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fractint-digest        Thursday, August 2 2001        Volume 01 : Number 585




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

Date: Tue, 24 Jul 2001 16:05:20 -0500
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) thanks and another stupid question

Cerridwen Connelly wrote:
>
> I can't recall how to make the square box
> appear on the screen to crop the fractal
> and "go in deeper".

You are probably speaking about the Zoom Box, which may be reached by
using the PAGE_UP keep on your keybaord.  You will then have many
options available while in that mode.  At this point, I suggest hitting
the F1-Key to acquire the various instructions.

You may wish to also runt the following from the Command Line:

      fractint.exe makedoc

This will generate a multi-page document with almost everything that you
would care to know about FractInt.

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

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

Date: Tue, 24 Jul 2001 17:06:59 -0400
From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) thanks and another stupid question

Try  "page up" or "page down"

- ----- Original Message -----
From: "Cerridwen Connelly" <[e-mail]>
To: <[e-mail]>
Sent: Tuesday, July 24, 2001 4:35 PM
Subject: (fractint) thanks and another stupid question


> Thank you Robin and Les!!!
>
> It works  now:-)
>
> Stupid question two:
>
> I can't recall how to make the square box appear on the screen to crop the
> fractal and "go in deeper". Does anyone know from this appalling
description
> what I am talking about and which keys to press?:-)
>
> *This is my final stupid question, I promise:-)
>
>
> Yn y Gwe,
>
> Cerridwen
> http://www.users.bigpond.com/catfishy
>
>
>
>
> --------------------------------------------------------------
> 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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------------------------------

Date: Tue, 24 Jul 2001 17:06:59 -0400
From: "Doug Stewart" <[e-mail]>
Subject: Re: (fractint) thanks and another stupid question

Try  "page up" or "page down"

- ----- Original Message -----
From: "Cerridwen Connelly" <[e-mail]>
To: <[e-mail]>
Sent: Tuesday, July 24, 2001 4:35 PM
Subject: (fractint) thanks and another stupid question


> Thank you Robin and Les!!!
>
> It works  now:-)
>
> Stupid question two:
>
> I can't recall how to make the square box appear on the screen to crop the
> fractal and "go in deeper". Does anyone know from this appalling
description
> what I am talking about and which keys to press?:-)
>
> *This is my final stupid question, I promise:-)
>
>
> Yn y Gwe,
>
> Cerridwen
> http://www.users.bigpond.com/catfishy
>
>
>
>
> --------------------------------------------------------------
> 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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------------------------------

Date: Tue, 24 Jul 2001 17:32:00 -0700
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) JPEGs & layers (was "saving files")

At 10:59 AM 7/24/01 -0400, cybersue wrote:
>Hello, Cerridwen (what a wonderful Celtic (?) name!) , The easiest way to do
>what you want is perhaps to save just the frame layers as a separate UPR,
>deleting all others (after saving, of course! :-)). Then render the frame
>UPR using the "Render to disk" command! The result will be a jpg file which
>you could then put into Photoshop and erase the center background black to
>transparent to use as a second layer over your own photos!

At 11:02 AM 7/24/01 -0400, cybersue wrote:
>So sorry, Cerridwen, I just realized that I was reading my "Fractint" mail,
>not my "UltraFractal" mail!

For anyone who *is* doing layers in Fractint, I wish to share a
trick which has made my JPEGs much better.  The program
I use to merge my layers has the annoying trait of having a
minimum compression ratio (won't generate a completely
non-compressed JPEG).  I have learned to save it first as a
24-bit color TIFF (I have no PONG-capable software), and
then do final adjustments and conversion to a mildly
compressed JPEG in a program with better compression
characteristics (in my case, PSP 2.0. Yes, 2.0!)  You still
have to live with artifacts, but they are less severe.


