jim Muth
[e-mail]


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

One_Wooly_Minibrot { ; time=0:02:50.11 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=multirot.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-3.54842305346022500/-3.09497819370686700\
  /73988.85/1/165 params=1/1.5/1/15/0.4/0 float=y
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  BlbBlaBka<3>Bj`PkEQlC<3>KmBJmBHmA<3>CmA<2>GmvymX<3>w\
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  jmkjmk<5>nmcombpma<3>rmX`mPJmI<2>WmK<5>HmH
  }

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) FOTD 15-07-00  (This is a Minibrot [7])
Date: 14 Jul 2000 22:34:25 -0400 (EDT)


FOTD -- July 15, 3000  (Rating 7)

Fractal visionaries and enthusiasts:

Today's fractal image most certainly is a picture of a Minibrot.
When I first saw it, I was tempted to state that the image is
not a Minibrot because it is only a picture of a Minibrot, but
then I realized that pictures of Minibrots are the real thing.
A picture of a Minibrot, and indeed of any fractal, is the
object itself.  Today's picture is a picture that was produced
without an object being photographed.  It is as close to an
actual Minibrot as one can possibly come.

This, along with the fact that two days ago I posted an image
that was not a picture of a minibrot, is why I named today's
picture "This is a Minibrot".

The formula that created the image is Z^(-0.6)+(Z^(-6)+(1/C),
another unexpectedly simple expression, which in this case has
produced a striking picture of a midget at the center of a
fractal spiral.

The parent fractal is a strangely twisted Mandel-shape, somewhat
too large to fit on the default screen.  An outzoom reveals the
entire figure, which has a prominent bud at its east edge.  From
this bud a prominent tail shoots out, but this tail is not the
normal infinitely deep filament, it is rather a broad area of
fascinating intricacies, with an obvious 'S'-shaped curve at its
center.  I found today's midget deep down in this curve.

The midget is better viewed than described.  That veiwing may be
accomplished by running the parameter file and waiting 8-1/2
minutes, or by going to the Usenet group:

          <alt.binaries.pictures.fractals>

or Paul Lee's web site at:

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

and downloading the GIF image file from there.

The fractal weather today was exciting to say the least, as the
most violent thunder-storm of the year pelted the Fractal
Central area with 2-inch (5cm) hailstones, torrential rain,
spectacular lightning, and high winds.  The wind and hail
stripped so many leaves from the trees that the fractal lawn
will need a raking.  The fractal cats took shelter in the
basement until the water started coming in.  Then they dashed to
the bedroom closet to weather the rest of the storm.  They are
just now venturing into the open.  Surprisingly, there was no
power failure, so the FOTD will go out on schedule.

The fractosophy is still on a simmer, but the pressure to
pontificate is building and the lid may blow at any time,
releasing the wisdom of the ages for all the world to see.  But
that time has not yet quite arrived, so check here tomorrow at
about this same time for possible enlightenment and certain
amusement.

Until then, take care, and be patient, for the best is yet to
come.


Jim Muth
[e-mail]


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

This_is_a_Minibrot { ; time=0:08:29.93 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+2.872362067538974/+1.227930592848623/2.7\
  04756e+007/1/137.499 params=1/-0.6/1/-6/0/0 float=y
  maxiter=1400 inside=0 logmap=137 periodicity=10
  colors=000Kmk<15>EGGEEEECC<3>D45<3>CEKCGSCIWCL`CNcCP\
  hCSmCUtCWw2SzCYwMbtWgselroqqyxp<16>yU_yTZyRYyPXyNWzL\
  U<3>vPXvQYuRZtSZpT_mU`iV`cVWYSU<2>VKOUHRTFTVER`DVfCU\
  lBXrA`s9du8g<3>y4bz3ax7_<6>oTQmWOl_N<2>hhIgkHhlF<3>l\
  mBmnAnn9on8<12>NZWLYYIW_<3>BTg<10>7Se7Se6Sd<3>5Sd4Re\
  5Sd<7>6ZZ6_Y6_X<2>6bV6cU4eW<6>FXOGWNIVM<3>OQH<3>UYDV\
  _CXaBYcA_d9fe1<2>PkLFmT<3>TrN<3>UuHUvGUwF<2>UyBUsF<3\
  >UwUUxYWya<8>mzWozWqzVszUuzUwzTxzTyzT<3>zzVzzVzzU<8>\
  zzQzzQzzQ<2>zzOzzOzzM<2>zze
  }

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) FOTD 16-07-00  (Shrimp Festival [5])
Date: 15 Jul 2000 22:49:20 -0400 (EDT)


FOTD -- July 16, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

What do you get when you take Z^(-1.2) add Z^(-2.3), multiply
the sum by -24 and finally add 1/C?  Why a basket of shrimp of
course.  Now I realize that a basket of shrimp is one of the
least expected things to come from a fractal formula, but what
can I say? -- the shrimp are in the picture, and I can't deny
the evidence of my own eyes.

True, it takes a bit of searching to pick out the shrimp, but
like those dirty words and pictures subliminally embedded in
commercial advertising, once they have been found, the shrimp
become glaringly obvious.  (Hmmm . . . I feel like making a
quick run to the seafood restaurant a mile or so down the road.)

Because of all the shrimp in the area of the midget in today's
FOTD picture, I named it "Shrimp Festival".  It's a different
kind of name, having none of the usual fractal connotations.
IMO, the artistic quality of today's picture is a come-down from
yesterday's.  I could honestly rate the effort at no more than a
5.

The parent fractal is an indescribable thing with smooth outer
edges and fractal debris filling the interior.  An obvious bit
of Mandeloid stuff surrounds a bay on the south edge of this
interior debris.  The scene of today's image lies in the second
valley of a side bud at the edge of this bay.

At a render time of 11 minutes, the parameter file is too slow
to be practical.  Therefore a download of the GIF image file is
strongly recommended.  That download may be found on the Usenet
network, posted to the binary group:

          <alt.binaries.pictures.fractals>

and on the Web at Paul Lee's site at the URL:

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

The fractal weather continues unsettled, with a very heavy
thunder-storm overnight being followed by another one this
afternoon.  We have now received over 4 inches (10cm) of rain in
24 hours.  The fractal cats are getting shell-shocked.  At least
the temperature is about as cool as it ever gets here (the
northeast corner of Baltimore, Maryland, USA) in July, with the
thermometer struggling to reach the mid-70's F (mid-20's C).

And I'm struggling to get the next round of fractal-oriented
philosophy started.  Unfortunately, I had no luck today, though
I'll try again tomorrow.

Until then, take care, and keep your fractals dry.


Jim Muth
[e-mail]


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

Shrimp_Festival    { ; time=0:11:11.51 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.5631088685160116/-0.303287451331795/1.\
  818684e+010/1/80 params=1/-1.2/1/-2.3/-25/0 float=y
  maxiter=1500 inside=0 logmap=216 periodicity=10
  colors=000vqz<3>vpzvozvqzvnzmlzunzupzumznmzulznlyulx\
  qkwukwukopgfkccf`_aTXXQTSKQNIMIFJBCFDBGEDGGFGHMG<3>N\
  TGOVGQXGRZGS`m<4>SZmSYmSYm<2>SXmSXmSWk<4>SUaSU_SUY<3\
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  aiIZlKXpN<21>NMJMLJMJI<2>KFIKEIL5E<3>JKMINOIRQHVR<24\
  >ND`NC`NBa<3>O8bM7d<18>`BNaBMbCL<3>eCHmDGwDFzDEzDDzD\
  A<3>zDGzDIzDJzDLzFMwGO<3>cKUZLVUMWPNYLOZ<3>ESdCTfBUg\
  <2>6Xl4Ym2Zp<14>Cm`Dn_EnZ<4>HtUIuTIvS<3>LzOJzK<3>NzP\
  OzQPzRQzS<6>RzT
  }

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: "succubus" <[e-mail]>
Subject: (fractint) colourmaps
Date: 16 Jul 2000 21:35:36 +1000

This is a multi-part message in MIME format.

------=_NextPart_000_07C0_01BFEF6D.C77D13C0
Content-Type: text/plain;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Hi,
Does anyone have any colourmaps colated other than those that come =
standard with fractint?

Does anyone have an explanation of ifs type fractals ie. what each of =
the numbers means & how fractint processes them. I haven't found enough =
info in fractint help.

Thanks in advance.

------=_NextPart_000_07C0_01BFEF6D.C77D13C0
Content-Type: text/html;
    charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN">
<HTML>
<HEAD>

<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type>
<META content=3D'"MSHTML 4.72.3110.7"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT color=3D#000000 size=3D2>Hi,</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2>Does anyone have any colourmaps =
colated other=20
than those that come standard with fractint?</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>Does anyone have an explanation of =
ifs type=20
fractals ie. what each of the numbers means & how fractint processes =
them. I=20
haven't found enough info in fractint help.</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>Thanks in =
advance.</FONT></DIV></BODY></HTML>

------=_NextPart_000_07C0_01BFEF6D.C77D13C0--


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

From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) colourmaps
Date: 16 Jul 2000 09:59:44 -0500

> succubus wrote:
>
> Hi,
> Does anyone have any colourmaps colated other than those that come
> standard with fractint?

Try this URL:

http://spanky.triumf.ca/pub/fractals/maps/

Cheers,

Bob

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

From: "Ton Koppens" <[e-mail]>
Subject: Re: (fractint) colourmaps
Date: 16 Jul 2000 22:56:11 +0200

Hi,

I've some 1400 colormaps collected over the last 5 years, ranging from ugly
to very nice.
If you're interested send me a private e-mail and I'll zip and forward them.

Greetings,

Ton


[e-mail]


-----Original Message-----


Hi,
Does anyone have any colourmaps colated other than those that come standard
with fractint?

Does anyone have an explanation of ifs type fractals ie. what each of the
numbers means & how fractint processes them. I haven't found enough info in
fractint help.

Thanks in advance.



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

From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) colourmaps
Date: 16 Jul 2000 16:18:50 -0500

Ton Koppens wrote:
>
> Hi,
>
> I've some 1400 colormaps collected over the last 5 years, ranging from ugly
> to very nice.
> If you're interested send me a private e-mail and I'll zip and forward them.
>

Please include me. Thank you.

