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fractint-digest       Tuesday, October 16 2001       Volume 01 : Number 604




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

Date: Mon, 8 Oct 2001 20:08:25 +0100
From: John Lewis <[e-mail]>
Subject: Re: (fractint) FOTD  08-10-01  (A New Seahorse Angle [4])

On Mon, 8 Oct 2001 10:49:17 EDT, [e-mail] wrote:
>
>FOTD -- October 08, 2001 (Rating 4)


I thought this appealing - I would have raised its rating to 7 at=

least.

John
- -- John Lewis, [e-mail] on 10/08/2001



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

Date: Tue, 9 Oct 2001 10:04:08 EDT
From: [e-mail]
Subject: (fractint) FOTD  09-10-01  (A Fractal in Paradise [9])

FOTD -- October 09, 2001 (Rating 9)

Fractal visionaries and enthusiasts:

Today's fractal image is one of those rare ones that rates a 9.
But once again I have only a few moments to write about it.  The
image results from a critical combination of Z, 1/Z and 1/C.

I named the picture "A Fractal in Paradise", mostly for
whimsical reasons.  The rating of 9 is an honest appraisal of
the image, which IMO is exceptional.

An added bonus is the relatively brief 12-minute render time
from the parameter file, though a download of the GIF image from:

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

or:

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

will be even faster.

The fractal weather today here at Fractal Central was sunny but
brisk, with a temperature of 57F 14C.  These conditions pleased
the cats, and the cats showed their contentment by sleeping
peacefully.  Thomas, the oversized yellow-orange one,
interrupted his rest long enough to come visit me for a
scratching under the chin which he repaid by giving me a brief
purr.  Tippy, the tabby, having much sleep to catch up on, had
no time to get scratched or purr, and slept through the entire
afternoon.

Even as I write these words, I see work piled on the table
across the room, waiting to be done.  I'll start by scanning the
envelope of photographs.  Then, when the day's tasks are
completed, I'll boot the fractal computer and return to the
world of fractals.  Until I reappear in 24 hours, take care, and
never surrender hope.


Jim Muth
[e-mail]


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

AFractalInParadise { ; time=0:12:23.20--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
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  }

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

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

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

Date: Wed, 10 Oct 2001 09:34:37 EDT
From: [e-mail]
Subject: (fractint) FOTD  10-10-01  (Criss-cross Midget [7])

FOTD -- October 10, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Today's fractal continues the same approach as yesterday's --
mixing portions of (Z) and (1/Z).  In today's case however,
there is a difference.  Instead of exactly Z and 1/Z, we
subtract some Z^(0.97) from some Z^(-1.15) before adding (1/C).

The parent fractal consists of a Mandeloid so distorted that its
parts are virtually unrecognizable.  It also has a smooth-edged
eye-shaped open area extending to the east.  Part of the Mandel
figure is obscured behind a circular disk at its origin, but a
rudimentary valley barely escapes being obscured.  Today's scene
is located in a cut-off thread of chaos that lies in the
northwest branch of this valley.

A fitting name for today's image eluded me.  There are many
themes that could be emphasized.  After studying the scene for
several minutes, I noticed the eight-armed cross, which could be
taken as two four-armed crosses, and named the picture
"Criss-cross Midget".  It's another above average image, but the
rating of 7 falls short of yesterday's superior 9.

Unfortunately, today's parameter file takes 44 minutes to render
- -- at least on my tired 200mhz Pentium machine.  A better way of
seeing the scene is to give Paul and Scott a chance to render it
from the parameter file and download the GIF image from their
web sites at:

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

and at:

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

The fractal weather today here at Fractal Central proved ideal.
After a frosty start, the warm sun boosted the temperature to
63F 17C, and brought out the fractal cats for a romp in the
yard.  They somehow managed to keep out of trouble for an entire
day.

As for me, I'm about ready to start another day's work.  With
any luck, I'll finish early and have time to find another
9-rated fractal.  If not a 9, a 5 or 6 image will do.  Until
next time, take care, and search for truth wherever it may be
found.