Happy fractalling,
        Bud


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

Date: Wed, 25 Jul 2001 08:12:08 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  25-01-00  (What a Midget [5])

Classic FOTD -- July 25, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Today's image is a harsh one, which takes 1-1/2 hours to render
from the parameter file.  Looking at it, I get the impression
that it could have been an 8-rated image, but somewhere along
the way something went wrong.  Maybe there's just too much muddy-
looking black.  In the end, I rated the image at an average 5
and named it "What a Midget".  The name is to be taken more as a
question than as an exclamation.

The image is part of the Z^(sqrt(2))+C fractal.  In today's
case, the pictured section of the fractal is located 6.283185307
out the infinite fractal spiral.  This number is two times pi.
I chose it because setting real (p2) of the MandelbrotBC1
formula to pi produces fractals with X-axis symmetry, and I
wanted to see what 2pi would do.  I found that it did nothing
extraordinary

The slow render time and less than great quality of today's
image make a download of the GIF image the better choice.  But
before visiting their web sites, give paul and Scott a chance to
render and post the image.  Those sites may 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 once again summer-like, with
humidity as high as the temperature, which reached 94F (34.5C).
The public complained, but the cats approved.

And I wish I had nothing to do, but the day is young and the
work is waiting.  Until next time, take care, and be efficient.


Jim Muth
[e-mail]


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

What_a_Midget      { ; time=1:27:57.45--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-0.30392296144667660/-0.870386112464632\
  30/7.247228e+008/1/-72.5 params=1.414213562373/0/6\
  .283185307/0 float=y maxiter=15000 inside=0
  logmap=2481 periodicity=10
  colors=0008R6AR7CR9ERAHRCJRDLRFNRGQRHSRJURKWRMZRN`\
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  B4cC5bC5bC6aD6aD7`D8`E5R4
  }

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: Thu, 26 Jul 2001 10:42:54 +0100
From: "Cerridwen Connelly" <[e-mail]>
Subject: (fractint) thanks - up and down:-)

Thank you Paul, Les and David for the "Page Up and Down" replies.

It works fine now and I am happily generating new additions to my art link
pages:-)

Yn y Gwe,

Cerridwen
http://www.technopagans.co.uk
http://www.pagantours.co.uk
http://www.users.bigpond.com/catfishy




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

Date: Thu, 26 Jul 2001 10:28:09 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  26-07-01  (A Skeletized Scene [5])

Classic FOTD -- July 26, 2001 (Rating 5)

Fractal visionaries and enthusiasts:

Due to a rush, today's discussion will be short.

Today's fragmented scene has a nearly-lost midget at the center.
The unusual effect is caused by coloring the outside area with
<fmod> rather than the usual <iter>.

The formula behind the image is (Z^2)+(0.2(Z^3))+C.  The parent
fractal is a figure with a string of bays, with many new valleys
to explore between the bays.  Today's scene lies in one of the
new valleys.  Noticing the skeletal effect of the picture, I
named it "A Skeletized Scene".  Due to the haste in which the
image was produced, I could rate it no higher than a 5.

The parameter file renders in 29 minutes on a Pentium 200mhz
machine.  The download of the GIF image from:

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

or from:

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

is far faster.  But give Paul and Scott a chance to render and
post the image before visiting their sites.

The fractal weather today was sunny and quite hot and humid
today, with a temperature of 97F 36C.  The fractal cats ignored
the heat and slept most of the day.

But I've got a bit of work to accomplish, so until next time,
take care, and patience is rewarded, but too much patience gets
nothing done.


