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fractint-digest        Friday, November 3 2000        Volume 01 : Number 505




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

Date: Mon, 30 Oct 2000 01:07:05 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  30-10-00  (Quintic Rectangle [4])

FOTD -- October 30, 2000 (Rating 4)

Fractal visionaries and enthusiasts:

I'm depressed today.  Maybe it's because yesterday I lost the
article that I spent several hours writing; maybe it's because
of the discouraging events on the fractal-art list.  Whatever
the reason, I seem to have no energy to write -- but I'll still
get in a few words.

Today's unimpressive picture is another view of the quintic
midget that appeared in the n-e-s-w picture of October 28.  This
time we see the midget from the Rectangular direction, which
shows the midget as a roughly rectangular hole with a pair of
tiny bridges across it.  The pattern around the midget and the
color palette are almost exactly the same as the image of 2 days
ago.

I named the picture "Quintic Rectangle" as a description.  I
rated it a lowly 4 because I don't think that much of it.  The
parameter file renders in under 5 minutes, which is slow enough
to make the download the better choice.

The GIF image has been posted to Usenet at:

          <alt.binaries.pictures.fractals>

and will soon be posted to the web at:

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

The fractal weather today was sunny but the 57F (14C) was too
chilly for the cats' outdoor adventure.  They spent the day
chasing spots of sunlight around the house instead.

And I'm going to spend the rest of the evening dozing in front
of the TV, with a junky horror movie playing.  But barring the
unexpected, I'll be here again tomorrow, with another fractal.
Until then, take care, and when the blues come calling, chase
them with a fractal.


Jim Muth
[e-mail]


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

Quintic_Rectangle  { ; time=0:04:44:04 -- SF5 on a P200
  reset=2001 type=formula formulafile=multirot.frm
  formulaname=multirot-XY-ZW-min function=flip/ident
  passes=1 center-mag=-0.00000000001373210/+0.00000000\
  000624286/6.317576e+009/0.5307/0/-72.66
  params=0/90/5/0/-1.077129325606079/-0.00275300534013\
  65/-1.077129325606079/-0.0027530053401365 float=y
  maxiter=1800 inside=0 logmap=128 periodicity=10
  colors=000cA_cA_cA_<3>cD_cD_aBY<3>iAXjAXlAXnAXpKUrOR\
  tTOvWKxZFzY0xW0vW0tV0lV0dT0ZS0TS0MQ0GQ0AP04N00N00M00\
  O00R30U60YA0aD0eI0hL0lP0qS0tX0y_0zc0zf4zcFt`PnY_jVid\
  SsZPzVO<3>zPTzNVzMV<2>zHbzGdzEezDgzBjzAlzAozAp<3>zAf\
  zAczAbyA`yA`0A07A0JA0XA0gA0sA0mA0<3>XA0SA1OA4JA6FA7A\
  AA6AC1AD0AG0AI0AJ<2>0AQ0AS0AT0AX<2>0Aa0Ac0Af0Ag0Ai0A\
  l0Am0Ao0Ar0As0Au0ApFAlSAgfAcsA`iAf_MlPZrFkx4yz9wy<2>\
  MspQqmVpl<3>lj`piYugXviTviQxiO<3>ykCzkAzk7zm4zm1<2>z\
  n0zn0xm0sm0mk3ik7djA_jFViIPiMLgPGgTAfX6f`0dc0dg0dj0_\
  d0Y_1VT4SP7PJAKDDH9GE3JB0MA0SB0XE0`H0fK0jM0oP0uS0yV0\
  zW0zQ0zM0zN0pJ3gMAYPJOSQFVY4Yf0_m0bu0fx4izDkzOnzXqzd\
  qzmqzoqzoqzpqzpqzrqzrqzsqzsqzuqzuqzvqzvqzxqz<3>zqzpq\
  z_qzIqzJqzLqzLqzrqzrqzsqzsqzuqzuqzvqzvqzxqz<3>yqzzqz\
  zqzzqzlqzlqzmqzmqzoqz<2>oqz
  }

frm:multirot-XY-ZW-min {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=(-z)^(p2)+c,
|z| <= 36  }

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


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

Date: Mon, 30 Oct 2000 18:46:38 +0100
From: "Thore Berntsen" <[e-mail]>
Subject: (fractint) Beta version of new animation utility for Fractint available

I'm working on a new animation utility for Fractint, and I need beta
testers. If You are interested please send me a mail [e-mail]

This animator can animate a lot of the parameters that You find in Par files
(including 3D!). It can do much more than just Zooming.

