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fractint-digest        Monday, January 15 2001        Volume 01 : Number 531




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

Date: Fri, 12 Jan 2001 14:56:16 +1300
From: <[e-mail]>
Subject: Re: (fractint) Philosopy

Chris Curnow <[e-mail]> said:

> Can I kick-start Jim into philosophy?
>
> It's not the parameters or formula that doesn't exist
> it's the map file.
>
> Try these three, a few seconds each to generate and
> the only difference is the colours:
>
>
You forgot my patented near-infrared colour maps - designed for people who
want to see leaping monkeys no-one else can without having to resort to drugs.

Morgan L. Owens
"I wouldn't complain if they didn't keep stealing my ultraviolet bananas."



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

Date: Thu, 11 Jan 2001 23:06:23 EST
From: [e-mail]
Subject: (fractint) C-FOTD  12-01-01  (The Budding Midget [6])

Classic FOTD -- January 12, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

To create today's fractal, I entered all 1's and 3's into the
M-Mix4 formula and let her rip.  Oh, I may have entered a single
'2' into real(p3) as the multiplication factor, but nobody's
perfect.

The resulting fractal is a distorted Mandeloid with a loop
attached.  This loop has sub-loops attached at regular
intervals, with tiny holes where the loops join.  To find
today's image, I chose one of these holes, which is in the shape
of a Mandelbrot midget, and dove into the debris cluttering its
East Valley.

The East-Valley nature of the scene of today's image is quite
apparent, as is the theme of smaller loops attached to larger
loops.  The smaller loops appear to be budding and breaking off
from the main feature, the effect which inspired the name "The
Budding Midget".  After studying and re-studying the picture, I
decided it rates a marginal 6, mostly because I like the purple
colors that fill it.

The parameter file renders in under 12 minutes at a resolution
of 640x480x256 on a Pentium 200 machine.  In a little over 12
hours, the GIF image file will be posted to Usenet at:

          alt.binaries.pictures.fractals

It should be available far sooner on the WWW at:

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

and at:

          <http://home.swbell.net/sdboyd56/fotd/>

The fractal weather today was unusually pleasant.  The sunny
skies and temperature of 56F (13C) had the fractal cats on the
porch from late morning until after 3pm, where they took turns
stretching in the sunlight and washing each other's faces.

Unfortunately, because of a major work rush, which requires two
jobs to be finished at the same time, I was prevented from
engaging in my intended philosophical pondering today.  But the
time is growing close when the philosophy will no longer be
able to be contained.  And that day might come before the week-
end passes.

So stay in touch with the FOTD, and never forget that patience
is rewarded.  Until next time, take care.


Jim Muth
[e-mail]


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

The_Budding_Midget { ; time=0:11:54.19 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+5.608365346018756/+0.652676256536578/187\
  481.4/1/80 params=1.333/-13.33/13.33/-1.333/-1.2/0
  float=y maxiter=1800 inside=0 logmap=223 periodicity=9
  colors=000f7Ji7Lg7Og7Qf7Td7Vd7Yc7`c7ca7d<3>_7o<3>f7p\
  g7pjAplBpmDroErpGrsJr<2>xNryPszSs<4>zZsz_vzaxzcyzdzz\
  fzzfz<3>zkzzmzzmz<2>zqzzszzszzpz<4>zhzzfzzdz<2>z_zzZ\
  zzWwzVt<4>zne<2>zzXzzUzvRzqOzmKzjHzf7za7zX6zV6zQ4zM4\
  zH3zE3zH7zJCxKGuNLrPPoQSlUXiY`dadaei_ilXmpTqqQurOysL\
  zs0zm0zh0xc0wZ0qU1pP3fK4jF6_09c0AS0CX0DN0FQ0GK0IF0JI\
  0IM0GM3GT9FTDF_IDaODgSCjYCnaAqfAvl9yp9zv7zz7zzAzzDyv\
  GtrJpmMkjPffSaa<3>c`Lf`Gi`D``PT``U`lU`xUez<3>UyzUzzS\
  zzQzzPzoOzaOzQIzO<3>0zC0zACzGQyMdsSskYzdczZizglznozn\
  pznsznvznxzpzzqzznzzhzsfzmVzfKz_NlLGT9M70Qg0d`6hj6nz\
  Amz7jzChz9gz7fz9hzAjzCmzDnzDpzFszGtzIwzJyyJzx<2>OzsP\
  zrPzpoBorHjsMguSdvWax__yfXzjTznQxmOukMrnJoqIltGiwDdz\
  Caz9_z7Xz6Tz3Qz1Oz0Qz1Sz1Tz1Xz1<2>`z1Yz4Xz7Vz9SzCQzD\
  PzGOzILzLJzMIzPGzQ
  }