Jim Muth
[e-mail]


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

A_Skeletized_Scene { ; time=0:29:49.15--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-3.517795082582847/-0.172268355153175/5\
  .450818e+011/1/-154.935/-0.116 params=1/2/0.2/3/0/0
  float=y maxiter=3000 inside=0
  proximity=0.047 outside=fmod periodicity=10
  colors=000DITDITCISCISCISBIRBIRBIRAIQAIQAIQ9JP9JP9\
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  RADPAAHAAKAAMAAPAARAAUAAT
  }

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


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

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

Date: Fri, 27 Jul 2001 10:09:50 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  27-07-01  (Billowing Billows [6])

Classic FOTD -- July 27, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

My opinion of the <tdis> outside fill option grows more
favorable every time I use it.  However, due to its flaw, the
tendency to revert to a flat color at high iteration levels, I
doubt that it will ever become my default method of exploration.
But it certainly can bring life to some otherwise nearly dead
fractals.

Today's image is a good example of the new life which the <tdis>
option can sometimes bring to ho-hum fractals.  When rendered in
the usual manner, with the usual equal-iteration bands, today's
image is just another fractal, the likes of which we've seen
hundreds of times before.  But when the new <tdis> option is
used, the image takes on a striking, almost three-dimensional
quality that makes it well worth being named Fractal of the Day.

The parent fractal of today's image is a Mandeloid with several
extra bays and valleys.  It was created by a simple combination
of small portions of Z^4 and Z^5.  On the surface it appears to
have little potential, and indeed, were it not for the <tdis>
option, I would have given up on the fractal before reaching the
scene of today's image.

I named today's picture "Billowing Billows" partly as a joke,
and partly because I like the sound of the words.  The rating
of 6 is fair.

The parameter file runs in 17 minutes.  The file of the GIF
image, which will be posted in an hour or so to:

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

and to:

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

will download in less than one minute.

The fractal weather today was cloudy, with a temperature of 88F
(31C) and a light shower in the afternoon.  The fractal cats
approved of everything but the rain.

And I'll approve of today's work once it's behind me.  The only
way I know to get the work behind me is to start, so that's what
I'm now ready to do.  But I'll return in the proper time with
another fractal.  The philosophy is also once again stirring, so
it stands to reason that it will soon make a long overdue re-
appearance.  Until tomorrow, take care, and search for fractals.


Jim Muth
[e-mail]


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

Billowing_Billows  { ; time=0:17:09.36--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-4.13027890934321500/+0.608256133526089\
  10/12033.82/1/-164.999 params=0.05/4/0.01/5/0/0
  float=y maxiter=1200 inside=0
  outside=tdis periodicity=10
  colors=000YTAXV9XX7XZ6X_5_c6bf6di6gm6jp6ls6gt8cu9Z\
  uBVvCRwDMwFIxGExHRhNbUTcTWcTYcT_cTacTcdSfdShdSjdSl\
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  tKbtKdsLfsLhsZMGYOEYQDYSB
  }

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

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

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Date: Sat, 28 Jul 2001 11:13:37 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  28-07-01  (Midget and a Half [6])

Classic FOTD -- July 28, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Today's fractal has been named "Halfway Midget".  I gave it this
name not because of its behavior, but because the generating
formula of its parent fractal is Z^(2.5)+C, and 2.5 of course is
halfway between 2 and 3.

Midgets in this range come in all shapes.  The shape of the
midget in today's picture, with the midget splitting along its
East Valley, is one of the most frequently seen.

I originally found today's midget by using the MandelbrotBC
formula.  But when the image was completed, I realized that the
second parameter was set to pi, and the formula was therefore
drawing the same image as Fractint's built-in manzpower formula
would draw.  I then rendered the image with the manzpower
formula, but found it too slow.  I finally turned to my own
MandelbrotN formula, and found that this formula draws the
identical image in 2/3 the time of the manzpower formula.

In my opinion, the most notable thing about the image is the
inconspicuousness of the branch cut discontinuities.  The breaks
are there, but they are so well hidden that unless looked for,
they would never be noticed.  All in all, it's a slightly-above-
average image, well worth the rating of 6.

Rendering the image with the fastest formula, MandelbrotN, takes
4-1/2 minutes.  Downloading the GIF image file is even faster,
but before going for the download, give Paul and Scott a chance
to post the image file to their web sites.