This program also has a module that can be used for converting the GIF files
that Fractint produces into AVI files.

The program is a MS Windows program, and it uses the DOS version of
Fractint.

Thore Berntsen
Norway
[e-mail]



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

Date: Tue, 31 Oct 2000 02:13:57 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  31-10-00  (Old Gold Minibrot [4])

FOTD -- October 28, 2000 (Rating 4)

Fractal visionaries and enthusiasts:

We'll have another short discussion today, since I lack both the
time and inspiration for a lot of fancy words.

The formula behind the image is Z^(-14)+2.5Z^(-1.4)+(1/C).  This
expression was calculated by the faithful MandelbrotMix4
formula, which never lets me down when I need a fractal in a
hurry and have little patience for a rigorous search.

I named the picture "Old Gold Minibrot" after the gold filaments
intricately weaved around the central midget, and rated it an
adequate 4.

The parameter file renders in 2-1/2 minutes, not too slow, but
still slow enough to make a download of the GIF image file from:

          <alt.binaries.pictures.fractals>

or from:

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

a reasonable alternate choice.

The fractal weather was near perfect today, with bright sunlight
and a temperature of 60F (15.5C), which so pleased the fractal
cats that they spent the afternoon sleeping on the porch.

That's it for tonight, until tomorrow, take care, and see you
then.


Jim Muth
[e-mail]


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

Old_Gold_Minibrot  { ; time=0:02:38.03 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-1.99346404717843900/+2.37985402910731000\
  /1843237/1/160 params=1/-14/2.5/-1.45/0/0 float=y
  maxiter=1200 inside=0 logmap=43 periodicity=10
  colors=000jAY<3>gAVfAUe9Tb8S_7R<2>R4KO3IL3HN9GF7BQJF\
  SIFcUO<2>riNwnMzsMwpK<3>chCZfAUd8<2>Fm2Jc5PV7UM9<3>o\
  5I<9>`9P_APYAQ<3>TBS<3>DRN9VM5ZL1aK<4>IgaMiePjh<3>an\
  v<4>`qp`ro`rn<3>_ui_vh_wg_xf_ye<3>WzNVzIUzETz9Tz5<3>\
  IzHGzKDzNBzPLzFVz6hz6<3>jzt<2>0zX`zRkzPuzNYzYBzh<2>L\
  zM<3>5zn2zu9zh<2>Tz9<2>yzO<3>Bzg<3>jzwszzkznczcXzT\
  <3>mzUqzUizZ<3>Ezr<3>IzxJzyMzy<3>WzyYzyRznLzd4z2<3>5\
  zPPzRhzTczY_zaWwf<2>JhsTcnacijcduiNrcK<3>PcCIcABc8\
  <3>_cbecjkcrqcy<3>fcbccXacSZzMWzGUzBEzo<3>NzSPzNHzhE\
  zg<3>VzeZzeYzf<8>XzkXzlXzl<2>XznXznVzl<3>OzgMzfKzdIz\
  cHzb<3>MzedzGizPmzX
  }

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, 01 Nov 2000 04:59:20 -0600
From: Bob Margolis <[e-mail]>
Subject: (fractint) Fractal Geometry Summer Workshop

Roger Bagula posted the following URL to a couple of the fractal
newsgroups. It may be of interest to the newbies amongst us who want to
know the mechanics behind the Mandelbrot and Julia Sets.

Bob

==========

Introduction to Fractal Geometry

Yale University, August 2000.

Michael Frame and Benoit Mandelbrot

http://classes.yale.edu/99-00/math190a/index.html

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

Date: Wed, 1 Nov 2000 07:26:45 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) FOTD  01-11-00  (Old Gold Minibrot [4])

FOTD -- November 01, 2000 (Rating 5)

Fractal visionaries and enthusiasts:

I'm posting this at 7:15am because last evening both internet
providers were inaccessible.