Bob

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

From: "Fernando Bresslau" <[e-mail]>
Subject: Re: (fractint) colourmaps
Date: 16 Jul 2000 21:32:49 -0300

This  calls another issue back. I┤ve recently downloaded some dozens of
other fractal progs which aren┤t so famous as frain or UF, and among them
was one which allowed you to easily change the colourmaps in a list in a
drop down menu, it was instantaneously and very nice. I miss this easy
access to maps in frain or UF. I suggest a key combination to change through
all the colourmaps in one directory. instead of pressing "e", "l", change to
the directory, arrow key, enter, we could use some ctrl+alt+shift+ nice
combination. I would really apreciate that to be in fractint┤s wish list.
Fernando Bresslau
http://www.fractal.art.br


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

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 17-07-00  (Mega-Minus Fractal [5])
Date: 17 Jul 2000 00:47:05 -0400 (EDT)


FOTD -- July 17, 2000  (Rating 5)

Fractal visionaries and enthusiasts:

For over 3 years I've been opening the FOTD discussion with the
introduction: 'Fractal visionaries and enthusiasts'.  The
description of a fractal enthusiast is obvious, but what is a
fractal visionary?

The truth is that I am not sure.  I simply invented the phrase
one day early in the life of the FOTD, and it kind of stuck
around.  The dictionary defines a visionary as a dreamer whose
ideas are impractical, and also as a seer -- one who sees
visions.  It would therefore appear that a fractal visionary is
a person who wastes too much time searching for fractals -- In
other words, someone like myself.

But is it truly a waste of time working with fractals?  I think
not.  After all, one must do something with their spare time,
and despite the words of some unenlightened critics, fractals
have become a form of art.  So a fractal visionary might well be
an artist -- an artist whose medium is numbers.  And there's
nothing impractical about that.

I named today's picture "Mega-Minus Fractal".  I gave it that
name because it shows what can be done by adding together
negative exponents of Z.  The formula that drew today's image
is 1.25(Z^(-0.5)+Z^(-10))+(1/C).  The parent fractal is near the
point of inversion -- too large to fit on the screen even at the
smallest magnitude available.

Ignoring the almost infinite extent of the entire fractal,
I directed my attention to a double-bay midget near the center.
I zoomed into a double valley separating the two large bays to
find today's midget.  Unfortunately, when I found it, I spent
too little time coloring it.  Thus the rating of an average 5.

The image of today's fractal is better viewed than described.
It may be viewed by running the parameter file and waiting
almost 7 minutes, or by downloading the fully-rendered image
from Usenet at:

          <alt.binaries.pictures.fractals>

or from the W.W.Web at:

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

The fractal weather today would have been ideal had it not been
for an hour-long dry lightning storm this afternoon, which was a
true spectacle, and sent the fractal cats scurrying for their
most secluded hiding places.  The temperature of 78F (25.5C) was
ideal, though unappreciated amid the turmoil.

The fractal philosophy went nowhere.  It might go somewhere
tomorrow; it might continue stagnated.  Check then to find out.
And until then, take care, and become a fractal visionary by
becoming one with your fractals.


Jim Muth
[e-mail]


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

Mega-Minus_Fractal { ; time=0:06:43.64 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+6.45906747057268800/+1.10441249439956900\
  /6873.396/1/7.499 params=1/-0.5/1/-10/0.25/0 float=y
  maxiter=1400 inside=0 logmap=98 periodicity=10
  colors=000sfPofNmfLkeJijH<3>af9_e6Yd7Wc8Ub8<3>PZAOXB\
  OWB<5>KPFJNFJMG<3>GHIFCJFFJ<3>CALB8MB7MA6N83M<27>dca\
  edbfeb<3>jjd<25>o_LoZLoZK<2>pYIqXHsXGuWG<2>yVDzVDzUC\
  zUBzTA<3>zUBzUCzUC<2>wUD<3>gVEcVE_cEXmE<3>SVF<10>CWI\
  BWI9WI<3>4WJ0XJ<16>NHJPGJQFJ<2>UCJVBKXAM<3>a6Ub5Wd4Y\
  e3_f2a<6>dAhdBicCjcDkcFl<3>bJsbKuaLwaMy<16>YdzYezXfz\
  XgzXhzYjz<18>UgzTgzTgz<3>Sfz6gz<2>Bfz
  }

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) FOTD 17-07-00  (Mega-Minus Fractal [5])
Date: 17 Jul 2000 08:49:36 GMT

On Mon, 17 Jul 2000 00:47:05 -0400 (EDT), Jim Muth
<[e-mail]> wrote:

>
>FOTD -- July 17, 2000  (Rating 5)
I think you underrated this one.

juice --have fun --harm none
INTP  web2.airmail.net/ebt

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

From: Jim Muth <[e-mail]>
Subject: (fractint) Re: FOTD 17-07-00
Date: 17 Jul 2000 19:43:56 -0400 (EDT)

At 08:49 AM 7/17/00 GMT, it was written:

>>FOTD -- July 17, 2000  (Rating 5)

>I think you underrated this one.

Remembering when a grade of 'A' in school was truly exceptional,
I rate my FOTD's conservatively.  For an image to rate a 9 it
must be truly exceptional.  For a rating of 10, the image must
be the best I have ever done.

Jim M.


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

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 18-07-00  (Holey Midget [6])
Date: 17 Jul 2000 22:52:26 -0400 (EDT)


FOTD -- July 18, 2000  (Rating 6)

Fractal visionaries and enthusiasts:

For almost a year I have given the FOTD's a rating somewhere
from 0 to 10 on my arbitrary scale of fractal worthiness.  To
this point the highest rating has been a 9, and the lowest, a 2.
Since June 1, the rating of the FOTD's has been as follows:

        Rating  0 --  0
        Rating  1 --  0
        Rating  2 --  0
        Rating  3 --  5
        Rating  4 --  7
        Rating  5 -- 12
        Rating  6 -- 13
        Rating  7 --  6
        Rating  8 --  1
        Rating  9 --  1
        Rating 10 --  0

As is true of most random distributions, most FOTD's have scored
near the middle of the scale.  As can be seen by plotting a
graph, the distribution is a roughly drawn version of the well-
known bell curve.  With a larger sample the curve would become
smoother.  The sample lacks 0's 1's and 2's because I reject
these poor quality fractals.  It lacks 8's 9's and 10's because
these exceptional fractals are quite difficult to create.  Since
June 1 the average rating has been 5.3, which shows that my
rating judgement is honest, and that I do not practice grade
inflation.

However I do appreciate those who tell me that I occasionally
under-rate my fractals.  And while appreciating the kind
comments, I never forget that beauty is in the eye of the
beholder.

And speaking of beauty, we have a FOTD to discuss.  Today's
image is a scene I found in the fractal created by the formula
10Z^(-6.67)+Z^(-0.667)+(1/C).  This formula draws a grossly
overblown thing which must be seen to be appreciated.  Today's
scene lies in a shallow valley near the extreme east edge of the
parent fractal.

The scene is that of the usual midget, in this case surrounded
by holes of all shapes and sizes.  Lots of holes is another
feature of fractals created by adding negative powers of Z.  The
holes may be made larger by increasing imag(p3), which defines
the escape radius, until the image becomes nothing but one big
hole, in which case the inside fill must be set to something
such as bof61 to create an image and resurrect the spirit of the
vanished midget.

At almost 1/4 hour, the parameter file is a slow one to
calculate.  The far wiser choice is to download the finished GIF
image from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather today finally settled down a bit.  The
partly cloudy skies, temperature of 86F (30C), and lack of
thunder brought out the best in the fractal cats, who were more
like their old selves as they chased each other around the yard.

The fractal philosophy is still stagnated however, but the
pressure to pontificate is still building, and when it breaks
loose anything might happen.  But the only thing that's going to
happen right now is that I'm going to shut down the fractal
shoppe and call it a night.  Until tomorrow, take care, and
fractals are good for the soul and spirit.


Jim Muth
[e-mail]


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

Holey_Midget       { ; time=0:13:37.73 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.203986748470977/-0.038709771549937/118\
  288.4/1/152.5 params=10/-6.67/1/-0.667/0/0 float=y
  maxiter=1500 inside=0 logmap=103 periodicity=10
  colors=000G0G<3>J0SK0VL0Y<3>P3j<2>S6mT7nW8o<3>fDsiEt\
  kGu<2>sJw<2>cQPZSEUT3VP2RP2KN1KL1KK1MIJCHP3GU7IUBJZE\
  KZILcMMcPNc<3>cSWfTTjUR<3>xYJv_KuaKsdKreKqiLohLnlLll\
  LkoMjoMhqMgsMfsM<2>boNanN`kO_kOZhOYhOXePWdPVbPUaPTZQ\
  SYQRWQQVQRVPSVPTVDUV1<3>`d2bf2dh2<3>jq2<9>NjdKigIhk<\
  3>9fz<3>TXNYUDaS3<9>GZPD_RB`T<3>3b`<3>EagGaiJakL`lm`\
  nk`pk`qm`sr`zw`zrZzmYzmXymWymVwmWtmWq<3>UYeHZbFZa<4>\
  LjlNmnOop<3>Sxx<3>HftEbsBZr<2>3Mo1Io0Lh<3>0VH0XA0Z4<\
  6>Q`DT`EX`F<3>j`J<3>0uq2qr3nrKjs<3>cXthUtmRurNuwKvzG\
  v<3>z3w<3>zBfzCbzEZzGVzIRzJN<3>zXMz`MzcM<8>zMEzKEzID\
  <3>zAA<2>zJK
  }

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: (fractint) Re: [philofractal] FOTD 18-07-00  (Holey Midget [6])
Date: 17 Jul 2000 22:41:38 -0500

Jim Muth wrote:
>
> For almost a year I have given the FOTD's a rating somewhere
> from 0 to 10 on my arbitrary scale of fractal worthiness.  To
> this point the highest rating has been a 9, and the lowest, a 2.
>

A bit of trivia, there have been two as high as "9", and interestingly
they have both been related to jungles:

    February 25, 2000  --  Jungle of Fractals
        June 01, 2000  --  Mandelbrot Jungle

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

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

From: Barry N Merenoff <[e-mail]>
Subject: (fractint) colourmaps
Date: 18 Jul 2000 04:03:17 -0400