The GIF image will be available for download at:

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

and at:

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

The fractal weather today was perfect.  The sunny skies, low
humidity, and temperature of 81F 27C made the cats as well as
myself happy.

Until next time, take care.


Jim Muth
[e-mail]


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

Midget_and_a_Half  { ; time=0:04:34.35--SF5 on a p200
  reset=2001 type=formula formulafile=slices.frm
  formulaname=MandelbrotN passes=1 center-mag=-0.923\
  23411769327450/-0.00079409795476115/2.610506e+008/\
  1/-14.999 params=2.5/0/0/0/0/0 float=y maxiter=3500
  inside=0 logmap=106 periodicity=10
  colors=000AfgAfhAeiAdiAcjAbkAakA_lAYl9Wm9Un8Sn8Qm8\
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  zc4zc4zc4zc4zc4zc6zc7zc9zcAzcCzcDzcFzcGzcHzcJzcKzc\
  MzcNzcPzcQzcRzcTzcUzcUzcU
  }

frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16
}

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

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

Date: Sun, 29 Jul 2001 10:57:24 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  29-07-01  (Creature Feature [7])

Classic FOTD -- July 29, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

I named today's picture of a Z^(sqrt(2))+C midget "Creature
Feature" because I found it on a Saturday evening, just as I was
ready to settle down to watch my traditional Saturday night
junky old creature feature on TV.  The image rates a 7 because
it shows a relatively new kind of midget.

But what is a creature feature?  To qualify as a creature
feature, a movie needs to meet certain low standards.  Most
importantly, it must violate so many scientific principles as to
be totally unbelievable.  A typical plot might be to have the
planet Earth torn in half by a magnitude 15 earthquake,
(impossible), and the two halves drift off in their own orbits.
(Also impossible.)  Of course, we would need a 'scientist' to
exclaim something like, "wow! what a trembler!", as the quake
happened.  (The word is temblor.)

Next, the special effects must be immediately obvious and
totally unconvincing.  Any invading alien monsters must look
like men in rubber suits, and not like actual alien life forms.
This leaves out most current movies with their computerized
effects that can be quite convincing.  These modern films can be
enjoyable, but they're not creature features.

The dialog of course must be so stereotyped as to be
predictable.  A line such as, "look George, an alien from outer
space!", can bring a dying movie back to life in a hurry.

Finally, in case all else fails, and to interest the ladies, the
movie must have a human relationship of the proper man-woman
kind.  And the viewers must spot the lovers before the lovers
recognize each other.

What does all this have to do with today's image?  Well, today's
image reminds me of an alien fungus growing on a man's arm,
which will soon turn the man into another alien fungus.

The fungus is actually the filaments shooting out from the
midget, which is located at the edge of a bay of its parent
fractal.  The parent is shaped quite like its child.

The parameter file renders in a quick 2-3/4 minutes, and is
about as much work as downloading the GIF image from:

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

or from:

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

The choice is left to the viewer.

The fractal weather today was pleasant but uneventful, with
partly cloudy skies and a temperature of 79F 26C.  The cats must
have approved, though they slept most of the afternoon.

Until next time and next fractal, take care, and see you then.


Jim Muth
[e-mail]


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

Creature_Feature   { ; time=0:02:42.30--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-0.56270101574334630/+0.915160418848623\
  90/160.9974/1/-155 params=1.414213462373/0/75.3/800
  float=y maxiter=3600 inside=0 logmap=47
  colors=00006R06R07S18T29U3AV4BW5CX6DY7EZ8F_9G`AHaB\
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  Zzzazzdzzgzzqzzpzzpzzozzo
  }

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: Mon, 30 Jul 2001 10:34:05 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  30-07-01  (Illusory Minibrot [7])

Classic FOTD -- July 30, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Today's fractal is a zoom into a curious image sent to me
yesterday by Lee Skinner.  I have named it "Illusory Minibrot"
because of the deceiving nature of its symmetry.  I rated it a 7
because in addition to its mathematical interest it is a
striking image.