This afternoon, (October 31), while browsing the fine selection
of fractals posted to A.B.P.F., I wondered whether such images
can honestly be called fractals.  Then, realizing how the idea
of what constitutes a fractal has changed in recent years, I
wondered whether the old-fashioned style images I post in the
FOTD can still be called fractals.  Since the nature of the two
styles of images is so different, I doubt that both can still
be considered fractals.

The images I create are done more in fun than with creative
effort, usually involving little more than flat iteration bands
and an adequate color palette.  Sometimes the time from boot-up
to completed image is less than 15 minutes.  Except for the CPU
speed increase, this is the same way I worked with fractals 10
years ago.

But in that time, fractal programs have changed.  They have
evolved into virtual graphic programs.  This is good, for it
gives the fractalist much additional creative opportunity,
albeit at the expense of that vague and debatable ideal, fractal
purity.

However, I feel that we have reached the point where fractal art
has become so far removed from the original idea of fractals that
the two can no longer be considered the same thing.  This in no
way reduces my opinion of the more artistic images, but I feel
that some distinction must be made between the type of images I
create and the type of images that appear on A.B.P.F.

Since the more artistic fractalists remain satisfied calling the
images they produce fractals, I will change the description of
my images from fractals to classic fractals.  The appearance of
the images themselves, as well as the discussion will remain
unchanged.

As a simple example, today's image explores the fractal that
results when the expression Z^(-14)+2.5Z^(-1.45)+(1/C) is
iterated.  I named it "The Lost Minibrot" because that title
seemed poetic, and not because I lost it, which obviously is not
the case.  The picture rates a perfectly average 5.  The
parameter file renders in a dragging 14 minutes, making a
download of the GIF image file from:

          <alt.binaries.pictures.fractals>

or from:

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

the far wiser choice.

The fractal weather today (Halloween) was perfect, and the cats
took full advantage of the perfection.  In the 61F (16C) degree
air they romped and frolicked until they exhausted themselves, a
time which is quite short for gloriously middle-aged classic
fractal cats.

I'll return tomorrow, (now later today), with another classic
fractal and more words of wisdom.  Until then, take care, and
regardless of what you call them, keep those fractals coming.


Jim Muth
[e-mail]


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

The_Lost_Minibrot  { ; time=0:17:02.17 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+1.85728145477441900/-0.23424119516995760\
  /5531863/1/162.499 params=1/-14/2.5/-1.45/0/0 float=y
  maxiter=1800 inside=0 logmap=204 periodicity=10
  colors=000X4A_5A_7A_8A<3>dEAfGAgHAhJAjIAlK9lL8lM7<9>\
  RF2OE2MD1<2>GB0EB0DC1<32>7eK7fL6gL<3>6jN<13>bqfdrhgr\
  i<2>ntnptoqqprtprjmrjjq`gq_dqUaqQ_<19>cmAco9bp8<3>`t\
  3<39>OGKOFKOEL<2>NBMNAMOBN<9>ODXODYODZOE_OE`<9>ONiOO\
  jOPk<2>OSnNTpOUn<3>OYjPZiP_hP`gPaf<3>_ebbfaeg`hi_<3>\
  ttWwwVzzU<18>zzBzzAzz9<2>zz7zz6zz6zz6<3>zz7
  }

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, 1 Nov 2000 22:34:02 +0100
From: "=?Windows-1252?B?UHVza+FzIElzdHbhbiBqci4=?=" <[e-mail]>
Subject: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

>What is necessary for an image to have midgets? should the power o Z be
>greater than 2??

Are 'midgets' the smaller Mandelbrot-shapes in the main Mandelbrot-set and
the small 'clones' in other sets?
If yes:
I think that the iteration should be trapped with some starting values (the
value of 'Z' should settle to a low value, instead of increasing toward
infinity). The Mandelbrot-set and the 'connected' Julia-sets have this
behaviour, the 'unconnected' Julia-sets and some other formulas -
type=sierpinski, type=unity - don't. This may depend on the exponent in use
for some formulas.


Sorry for posting this so late, I forgot to send it.




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

Date: Thu, 2 Nov 2000 15:01:10 +1300
From: <[e-mail]>
Subject: Re: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

=?Windows-1252?B?UHVza+FzIElzdHbhbiBqci4=?= (if that is the writer's name)
said:
> >What is necessary for an image to have midgets? should the power o Z be
> >greater than 2??
>
In the dynamic? As in z^2+c? I guess you mean "greater than or equal to 2".
Lemme just switch to Fractint for a sec...