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 Jan 2001 20:26:50 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Fw: Higher resolution

On 11 Jan 01 at 14:44, Kennan C Herrick wrote:

> Hi David-
>
> Thanks kindly for your response.  A few comments that
> might be of interest...
>
> On Wed, 10 Jan 2001 21:11:55 -1000 "David Jones"
> <[e-mail]> writes:
> > IIRC, that's the chipset on a Diamond video adaptor we
> > have around here (in use at the moment on a Linux box).
> > Ran Fractint 19.x quite happily at resolutions up to
> > 1024x768 or 1280x1024 (I forget which). But I wasn't
> > running it under W95, I run it under OS/2. In W95, it
> > would happily freeze the system as Windows and Fractint
> > fought over who controlled the video.
> >
> > You might try this. Shutdown W95 to a DOS prompt, then
> > change to your Fractint directory and try running
> > Fractint that way. If it works fine, then it's a
> > conflict with Windows.
>
> It does work fine.  But when, in Fractint, I use
> <esc><del> & then select the several higher-resolution
> video modes, I find, as you no doubt are aware, that the
> images come up smaller on the screen.

Mine never came up smaller on screen, except for some
PARs that set it to weird view modes for their own
reasons.

> I then have to go to <v> & set the several window
> options to get a full-screen image in, say, 800x600
> mode.  It puzzles me as to why anyone would want a
> smaller image than full-screen.

IIRC, according to the Fractint docs, it's there to speed
up rendering. Basically, Fractint dates back to the days
of very slow computers - perhaps even the famous IBM XT.
Rendering even a 320x200 fractal could take quite awhile!
Having the view option set to a "postage stamp" (that's
how I think of it) image let even slow machines render
something relatively fast. Useful for quick exploration.
Once you found an area that you wanted to explore in
greater detail, you could switch the view back to normal,
pick your desired resolution, and let it crank until it
was done.

> Another interesting thing:  Although I am back under
> Windows now, for doing this email, I seem to recall
> that, once I had established Fractint in, say, 800x600
> full-screen, I could load a .gif image that I had
> previously saved when in the 648x480 screen under
> Windows, show it on that enhanced-resolution full
> screen, and then save it again (with a new filename).
> Then, back under Windows and re-loading Fractint, I
> could display that newly-saved image; necessarily, of
> course, in only the 640x480 mode.  But then I found (or
> think I found; I must check again) that the increased
> quantity of pixels, brought about by having saved it
> from the 800x600 screen, were there when I zoomed in.

Actually, when you zoom in on a fractal in Fractint, the
fractal is recalculated at the higher magnification,
revealing more detail than was in the original in the
first place.

> So that appears to be a way for me to realize the
> greater resolution that I want--but what a pain in the
> butt it is!

You can also render an image using one of the disk video
modes. Don't know about Fractint v20 (haven't done
anything that big in it) but I've rendered fractals out
to 2048x2048 using a disk video mode. Fractint displays a
text message while rendering, and when it's done. Then
you just press the usual S key to save the generated (but
invisible) image as a GIF. It will probably be saved in
your Fractint directory, where you can open and work with
it using your preferred graphics converter.

> For your info, the reason I want the higher resolution
> is so that I can take the .gif file, convert it to .tif,
> and then import that into my CAD program as a "template"
> for drawing a vector-format figure.  That, in turn, I
> can subsequently export, in .dxf format, for the purpose
> of fabricating a physical object in the form of the
> fractal.

Actually, I think it's the best way to accomplish what
you want!

> Such a roundabout way to do that but I don't know any
> better.  I used to have a raster:vector conversion
> utility, and used it occasionally, but found that it
> made pretty much of a hash of the very-complex
> fractals.  Turned out better, although tedious, to
> replicate them visually using the CAD program.

Yes, I discovered that, too. Wanted to vector trace some
scanned photos - had a trace program that claimed it
could do it. Ended up with nothing useful. I had better
luck importing the photo and tracing over it in
CorelDraw.