Jim Muth
[e-mail]


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

Criss-cross_Midget { ; time=0:44:43.00--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
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  }

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

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

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

Date: Thu, 11 Oct 2001 01:31:48 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Fractalus down

I was wondering why the PhiloFractal posting of Jim's FOTD never showed
up this morning so I could create the web page.  Finally found out the
reason late in the evening from a posting to the Yahoo eGroup:


    Janet Preslar posted to Fractal-World:
    >
    > Damien has asked me to post that the Fractalus server has
    > had a "catastrophic hardware failure" and will be offline
    > until sometime Friday.  This affects not only the Fractalus
    > website but all the mailing lists hosted there.  He'll be
    > posting here when everything is up and running again.
    >


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

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

Date: Thu, 11 Oct 2001 11:38:32 EDT
From: [e-mail]
Subject: (fractint) FOTD  11-10-01  (Fractal Thursday [6])

FOTD -- October 11, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

With the philofractal list down for a couple days, I'm taking
advantage of the philosophical time-out to catch up on some
humdrum everyday work that has been accumulating the past week
or so.  When the list comes back online, I'll pontificate with
the philosophical pondering I've been doing.

In the meantime the fractals keep coming.  Today's image
features a return to the Mandelbrot set for a view of a midget
never before seen.  (Almost all deep midgets in the M-set have
never been seen.)  This time we journey out the negative stem to
the fourth valley, the one I call Triple-Scepter Valley.

Today's midget lies in a spiral of this fourth valley, a fact
that is verified by the abundance of spirals surrounding the
midget.  I had intended on trying the <tdis> outside option on
this image, but when this option is used, the rendering speed
slows down for some reason by a factor of over 20.  The normal
equal-iteration-bands method of coloring produces an image every
bit as worthwhile, which rates an above-average 6.

With no immediate ideas for a better name, I named the image
"Fractal Thursday".  It's a fair description of the time in
which the image was found.  The parameter file runs in 3
minutes.  Paul and Scott will have the image posted to their web
sites within the hour.  Those web sites can be found at:

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

and at:

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

The fractal weather today was sunny and warm.  The temperature
of 75F 24C kept the cats out in the yard most all day.  When the
weather is good and the cats are outside, they are happy cats.
Therefore the cats were happy all day.

And I'll be a bit happier when I get a bit of this backed-up
work finished.  So until next time, which will be tomorrow, take
care, and the rest will be easy.


Jim Muth
[e-mail]


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

Fractal_Thursday   { ; time=0:03:23.01--SF5 on a P200
  reset=2002 type=mandel passes=1
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  }

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

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

Date: Thu, 11 Oct 2001 13:47:36 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) FOTD  11-10-01  (Fractal Thursday [6])

[e-mail] wrote:
>
> When the list comes back online, I'll pontificate
> with the philosophical pondering I've been doing.
>

I noticed that you sent a single copy of the FOTD yesterday, as opposed
to a CC'ed version to the Philofractal list.  Which means that
Wednesday's philosophy may be lost if all recently sent email on
Fractalus is gone.

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

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

Date: Thu, 11 Oct 2001 15:06:28 EDT
From: [e-mail]
Subject: (fractint) Re: FOTD 11-10-01

Paul Lee wrote:

>I noticed that you sent a single copy of the FOTD
>yesterday, as opposed to a CC'ed version to the
>Philofractal list.  Which means that Wednesday's
>philosophy may be lost if all recently sent email
>on Fractalus is gone.

No problem.  I've got the missing philosophy on hold
and I'll post it when the philofractal list comes
back online.

Jim M.

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

Date: Thu, 11 Oct 2001 22:42:15 EDT
From: [e-mail]
Subject: (fractint) FOTD  12-10-01  (Fractal Flinders [6])

FOTD -- October 12, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Sometimes, perfectly good fractals turn into a mass of bits and
pieces -- flinders that is -- and today's image is a perfect
example of this fractal disintegration.

I started with a perfectly good fractal -- the figure created by
the formula Z^1.5874+C (the 1-1/2 root of 2) -- and investigated
the area 6 levels up the logarithmic spiral.  I chose a
perfectly ordinary appearing valley to delve into, but I had not
gone far when the whole fractal world disintegrated around me.