Well, I found a recognisable Mandelbrot midget - a slightly nicked z^2+c-like
one - in z^1.9+c.

> Are 'midgets' the smaller Mandelbrot-shapes in the main Mandelbrot-set and
> the small 'clones' in other sets?
>
Yes; also called "minibrots" or sometimes "atoms".

> If yes:
> I think that the iteration should be trapped with some starting values (the
> value of 'Z' should settle to a low value, instead of increasing toward
> infinity). The Mandelbrot-set and the 'connected' Julia-sets have this
> behaviour, the 'unconnected' Julia-sets and some other formulas -
> type=sierpinski, type=unity - don't. This may depend on the exponent in use
> for some formulas.
>
The Mandelbrot Set and its Julia sets are defined by this property (z's being
bounded in magnitude): points within the set lead to bounded orbits, orbits
starting from points outside diverge towards infinity. In "unconnected" Julias
(or "dusts"), the set is - what topologists would call - of measure zero,
which is to say that the points of the set are isolated from each other. At
any finite resolution, therefore, all you see are points _outside_ the set.

In the Unity fractal, the set is the unit circle (hence the name): the fractal
fun & games is a consquence of the method for finding it.

I leave Sierpinski's gasket as an exercise for the reader.

None of this really helps in determining when (and where) midgets should
occur: the question gets even harder when you consider that some of these
midgets (an infinite number, in fact - nay, the vast majority) are so badly
distorted that they're often unrecognisable.

Morgan L. Owens
"Lesser fleas."

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

Date: Wed, 1 Nov 2000 18:38:37 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Fractal Geometry Summer Workshop

The book "Turbulent Mirror" has a very good discussion
and explanation of fractals that would be very good for
newbies to fractals.

On  1 Nov 00 at 4:59, Bob Margolis wrote:

> Roger Bagula posted the following URL to a couple of the
> fractal newsgroups. It may be of interest to the newbies
> amongst us who want to know the mechanics behind the
> Mandelbrot and Julia Sets.

Another blast of bits from David
http://home.hawaii.rr.com/aliasjj/   http://www.hawastsoc.org/
For the best Hawaii & Pacific Basin surf forecast:
    http://www.surfreporthawaii.com

Random Thought for this Nanosecond
Sorry - insufficient processing power. Upgrade brain (y) (n)? (D.Jones)



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

Date: Wed, 1 Nov 2000 18:38:36 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) FOTD  01-11-00  (Old Gold Minibrot [4])

On  1 Nov 00 at 7:26, Jim Muth wrote:

> Since the more artistic fractalists remain satisfied
> calling the images they produce fractals, I will
> change the description of my images from fractals to
> classic fractals.

Wrong choice. *real* fractals. IMHO, fractal images using
layering et al - whether or not the layering is done in
the fractal generator or in a separate program - are
post-processed, and no longer fractals to me.

Another blast of bits from David
http://home.hawaii.rr.com/aliasjj/   http://www.hawastsoc.org/
For the best Hawaii & Pacific Basin surf forecast:
    http://www.surfreporthawaii.com

Random Thought for this Nanosecond
Observe with the eyes; work with the hands. (D.Jones)



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

Date: Thu, 2 Nov 2000 00:25:51 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) Classic FOTD 02-11-00 (Meteor Impact [6])

Classic FOTD -- Nov. 02, 2000 (Rating 6)

Fractal visionaries and enthusiasts:

I hope I've got everything right tonight.  Last night, when I
tried to post my FOTD, I found both Mindspring (Earthlink) and
AOL inaccessible.  Finally, early this morning, when I gained
access, I forgot to update the image name.  But no harm done --
the image wasn't that good anyway.

Today's image is better, at least good enough to rate a somewhat
above average 6.  The brilliant object in the picture reminds me
of a meteor plunging through earth's atmosphere on its way to a
surface impact, which is why I named the image "Meteor Impact".

The actual meteor is a midget in a remote part of the Z^1.195+C
fractal.  And I did touch up the colors in a graphic program.