An IFS fractal is generated by a set of transformations represented by 3x=
2
matrices indicating
an affine transformation (rotation, scaling, and shear) followed by a
translation (slide). I don't
know the details, but the numbers are probably parameters of these
transformations. The
fractal is defined by the criterion that it is the union of the specified=

transformations of itself.
The exact fractal can be found by a depth-first search of the tree of
successive transformations
performed on a representation of the unit square, where each branch ends
when the area of
the resulting parallelogram is less than one pixel. (This is guaranteed b=
y
the requirement that
the affine component is contractive (absolute value of determinant less
than one).
Fractint, however, (at least the version I had) uses a Monte-Carlo
approximation in which a
random sequence of transformations is applied to a single point. This has=

the disadvantage of
taking exponential time in the number of zooms. =


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From: Guy Marson <[e-mail]>
Subject: Re: (fractint) FOTD 18-07-00  (Holey Midget [6])
Date: 18 Jul 2000 12:55:57 +0200

Hi Jim,

nice are the majority of your creations! I am trying desperately to find
nice corners with "invert=1" (in the y-screen) but no chance until now.. Or
does somebody know a way to find +/- the same corners with invert=1 (or
invert=any other value)?

cheers,

Guy


>
>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]
>Get Commands:   [e-mail] "help"
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>Unsubscribe:    [e-mail] "unsubscribe fractint"
>


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From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 19-07-00  (Destiny [8])
Date: 18 Jul 2000 22:25:17 -0400 (EDT)


FOTD -- July 19, 2000  (Rating 8)

Fractal visionaries and enthusiasts:

I like today's fractal.  I like it enough to have considered
giving it a rating of 9, but a second appraisal convinced me
that it is honestly worthy of a lesser but still outstanding
rating of 8.  The bands in the purple areas are just a bit too
obvious.  With more time I could have done better.  (Those 9's
are indeed difficult to come by, and those 10's happen only a
few times in a lifetime.)

The iterated formula Z^(-0.5)+10Z^(-10)+(1/C) that produced the
image draws a many-lobed figure, somewhat too large for the
default screen, with a double-lobed bay at the east end.  The
scene of today's FOTD lies deep in the shoreline of that bay.

The parameter file is another slow one, rendering in just under
12 minutes on a Pentium 200mhz.  The GIF image with its data
intact has been posted to:

          <alt.binaries.pictures.fractals>

and to:

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

Whether or not one gets the data information depends on the
particular software that person is running.

The fractal weather was quite warm today, with a temperature of
89F (31.5C) that the cats found enjoyable.  The perfection was
marred slightly by a light shower in the afternoon, but it was
not enough to dampen the cats' enthusiasm.

The philosophy floundered and foundered as I tried to determine
the meaning of life.  I decided that the meaning of life is to
find fractals, but then I started wondering about the meaning of
searching for fractals.  About that time a customer called on
line number 2 and I had more important things to attend to.

I might tackle the meaning of life question tomorrow, but it's
still only about a 10 percent chance.  I'll have another
glorious fractal for certain however, so check back then to be
amazed, delighted, entertained, and lots of other enjoyable
things.

Until tomorrow, take care, and cherish your day.


Jim Muth
[e-mail]


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

Destiny            { ; time=0:11:42.17 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.69908857211162900/+0.00706571833280151\
  /7.96032e+009/1/82.5 params=1/-0.5/10/-10/0/0 float=y
  maxiter=1350 inside=0 logmap=225 periodicity=10
  colors=000zYAzYCzWDxUEsRFnOGjNHfLIaIKVGLNEMGDN9CO009\
  49975F98HC4KE0IG5LH0OK0RN0VQ0XU0`W1cY2ea4id5kh6pj7rn\
  8vq9xs8zsAzrDzqEzpGznHzmKxkMxjNwiQwhRwfUveWvdXvc_ua`\
  u`cs_dsYfsXirWjrVmrUnq<2>QupOwpNxsMzvMzxQzxSzz<3>azz\
  dzzfzzhzzizzizzixziwzjuzjrxjqwjnvjkukjskhrkerkdrkarm\
  _qmYqkWqjUqjSpiQphNnfMkeKieHedGicEfdCcc9YfAajA_nCdqC\
  auC_xDdzDazA_zD`zF`zG`zIazLazMazOazQcxScwVc<2>v_duad\
  sdeseerherieujfvkhuhdueauc_u`XsYVsWSsSQ<2>rLIrIGrGEq\
  ECqA9<2>p42p10p00<2>q10r42r65r77s99sCAsEDuGFuHHuKKvM\
  MvON<3>wXXx__x`axcczeezhhzijzkmznpzqq<2>zwxzzzzzzzzz\
  zzzxzzvzzuxz<2>nvzkuziszhrzerz<2>_nzXmzWkzUkzRjzQizN\
  hzLfzKfzIhzIhzIiwIivIisHjqHjnHkmHkjHkhHmf<2>Gn_GnYGp\
  WGpUFpRFqQFqNFqLFrKFrHEsFEsDEsCEu9Eu7Cv5Eu6Fu6Gu7Hs7\
  <3>Mr9NrAOrAQqCRqCUqD<2>XpEYpF_nF`nGanGcpF<2>fpF
  }

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) FOTD 20-07-00  (A Eutectic Mixture [9])
Date: 19 Jul 2000 23:55:51 -0400 (EDT)


FOTD -- July 20, 2000  (Rating 9)

Fractal visionaries and enthusiasts:

No, there is no mistake.  Today's FOTD actually rates a 9 -- at
least in my opinion.  This is only the third time since I began
rating my FOTD's this past Feb 6th that I have been able to give
such a distinguished rating to a fractal.  I almost gave a
rating of 9 to yesterday's FOTD, but now I'm glad that I settled
for the 8, since today's picture is notably better and well
worth the 9.  Now if I can only find a 10 . . .

I gave the coloring of today's image the extra effort that I
failed to give yesterday's picture, and that extra effort made
the difference, as both underlying images have about the same
potential.  I named today's picture "A Eutectic Mixture" because
the parent fractal appears to be the best that can be obtained
from this particular alloy of negative powers of Z.

The iterated fractal formula that drew today's image is
Z^(-0.09)+15Z^(-15)+(1/C) -- a harmless expression that leaps to
life when it is iterated.  The parameter file takes over 18
minutes to render on a Pentium.  The GIF image file saves time
by downloading in a far shorter time.  That download may be
found on Usenet at:

          <alt.binaries.pictures.fractals>

and on the Web at:

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

The fractal weather today was cloudy and remarkably cool for
this, the hottest time of year.  The afternoon temperature of 62F
(16.5C) was quite a bit too chilly for the cats.  The steady
light rain that set in during midday took all thoughts of the
outdoors from their minds.

I was too busy fractaling to do much philosophizing today.  I'll
be fractaling again tomorrow, so there's no guarantee that I'll
have philosophy then either.  But check anyway.  Sometimes the
strangest things happen.

Until next time, take care, and a great fractal can turn a
cloudy day sunny.


Jim Muth
[e-mail]


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

A_Eutectic_Mixture { ; time=0:18:37.79 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+4.69537095997045400/+0.32186770158987670\
  /4.039309e+010/1/-107.499 params=1/-0.09/15/-15/0/0
  float=y maxiter=2100 inside=0 logmap=368
  periodicity=10
  colors=000R0I<3>S0LT0MT0NU0OU0PW0Q<2>X0TY0UY0T<3>_0P\
  `0O`0Na0Ma0Kb0Jb1J<14>IAGGAGFBGDCGCCFBDF9CF8AF6CF5CF\
  2DG<24>_`BaaAbbA<3>geA<3>OiSJjXEj`<3>FmUFmSFnQFoPFoN\
  IpLPpJ<3>hsDmsBmt9ru9wt8wq8qn7lk7gh6<2>P_5OX5<3>SL3T\
  I3UF2VC2V81<20>a9Ab9Ab9B<2>c9Cc9Ce7A<6>VKIUMJSOK<2>O\
  UNMWOJYR<8>QWMRWLSWLTWK<3>WTIXSIXRHYQHZPG<3>nLErKEvK\
  DzVB<3>iTFeTHaTK<3>LSWERZBUaIYd<2>khmilp<11>JrJHsGFs\
  D<3>6u2<17>FhWGhYGgZ<2>IecIdeHad<3>IggZXL
  }

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) FOTD 21-07-00  (The Elephants Walk [3])
Date: 21 Jul 2000 01:34:36 -0400 (EDT)


FOTD -- July 21, 2999 (Rating 3)

Fractal visionaries and enthusiasts:

Today's FOTD, which is quite a come-down from yesterday, shows
some elephants.  I named the picture "The Elephants Walk"
because that's what the elephants appear to be doing.

For purposes of clarification, various parts of the Mandelbrot
set have been given descriptive names such as Seahorse Valley,
Elephant Valley, Scepter Valley, etc.  The names refer to the
shapes of the features in these valleys, and a bit of
imagination is necessary of course to see the vague resemblance
to the objects the valleys are named after.

Perhaps the easiest things to find are the guardian elephants
trotting out of East Valley, the valley that begins at 0.25 on
the X-axis of the M-set.  In this area, each elephant is aligned
with one Mandelbrot bud, and stands guard over its bud,
protecting the bud from whatever it is that attacks Mandelbrot
buds.

Today's fractal shows two complete though strangely distorted
elephants, and the front part of a fragmentary third elephant.
The elephants are nice, but we've all seen the East Valley
elephants many times, so to make things more interesting, I have
captured a view of the elephants from an entirely new direction
-- the direction I call Oblate, which consists of the planes of
the Julibrot defined by the imag(c) and real(z) axes.  In
today's tilted picture the narrow diagonal line is oriented in
the imag(c) direction, with the positive direction toward the
upper right, while the perpendicular direction is real(z).

The elephants are obvious enough, but where are the buds they
are guarding?  The secret is that the one-bud-per-elephant
arrangement is true only in the Mandelbrot orientation.

Actually, one bud appears in today's picture, but it appears so
distorted that it would never be recognized.  Look carefully at
the straight-edged features extending diagonally from the lower
left to the upper right of today's image.  Pay special attention
to the hair-thin straight line.