Such disintegration usually signals a dead end of the search.
Not in today's case however.  This left-over chaos is filled
with debris, which in itself forms recognizable repeating
patterns.  And as an added attraction, the chaos is overflowing
with deficient midgets of all sizes and shapes.

The overall effect of the image is one of fractal flinders
floating in a vast space near a relatively unimpressive midget.
The pieces almost appear to be drawn down into the midget as
though it were a black hole.  I first thought of naming the
image "Black Hole", but decided on "Fractal Flinders", a title
with a more attractive sound.

The 16-minute render time will leave some impatient.  The
1-minute download of the finished GIF image from the W.W.Web at:

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

or at:

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

will be far more satisfying for these impatient ones.

The fractal weather today featured blue skies, puffy cumulus
clouds, gentle breezes, and a temperature of 79F 26C.  All in
all it was a perfect Autumn day, which left the fractal cats
purring with contentment.

No philosophy will be lost while the philofractal list is down.
I'm still writing my thoughts, and saving them in a separate
file.  The accumulated wisdom will appear as soon as the
philofractal list is once again up and running.

That's it for today, fractal fans.  It's time to shut down the
fractal shoppe and call it an evening.  But the next FOTD will
appear in two wags of a . . . a pussy cat's tail.  Until then,
take care, and I have not yet begun to explore.


Jim Muth
[e-mail]


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

Fractal_Flinders   { ; time=0:16:31.13--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=+0.51849225088358700/-0.546491304449809\
  /24561.24 params=1.5874/0/6/0 float=y
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  }

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

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

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

Date: Sat, 13 Oct 2001 10:13:40 EDT
From: [e-mail]
Subject: (fractint) FOTD  13-10-01  (V For Victory [5])

FOTD -- October 13, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

For today's fractal we take a trip to the East Valley area of
the Mandelbrot set to check a midget lying deep on one of the
arms of a 17-armed star of a tiny bud.  While finding the
midget, I had the Fractal Central radio tuned to a talk program,
and the talk was all about war.  Then, when the very fast image
was finished, I noticed that some of the elements vaguely
resemble the letter 'V'.  Feeling a touch of patriotism, I named
the image "V For Victory", a slogan that was popular during WWII.

The magnitude of the image is right in the range where arbitrary
precision math cuts in.  In today's image, the slowdown is so
large and the improvement so small that I included the
mathtolerance command in the parameter file to force the program
to use the high-speed standard math routine.

Unsure of how to rate the image, and following the principle of
'when in doubt, make it average', I settled on a rating of a
generic 5, though a 6 would also be reasonably close.  I always
tend to under-rate images in the classic M-set.  They seem to
come just a bit too easily.

The parameter file runs in slightly over 1 minute using standard
math, and in slightly under 2 hours using the slightly more
accurate arbitrary precision math.  Those who wish to see the
most accurate rendering should remove the mathtolerance command
from the parameter file and prepare for a wait.

Those who can't decide which math to use should visit the
W.W.Web at:

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

or at:

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

and pick up the image from there.

The fractal weather today (Oct 12) was ideal, with blue skies,
puffy clouds, and a cat-pleasing temperature of 77F 25C.  More
of the same is expected this afternoon.

When I last checked, the philofractal list was still down, so
the philosophy will be held for at least one more day.

Until next time, take care, and be up and running.


Jim Muth
[e-mail]


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

V_For_Victory      { ; time=0:01:10.46--SF5 on a P200
  reset=2002 type=mandel passes=b mathtolerance=/1
  center-mag=+0.28174961344731050/-0.009596893105776\
  96/1.528115e+013/1/-117.488176390760771/-0.0292145\
  165871739859 params=0/0 float=y maxiter=18000
  bailout=6 inside=255 logmap=1637
  colors=000nl0rk0of0lc0i`1fY1cT3`Q4YN4VK6SG7PD7MA9J\
  7AG3AD0CA0D70D0VX0zn0zg0zc0z_3zV7zQAzM9wP9tS9pT7lX\
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  GKQGPPETMEfKEnJEvGDzDDvADg7Dg4Dg1Dg0Dg0Dg0Dg0Hn7Kr\
  ENwKQzSTz_Xzd_zcYzcXzcVzcTwaSraQoaPpaNraMt`Kv`Jw`H\
  x`Gz`EzdDzgDzlCzoCziEzdGz`HzXKzQMzMNzHQzDSz7Sz3Sz0\
  Sz0SzGSzKSzQSzXSz`SzfKzk9zp0zv0zt0zr0zp0zo0zk1zg4z\
  d9zaCzYEzVJzSMzPPzMTzHXzE_zCcz9fz6izKGzY0zzKzxNzxP\
  zxQzxTzxVzxXzx_zYpzaozzzz
  }