When I run the image through a graphic program, I never change
it so much that it cannot be defined in a parameter file, so
running the parameter file will produce exactly the same image
as has been posted to:

          <alt.binaries.pictures.fractals>

and to:

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

The fractal weather was perfectly perfect all day, with a
temperature of 62F (16.5C) and not a single cloud to mar the
deep blue sky.  The fractal cats showed approval by lounging in
the yard for several hours, trying to decide what trouble to get
into.

My philosophical muse has been absent ever since I lost that
long FOTD article a few nights ago.  I'm hoping she'll return
before too long.  Until tomorrow, take care, and be good, but
not too good.


Jim Muth
[e-mail]


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

Meteor_Impact      { ; time=0:12:00.00 -- SF5 on a p200
  reset=2001 type=formula formulafile=branchct.frm
  formulaname=MandelbrotBC passes=1
  center-mag=-2.72959302366478800/+9.28940913170944800\
  /74.45881/1/90 params=1.195/0/4.671/0 float=y
  maxiter=75000 inside=255 logmap=22 periodicity=10
  colors=000B00B00E00G00H00L00M00P00R00U00V00X00_00_00\
  b00b00d00<2>e00e00g00<2>h00h10j10<2>k10k10m20n20n40p\
  40p40q60q60r60t70t70v90v90w90wB0yB0zB0zD0<2>zE1zE1zG\
  2zG2zG4zH4zH6zJ6zJ6zJ7zL7zL9zL9zMBzMBzL7zMB<3>zMHzMJ\
  zOM<3>zOSzOUzPX<3>zPbzPdzPezRhyRjyRkwRmwRnvRpvSrtStt\
  SvrSwrSyqSzqUzpUzpUznUznUzmUzqMzmUzhazdhyakrXkkSkePk\
  _RkYSkYUkXVkXXkVYkVYkR<2>bkadkddkg<3>jkrJkm<2>apzgqz\
  mrzrtzyvzzwzzyz<23>zzyzzyzzy<3>zzyzzzzzyzzvzzrzzpzzk\
  zzhzzezzbzzYzzVzzSzzPzzLzzHzzEzzBzz6zz2zz0zz0zz0zz2z\
  z4zz4zz4zz4zz6zz6zz6wz6tz7qz7pz7mz7kz7kz9<2>kz9nzBqz\
  BtzBwzBzzDzzDzzDzzDzzBzzD<5>zzEzzEzzEzzG<6>zzHzzHzzJ\
  <2>zzJzzJzzL<6>zzMzzMzzO<3>zzOzzSzzz
  }

frm:MandelbrotBC = { ; Z = Z^E + C
  e=p1
  p=real(p2)+PI
  q=2*PI*trunc(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<100
}

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


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Date: Thu, 02 Nov 2000 13:27:53 +0100
From: Ralph Feltens <[e-mail]>
Subject: Re: (fractint) FOTD  01-11-00  (Old Gold Minibrot [4])

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
Hi there
<p>I'm just another one of those people that after years of using fractint
were lured to Ultrafractal and its layering capabilities. IMO, layering
per se is not a sufficient reason to reject the resulting picture as not
being a fractal any more. For as long as you are using the same formula
and coordinates for all of the layers, the underlying fractal shape will
stay invariant.
<p>The use of different coloring (& layering) algorithms, of course,
can lead to remarkably diverse results. But if you felt so inclined, you
would still be able to reproduce the fractal by using a single coloring
algorithm (probably a quite complex one) in a single layer image à
la fractint (missing true color support or other limitations that are program-
but not fractal-specific not being taken into consideration). So the use
of layering techniques should not be irreconcilable with "fractal purism".
<p>There are always some arbitrary choices to be made when generating a
fractal, even a simple one in fractint: choice of colormap, spread of the
colormap (e.g. log mapping), bailout radius (effects the position of the
color bands). Not to speak of the choices nessessary to generate one of
the beautiful orbit type fractals made popular by <a href="http://members.home.net/mbfractals/">Paul
Carlson</a> ...
<p>Regards
<p>Ralph Feltens
<p>PS. Somebody on this list (was it Jim Muth?) already stated the fact
that all we see is not a fractal, but the image of a fractal ...
<p>David Jones wrote:
<blockquote TYPE=CITE>On  1 Nov 00 at 7:26, Jim Muth wrote:
<p>> Since the more artistic fractalists remain satisfied
<br>> calling the images they produce fractals, I will
<br>> change the description of my images from fractals to
<br>> classic fractals.
<p>Wrong choice. *real* fractals. IMHO, fractal images using
<br>layering et al - whether or not the layering is done in
<br>the fractal generator or in a separate program - are
<br>post-processed, and no longer fractals to me.</blockquote>
</html>