Depending on your CAD program, you might investigate
writing a fractal generator using it's macro/programming
language (doesn't AutoCAD still use AutoLisp?). If you
implemented something like Fractint's boundary tracing
method, you could have the fractal already generated as
a vector curve for each color boundary.

Of course, you could end up generating a *really enormous
file* that way! ;-)

> If it still doesn't run your
> > desired resolution, there's a chance your video adapter
> > doesn't support VESA video modes (many accelerated,
> > Windows-optimized ones don't). IIRC, there's a utility
> > available that can check for those modes, and tell you
> > what codes to feed Fractint to enable it to use them ...
> >
> > You might also check to see if there are more recent
> > Windows video drivers for that adapter - maybe they fixed
> > whatever is keeping Fractint from working.
>
> I checked their website and no additional/later drivers
> are available. The S3 board seems to support VESA since
> Fractint's VESA modes display all right when under DOS
> only.  Do you suppose other people, using other boards
> perhaps, have no problem with running Fractint under Win
> 95 and in the several enhanced video modes?  From my
> experience, I shouldn't think so.

Other boards may work fine under W95. My old ET4000 SVGA
adaptor would do 1024x768 without any problems, but it's
a dumb SVGA board (no Windows acceleration). On a lark, I
installed Fractint on my office PC, an IBM PC750 with an
S3-based integrated display adaptor. I discovered by
accident that Fractint would do 1600x1200 on it with the
old IBM P50 monitor attached to it ... (Found some lunch
time entertainment!)

Fractint won't display anything better than 640x480 on my
current display adaptor, an Elsa GLoria Synergy. The Elsa
doesn't support any other VESA modes according to the
vesacfg program. :-( Maybe I'll have better luck on
the 3dfx Voodoo3 card on my new PC.

> > On 10 Jan 01 at 10:49, Kennan C Herrick wrote:
> >
> > > Would anyone have any info on running Fractint v. 20.0 @
> > > better than 640x480 resolution using an S3 Trio 32/64
> > > PCI adapter board containing a "764V+(765)Rev B" chip
> > > set (whatever that is!)?
> > >
> > > Whether or not that adapter is initially set for my
> > > preferred mode, 800x600x16-bit color, under Win 95, I
> > > can only get Fractint to work in 640x480 modes; full
> > > screen or window makes no difference in that regard. I
> > > don't want the colors so much as enhanced
> > > pixel-resolution, on-screen and in saved files.
> > >
> > > I'm not a Windows/DOS wonk so could use help if anyone
> > > has it--beyond what I could glean from fractint.doc.
>
> Thanks again for your help...

You're welcome, for what little it's been so far ... ;-)

David
[e-mail]


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

Date: Fri, 12 Jan 2001 20:58:12 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) C-FOTD  13-01-01  (Challenging Midget [8])

Classic FOTD -- January 13, 2001 (Rating 8)

Fractal visionaries and enthusiasts:

A few days ago I received an e-mail from a fractal fan, asking
me to tell more about fractals.  Since I had no idea of where
'more' started, I didn't know quite what to tell.  But once I
sat at my keyboard this morning to reply to the e-mail, the
philosophical muses came to life, and the words flowed almost of
their own accord.  The following four paragraphs are a slight
revision of the letter I sent earlier today.  Perhaps the
philosophy is once again ready to arise.

My interest in fractals is mathematical, artistic, and philosoph-
ical.  Mathematically, fractals are simply graphs of iterated
mathematical functions.  Artistically, fractals offer a means of
expressing one's artistic aspirations, though I consider the
importance of this aspect to be somewhat exaggerated.  My main
interest lies in the philosophical aspect of fractals.

Perhaps the question most often asked about fractals is, "what
are they?"  In addition, I often wonder, "are fractals real?"
The answer can only be, "fractals are the things numbers do, and
numbers are pure abstractions".  The Mandelbrot set does not
exist in the sense that a tree does.  No one will ever find a
'real' Mandelbrot set; they will find only pictures of it.  The
M-set exists only because human beings evolved with the sense of
vision, and to better understand the workings of math functions,
find it helpful to turn the functions into pictures.  In
essence, the Mandelbrot set exists only because we created it
with our minds and sustain it with our computers.