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

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Date: Sun, 14 Oct 2001 10:16:57 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  14-10-01  (Fracler [8])

FOTD -- October 14, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

When today's parameters are entered into the MandelbrotMix4
formula, the resulting fractal looks like a snail with its head
out of its shell, facing east.  Today's image is located in a
narrow cleft of disconnected chaos near the edge of the back of
the snail's neck.

Actually, today's midget lies in the northern suburbs of a
larger midget in the area.  The larger midget, which is a less
spectacular version of the midget in today's image, can be seen
by resetting the log palette to zero and backing out three zooms.

The generating formula subtracts 1.4 parts of Z^(-1.17) from 1.4
parts of Z^(0.87), then adds (1/C) to create the parent fractal
snail.  The image itself reminds me of an alien flower, thus the
name "Fractal Flower", which I shortened to "Fracler".  Since I
think the image is quite good, I rated it at an exceptional 8.
Others may have a different opinion.

On my worn-out but still eager Pentium 200mhz machine, the
parameter file renders in just under 13 minutes.  Much time can
be saved by picking up the GIF image from the W.W.Web at:

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

or at:

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

With blue skies, puffy white cumulus clouds, and a temperature
of 79F 26C, the fractal weather today here at Fractal Central
was once again perfect.  And the cats must have agreed, because
they spent most of the day in the outdoor world.  To add to the
excitement, Tippy, the active one, actually caught a mouse and
brought it to the door to show me.  The mouse appeared to be
unharmed, so after praising Tippy, I took the mouse and returned
it to the yard.  As it scampered away, I warned it to be more
alert for predator cats the next time.

The philosophy is accumulating while the philofractal list,
having suffered a 'catastrophic' failure, (reminds me of the
WTC), remains down.  When, and now I'm beginning to wonder if,
the list once again becomes operational, I'll have lots of
controversial philosophy to share.  Until then, the fractals
will continue appearing at a rate of one per day on the Fractint
list, together with lots of fractal talk, but little philosophy.

The next fractal will appear right here in about 24 hours.  Take
care, and when the going gets tough . . . what *do* the tough do?


Jim Muth
[e-mail]


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

Fracler            { ; time=0:12:53.13--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-1.039444410280139/+0.71916981442691810\
  /5.739517e+007/1/-137.499999948393366/1.5697518258\
  1675643e-007 params=-1.4/-1.17/1.4/0.87/0/5 float=y
  maxiter=2500 inside=0 logmap=253 periodicity=25
  colors=000Q0WS0UT0SU0PV0NW0KY0J_0Na1Qc2Ud4Ye5ah6di\
  8hj9kmAonBsoCvmEtkFsjGriIphJogKmeLkcLjbNi1EO5GP8IP\
  AJQEKQGLQJNSNOSVPTSQTUPTUOJTNJGL9KL8NO8PR6TT6VW5YZ\
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  zY0za0zZ0zW0zU0zS0yP0vN0uK0sI0pF0oC0mA0kB0iC0hC0dB\
  0aA0Y90U80Q60N50J40F20B10800400000211542852A84C94F\
  B5IC5KF6NG6PJ8SK8UN9WO9ZQA_SAaQ8aQ5bQ2bQ1cQ0cQ0cQ0\
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  egPyscvrburasparp_ppZnoZmoYkoYUSmB4zNAzWGyeLwoSvyY\
  uzbttchecYScLEcAehZzmuzksujrojojinehk_hjVghQigKkdF\
  ncApa4s_0uY0wW5zYGzYSzZbzZmz_wz_zz_zzbyzcuzdrzenzg\
  ozcpz_pzWrzTrzPQzZ0zhzzCyzFpzIhzK_zNTzOKzQBzT2zV0z\
  W4zLCzAKz0LzELzSLzcOzaPzZ
  }

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

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


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

Date: Mon, 15 Oct 2001 13:08:05 +0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) FOTD 13-10-01 (V For Victory [5])

>Unsure of how to rate the image, and following the principle of
>'when in doubt, make it average', I settled on a rating of a
>generic 5, though a 6 would also be reasonably close.  I always
>tend to under-rate images in the classic M-set.  They seem to
>come just a bit too easily.