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Date: Fri, 3 Nov 2000 12:16:44 +1300
From: <[e-mail]>
Subject: Re: (fractint) FOTD  01-11-00  (Old Gold Minibrot [4])

Ralph Feltens <[e-mail]> said:

> <p>There are always some arbitrary choices to be made when generating a
> fractal, even a simple one in fractint: choice of colormap, spread of the
> colormap (e.g. log mapping), bailout radius (effects the position of the
> color bands). Not to speak of the choices nessessary to generate one of
> the beautiful orbit type fractals made popular by <a
href="http://members.home.net/mbfractals/">Paul
> Carlson</a> ...
>
Having seen some of the par files that Ultra Fractal uses, it seems that
"arbitrary choices" make up the vast bulk of the task - layering/compositing,
colouring, etc., but where's the fractal declared?

Morgan L. Owens
"The Gimp uses smaller scripts"

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Date: Thu, 2 Nov 2000 23:41:03 -0200
From: "Fernando Bresslau" <[e-mail]>
Subject: Re: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

Thanks for the answers. yes, I was meaning the small mandelbrot copies in
the z^something + c fractal. Actually, the mandelbrotmix4, which is a
generalization of the previous formula. It happens sometimes that you hit on
a fractal (by choosing the exponents and multipliers in the formula) that
has lots of midgets quite visible and obvious. Other times that┤s isn┤t
true. In some cases you get an unconnected set, others the seems to be
conected, but hasn┤t midgets, not even deformed ones.
the mm4 formula is nice because it initializes the pixels (I think) in a way
that we get undeformed midgets.
So the question was which is the condition to the existence of midgets (even
deformed ones) and I add now another one: when does a set get diconected?
maybe it would be good to concentrate the analysis to the mm4 formula, which
is namely
z=k*((a*(z^b))+(d*(z^f)))+c

being k, a, b, c, f the parameters at the z screen.

Tahnks,
Fernando Bresslau


- ----- Original Message -----
From: <[e-mail]>
To: <[e-mail]>
Sent: Thursday, November 02, 2000 12:01 AM
Subject: Re: Midgets - Re: (fractint) FOTD 29-10-00 (The Green Goblet [5])


> =?Windows-1252?B?UHVza+FzIElzdHbhbiBqci4=?= (if that is the writer's name)
> said:
> > >What is necessary for an image to have midgets? should the power o Z be
> > >greater than 2??
> >
> In the dynamic? As in z^2+c? I guess you mean "greater than or equal to
2".
> Lemme just switch to Fractint for a sec...
>
> Well, I found a recognisable Mandelbrot midget - a slightly nicked
z^2+c-like
> one - in z^1.9+c.
>
> > Are 'midgets' the smaller Mandelbrot-shapes in the main Mandelbrot-set
and
> > the small 'clones' in other sets?
> >
> Yes; also called "minibrots" or sometimes "atoms".
>
> > If yes:
> > I think that the iteration should be trapped with some starting values
(the
> > value of 'Z' should settle to a low value, instead of increasing toward
> > infinity). The Mandelbrot-set and the 'connected' Julia-sets have this
> > behaviour, the 'unconnected' Julia-sets and some other formulas -
> > type=sierpinski, type=unity - don't. This may depend on the exponent in
use
> > for some formulas.
> >
> The Mandelbrot Set and its Julia sets are defined by this property (z's
being
> bounded in magnitude): points within the set lead to bounded orbits,
orbits
> starting from points outside diverge towards infinity. In "unconnected"
Julias
> (or "dusts"), the set is - what topologists would call - of measure zero,
> which is to say that the points of the set are isolated from each other.
At
> any finite resolution, therefore, all you see are points _outside_ the
set.
>
> In the Unity fractal, the set is the unit circle (hence the name): the
fractal
> fun & games is a consquence of the method for finding it.
>
> I leave Sierpinski's gasket as an exercise for the reader.
>
> None of this really helps in determining when (and where) midgets should
> occur: the question gets even harder when you consider that some of these
> midgets (an infinite number, in fact - nay, the vast majority) are so
badly
> distorted that they're often unrecognisable.
>
> Morgan L. Owens
> "Lesser fleas."
>
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Date: Thu, 02 Nov 2000 20:39:42 EST
From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Re: Meteor