This line is what I call a bridge.  Bridges appear all the time
in the four odd planes of the Julibrot figure.  This bridge is
actually the tip of a Mandelbrot valley sliced from the side,
and the diagonal empty space between the line and the main
diagonal straight-edge is the open inside of one of the buds
along the southern edge of East Valley.

The reason the buds appear as straight lines is that they are
actually four-dimensional hypercylinders in the 4-D Julibrot
figure -- a shape impossible to visualize with mere 3-D minds.
I find it most curious that these straight bridges continue
their way wherever they are unobscured regardless of the low-
iteration material surrounding them.  In fact, as can be seen in
several places in today's picture, the bridges actually attract
the low-iteration material to themselves, and increase their
mass by absorbing this material.

The parameter file of today's image takes 5-1/2 minutes to
render on a P200 machine.  The GIF image file downloads in less
than half that time from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather today was partly cloudy and quite cool for
July.  The temperature of 79F (26C) must have suited the fractal
cats perfectly, for they spent several hours outdoors, romping
in the yard.

The philosophy made little progress however.  But tomorrow is
another day, (it always is), and some surprise philosophy could
appear then.  Check in to see what happens.  Until next time,
take care, and don't lose your head in the fourth dimension.


Jim Muth
[e-mail]


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

The_Elephants_Walk { ; time=0:05:20.22 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=multirot.frm
  formulaname=multirot-XY-ZW function=ident/flip
  passes=1 center-mag=+0.3181278040886614/-0.013000620\
  65059610/275.3077/0.04602/0.659/80.235
  params=0/90/0/0/0.285/0 float=y maxiter=2500
  inside=0 logmap=14 periodicity=0
  colors=000YGU<3>`JXaKYbLZcM_dO`eRagUb<3>nfhpijrklsmm\
  qli<2>hd_daX`YUYVRTSN<3>FGABD78A4571<3>PPNUTSYXX<3>M\
  RRKQPHPOENMBML8RJ6TI7YH8cH9iHAmHDoG<4>RXEUTDXQD<3>gB\
  B<7>VOVTQYRS_QTbOVdNWf<3>F_sD`vC`v<3>A_vA_vA_v<6>Ccs\
  CcrCdr<2>DeqDfpGfkDfp<6>FimFjmFjl<3>Glk5hi<3>8Ta9P_9\
  O_AN`<3>CXdDZeDafEcgFehKciPajU_mZYl<2>kSl<3>iKliIlhG\
  lhElhClgBl<58>KfkKgkJhk<3>IjkHjnHkqGktGmwMmz<3>JmrIm\
  pHmnGmlImj<3>HmaHm_HmYHmW<4>HmXHmXHmXHmYHmYHmY<2>HmZ\
  HmZImZJm_<3>KmW
  }

frm:multirot-XY-ZW {; draws 6 planes and many 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))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(z)+c,
|z| <= 36  }

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


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

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 22-07-00  (A Swarm of Leeches [5])
Date: 21 Jul 2000 22:35:25 -0400 (EDT)


FOTD -- July 22, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

Do leeches come in swarms?  I don't know, but if a group of
giraffes is called a tower and a group of crows is called a
murder, why can't a group of leeches be called a swarm?  Yes, I
realize that a group of blood-sucking leeches is not the most
artistic fractal thing in the world, but it is different, and
when I saw today's curious image, I couldn't help but seeing a
midget surrounded by clinging, sucking leeches.  That's when
the name "A Swarm of Leeches" came to mind.

The iterated fractal formula that drew the image is another of
my whimsical ones:  Z^(-sqrt(2))+5Z^(sqrt(2))+C.  Like the
parameters I use with most of my M-Mix4 formula fractals, the
parameters of today's image were chosen basically at random.  I
simply turned off my brain and put my fingers on automatic.
(Not that it made much difference.)

The parent fractal of today's scene is a small Mandeloid that is
eroding at the edges.  I found today's scene in the northeast
corner of the main bay, deep in a very loosely wound spiral,
somewhat away from the area that is disintegrating.  Other parts
of this fractal appear quite promising; I may be looking further
into it in the near future.

At just under 10 minutes on a Pentium, the parameter file is a
slow one.  But relief for irritation may be found on Usenet at:

          <alt.binaries.pictures.fractals>

and on Paul Lee's site on the W.W.Web at the URL:

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

where the GIF image has been posted with all its data.

The fractal weather today was partly cloudy and quite pleasant,
with a temperature of 84F (29C) which made the cats happy.  A
sudden short but torrential shower at nightfall brought the day
to a cool and satisfying close.

The philosophy is once again stirring, so all you fans of the
fantastic philosophical pontifications won't have long to wait.

As for me, I'm going to take a few minutes to check other parts
of the fractal that contains today's image.  And then I'm going
to shut the place down, feed the cats, and call it a night.
Until tomorrow, take care, and leeches might be repulsive, but
every one of them is a sucker.


Jim Muth
[e-mail]


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

A_Swarm_of_Leeches { ; time=0:09:49.14 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.03234114002211268/+0.0758542959983652/\
  1.416931e+008/1/-25 params=1/-1.4142/5/1.4142/-0.83/0
  float=y maxiter=900 inside=0 logmap=106 periodicity=9
  colors=000KXoKXo<3>HTgGSeFRdKQbPP`<3>h9Sj0P<3>oLSpQS\
  rVT<2>uhVujVtkVrjSphQ<3>eXFcUC`RA<2>SJ0SI2SI3<10>DJG\
  BJHAJI<3>5JM<8>bVWfWXjXYmZZ<2>zb`<18>RKsPJtNIu<3>GEx\
  <3>KSbLWYMZSNbNNeI<2>cg`ihfpgn<12>amP`nN_nL<2>XpFWpD\
  UsD<12>eNBfLBgIB<2>jBBk8Bj5A<14>kGOkHPkIQ<3>kKT<3>op\
  PtyO<8>SrRPqSLpS<2>CnT9mT4nU<11>PjIRjHTiGViFWiEYhD<3\
  >dj9fk8gk8<9>jpHjqIjqJ<3>ksMdtcZtc<3>dvcfwcgwbixa<3>\
  ozSpzQozR<8>mzUGzd
  }

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) FOTD 23-07-00  (A Patch of Briars [5])
Date: 22 Jul 2000 22:23:37 -0400 (EDT)


FOTD -- July 23, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

Today's FOTD picture has a prickly feel about it.  It seems
rather thorny in overall appearance, all of which justifies the
name I gave it -- "A patch of Briars".  My first impulse when I
saw the scene was to name it something like "Barbed Wire", but
the briar patch name won out because of its more poetic sound.

The fractal formula that drew the image is surprisingly simple --
-0.8(Z^1.5)-0.8(Z^(-0.5))+(1/C), which was calculated as usual
by the M-Mix4 formula.  The finished product was livened a bit
in a graphic program.

The parameter file runs in a bit under 3 minutes, leaving it up
to the viewer to decide whether the easiest way to see the FOTD
is to run the parameter file or to download the GIF image from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather today was perfect, though some showers
passed close by during the afternoon.  The partly cloudy skies
and temperature of 84F (29C) were just what the cats ordered.

There's good news for philosophy fans -- my muse is once again
speaking.  It will take a day or two to fine tune the
composition, but the topic is already determined.  Actually, it
was a letter that appeared earlier Saturday on the philofractal
list that supplied the inspiration.

For the moment my calendar clock tells me that it's Saturday
evening, and two of my favorite shows will soon be on TV -- 'Red
Dwarf' and 'Doctor Who'.  So I've got to hurry and shut down the
fractal shoppe to settle into my overstuffed chair for a late
evening of TV viewing.

Until tomorrow, take care, and for the life of your fractal,
don't turn off that computer.


Jim Muth
[e-mail]


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

A_Patch_of_Briars  { ; time=0:02:40.34 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.76022595650848300/+1.14392397091661000\
  /4403963/1/119.999 params=1/1.5/1/-0.5/-1.8/0 float=y
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  pn9pl<3>9pk9pk9pi9pi9pg<3>9pf9pf9pd9pd9pd9pb<2>9pa9p\
  a9p_9p_9p_9pY<3>9pX9pX9pV9pV9pV9pT9pT9pR<3>9pQ9pQ9pO\
  <3>9pN9pN9pL9pL9pJ<3>9pI9pI9pG9pG9pG9pE9pE9pE
  }

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: "succubus" <[e-mail]>
Subject: Re: (fractint) colourmaps
Date: 23 Jul 2000 19:52:08 +1000

Thank you for all the colourmaps & information. I will be trying them out
over the next month or so.
regards,
regina
-----Original Message-----


An IFS fractal is generated by a set of transformations represented by 3x2
matrices indicating


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From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 24-07-00  (Ring Around a Midget [7])
Date: 24 Jul 2000 01:06:29 -0400 (EDT)


FOTD -- July 24, 2000 (Rating 7)

Fractal visionaries and enthusiasts:

Today's fractal is a picture of a ring around a midget, so
that's what I named it.  The iterated formula started as a
whimsical -11Z^(-1.1)-Z^(-11), but I soon found that setting
real(p3) to -1.99, which multiplied the original expression by
-0.99, made the fractal far more interesting and resulted in a
final image that rates a 7.

The parent fractal is too large to fit on the default screen,
and must be given one outzoom before it is all visible.  When
this is done, a curiously distorted Mandeloid comes into view,
with a negative tail that leads in a graceful curving arc into a
dazzling basin quite unlike any I've seen until now.

Naturally, upon finding something I've never before seen in a
fractal, my immediate impulse is to dive into it in search of
midgets.  On my dive today I came up with a midget and a fractal
picture that rates a 7.

At 10-1/2 minutes, the parameter file is annoyingly slow to
render.  But don't despair, for relief is but a few mouse clicks
away, waiting at the Usenet site:

          <alt.binaries.pictures.fractals>

and at the Web site:

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

where the GIF image has been posted in all its unfathomable
glory.

Though today's fractal rates an above average 7, the fractal
weather rated a below average 3.  The temperature of 78F (25.5C)
was comfortable enough, but it was cloudy, and the forecast or
rain all week added to the depression.  The fractal cats, who
seldom get depressed, spent over an hour in the yard before
retiring to their favorite chairs for the evening.

The philosophy is moving along in high gear, and will soon
appear on the philofractal list.  But it's not quite ready yet,
so a bit more patience will be required.