I rate images (and music, for that matter...) by how good the end result is,
not how easy or otherwise it was to create. By my scale, this image should
rate nearer 8, if only for the cool colour scheme.

Thanks.
Andrew.



_________________________________________________________________
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------------------------------

Date: Mon, 15 Oct 2001 13:11:43 +0000
From: "Andrew Coppin" <[e-mail]>
Subject: Re: (fractint) FOTD 14-10-01 (Fracler [8])

>From: Jim Muth <[e-mail]>
>Reply-To: [e-mail]
>To: [e-mail]
>Subject: (fractint) FOTD  14-10-01  (Fracler [8])
>Date: Sun, 14 Oct 2001 10:16:57 -0400 (EDT)
>
>
>FOTD -- October 14, 2001 (Rating 8)
>
>Fractal visionaries and enthusiasts:
>
>The generating formula subtracts 1.4 parts of Z^(-1.17) from 1.4
>parts of Z^(0.87), then adds (1/C) to create the parent fractal
>snail.  The image itself reminds me of an alien flower, thus the
>name "Fractal Flower", which I shortened to "Fracler".  Since I
>think the image is quite good, I rated it at an exceptional 8.
>Others may have a different opinion.

I for one agree with that particular rating. (If I thing an image is
over-rated, I generally don't bother to post a message saying so. I guess
I'm just NICE or something...)

THanks.
AnDRew.


_________________________________________________________________
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------------------------------

Date: Mon, 15 Oct 2001 09:20:43 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  15-10-01  (Fractal Bagel [5])

FOTD -- October 15, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Fractals are total abstractions.  There is no 'real' Mandelbrot
set or Julia sets lurking in as-yet-undiscovered hiding places.
It is all about numbers and the things numbers do.

But we are a part of reality and cannot escape it.  Our minds
are wired to see 'real' objects even where none exist.  Perhaps
the strongest evidence of this wiring is the way we so often
invent then actually see faces in random patterns such as clouds.

I could find no face in today's image, though I did find a
bagel.  In fact, the whole scene is of one big bagel, which is
why I named the image "Fractal Bagel".  The midget lies in a
chaotic filament on the northwest border of the fractal that
results when the expression Z^1.44225+C is iterated by the
MandelbrotBC1 formula, using the <recip> function.  I chose the
value 1.44225 as the exponent of Z because it is the cube root
of 3, and whole-number roots of whole numbers seem to make more
interesting images.  The rating of 5 is average, and says
nothing about the image.

The proper function to use with the MandelbrotBC1 formula is
<floor>, but most other functions also produce interesting
fractals.  In today's case I used the <recip> function to see
what it would do.

On my machine, the parameter file takes over 1/2 hour to run.
But my machine is old and tired, and most machines will render
the image in less than 15 minutes.  Those who would rather do no
rendering at all can find the GIF image posted to the W.W.Web at:

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

and at:

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

The fractal weather today (Sunday) suffered a setback, with only
a few brief periods of sun and too much wind for the sensitive
fractal cats.  The temperature of 75F 24C was pleasant enough,
but the wind limited the cats to a couple brief outings.  A
heavy shower fell after dark, bringing a less-than-perfect end
to the inauspicious day, but by this time, the cats had long
since given up and settled into the world of sleep.

The philofractal list is still down, so the philosophy is still
in cold storage.

And I'm hot to get the day's work started.  Until next fractal,
take care, and fractals are real because we see them, but are
they really real.