Cool image. I can hear the "disaster" music from Armageddon when I see it...
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Date: Thu, 02 Nov 2000 20:43:45 EST
From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) A remark on fractal "purity"

Purity is clearly not a black and white distinction. Some would say that
only the spare elegance of boundary scan/MIIM/distance estimator images are
truly pure. Others include heavily post-processed images whenever the basic
fractal image is enhanced rather than obfuscated or mutilated by the
post-processing. I'd say it's a continuum, but that it's reasonably pure as
long as the basic fractal is clear -- for example in some of the images I've
experimented with recently, including anti-aliased images (done by making
large images in D&C mode and resampling in Corel Photo-Paint) and truecolor
images (I make three separate greyscale images, with different logmap
settings, and use Corel's Combine Channels option to merge them as the red,
green, and blue components of the result). The results look pretty "pure" to
me...
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Date: Thu, 2 Nov 2000 23:33:38 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) Classic FOTD 03-11-00 (Ionized Mandelbrot [7])

Classic FOTD -- November 03, 2000 (Rating 7)

Fractal visionaries and enthusiasts:

Today's striking fractal was created by a rather unusual formula
- -0.002*(Z^1000)+0.02*(Z^(-2))+(1/C).  The parameters were chosen
entirely at random, as are the parameters for nearly all my
fractals.

I named the image "Ionized Mandelbrot" because of the fuzzy,
purplish-blue aura around the midget, which reminds me of the
ionized glow in a vacuum tube.  Since the picture is better than
the past few days' efforts, I rated it an above-average 7 on my
0-to-10 scale of fractal worth.

A day or so ago, a message was posted to the Fractint list,
asking what was necessary for a fractal to have midgets.  The
truth is that after working with the MandelbrotMix4 formula for
over a year, I just don't know.  To begin, it is difficult to
define exactly what a midget is.  Many fractals are filled with
holes that I do not consider midgets.  By a 'midget' I usually
mean a tiny, often distorted, classic Mandelbrot shape embedded
in a larger fractal.  These tiny Mandelbrot shapes are sometimes
called 'atoms'.

The easiest answer would be that midgets are present in all
fractals of the form Z^n+C, where 'n' is greater than 1 and Z is
initialized at the critical point of the formula.  But the
midgets are almost impossible to find in fractals where 'n' is
less than 1.2.  As 'n' is increased to higher values, the
midgets become easier to find, but ever less interesting,
eventually degenerating into boring lopsided circles.

The M-Mix4 formula automatically initializes Z to a critical
point of the iterated formula, but not all formulae have
midgets, and in many other fractals only certain limited parts
have midgets.  I have much more to discover about when and where
midgets

I'll return to the topic of midgets in a day or two.  For now
it's time to give a reminder that today's image takes 8 minutes
to render from the parameter file, and only a minute or so to
download from:

          <alt.binaries.pictures.fractals>

or from:

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

The fractal weather today was perfect, with sunny skies and a
temperature of 68F (20C), which lured the fractal cats onto the
porch and then into the yard, where they sampled the cat-mint
plant.

The philosophy is still sleeping, but I've got a few hours to go
yet in my day.  It's just enough time to find a fractal and
catch up on the fractal-art list, which has suddenly come alive.
Until tomorrow, take care, and do fractals exist as real objects,
or are they mere thoughts -- or are they both?