Much is also made of the fractal nature of the real world.  We
hear about the fractal nature of trees, ferns, clouds, coast-
lines, etc.  These things do indeed have a fractal surface
appearance, but they are not true fractals in the mathematical
sense.  A true mathematical fractal continues unchanged to
infinity regardless of how much it is magnified.  The 'real
world' fractal objects such as trees and clouds ultimately break
down into individual cells and water droplets, and finally into
atoms, which no one shall ever observe directly.

But according to quantum theory, atoms also are nothing more
than convenient pictures, models created in human minds from
mathematical functions.  And I have heard it said that numbers
themselves are creations of the human mind.  So is the 'real
world' the world's greatest fractal?  The answer to this
challenging question is what I am currently seeking.

Another challenging question is why I named today's C-FOTD
"Challenging Midget"  I'm sure I had a good reason for such a
provocative name, but the reason totally eludes me.  Regardless,
it's a fine fractal, which renders from the parameter file in
under 3 minutes.

The iterated expression, -5.5Z^(-0.5)-5.5Z^(0.5)+(1/C), as are
so many of mine, is totally whimsical.  The fractal it draws at
first appears to be a total loss, but a close examination soon
reveals tiny areas of promise.  Today's midget lies in one of
these promising areas.

It's a lively little midget, centered as it is in its square of
chaos, with gracefully curving arms radiating from the four
corners before an electric violet background.  The midget is so
lively in fact that I rated the image a lofty 8, a level rarely
reached on my conservative scale of fractal worth.

Since the parameter file takes only 2 minutes to complete,
running the file is most likely the fastest way to view the
image.  But for those who find running parameter files too much
of a hassle, the GIF image will soon be posted to:

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

and to:

          <http://home.swbell.net/sdboyd56/fotd/>

In 15 hours the image will also be posted to the Usenet group:

          alt.binaries.pictures.fractals

though by that time everyone who wants to see the image will
most likely already have seen it.

The Usenet postings will continue to be delayed by 12+ hours
until I solve my technical difficulties, a task that I have no
intention of tackling in the near future.

The fractal weather today here at Fractal Central was once again
comfortable, though not nearly as mild as yesterday.  The partly
sunny skies and temperature of 42F (5.5C) lured the fractal cats
onto the porch and into the yard, but once in the yard they
quickly decided it was a bit too chilly, and soon returned to
their radiators.

And this leaves me with nothing to do but shut down the fractal
shoppe and call it a night.  I'll watch a junky old movie if I
can stay awake.  Until tomorrow, take care, and beware of the
fractal witch.


Jim Muth
[e-mail]


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

Challenging_Midget { ; time=0:02:42.96 -- SF5 on a p200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.05445382910798185/+0.01773957995824642\
  /8.333333e+007/1/4.999 params=1/-0.5/1/0.5/-6.5/300
  float=y maxiter=1300 inside=0 logmap=45 periodicity=9
  colors=000bFz<2>cKz`FzYDzWCzT9wP8tO6oL3kJ1hG0eD0bC0Y\
  <2>40O10L00I10L10M10O11P34R39T3CV3FW4JZ4M`4Rb4Vc6Ye6\
  bf6eh6hj8mm8po8vp8yr<2>9zw9zyCzvFztIzpLwoOrkRojVjfWf\
  e<3>hRWkMToJRrFOtCMw8Jz4Iz0Fz0Dz0Az09z08z09z0Az0Az0C\
  z0Dz0Dz0Fz0Fz0Gz0Iz0Iz0Jy0Lw0Lv0Mv0Mt0Or0Pp0Pp0Ro0Tm\
  0Tk0Vk0V`0TR3RI9R9FP0LP0RO0YO0`L0bJ0eI0fG0jD0kC0oA0p\
  91t63v44y38z19z0Az0Dz0Fz0Gz0Iz0Iz0Jz0Jz0Lz0<2>Mz0Mz0\
  Oz0Oz0Pz0Pz0Rz0Rz0Rz0Pz0Oz0Mz0Mz0Lz0Jz0Jz0Iz0Gz0Fz0F\
  z0Dz0Cz0Cz0OzAZzYfzZpz`yzbzzbwzcmzcczcVze<2>3zf0zf0z\
  f0zj0zk0zo3zp8ztCzvFzyJzzOzzRzzWzwZzoczffzZkzRozJtzC\
  wz4zz0<3>zz0zz4<3>zzZzzfzzozzwzzzzzvyzorzhkzbezWZzO<\
  3>Az0Cz4Dz9DzDFzIFzMGzPGzVIzZIzcJzhJzkkz0oz0pz6rzAvz\
  GwzMyzRzzYzzczzh`zz8zz<3>IzzLzzOzzPzzVzjYzPVzRRzTOzT\
  LzVIzWFzWCzY9zZ6zZ3z`0zb<2>0zc0z`0zZ0zW0zV0zR`ztbzw
  }