Jim Muth
[e-mail]


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

Fractal_Bagel      { ; time=0:34:17.78--SF5 on a P200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=recip passes=1
  center-mag=-1.08717603028377500/+1.205061829294592\
  00/1.889778e+011/1/42.4995365922868444/-0.00193853\
  530842458266 params=1.44225/0/0/0 float=y
  maxiter=45000 inside=0
  colors=000ebHfcFgcEhdDieCjfBkfAlg9mh8ni7oi6nj7nj8n\
  j9njAnjBmjCmjDmjEmjFmjGmjHlkIlkJlkKlkLlkMlkNkkOkkP\
  kkQkkRkkSkkTjlUjlVjlWjlXjlYjlZil_il`ilailbilcgpjil\
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  Q4YP3XO2XN2XMa_Lb`Kc`JdaI
  }

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

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


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

Date: Tue, 16 Oct 2001 09:59:45 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  16-10-01  (New Eastern Angle [7])

FOTD -- October 16, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

The well-known Mandelbrot set is actually a slice through the
center of a less-known four-dimensional object known to Fractint
users as the 'Julibrot'.

Since the Julibrot is four-dimensional, the M-set does not cut
the Julibrot in half, but it does slice a two-dimensional hole
all the way through it.  All the 'perturbed' M-sets are parallel
to the 'true' set, and taken as a single unit, form the Julibrot.

The many Julia sets are also slices through the Julibrot.  The
2-D Julia sets also cut the 4-D Julibrot in parallel slices, and
when taken as a single unit, form the same Julibrot.  The
difference between the Julia sets and the Mandelbrot sets is the
direction in which they cut the 4-D Julibrot.

The Julia sets are oriented in a direction completely
perpendicular to the Mandelbrot sets.  This relation is not the
same as that of perpendicular planes in normal 3-space, such as
a wall and ceiling, which must always intersect in a line and
have common sets of parallel lines.  In the 4-D Julibrot, M-sets
and J-sets intersect in only a single point, and every line in
every M-set is perpendicular to every line in its intersecting
J-set.

Just as M-sets and J-sets are slices in different directions
through the same four-dimensional Julibrot object, there are
many other directions in which this 4-D object may be sliced.
Today's 7-rated image, which I have named "New Eastern Angle"
shows East Valley of the M-set sliced in one of these new
directions.

Since the slice is in a new direction, there are no Mandelbrot
elephants, buds, or brain-like Julia sets to be seen.  What is
visible is totally unlike any M-set or J-set, and must be seen
to be appreciated.   The image can be seen by running the
attached parameter file or by picking it up from the W.W.Web.

The parameter file runs in exactly 7 minutes on my worn-out
Pentium 200mhz machine with a noisy fan.  Most of the 7 minute
render time is spent on the bottom 1/2 inch of the image.  The
pre-rendered GIF image downloads in even less time from the
W.W.Web at:

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

or at:

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

But before going for the download, give Paul and Scott a chance
to render and post the image.

The fractal weather today here at Fractal Central was once again
perfect, with sunny skies and a temperature of 71F 21.5C.  The
fractal cats agreed, and showed their pleasure by spending most
of the afternoon lurking in the yard, watching the squirrels,
who are busy gathering their nuts for the coming Winter.

Seeing no signs of life yet from fractalus.com, I once again
filed away the day's philosophy until and if fractalus has a
resurrection.

It's now time to file away the fractals and turn to more
profitable but less enjoyable activities.  Until tomorrow, take
care, and be sharp.


Jim Muth
[e-mail]


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

New_Eastern_Angle  { ; time=0:07:00.73--SF5 on a p200
  reset=2002 type=formula formulafile=allinone.frm
  formulaname=multirot-XZ-YW-new passes=1
  center-mag=+0.60570814332461560/+0.250416550291830\
  40/8155.282/0.0003492 params=0/57/2/0/0/0/0/1e-005
  float=y maxiter=45000 inside=0 logmap=135
  colors=000SUhTUiUUjVUkWUlXUmYUnZUo_Up`UqaUrbUsbUtb\
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  KUKLUKMUKNUKOUKPUKQUKRUKS
  }

frm:multirot-XZ-YW-new {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p3, c=e*imag(pixel)+p4:
z=z^(p2)+c,
|z| <= 36  }

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


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

End of fractint-digest V1 #604
******************************