Until next time, take care, and don't do anything naughty, or
you might turn into a fractal.


Jim Muth
[e-mail]


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

RingAround_aMidget { ; time=0:10:36.14 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-5.34265200320681500/+7.73134099829820100\
  /6.046723e+011/0.9999 params=-11/-1.1/-1/-11/-1.99/0
  float=y maxiter=1200 inside=0
  logmap=234 periodicity=10
  colors=0002742723873AB4BG4EK5HO<3>7Ke7Ki8Ln8Mr8Mv<9>\
  cdygfyjhy<3>voz<3>kMkiEgf7cd0`<3>hIkiMnjQpf1VZQLRnC<\
  3>T_NUWPUSSUPU<3>iOblOdbIUTDJJ89<6>aWNdZPgaR<3>qnZ<3\
  >cTb`NcYIbRD`NE_PFZSGaTHeXIhXJkYKp<2>ZNwZOyZOzYNy<3>\
  XNpWNnWMk<3>UMfUMeUMd<3>NDULBSJ9PI7N<3>CCNBEN9FN8GN7\
  HN<8>UFLWFLZFL<3>gFL<3>s_ivdopbej`We_M<7>gbFgbEgbD<2\
  >gcAgcAeaB<8>ROGQMHOLH<3>IFJ<3>gA9m96s84y72<3>`F5UG5\
  OI6<2>6N7<5>WQC_QDcRE<3>tSH<2>L0F<3>okTvvWpwV<3>VyVP\
  zVKzV<7>8tD7tB5s9<2>1q30q11jD<3>5Jw<3>LDmPCkTBi<11>r\
  3q
  }

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) FOTD, 25-07-00  (Midget with Zipper [7])
Date: 24 Jul 2000 22:31:05 EDT


FOTD -- July 25, 2000 (Rating 7)

Fractal visionaries and enthusiasts:

I've heard of fractal seahorses and elephants, and all kinds of
other interesting fractal configurations.  But until today I had
never heard of a fractal zipper.  All that changed this evening
however, when I went diving into an interesting looking area of
a fractal closely related to the parent fractal of yesterday's
"Ring" picture.  In fact, the zipper that in today's picture
weaves around the central midget in eight waves is nothing more
than an amplified version of the ring that was so prominent in
yesterday's image.

And yes, I must confess that I have sinned.  I increased the
contrast of the original Fractint GIF image by 15 percent in a
graphic program.  But since the same thing could have been done
with more effort in Fractint itself, we'll still consider the
image up to my usual standards of fractal purity.

I named today's picture "Midget with Zipper" for obvious
reasons.  I rated it a 7 because I like the image more than
average.  For those who choose to view the zipper, (which is not
open), by running the parameter file, the wait will be about 10
minutes.  Those who would rather download the finished image,
will find it posted as usual to:

          <alt.binaries.pictures.fractals>

and to:

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

The fractal weather was cloudy and cool with steady light rain
all day.  The temperature of 64F (18C) and the wetness kept the
cats snug indoors from dawn until dusk.

Speaking of foul weather, the cats are testy due to being
housebound all day, and I hear them getting into trouble
downstairs.  I'd better shut down the fractal shoppe and calm
Thomas and Tippy.  Until next time, take care, and does it
really matter what mind is?


Jim Muth
[e-mail]


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

Midget_with_Zipper { ; time=0:09:45.29 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-14.67421731461308/+3.061215278356668/1.3\
  16117e+008/1/54.999 params=-11/-1.1/-1/-11/-1.93/0
  float=y maxiter=1000 inside=0 logmap=184
  symmetry=none periodicity=10
  colors=00007E07N08J09Q0BO0CS0ER0FV0HV0IY<3>0Nb0Oc0Ob\
  0S_0VY<2>CbQHdNKgK<3>_q9cs7gv4ix1mzJqz_uzZxzYuzHrz0<\
  2>kzChzHfxKcxO`xU<2>_xc_xc_xc_wbZuUSrK<4>MgHKdHJcHI`\
  FHZFFWEEVECSCBQC9OCxNzzNzzOzzQzxRznSzhSzbUwZVuRWsOYq\
  MYnJZlH_kE`hBbf8bd<2>9SY9OW9MUBIRBFOBBNB8KB4IB1H94F9\
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  4d04k05o05u09o0Cl0Fh0Jc0M_0OW1<3>`F7cB8f59i1Bl0Cn0Ch\
  0Hb4JW9NQFQJKUCQW5V_0_b4`Z8`VCbRHbNKcKOcHSfC<2>cm1fo\
  2hr4ku4mw5oz7<3>zz9zzBzzCzzCzzE<3>`zJVzKOzMIzNBzO4zQ\
  0zQ1zR4zS7zS9zU
  }

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) FOTD 26-07-00  (Fractal Potpourri [4])
Date: 25 Jul 2000 23:41:09 -0400 (EDT)


FOTD -- July 26, 2000 (Rating 4)

Fractal visionaries and enthusiasts:

Today's fractal is a come-down from yesterday's, but it still
rates a 4, which equals only slightly below average.  The
picture was created by the formula 1.1(Z)-3.1(Z^(-2))+(1/C).

The parent fractal, which lies off the northwest corner of the
default screen, is a nearly circular Mandeloid with an excess of
undersized buds lining the shoreline.  Today's scene lies
slightly inland from the northernmost part of the shore.

I named the picture "Fractal Potpourri" because it is a mixture
of anything and everything, with no definite theme to lock onto.
Due to a slightly busier day than expected, I had to be frugal
on the coloring of the image.  But I gave it a run through a
graphic program to bring out some of the zip that I neglected to
give it when I worked with it.

The parameter file makes the impatient fractalist wait over 10
minutes.  A quick trip on the internet to:

          <alt.binaries.pictures.fractals>

or to:

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

will produce the image in 1/10th the time.

Though the fractal weather today was cloudy, no rain fell.  The
temperature of 76F (24.5C) was good enough for the fractal cats,
Thomas and Tippy, who somehow managed to be on their best
behavior all day.

It was also a good day for the philosophy, but I got it all out
of me in replies to letters on the philofractal list.  I'll try
again tomorrow to amuse, entertain and enlighten with my
one-of-a-kind philosophy.  And hopefully I can keep the
philosophy from changing into armchair science.

And now it's time to accept the fact that all good things must
come to an end.  Today's FOTD has ended, but the moment has been
prepared for, and more FOTD's are waiting in the wings.  The
next will appear in only 24 hours.  Until then, take care, and
don't let that fractal break you up.


Jim Muth
[e-mail]


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

Fractal_Potpourri  { ; time=0:10:11.60 -- SF5 on a p200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.52471990205487250/+1.68018131750088800\
  /3.623226e+008/1/-30 params=-3/-2/1/1/0.1/0 float=y
  maxiter=1500 inside=0 logmap=195 periodicity=10
  colors=000C03C04<2>G03I41J90LF0MJ0MP0LT0J_0Jc0Vg0<2>\
  yu0zx00zM0sV6jcCajITsMMzLOz<3>LOzLPzLPz<2>LPzQ`zVjz`\
  uzdzxVlSMV0ST1<3>oSJuSOzSSzSXzQTzPSyOQvMPuLOsLMvMQyP\
  TzSYzV`zXc<2>ygOvjJsmFor9lu4ix0fz0cz0`z0av0aj0c_0cP3\
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  2>aQxfSzjTzcVzYXu<3>AaM4cD0d40f0<2>0j07l0Dm0Lo0Qp0Vr\
  3Ys4au6dv9ixAlyCfzA`zAXzAQzAMzAGzACzAJzF<3>fzTlzXrz`\
  xzcyzf<3>yzlzzmzzozzpzzrzzsxzlSz3
  }

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) FOTD 27-07-00  (Lotus [4])
Date: 27 Jul 2000 00:02:32 -0400 (EDT)


FOTD -- July 27, 2000 (Rating 4)

Fractal visionaries and enthusiasts:

Today's fractal is a quickie, as will be today's discussion.  A
combination of an unexpected rush job and a flooded fractal
basement left no time at all for hunting fractals.  As a last
resort I made do with the first midget I stumbled upon.

The formula behind today's image is 0.7(1/Z)-1.25(Z)+(1/C),
values I entered entirely at random.  After locating the midget,
I left the computer to attend to other matters, such as bailing
out the basement.  When I returned to the screen and saw the
finished image, I thought, 'how like a lotus'.  I immediately
named the picture "Lotus".

The parameter file takes 18 minutes to run.  The GIF image
downloads much faster from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather today was cloudy with steady sometimes heavy
rain.  As a result of the outside wetness, the cats spent the
afternoon sulking in the living room.  The temperature of 68F
(20C) gave no hint that the average temperature at the end of
July is around 90F (32C).

The philosophy went nowhere, nor is it likely to do much
tomorrow, which will be another hectic day.  But hectic or not,
I'll be here on schedule with another fractal, most likely a
midget, and a few words about the picture.  Until then, take
care, and see you in 24 hours.


Jim Muth
[e-mail]


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

Lotus              { ; time=0:17:54.95 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.03443851345909527/-0.24455925728354620\
  /1.204285e+009/1/52.499 params=-1.25/1/0.7/-1/0/0
  float=y maxiter=1800 inside=0 logmap=333 periodicity=9
  colors=00000T01Y<3>0DS0GQ0JP0MO0QO0TM0XL<3>0gF0jD0mC\
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  XQSYPSYOSYMQ_LQ_JQ_IQ_FQ`<3>9Pa7Pa3Qc4Pa6Pa7O`7O`9M_\
  AM_CLYCLYDJXFJXGIVGIVIGTFFF000FFFJGT<2>QPcSSgVXl<2>a\
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  ljYl<3>iOliMliJliGlgFl<3>g4lg1ld0jg0li3mj6ml9omCooFp\
  pIprLrsOruQsvTsyXuz_vzavzdx<3>zpzzszzvzzyzvzgdzMfzP<\
  2>jzTlzVlzY<2>pzarzcrzf<2>vzjxzlxzmuzfsz_<2>xzFyz9zz\
  1<3>zz0zz0zz1<3>zzDzzGzz0zz7zzJzzTzzdzzr<5>zzazzczza\
  zz`
  }

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) FOTD 28-07-00  (Carousel [5])
Date: 27 Jul 2000 23:44:42 -0400 (EDT)


FOTD -- July 28, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

While cleaning the muddy coating from the floor in the basement,
my thoughts drifted to jollier things.  What could be more jolly
than a ride on a carousel, holding a big puff of pink cotton-
candy as you go round and round?