A quick glance seems to show 32 filaments entering from the
border of the image, but by the time the reddish teeth jutting
into the blue area are reached, the symmetry has dropped to 16.
Things are not as they appear however, for both of these
apparent symmetries are false.  The symmetry of the whole
picture is one big illusion.

Out beyond the 16 encircling yellowish arms, the actual symmetry
is 8.  Look closely at those 16 rusty-red teeth.  They are not
identical, but alternate between two different varieties, making
the complete circle consist of 8 groups of 2.  The smaller teeth
have one long filament attached, while the larger teeth have 3,
giving a total of 32 filaments extending out beyond the image
border.

The reason for this pseudo-symmetry is not altogether clear,
though it is certainly connected to the periodicity of the area
and perhaps to the value of the exponents of the generating
formula.  Regardless, it is a promising area to investigate,
which I will likely be exploring in the not-too-distant future.

The image takes 18 minutes to render on my machine, which is an
old-style Pentium running at 200mhz.  Within an hour or two, the
file of the completed GIF image will be posted to:

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

and to:

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

The fractal weather today featured clouds, light rain, and a
most un-summer like temperature of 64F 18C.  The cats complained
a bit, then went to sleep.  I notice that the cats are romping
less and sleeping more as the months and years pass.  They must
be starting to feel their age.

As for myself, I'm feeling the need to get some work done.  So
until next time, take care, and don't write off the philofractal
list as dead yet.  I've got a lot of controversial stuff yet to
discuss.  All I need is the time to sit down and write it.


Jim Muth
[e-mail]


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

Illusory_Minibrot  { ; time=0:18:34.17--SF5 on a p200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=-4.28968168524079100/+0.751079008850680\
  90/1.517355e+012/0.9996/-175.008/-0.043
  params=0.05/4/0.01/5/0/0 float=y maxiter=1800
  inside=0 logmap=373 periodicity=10
  colors=000M6FL4EK2CJ0BI1DI1EH2FH2GG2HG3IF3JF3KE4LE\
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  zKmzKmzKmzKmzKmzLmzLmzOmz
  }

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

Date: Tue, 31 Jul 2001 09:14:43 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  31-07-01  (Smoky Joe Midget [7])

Classic FOTD -- July 31, 2001 (Rating 7)

Fractal visionaries and enthusiasts:

Long ago, before the bridge across the Chesapeake Bay was built,
there used to be a ferry that carried travelers to the eastern
shore.  That ferry was named "Smoky Joe".  I never had the
pleasure, or displeasure, of riding on that ferry, but my father
rode it often, and frequently told of the thick black clouds of
oily smoke that belched from the funnel whenever the ancient
engines were running, sometimes choking the passengers and
always marking the ferry's position even when the boat itself
was below the horizon.

For some strange reason, today's fractal reminds me of a ferry
boat that I have seen only pictures of.  The outer features
surrounding the central midget do have a rather smoky effect,
and the streaks of orange-red could be the reflection of a fire
in a coal furnace, so I guess the name is justified.

The formula Z^3+0.225(Z^5)+C is responsible for the smokiness,
as well as everything else in the image, except for the
coloring, which was created by the <tdis> inside fill option
aided by myself.  The rating of an above-average 7 is justified.

The render time of a little over 8 minutes is slightly slow, but
worth the wait.  And as always, those who lack the computer time
to render from the parameter file may see the image by visiting
Paul's web site at:

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

or Scott's at:

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

and downloading the GIF image from there.  Give Paul and Scott a
chance to first post the image of course.

The fractal weather today was average, with a temperature of 81F
27C and big puffy white clouds that occasionally dropped a few
large raindrops but never released their full potential.  The
fractal cats showed their approval by spending several hours in
the yard, dodging the few raindrops.