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, 13 Jan 2001 13:58:04 -0800
From: "Diana L. Dubel" <[e-mail]>
Subject: (fractint) Question on the Mandelbrot Fractal

Math and Fractal groupies,

I am trying to understand the guts of computation of values in the
Mandelbrot set, and am a little confused.

I have seen printout's of the computer computation of values for the
Mandelbrot set.

For example;

z(0) = c = pixel;
z(n+1) = z(n)^2 + c
bailout = 4
etc.

Does the computer pick a pixel point on the complex plain and square it, add
c, [repeat many times], and determine if it is less than 4, for example?

Or does it do a computation of the encirclement set?  In that case it would
determine a limit as "l" approaches infinity of the log(base2) of the
modulus of z sub l, over 2^{l}, and check to see if this is less than 2^k, z
sub 0 = c.

I have studied Chapter 14 in "Chaos and Fractals" in detail, but am not
understanding some of the applications.

Thanks,

Diana
========================================
Diana L. Dubel  :-)

E-mail - - - [e-mail]


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

Date: Sat, 13 Jan 2001 14:02:59 -0800
From: "Diana L. Dubel" <[e-mail]>
Subject: RE: (fractint) Question on the Mandelbrot Fractal

Note than in my message above, "l" is the letter L.

So, the paragraph below---

> Or does it do a computation of the encirclement set?  In that case it
would
> determine a limit as "l" approaches infinity of the log(base2) of the
> modulus of z sub l, over 2^{l}, and check to see if this is less than 2^k,
z
> sub 0 = c.

might be written as---

> Or does it do a computation of the encirclement set?  In that case it
would
> determine a limit as "L" approaches infinity of the log(base2) of the
> modulus of z sub L, over 2^{L}, and check to see if this is less than 2^k,
z
> sub 0 = c.



- -----Original Message-----
From: [e-mail]
[mailto:[e-mail]]On Behalf Of Diana L. Dubel
Sent: Saturday, January 13, 2001 1:58 PM
To: Fractint@Lists. Xmission. Com
Subject: (fractint) Question on the Mandelbrot Fractal


Math and Fractal groupies,

I am trying to understand the guts of computation of values in the
Mandelbrot set, and am a little confused.

I have seen printout's of the computer computation of values for the
Mandelbrot set.

For example;

z(0) = c = pixel;
z(n+1) = z(n)^2 + c
bailout = 4
etc.

Does the computer pick a pixel point on the complex plain and square it, add
c, [repeat many times], and determine if it is less than 4, for example?

Or does it do a computation of the encirclement set?  In that case it would
determine a limit as "l" approaches infinity of the log(base2) of the
modulus of z sub l, over 2^{l}, and check to see if this is less than 2^k, z
sub 0 = c.

I have studied Chapter 14 in "Chaos and Fractals" in detail, but am not
understanding some of the applications.

Thanks,

Diana
========================================
Diana L. Dubel  :-)

E-mail - - - [e-mail]


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

Date: Sat, 13 Jan 2001 15:42:13 -0800
From: "Osher Doctorow" <[e-mail]>
Subject: (fractint) Lapidus-Frankenhuysen Quantum Fractal Billiard Table Conjecture - Doctorow