Nothing could.  But we have no carousel, so we'll have to settle
for a view of a fractal carousel, which is certainly better than
nothing.  Today's fractal picture of an abstract carousel gives
such a view.  It features a midget that exists deep down in the
oversized fractal that results when the formula
2(Z^(-2))+0.3755(Z^2)+(1/C) is iterated.

Actually, I named today's picture "Carousel" because of the
carnival-like effect of all the bits and pieces of color.  And
the outer pink ring is indeed close to the color of cotton candy.

But with all good news comes some bad news.  The bad news about
today's FOTD is that it is one of the slowest in months, taking
well over an hour to render even on a Pentium 200mhz.  The bad
news is relieved however by the fact that the GIF image file has
been posted to:

          <alt.binaries.pictures.fractals>

and to:

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

from where it may be downloaded in a minute or so.

The fractal weather remained cloudy and very damp all day.  The
temperature of 78F (25.5C) was pleasant enough, but the wet
grass kept the cats confined to the porch all afternoon.  And
the wet basement kept me confined down there on mopping duty for
a good part of the afternoon.

The fractosophy is still simmering, but it's not yet finished.
It's hard to wax philosophical when one is cleaning a layer of
sticky mud from the basement floor.  If all goes well, the
philosophy will be ready to be made public this weekend; if not,
who knows when it will appear.

But regardless of when the philosophy appears, I'll appear again
tomorrow at this same time and place.  Until then, take care,
and the number of fractals is more infinite than infinity.


Jim Muth
[e-mail]


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

Carousel           { ; time=1:07:48.42 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-1572.36433456487/+5948.717668412058/1392\
  66.5/1/-157.5 params=2/-2/0.3755/2/0/0 float=y
  maxiter=10000 inside=0 logmap=1405 periodicity=0
  colors=000OmR<3>HscGugEvjCxmByp<2>O1C<7>cBceCggEj<3>\
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  >Lzm<3>_zUWzL<3>SzKSzKQzO
  }

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) FOTD 28-07-00  (Carousel [5])
Date: 27 Jul 2000 23:44:42 -0400 (EDT)


FOTD -- July 28, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

While cleaning the muddy coating from the floor in the basement,
my thoughts drifted to jollier things.  What could be more jolly
than a ride on a carousel, holding a big puff of pink cotton-
candy as you go round and round?

Nothing could.  But we have no carousel, so we'll have to settle
for a view of a fractal carousel, which is certainly better than
nothing.  Today's fractal picture of an abstract carousel gives
such a view.  It features a midget that exists deep down in the
oversized fractal that results when the formula
2(Z^(-2))+0.3755(Z^2)+(1/C) is iterated.

Actually, I named today's picture "Carousel" because of the
carnival-like effect of all the bits and pieces of color.  And
the outer pink ring is indeed close to the color of cotton candy.

But with all good news comes some bad news.  The bad news about
today's FOTD is that it is one of the slowest in months, taking
well over an hour to render even on a Pentium 200mhz.  The bad
news is relieved however by the fact that the GIF image file has
been posted to:

          <alt.binaries.pictures.fractals>

and to:

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

from where it may be downloaded in a minute or so.

The fractal weather remained cloudy and very damp all day.  The
temperature of 78F (25.5C) was pleasant enough, but the wet
grass kept the cats confined to the porch all afternoon.  And
the wet basement kept me confined down there on mopping duty for
a good part of the afternoon.

The fractosophy is still simmering, but it's not yet finished.
It's hard to wax philosophical when one is cleaning a layer of
sticky mud from the basement floor.  If all goes well, the
philosophy will be ready to be made public this weekend; if not,
who knows when it will appear.

But regardless of when the philosophy appears, I'll appear again
tomorrow at this same time and place.  Until then, take care,
and the number of fractals is more infinite than infinity.


Jim Muth
[e-mail]


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

Carousel           { ; time=1:07:48.42 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-1572.36433456487/+5948.717668412058/1392\
  66.5/1/-157.5 params=2/-2/0.3755/2/0/0 float=y
  maxiter=10000 inside=0 logmap=1405 periodicity=0
  colors=000OmR<3>HscGugEvjCxmByp<2>O1C<7>cBceCggEj<3>\
  oIx<2>7cJ<3>AoHBrGCuGCxG<2>FQv<7>L_fL`dMab<3>OeV<3>R\
  ULRRJSWN<2>Vk`<8>hS`jQ`kO`<3>qG`LPh<7>DgWCjVBlT<2>8s\
  O7uN8lV<2>BOr<3>WXU<7>RURQURQUR<3>OTQ<3>WWKYXI_XH<3>\
  HWfCWm7Ws3Wy<3>5iU5lM5oF<4>WeP`dQebSk`UpZWzVUzWZ<3>k\
  VLgUHcUE_UAXU7<2>8514I90VH<3>6ZO7ZP8hRA`T<2>DbX<3>ZR\
  McOKaLHcIErUBXC8V95T62K30T43U56e69V7B<3>XBMYCPYDSZEU\
  ZFw_Gr_GmZIhYKP<2>VQ6VR0WS1<5>_X3`Y3aY3<3>c`4<3>QiIM\
  kLJmOGoRXpHmq7<4>PvM<2>ByV<3>`z`fzalzb<3>_zgXziUzj<2\
  >Lzm<3>_zUWzL<3>SzKSzKQzO
  }

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) FOTD 29-07-00  (Juliana [5])
Date: 29 Jul 2000 00:21:05 -0400 (EDT)


FOTD -- July 29, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

For today's fractal we return to that most basic of all fractal
formulae, Z^2+C.  Normally, this formula would draw some nice
Julia sets, or a nice scene in the Mandelbrot set, but today it
has drawn nothing like the familiar fractals.

Something has gone wrong.  What we see does not resemble a Julia
set, nor does it look like a Mandelbrot image.  It resembles a
Mexican pattern, but that pattern has been distorted in a
strange way.

The secret is that I have drawn a slice in a new direction
through the four-dimensional Julibrot figure.  What appears on
the screen is actually part of the valley at -1.368 of the
M-set.  It appears so strange because it is sliced in an
unfamiliar direction, which is oriented 52-1/2 degrees from the
rectangular direction toward the Julia direction.

This direction is impossible to visualize with our 3-D minds,
but it cuts the Julibrot in some quite unusual slices, a few
more of which I may use as FOTD's in the near future.  The
narrow vertical open area along the picture's Y-axis is actually
the narrow space between the two branches of the valley located
at -1.368 on the X-axis of the M-set.

I named the picture "Juliana" because its orientation is closest
to the Julia direction.  The draw time of 10-1/2 minutes is my
best estimate, since the image was rendered on three different
machines running at three different speeds.  But regardless of
the draw time, there is no uncertainty about the minute or so it
will take to download the GIF image from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather today was variably cloudy and very humid,
with a temperature of 85F (29.5C) that drew the cats into the
yard, where they chattered at the house sparrows.  The day ended
with a torrential thunder-storm, which drove the cats into
hiding and re-flooded the fractal basement.

Due to the very busy day, the philosophy went nowhere.  Tomorrow
I'll once again have to dry out the basement, but while doing
so, I could think of some incredible philosophy.  If I do, it
will appear in tomorrow's FOTD.  Check back in 24 hours to see
how the day will evolve.

Until next time, take care, and fractals forever.


Jim Muth
[e-mail]


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

Juliana            { ; time=0:10:31.91 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=multirot.frm
  formulaname=multirot-XY-ZW function=flip/ident
  passes=1 center-mag=-0.17524/2.35922e-016/58.12843/0\
  .3623/90 params=52.5/90/0/0/-1.3681038846/0 float=y
  maxiter=120000 inside=0 logmap=25 periodicity=10
  colors=000bVzaUzaUzaSz<3>aRzaQzaQz_Qz_Oz<5>_Mz_Mz_Kz\
  <3>ZJzZIzZIz<2>ZHzZHzYIz<4>YJzYKzYKzYKzYMzYMyXMyXMw<\
  2>XNuXOuXOsXOsXQrXQrXQqXKnXQqXVsXZvXcyXizXmzXrzXwzXz\
  zUvzSrzRmzOizNczM_zIOzKXzMbzNjzOqyQywSzyRzvQzsOzrNzo\
  MznKzkJzjIygHwfFwcEvbDu_BuZAsX8rU7qS6qQ4oO3nM2nK0mI0\
  kH0kE0jD0iA0s00i80ZI<2>B4fA8b8BZ7EX6IS6KO4NM3RI2UE0a\
  D2XB8RAFN8MI7RD6Y84c33j02o00u44yE7zOAzYDzVFzSIzRK<2>\
  zKSzIVzHYzE_yBbyAew7gz7mw6ju6is6gq4fo4em4cj3bi3af3_e\
  3Yb2X_2VZ2UX0S<2>Q0OO0NM0KK0JI0IF0HE0FB0EA0D70B60AA3\
  7EA6HF4KM3NR2RY0Ub0Yi0_n0cu0cz0fz0iv0kr0mm2oi4re7uaA\
  vXDySFzOIzKKyNOvORsRVoSYmU_jXcfYfc_jaamYboVesSfvOizM\
  jzMqzJkzIgzHczE_wDXuBSsAOq7Kn6Hk4Di38g46m44qB2rI0s<2\
  >a0wg0yo0zm0yj0vi0sf0qe2nb3ka6iZ7fYAcVBaUE_RFYOIVNJS\
  KMQJNNHQKFRIDUFBVD8YA8a4<2>4UE0700400306DNMMj
  }

frm:multirot-XY-ZW {; draws 6 planes and many 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))+p2,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3:
z=sqr(z)+c,
|z| <= 36  }

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


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

From: "Fernando Bresslau" <[e-mail]>
Subject: Re: (fractint) FOTD 28-07-00  (Carousel [5])
Date: 28 Jul 2000 22:35:57 -0300

Hi Jim!
One week without internet access and you surprise me with very nice images.
I just can┤t agree with you ratings, Ziper, Potpuri and Lotus are all above
average images, IMHO.