It's now 9am of the last day of July, and time to get a bit of
work done.  I'll return as always at the proper time.  Until
then, take care, and brace yourself for imminent philosophy.


Jim Muth
[e-mail]


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

Smokey_Joe_Midget  { ; time=0:08:17.96--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.02671087209221384/-1.928837536631981\
  00/6.528213e+012/0.9999/-127.48/-0.023
  params=1/3/0.225/5/0/0 float=y maxiter=1200
  inside=0 outside=tdis periodicity=10
  colors=000CbSAXU8OWELSKJPQHLWFI_DFUHMZKTYOhWRmVVrU\
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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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Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
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Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Wed, 1 Aug 2001 10:28:43 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  01-08-01  (A Midget in a Quandary [8])

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

Fractal visionaries and enthusiasts:

On the surface, today's image resembles a piece of pop art.
Actually it's "A Midget in a Quandary", which is the name I gave
to the image.

The midget's problem lies in its symmetry.  Clearly, the midget
is a quadratic one, but where is the 2,4,8,... symmetry that
normally appears around such midgets?  Instead of a 4-way and an
8-way symmetry, we have a very well defined 6-way symmetry, and
this is not a pseudo-symmetry, it is a true 6-way symmetry.

To make matters worse, the 6-way symmetry breaks down into a
36-way symmetry as it nears the midget.  This would be expected
in a fractal created by a formula such as Z^6+C, but today's
fractal was created by a combination of Z^3 and Z^4, giving no
reason at all for the 6-way symmetry.

Features with 3-way symmetry also fill the image.  The most
prominent of these are located in the six radiating arms, though
no midgets lie at the center of these 3-way features.  And the
area within the 36-way symmetry breaks down into the kind of
non-symmetrical chaos that would be expected around the
fragmentary midgets of a perturbed fractal.  But a closer
examination of today's midget shows that it is intact.

All-in-all, today's image is a real mystery.  If I were rating
it according to its appearance alone, I would give it a 6.  But
when the puzzling mathematical aspect is considered, the picture
is well worth its rating of 8.

At a bit over 10 minutes, the parameter file renders reasonably
quickly.  And as always, the GIF image will soon be posted to
the web sites of Paul and Scott 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 of the pleasant uneventful summer
variety, with hazy sun and a temperature of 81F 27C that pleased
the cats.  To please me however it will be necessary for the
day's work to be behind me.  And it's now time to set out on the
road to pleasure.  So until next time, take care, and start
looking forward to philosophy of the fantastic kind.


Jim Muth
[e-mail]


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

AMidgetInAQuandary { ; time=0:10:39.17--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=1
  center-mag=+0.44736824626302050/-0.000845686608124\
  88/1.476198e+007/1/-22.499 params=1/3/-0.35/4/0/0
  float=y maxiter=2600 inside=0
  logmap=154 periodicity=10
  colors=00060020000000200600A0DE0HH0IL0LP0QU0VYbYan\
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  zzzzzzzzszzezzUzzHzz6zz0zz0zz0zz0zz0zz0zz0zz0zzAzz\
  HzzPzzYzzezzkzzszzzzzzzzP
  }

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

Date: Thu, 2 Aug 2001 10:31:56 -0400 (EDT)
From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  02-08-01  (Simply Amazing [9.5])

Classic FOTD -- August 02, 2001 (Rating 9.5)

Fractal visionaries and enthusiasts:

Today's image, which is from the same area of the same parent
fractal as yesterday's, is impossible.  It's incredible.  It has
no right existing.  But here it is.  I rated it a 9-1/5 because
in the mathematical sense, and with no exaggeration, it is the
most unusual fractal I have ever seen.  (Artistically however it
is not all that much.)

I have long noticed that the midgets I find in the fractals
created with the MandelbrotMix4 formula are all of the quadratic
variety.  That is, they are all shaped like miniature Mandelbrot
sets.  At the same time, I have heard rumors that midgets of
other higher orders are possible if only one knew enough math to
find them.