From: Osher Doctorow, Ph.D. [e-mail], Sat. Jan. 13, 2001 3:29PM

M. L. Lapidus and M. van Frankenheusen (University of California Riverside -
although most of their work was done in France and Vienna) in their volume
Fractal Geometry and Number Theory, Birkhauser: Boston 2000 (and especially
Lapidus' numerous papers on which it is based) give a conjecture of Lapidus
that an analogue of the Gutzwiller Trace Formula of quantum chaos theory
holds on some dynamical system associated with any self-similar fractal drum
viewed, e.g., as a billiard table.  A self-similar set in R^d is a union of
N scaled copies of itself generated by similarity transformations with
various scaling ratios.  A fractal drum is a bounded open subset of R^n
having a fractal boundary.  Most of the book studies the simpler
one-dimensional case of fractal strings and fractal sprays which are their
higher dimensional analogues and develops a theory of complex dimensions
that relate the geometry and spectrum of the fractal string.  M. C.
Gutzwiller of IBM is one of the quantum/classical chaos pioneers, and much
of his work is summarized in the volume Chaos in Classical and Quantum
Mechanics, Springer: Verlag, New York 1990.  Logic-based probability (LBP)
connects strongly with Lapidus and Frankenhuysen's work via the Riemann zeta
function functional equation and the "kernel" of the series representation
of the exponential function, but the conjecture is especially related to LBP
because one of its main conclusions is that boundaries (including fractal
boundaries) are generalized maximum entropy/maximum LBP optimal.

These directions of research into fractals and chaos complement a second LBP
direction of research into them via Brownian (fraction, fractal) bridges and
Brownian motion and Brownian snakes/excursions etc., which relate to LBP via
their close connection with the uniform empirical process and in turn the
latter's relationship to uniformly distributed random variables.  They are
to be contrasted with research into fractals via composition, especially
infinite composites of functions of form fofofo..., i.e., via iteration as
with computer programs for the composite function.  Composition/iteration
gives us concrete geometrical pictures of fractals and chaos, which in my
opinion needs to be complicated by the more abstract theory of the above two
directions.

Osher Doctorow
Doctorow Consultants, Ventura College, West Los Angeles College, etc.


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Date: Sat, 13 Jan 2001 16:12:53 -0800
From: Kennan C Herrick <[e-mail]>
Subject: Re: (fractint) Fw: Higher resolution

Thanks for the info!  I downloaded ves2acfg & ran it but it appears to
report no VESA capability: the screen just comes up blank; no info there.
 Curious...because under pure DOS, Fractint >works< in several of its
"VESA" video modes.

Ken Herrick

On Thu, 11 Jan 2001 14:14:30 EST [e-mail] writes:
> <<IIRC, there's a utility
> available that can check for those modes, and tell you
> what codes to feed Fractint to enable it to use them ... >>
>
> This links to the page on Sylvie Gallet's site wherein she makes
> available
> the utility
> ves2acfg which can be used to discover which modes your system uses
> so that
> you may then customize your set-up for best effect.
> Cheers!
> ~renrad
>
> <A
>
HREF="http://www.fractalus.com/sylvie/linke.htm">http://www.fractalus.com
/sylv
>
> ie/linke.htm</A>
>
> --------------------------------------------------------------
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Date: Sat, 13 Jan 2001 16:03:58 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Fw: Higher resolution

Maybe the W95 video driver isn't letting VESA2CFG do
what it needs to do with the video card to determine the
video modes. You might try booting to a DOS prompt and
run VESA2CFG. Note down what it reports, then you might
modify the appropriate Fractint video file to add those,
and see if they work under W95.

If they still don't, it sounds like the W95 driver
doesn't support VESA modes for your adaptor. At that
point, I don't know what you could do beside changing to
a different display adaptor.

Good luck!

David
[e-mail]

On 13 Jan 01 at 16:12, Kennan C Herrick wrote:

> Thanks for the info!  I downloaded ves2acfg & ran it but
> it appears to report no VESA capability: the screen just
> comes up blank; no info there.
>  Curious...because under pure DOS, Fractint >works< in
>  several of its
> "VESA" video modes.


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Date: Sat, 13 Jan 2001 22:04:09 EST
From: [e-mail]
Subject: (fractint) C-FOTD  14-01-01  (Challenge Variation [6])

Classic FOTD -- January 14, 2001 (Rating 6)

Fractal visionaries and enthusiasts:

Today's C-FOTD is a closer view of the midget at the center of
yesterday's "Challenging" image.  I named it "Challenge
Variation" accordingly.  Since too much of a good thing is not
always as good as it seems, I rated today's image a 6, a
two-point come-down from yesterday's image.

In today's image the maxiter has been lowered to 500, a value
barely enough to resolve the midget, and the color palette has
been changed from a somber violet theme to a joyous celestial
blue.  The lacework effect in the elements surrounding the
midget is an illusion created by the coloring.