Fernando Bresslau
http://www.fractal.art.br


----- Original Message -----
Cc: <[e-mail]>
Sent: Friday, July 28, 2000 12:44 AM


>
> FOTD -- July 28, 2000 (Rating 5)
>
> Fractal visionaries and enthusiasts:
>
> While cleaning the muddy coating from the floor in the basement,
> my thoughts drifted to jollier things.  What could be more jolly
> than a ride on a carousel, holding a big puff of pink cotton-
> candy as you go round and round?
>
> Nothing could.  But we have no carousel, so we'll have to settle
> for a view of a fractal carousel, which is certainly better than
> nothing.  Today's fractal picture of an abstract carousel gives
> such a view.  It features a midget that exists deep down in the
> oversized fractal that results when the formula
> 2(Z^(-2))+0.3755(Z^2)+(1/C) is iterated.
>
> Actually, I named today's picture "Carousel" because of the
> carnival-like effect of all the bits and pieces of color.  And
> the outer pink ring is indeed close to the color of cotton candy.
>
> But with all good news comes some bad news.  The bad news about
> today's FOTD is that it is one of the slowest in months, taking
> well over an hour to render even on a Pentium 200mhz.  The bad
> news is relieved however by the fact that the GIF image file has
> been posted to:
>
>           <alt.binaries.pictures.fractals>
>
> and to:
>
>           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
>
> from where it may be downloaded in a minute or so.
>
> The fractal weather remained cloudy and very damp all day.  The
> temperature of 78F (25.5C) was pleasant enough, but the wet
> grass kept the cats confined to the porch all afternoon.  And
> the wet basement kept me confined down there on mopping duty for
> a good part of the afternoon.
>
> The fractosophy is still simmering, but it's not yet finished.
> It's hard to wax philosophical when one is cleaning a layer of
> sticky mud from the basement floor.  If all goes well, the
> philosophy will be ready to be made public this weekend; if not,
> who knows when it will appear.
>
> But regardless of when the philosophy appears, I'll appear again
> tomorrow at this same time and place.  Until then, take care,
> and the number of fractals is more infinite than infinity.
>
>
> Jim Muth
> [e-mail]
>
>
> START 20.0 PAR-FORMULA FILE================================
>
> Carousel           { ; time=1:07:48.42 -- SF5 on a P200
>                      ;  Version 2000 Patchlevel 9
>   reset=2000 type=formula formulafile=critical.frm
>   formulaname=MandelbrotMix4 function=recip passes=1
>   center-mag=-1572.36433456487/+5948.717668412058/1392\
>   66.5/1/-157.5 params=2/-2/0.3755/2/0/0 float=y
>   maxiter=10000 inside=0 logmap=1405 periodicity=0
>   colors=000OmR<3>HscGugEvjCxmByp<2>O1C<7>cBceCggEj<3>\
>   oIx<2>7cJ<3>AoHBrGCuGCxG<2>FQv<7>L_fL`dMab<3>OeV<3>R\
>   ULRRJSWN<2>Vk`<8>hS`jQ`kO`<3>qG`LPh<7>DgWCjVBlT<2>8s\
>   O7uN8lV<2>BOr<3>WXU<7>RURQURQUR<3>OTQ<3>WWKYXI_XH<3>\
>   HWfCWm7Ws3Wy<3>5iU5lM5oF<4>WeP`dQebSk`UpZWzVUzWZ<3>k\
>   VLgUHcUE_UAXU7<2>8514I90VH<3>6ZO7ZP8hRA`T<2>DbX<3>ZR\
>   McOKaLHcIErUBXC8V95T62K30T43U56e69V7B<3>XBMYCPYDSZEU\
>   ZFw_Gr_GmZIhYKP<2>VQ6VR0WS1<5>_X3`Y3aY3<3>c`4<3>QiIM\
>   kLJmOGoRXpHmq7<4>PvM<2>ByV<3>`z`fzalzb<3>_zgXziUzj<2\
>   >Lzm<3>_zUWzL<3>SzKSzKQzO
>   }
>
> 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]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"


__________________________________________________
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Talk to your friends online with Yahoo! Messenger.
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-------------------------------------------------------------------------------

From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD 30-07-00  (An All-New Midget [6])
Date: 29 Jul 2000 22:21:08 -0400 (EDT)


FOTD -- July 30, 2000 (Rating 6)

Fractal visionaries and enthusiasts:

Today's FOTD features an all new midget.  Yes, this particular
midget, though it has potentially existed for longer than all
eternity, has never before been seen by the eyes of Man, or the
eyes of Cats.  I present it here today in its premier appearance
-- the midget that against all odds *was* discovered.

I named the picture "An All-New Midget" simply because that's
what it is.  I rated it a 6 because at the moment I consider it
to be slightly above the FOTD average.  Tomorrow I might feel
different, but today's opinion is the one that counts.

What are the chances that this particular midget would ever see
the light of day?  One in a million, one in a googol, one in a
googolplex^googolplex?  Actually, since the number of
undiscovered midgets in the infinity of undrawn fractals is a
number beyond infinity, the chances of this midget ever being
seen are zero -- exactly as great as the chances of my ever
having been born.

Yet despite these overwhelming odds, the midget was discovered
and I was born.  And the midget actually made it onto the honor
roll of midgets worthy of being chosen Fractal of the Day.

The fractal formula that was iterated to uncover this midget is
Z^(-7.071)+Z(-0.7071)+(1/C), an obviously whimsical expression
that I entered totally at random.  The parameter file takes 1/4
hour to render even on a fast Pentium, so to avoid impatience, a
quick trip to the Usenet group:

          <alt.binaries.pictures.fractals>

or to Paul Lee's web site at:

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

is strongly recommended.

The fractal weather was much improved today, which turned out
partly cloudy, with a temperature of 83F (28C).  The lack of the
daily deluge met with the approval of the fractal cats.

Curiously enough, last year at this time the local farmers were
praying for rain.  Their prayers have been generously answered,
but now they're praying for the rain to stop.  I guess they
should have been more specific about the amount of rain they
asked for.

My philosophy is still coming, as it always is, but it's not yet
here.  It may arrive tomorrow, it may not.  But an FOTD most
certainly will arrive tomorrow, so check back then to see the
eighth wonder of the world.

Until then, take care, and befriend a lost Mandelbrot midget.


Jim Muth
[e-mail]


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

An_All-New_Midget  { ; time=0:14:19.74 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.41054321687411460/+0.58664493306153620\
  /3457899/1/52.499 params=1/-7.071/1/-0.7071/0/0
  float=y maxiter=1800 inside=0 logmap=163 periodicity=9
  colors=000TO_<7>_Vf`WgaXh<3>e`lZXn<3>7Hm1Em9Gm<2>XKl\
  cLicMgcMg<3>cOacO`eO_eOYePX<6>QROORMMRL<2>FSHDSG9RE<\
  24>`cIadIbdI<3>ffI<3>iId<23>K6KJ5JI5I<3>E3EA2F<8>UBC\
  WCCZDC<3>fGB<21>UZ7T_7S`6<2>Rc6Qd6Oc7<8>`j6ak6bl6<3>\
  ho6jp6lp6<3>ts6vt6xu6zv6zv6<3>ntIktKhtN<2>_sWXsYUqWR\
  oV<3>`hQcfPeeO<3>oZJ<7>fM_eKadJc<3>`Dk<3>uDo<5>rNuqP\
  vqQwqSxpUy<3>n_znazmbzmdzmez<2>afzYfzVez<2>UgzMgz<2>\
  Thz
  }




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


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Post Message:   [e-mail]
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-------------------------------------------------------------------------------

From: DeBow Freed II PhD <[e-mail]>
Subject: ATTN Jim Muth:Re: (fractint) FOTD 28-07-00  (Carousel [5])
Date: 30 Jul 2000 13:26:25 -0500

ME too

Fernando Bresslau wrote:

> Hi Jim!
> One week without internet access and you surprise me with very nice images.
> I just can┤t agree with you ratings, Ziper, Potpuri and Lotus are all above
> average images, IMHO.
>
> Fernando Bresslau
> http://www.fractal.art.br
>
> ----- Original Message -----
> From: "Jim Muth" <[e-mail]>
> To: <[e-mail]>
> Cc: <[e-mail]>
> Sent: Friday, July 28, 2000 12:44 AM
> Subject: (fractint) FOTD 28-07-00 (Carousel [5])
>
> >
> > FOTD -- July 28, 2000 (Rating 5)
> >
> > Fractal visionaries and enthusiasts:
> >
> > While cleaning the muddy coating from the floor in the basement,
> > my thoughts drifted to jollier things.  What could be more jolly
> > than a ride on a carousel, holding a big puff of pink cotton-
> > candy as you go round and round?
> >
> > Nothing could.  But we have no carousel, so we'll have to settle
> > for a view of a fractal carousel, which is certainly better than
> > nothing.  Today's fractal picture of an abstract carousel gives
> > such a view.  It features a midget that exists deep down in the
> > oversized fractal that results when the formula
> > 2(Z^(-2))+0.3755(Z^2)+(1/C) is iterated.
> >
> > Actually, I named today's picture "Carousel" because of the
> > carnival-like effect of all the bits and pieces of color.  And
> > the outer pink ring is indeed close to the color of cotton candy.
> >
> > But with all good news comes some bad news.  The bad news about
> > today's FOTD is that it is one of the slowest in months, taking
> > well over an hour to render even on a Pentium 200mhz.  The bad
> > news is relieved however by the fact that the GIF image file has
> > been posted to:
> >
> >           <alt.binaries.pictures.fractals>
> >
> > and to:
> >
> >           <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
> >
> > from where it may be downloaded in a minute or so.
> >
> > The fractal weather remained cloudy and very damp all day.  The
> > temperature of 78F (25.5C) was pleasant enough, but the wet
> > grass kept the cats confined to the porch all afternoon.  And
> > the wet basement kept me confined down there on mopping duty for
> > a good part of the afternoon.
> >
> > The fractosophy is still simmering, but it's not yet finished.
> > It's hard to wax philosophical when one is cleaning a layer of
> > sticky mud from the basement floor.  If all goes well, the
> > philosophy will be ready to be made public this weekend; if not,
> > who knows when it will appear.
> >
> > But regardless of when the philosophy appears, I'll appear again
> > tomorrow at this same time and place.  Until then, take care,
> > and the number of fractals is more infinite than infinity.
> >
> >
> > Jim Muth
> > [e-mail]
> >
> >
> > START 20.0 PAR-FORMULA FILE================================
> >
> > Carousel           { ; time=1:07:48.42 -- SF5 on a P200
> >                      ;  Version 2000 Patchlevel 9
> >   reset=2000 type=formula formulafile=critical.frm
> >   formulaname=MandelbrotMix4 function=recip passes=1
> >   center-mag=-1572.36433456487/+5948.717668412058/1392\
> >   66.5/1/-157.5 params=2/-2/0.3755/2/0/0 float=y
> >   maxiter=10000 inside=0 logmap=1405 periodicity=0
> >   colors=000OmR<3>HscGugEvjCxmByp<2>O1C<7>cBceCggEj<3>\
> >   oIx<2>7cJ<3>AoHBrGCuGCxG<2>FQv<7>L_fL`dMab<3>OeV<3>R\
> >   ULRRJSWN<2>Vk`<8>hS`jQ`kO`<3>qG`LPh<7>DgWCjVBlT<2>8s\
> >   O7uN8lV<2>BOr<3>WXU<7>RURQURQUR<3>OTQ<3>WWKYXI_XH<3>\
> >   HWfCWm7Ws3Wy<3>5iU5lM5oF<4>WeP`dQebSk`UpZWzVUzWZ<3>k\
> >   VLgUHcUE_UAXU7<2>8514I90VH<3>6ZO7ZP8hRA`T<2>DbX<3>ZR\
> >   McOKaLHcIErUBXC8V95T62K30T43U56e69V7B<3>XBMYCPYDSZEU\
> >   ZFw_Gr_GmZIhYKP<2>VQ6VR0WS1<5>_X3`Y3aY3<3>c`4<3>QiIM\
> >   kLJmOGoRXpHmq7<4>PvM<2>ByV<3>`z`fzalzb<3>_zgXziUzj<2\
> >   >Lzm<3>_zUWzL<3>SzKSzKQzO
> >   }
> >
> > 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) FOTD 31-07-00  (Undersea World [5])
Date: 30 Jul 2000 23:44:04 -0400 (EDT)