Until today, I have found higher-order midgets only in formulas
such as Z^(2.99)+Z^(3.01)+C, which doesn't count, because such a
formula is basically 2(Z^3)+C, and the fractal it draws is the
expected cubic.  Today however I finally found an elusive higher-
order midget.

But this is not all.  Not only did I find a cubic midget, but
right beside it and in the same frame I found an order-6 midget.
The cubic is not all that unexpected, since the generating
formula combines portions of Z^3 and Z^4, but the order-6 midget
is a total surprise.

Yesterday's image, which showed a quadratic midget with 6-way
symmetry, hinted at something very unusual in the area, but not
until I stumbled upon today's scene did I realize how unusual.
The more mathematically erudite may see what is happening and
understand how a scene such as today's is possible.  For myself,
I enjoy mysteries, and I'll consider today's image a mystery.
But I'm going to do a lot of exploring around the area of
today's image to see what other wonders I can uncover.

I have named today's image "Simply Amazing".  That is how I felt
when I saw it, so that's what I named it.  The parameter file
renders in just under 5 minutes, making it a toss-up whether to
run the parameter file or download the finished GIF image from:

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

or from:

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

The fractal weather today was more typical summer stuff, with
hot sun and a temperature of 88F 31C.  The cats, who enjoy such
conditions, were kept happy.

The clock over my desk tells me that it's already past the time
when I should get to the waiting work.  So until the next FOTD,
take care, and who knows what strangeness lurks deep in the
world of fractals.


Jim Muth
[e-mail]


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

Simply_Amazing     { ; time=0:04:53.85--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotMix4 function=ident passes=t
  center-mag=+0.44864363812428920/+0.000055024630770\
  93/72716.29/1/72.5 params=1/3/-0.35/4/0/0
  float=y maxiter=3000 inside=0 logmap=72
  colors=000SGUSGUTOZUWbVcfWkkXsoXzs`qodhlg_ikRfoIcr\
  9`zFSi`cUvn`rcfoTmkIsh7rc8q_8pW9oS9nOAmKAlGBkCBcaF\
  WzIMeEDLA40636E2CM2HT1N`1SgAG_I5SR7P_9NgBKpDIxFGfE\
  SPDc7Co57o7Am8CkAEiBGgDIeELcGNaHP_JRYKTWMWUNYSP_QQ\
  aOScMTeKReJPeJOeJMeILeIJeIIeHGeHFeHIaKKYMNUOPRQNPT\
  LNWKMYMPZNSZPU_QX_SZ_Ta`Uc`Wf`XiaZka_naapbbsbcubeu\
  dfuehufiuhkuilujnuloumqunruptuquurwutxuuyuvW5qZAr`\
  ErcJseNshStjWtm`toduriutmvwrv7X79Y9AZAC_CD_DF`EGaG\
  IaHJbILcKMcLNdNPeOQePSfRTgSVgTWhVYiWZiX_jZak_bladl\
  bemcgnehnfjogkpilpjnqlormqrnrspttqutrwutxvuQP8SRBT\
  SDVUFWVHYWJZYL`ZNa_PbaRdbTecVgeXhfZjh`kibmjdnlfomh\
  qnjrpltqnurpwtrxutoyTpxUpxVpxWqxXqxYqxYqxZrx_rx`rx\
  arxasxbswcswdtwetwetyftyguzhuziuzjuzjvzkvzlvzmwznw\
  znwzowzpxzqxzrxzrxzsyztyzuyzvazRczUezWgzZiz`kzcmze\
  nzhpzjrzmtzovzrxzt5zu7zv8zvAzvBzvDzvEzvGzvHzvJzvKz\
  vMzvNzvPzvQzvSzvJzpNzsQzu
  }

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

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


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End of fractint-digest V1 #585
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