The 4-1/2 minute render time of the parameter file is far better
than the 15-hour wait for the GIF image file to be posted to
Usenet at:

          alt.binaries.pictures.fractals

However in an hour or so the image file will be available on the
Web at the following two URL's:

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

          <http://home.swbell.net/sdboyd56/fotd/>

After a very frosty start, the fractal weather was ideal for
cats most of the day, with bright sunshine and a temperature of
45F (7C), which lured the dynamic duo into the yard, where they
passed the afternoon investigating whatever they found there to
investigate.

As for me, I've about had it for the day.  It's 9:50pm of
Saturday evening, and almost time to toss reason to the winds
and watch the junkiest old sci-fi or horror movie I can find in
my vast collection of junk.  I won't know what it will be until
the tape starts playing.

Until tomorrow, when some fractosophy is likely to appear, take
care, and keep your fractals handy.


Jim Muth
[e-mail]


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

ChallengeVariation { ; time=0:04:30.84 -- SF5 on a p200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.054453829082191/+0.017739580012905/8.4\
  739e+008/1/-35 params=1/-0.5/1/0.5/-6.5/300 float=y
  maxiter=500 inside=0 logmap=65 periodicity=10
  colors=0002es0csTXzzRziXuRagAeX0s_0za0zW0zP0zL1zR2uW\
  4la4de5Xk6Pr8Iw8Az5Dz2Gx1Ix0Lw0Ou0Pu0Ts0UszDzz9ur6eg\
  4TZ1FP02G00R80_J0iX1si4zx8zzAzzGzpMzeTwXZrOdnFkk6rd9\
  kZAdUDZOFTIGMDJG8LA4M5FJ9PGD_DGlALx8Pz6TrJI_W8Ji04w0\
  0z00z06z0Fz0Oz2Xz6ezCnzGssMxlTzdZzZczUZzPWwLTsGPpDMr\
  9Pr5Rs1Ts0UZArFMzLTzPZrWdg_kXdpO2sRz9DwGAlO8cU5Ua4Lg\
  1Cp05w0Fu2Ou6XuAeuFpuJzuOzuTrsGar6Lp06n0Gc0PU2ZLAiAJ\
  s2Tz0az0iz0lp5ndFpUPrL_sRepXklcpkiwgpzduzcUpL6a40O0R\
  T0zX6idIIlU0ue5xgIziWzkizkkzXlzJnz8px0rw0gz0Zz0Pz4Gz\
  A8zGi0cd0a_6_WDZRLXMTiI_sTWz<2>zIznOzcWzZczWczRczOcz\
  LWzWOzdGzp9zz5zz5zz4zw2zr1zk8zeDz_JzWJzZTzaUzdWzgczk\
  kzlszgizcazZWzWPzaUzgZzlczsgzxlzzizzgwzkpsnekr_<2>Oz\
  IGzLMzJTzIZsIduGkwFrxFxzDzzCzzCzzDxzFrzGlzIezJazJczG\
  czFdzDdzAez9ez8gz6gz4iz2iz1kz0<2>lz0iz0ez4cz8_zDXzIU\
  zMRzTOzX<4>Azw8zx5zz4zzLzrCzs
  }

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

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

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

Date: Sun, 14 Jan 2001 19:01:18 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Question on the Mandelbrot Fractal

At 13:58 13/01/2001 -0800, Diana wrote:
>Math and Fractal groupies,
>
>I am trying to understand the guts of computation of values in the
>Mandelbrot set, and am a little confused.
>
>I have seen printout's of the computer computation of values for the
>Mandelbrot set.
>
>For example;
>
>z(0) = c = pixel;
>z(n+1) = z(n)^2 + c
>bailout = 4
>etc.
>
>Does the computer pick a pixel point on the complex plain and square it, add
>c, [repeat many times], and determine if it is less than 4, for example?

That's basically it. To be precise, I'll use a real example.

Mandel (XAXIS) {
   c = z = pixel:
    z = sqr(z) + c
     |z| <= 4
   }

The first line here includes a note about the symmetry of the fractal.
For each pixel (representing a certain point in the complex plane whose
coordinates are stored in the variable "pixel") that Fractint bothers to
calculate, it goes through the following process.

1) It does the initialisation calculations (the stuff up to the colon)
_once_. Then it enters the loop.