FOTD -- July 31, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

Today's discussion will be short because even though it is a
Sunday, I was busy most of the day finishing a job which must
be at the printer's tomorrow morning.

But despite the rush, I found time to find a fractal.  Don't ask
how I find the time to locate all these fractals -- it's as much
a mystery to me as it is to anyone.  Today's FOTD resembles a
midget under a shallow layer of water.  I named it "Undersea
World".

The formula that I used to draw the image is the MandelbrotMix4,
which calculated the expression Z^(-0.95)+Z^(-2.95)+(1/C).  I
have decided to give this overworked formula a rest for the
month of August, and concentrate on things such as new and
unfamiliar slices through the four-dimensional Julibrot figure,
which is the sum of all Julia sets and all warped Mandelbrot
sets.

The parent fractal is a multi-lobed Mandeloid consisting of the
typical fragmented debris that results when negative exponents
of Z are calculated.  But toward the center top lies a strangely
different area.  It is in this area where I found my midget.
The image rates an average 5 on my scale, since I can't imagine
something found in such haste having above-average value.

The parameter file is another slow one, so the trip to:

          <alt.binaries.pictures.fractals>

or to:

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

is strongly recommended.

The fractal weather today was partly cloudy and oppressively
humid with a heavy thunder-shower in the afternoon that caused
local flash-flooding.  Luckily, the rain fell just short of
again flooding the fractal basement.  The temperature of 84F
(29C) was ideal for cats, but cats don't like wet grass, so the
fractal cats spent the day indoors.

Needless to say, with all the work and the rain that threatened
to flood the basement, I found no time to philosophize today,
and probably will find no time again tomorrow.  But sooner or
later the philosophy will come, and when I philosophize, I
philosophize with no holds barred.

So until tomorrow, take care, and be at peace.


Jim Muth
[e-mail]


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

Undersea_World     { ; time=0:30:39.40 -- SF5 on a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-0.05943680542175839/+1.33301484757948400\
  /2.015923e+008/1/-125 params=1/-0.95/1/-2.95/0/0
  float=y maxiter=3000 inside=0 logmap=656 periodicity=9
  colors=000oidpmfppgdqZUqQWYcJqHKUwmwr<3>RStLKtGCt`Gn\
  uKi<7>bRh`ShZTh<3>QWhXeVbnH<3>RWTORWMNZ<3>A4jwwm80lZ\
  SVyrD<2>_Za<8>WZXWZWVZW<3>UZUJTL9ND<3>HDTJAXL8`N5dO3\
  h<3>kFfyGi<3>XLYQMVDM`JNTOOMUPE`R1<3>TQMSQSQQX<2>LQk\
  <3>0Hd<3>bUFlX9u_3SDCQYBMsA<5>WlGYjHZiI<3>edN<6>afB`\
  fA`f8<3>Zf2<3>jPMmKRpGWsB`v7e<3>lDljFngGpeIrcJs<9>`Q\
  l`Rk`Sj<3>_UhUYdO`aIok<2>IH9abWuwqsGF<2>C7M<3>PPFSUD\
  VYC<3>fo5mv0<3>`jGYgKUdO<2>LW_PfvITc8J6<2>G7p<7>PSXQ\
  VURXS<2>UdKVgIVlB<3>WcSX`XXZ`XXdZXg<8>LHpKGqIEr<2>E9\
  uC7vA5y<3>D7sD7rG6p<2>P6j
  }

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) FOTD 01-08-00  (Seahorse Valley [5])
Date: 31 Jul 2000 22:23:41 -0400 (EDT)


FOTD -- August 01, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

Every fractalist is familiar with the classic Mandelbrot set.
The most popular area of the M-set is the valley at -0.75 on the
X-axis, otherwise known as Seahorse Valley.  This valley is
filled with fractal scenery of the most interesting kind, making
it the most rewarding area to explore, especially for the
fractal newcomer.

Seahorse valley also has a Julia aspect, which appears as a
string of roughly circular bays, the shorelines infinitely
divided into identical smaller bays.  because of its self-
similarity, this Seahorse Valley Julia set is less interesting
than the Mandelbrot aspect of the valley.

The Seahorse Valley Julia set is merely the completely
perpendicular plane of the four-dimensional Julibrot that
intersects the M-set at the point -0.75 on the X-axis.  But
since Seahorse Valley is actually a four-dimensional object, it
can be sliced in infinitely many other directions.  Today's FOTD
is a slice through Seahorse Valley in one of these new
directions.

The orientation of today's image is but 0.1 degree removed from
the Julia direction, but look at the difference that 1/10 degree
has made.  The familiar Seahorse Valley Julia figure is there,
rotated to a 35-degree angle, but it is filled with a most
incredible background consisting of parallel bands of color.
This background is actually a grossly enlarged side view of the
wall of Seahorse Valley.  The diagonal pink strip marks the line
where the north and south branches of the valley almost meet.

The maxiter of the image is a whopping 2,000,000, and every
iteration is used, since the part of the valley that we're
viewing from the side lies extremely close to the X-axis of the
M-set, where the iterations are well over 1,000,000.

I named the picture "Seahorse Valley" because even though it's
not immediately apparent, it's the Seahorse Valley part of the
Julibrot that we're viewing.  Since the interest of this image
is more mathematical than artistic, I can rate it only an
average 5.  With such a high maxiter, the parameter file takes
well over an hour to render even on a fast Pentium, but being
merciful, I have posted the GIF image to:

          <alt.binaries.pictures.fractals>

The image is also available on Paul's web site at:

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

The formula that drew the image and will draw many more FOTD's
this month of August was posted to the Fractint list last July
by John Goering.  It is the only formula that draws all possible
oblique angles through the 4-D Julibrot.  Unfortunately the
formula is limited by its inability to enter variable starting
points of Z, but this is a limit of the Fractint program, a
limit which could be easily overcome with 2 more variable
parameter entries for type=formula.

The fractal weather today was mostly cloudy and very muggy, with
only a little sun.  Later in the afternoon a light thunder-
shower passed over, but by that time the fractal cats had
already taken their daily romp in the grass.

In the sultry conditions the philosophy languished, but tomorrow
is but 24 hours off.  Check then for a 25 percent chance of
finding philosophy.  Until then, take care, and don't work
yourself into a fractal sweat.


Jim Muth
[e-mail]


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

Seahorse_Valley    { ; time=1:03:21.27 -- SF5 0n a P200
                     ;  Version 2000 Patchlevel 9
  reset=2000 type=formula formulafile=julibrot.frm
  formulaname=SliceJB passes=1
  center-mag=-0.00309701/-0.00597368/0.9861933/1/-35
  params=0.4995/0.5/0.499/0.5/-0.75/0 float=y
  maxiter=2000000 inside=0 logmap=yes periodicity=0
  colors=000KSh<3>KbmKdnKgpKjqKlrKnsKovKptKorKopKnn<12\
  >bdRccPebNfbLhaJi`HkZFmXEoVErTKuRQ<4>pHVoFWmDX<18>SB\
  oRBpQBq<3>MBt<8>IV_IXYIZW<3>GfN<2>G`J6ZU8XSAWR<10>Ti\
  DUjCWkB<2>`o7bp6bp6cq5<3>OY4KT4TP4VT3WT3VU3XV3ZV3YW3\
  ZW3_W3`W1_X3<2>a_7aa9adAafC<3>bkIblJcmLcnMcpO<2>dtSd\
  vUcxWdwV<7>k_NlXMmULnRK<2>oII<4>eNScOU<4>UTrSSwTQrTN\
  m<2>UGZUDUUBRU9R<5>_CK`DJaDI<3>eFEfKJ<3>jK_kKclKd<3>\
  pKhqKirKi<3>vMmwNnwNo<5>wQuwRvwRwwSxwSy<33>whz
  }

frm:SliceJB {; by John R. H. Goering, July 1999
  pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1),
  b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), ca=cos(a),
  cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d),
  sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
  q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg,
  s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s):
  z=z*z+c
  |z|<=9
  }

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


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