Jim Muth
[e-mail]


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

Ionized_Mandelbrot { ; time=0:08:08.58 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+7.625829827008553/+0.00937269972207/3.58\
  9962e+011/1/129.992/0.007 params=1/1000/-10/-2/-1.00\
  2/5000 float=y maxiter=1400 inside=0
  logmap=168 periodicity=10
  colors=000805A07C08D0CF0DG0FI0IJ0JL0L<5>L0eL0hL0k<3>\
  L1yL2zL2zL4zLOzDUzKYz0az0hz0oz0pz0ps1np<2>FehJceO`a<\
  3>dPQhMOkJLnIOoGQpGTrFWsDZuDaxCdyCgzAiz8l<2>z7uy4lr1\
  e<3>T0AM01G00I00J00J02L04M07M0AO0CO0FP0IQ0JQ0MS0PS0Q\
  W0TZ0Vc1We4Zi5`l7apAdsCexDgzGizIkzJlzLn<3>yWevZcsaap\
  dZngYkiVhlTeoQcrP`uMYxLWzJVvMVrPVnQTkTTgVTcYSZ`SWaSS\
  dQOeQJhQGiPM`OQZMWYM`WQWV<3>lFPTLOQMPOOSLPVGSQDTOAVJ\
  7WG2ZD0`80a50c20hA0lI<2>0ya<2>0zv0zz0zz0zy0xy0py0iy0\
  cy0Wy0Px0Ox<3>0Qx0Vr<3>0ha0lY0oT0sO0xJ0zF<2>0z10z00z\
  41zA4zGAzM<2>OydSviWuh`xg<3>pnauk`yhZzF0<2>n1Mi0Ve0a\
  c0hh0en4csC`xJYzQVzYSzdQ<2>zhOziOzkM<2>yoLvpMsrOrsPo\
  uQlvSkxThyTgzVdzWazY`zZYz`Wz`szGzz0zz1zz5zzAzzFzzI<2\
  >yzVvzYuzarzepziozlrzh<3>xzSyzOzzJ<3>zz14z05z17z2
  }

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, 03 Nov 2000 08:42:35 CET
From: "Baerbel Strauch" <[e-mail]>
Subject: [none]

hi there,
i┤m a big admirer of the fractal-art and i love your page...i would like to
know:
is there a beginners manual for working with/on fractals; some explanations
, photographs, webpages... i┤m also intetested in books.
i┤d love to create my own fractals!
thank u,
           bΣrbel
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Date: Fri, 03 Nov 2000 01:56:51 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Re:

BΣrbel Strauch wrote:
>
> hi there,
> i┤m a big admirer of the fractal-art and i love
> your page...i would like to know:
> is there a beginners manual for working with/on
> fractals; some explanations, photographs, webpages...
> i┤m also intetested in books.
> i┤d love to create my own fractals!
> thank u,
>
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

SHORT AND SIMPLE:  The fractal related newsgroups, discussion lists, and
websites get a lot of requests regarding fractal information.  The
following is by no means an exhaustive listing.  (For the exhaustive
list see the next section of this document.)  Just below is a listing of
a few of the programs (some freeware; some shareware) frequently used by
persons posting to the newsgroup.

Flarium/Iterations/Tiera-Zon/Sterling-ware/and others....
http://www.eclectasy.com/Iterations-et-Flarium24/
(mirror) http://www-hs.iuta.u-bordeaux.fr/ferguson/

Fractal ViZion/Fractal ZPlot/and others....
http://www.geocities.com/SoHo/Lofts/5601/

Fractint
http://spanky.triumf.ca/www/fractint/

Fractal eXtreme
http://www.cygnus-software.com/

Fractal Orbits 32
http://spanky.triumf.ca/pub/fractals/programs/ibmpc/windows/fo32201.zip

UltraFractal
http://www.ultrafractal.com/


For the MAC:
  FracPPC & Fractal Domains
     http://www.fractaldomains.com/
other MAC programs:
  http://hypertextbook.com/chaos/92.shtml
  http://spanky.triumf.ca/pub/fractals/programs/MAC/
  http://iq.tvsoft.com/~dplatt/mac/
  http://www.swin.edu.au/astronomy/pbourke/


+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

For an exhaustive list of fractal generators, galleries featuring
fractals, and other fractal related information, go to the following:

    http://home.att.net/~Paul.N.Lee/Fractal_Software.html
and
    http://home.att.net/~Paul.N.Lee/Fractal_Links.txt
and
    http://home.att.net/~Paul.N.Lee/Fractal_Census.html

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++


Sincerely,
P.N.L.
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End of fractint-digest V1 #505
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