2) Fractint then does the calculations in the loop (z = sqr(z)+c, here).

3) Fractint checks the test (|z|<=4) to see if it's still true. Note that
in Fractint |z| is the _squared_ modulus - it's a lot cheaper to calculate
than the modulus itself. So that test is actually checking to see if the
magnitude of z is still no more than 2 (it is a fact of the Mandelbrot set
that any trajectory that gets further from zero than this could not have
originated from any point within the set).
  If the test fails, then the loop ends and Fractint has what it needs to
specify a colour. If the test passes of course, then we go round again for
another iteration (unless we get bored).

Morgan L. Owens
"Okay, it's not the most advanced programming language. But it's simple and
fast and it works."



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

Date: Sun, 14 Jan 2001 05:56:31 -0800
From: "Diana L. Dubel" <[e-mail]>
Subject: RE: (fractint) Question on the Mandelbrot Fractal

Thanks to David and Morgan for responding to my question.

I had thought what you were saying was the case, but I was confused by the
depth of the treatment in the "Chaos and Fractals" book.  I sometimes wish
that authors would get down to basics.

I also looked up the definition in the CRC Standard Mathematics Tables and
Formulae book.  It says:

"Alternately, the Mandelbrot set consists of all points c for which the
discrete dynamical system, z(n+1) = z(n)^2 + c with z(0) = 0 converges."

Your responses, and this definition, I can understand.

Thanks,

Diana

- -----Original Message-----
From: [e-mail]
[mailto:[e-mail]]On Behalf Of Morgan L. Owens
Sent: Saturday, January 13, 2001 10:01 PM
To: [e-mail]
Subject: Re: (fractint) Question on the Mandelbrot Fractal


At 13:58 13/01/2001 -0800, Diana wrote:
>Math and Fractal groupies,
>
>I am trying to understand the guts of computation of values in the
>Mandelbrot set, and am a little confused.
>
>I have seen printout's of the computer computation of values for the
>Mandelbrot set.
>
>For example;
>
>z(0) = c = pixel;
>z(n+1) = z(n)^2 + c
>bailout = 4
>etc.
>
>Does the computer pick a pixel point on the complex plain and square it,
add
>c, [repeat many times], and determine if it is less than 4, for example?

That's basically it. To be precise, I'll use a real example.

Mandel (XAXIS) {
   c = z = pixel:
    z = sqr(z) + c
     |z| <= 4
   }

The first line here includes a note about the symmetry of the fractal.
For each pixel (representing a certain point in the complex plane whose
coordinates are stored in the variable "pixel") that Fractint bothers to
calculate, it goes through the following process.

1) It does the initialisation calculations (the stuff up to the colon)
_once_. Then it enters the loop.

2) Fractint then does the calculations in the loop (z = sqr(z)+c, here).

3) Fractint checks the test (|z|<=4) to see if it's still true. Note that
in Fractint |z| is the _squared_ modulus - it's a lot cheaper to calculate
than the modulus itself. So that test is actually checking to see if the
magnitude of z is still no more than 2 (it is a fact of the Mandelbrot set
that any trajectory that gets further from zero than this could not have
originated from any point within the set).
  If the test fails, then the loop ends and Fractint has what it needs to
specify a colour. If the test passes of course, then we go round again for
another iteration (unless we get bored).

Morgan L. Owens
"Okay, it's not the most advanced programming language. But it's simple and
fast and it works."



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

Date: Mon, 15 Jan 2001 22:33:25 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: RE: (fractint) Question on the Mandelbrot Fractal

At 05:56 14/01/2001 -0800, Diana wrote:
>Thanks to David and Morgan for responding to my question.
>
>I also looked up the definition in the CRC Standard Mathematics Tables and
>Formulae book.  It says:
>
>"Alternately, the Mandelbrot set consists of all points c for which the
>discrete dynamical system, z(n+1) = z(n)^2 + c with z(0) = 0 converges."

Well, there you go - even the CRC isn't infallible! All you can say about
the trajectory of a point within the set is that it remains bounded; it
could converge, or it could be periodic (with any integer period), or it
could indeed be chaotic (ie., with infinite period).

Morgan L, Owens
"1, -1, 1, -1, 1, -1, 1, -1, ..."



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

End of fractint-digest V1 #531
******************************