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fractint-digest        Monday, November 6 2000        Volume 01 : Number 506




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

Date: Fri, 3 Nov 2000 10:08:02 -0200
From: "Fernando Bresslau" <[e-mail]>
Subject: (fractint) Re:

Hi, BΣrbel. I myself work mostly with two programs: fractint and
Ultrafractal. Both of them have nice webpages, with lots of info, including
for beginners. So I sugggest you take a look at  www.fractint.org and
www.ultrafractal.com where you will find links to downloads of the programs
and to resources, tutorials and goodies for beginners.
Thak you for your interest,
Fernando Bresslau
http://www.fractal.art.br

- ----- Original Message -----
From: "Baerbel Strauch" <[e-mail]>
To: <[e-mail]>
Sent: Friday, November 03, 2000 6:42 AM


> 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
> _________________________________________________________________________
> Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.
>
> Share information about yourself, create your own public profile at
> http://profiles.msn.com.
>
>
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------------------------------

Date: Fri, 3 Nov 2000 10:17:19 -0200
From: "Fernando Bresslau" <[e-mail]>
Subject: Re: (fractint) Classic FOTD 03-11-00 (Ionized Mandelbrot [7])

Thanks, Jim, for the nice answer and for the nice midget... I┤ll start
iterating formulas with z┤s bigger than 1.5, maybe a lot bigger, like
1e20...
Fernando Bresslau
http://www.fractal.art.br



- ----- Original Message -----
From: "Jim Muth" <[e-mail]>
To: <[e-mail]>
Cc: <[e-mail]>
Sent: Friday, November 03, 2000 2:33 AM
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, 3 Nov 2000 13:38:24 -0500
From: "Barry N. Merenoff" <[e-mail]>
Subject: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

Message text written by INTERNET:[e-mail]
>I think that the iteration should be trapped with some starting values<

That's an interesting idea. Could you please elaborate on it? Or maybe se=
nd
a sample Par?

Sincerely,
        Collin

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

Date: Fri, 3 Nov 2000 14:13:01 -0500
From: "Barry N. Merenoff" <[e-mail]>
Subject: Re: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

Message text written by INTERNET:[e-mail]
>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.<=


Not quite. A dust has a "topological dimension" of zero. A connected Juli=
a
has a topological dimension of one, and a fractal with a decorated interi=
or
has a topological dimension of two. Note that the topological dimension i=
s
always an integer, and is not the quantity usually referred to as
dimension. That usual quantity is the Hausdorff dimension, which is alway=
s
greater than the topological dimension, and may be fractional. The measur=
e
of a fractal is in units of length to the power of the Hausdorff dimensio=
n.

For example, the Sierpinski Gasket has a topological dimension of 1 and a=

Hausdorff dimension of 1.585. The measure is proportional to the 0.7925
power of the bounding triangle's area.

The Mandelbrot Set, with a solid-color fill, has a topological dimension =
of
1 and a Hausdorff dimension of 2, but its measure is zero. Because the
topological dimension is 1, the measure includes only the boundary, not t=
he
interior. A Hausdorff dimension of 2 indicates that the measure is in
ordinary units of area. This means that the boundary forms structures tha=
t
appear to be filled in with a boundary-only area, but which when magnifie=
d
are always seen to be merely a curve.

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

Date: Fri, 3 Nov 2000 14:19:46 -0500
From: "Barry N. Merenoff" <[e-mail]>
Subject: Re: (fractint) Fractal Geometry Summer Workshop

Message text written by INTERNET:[e-mail]
>The book "Turbulent Mirror" has a very good discussion =

and explanation of fractals that would be very good for =

newbies to fractals.
<

I thought "Turbulent Mirror" was too philosophical. "Fractals Everywhere"=

sticks more to the subject.

Sincerely,
        Collin

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

Date: Fri, 3 Nov 2000 14:27:57 -0500
From: "Barry N. Merenoff" <[e-mail]>
Subject: Re: (fractint) FOTD  01-11-00  (Old Gold Minibrot [4])

Message text written by INTERNET:[e-mail]
>but where's the fractal declared?<

Mathematically speaking, the actual fractal is an abstract concept.
Different choices of rendering the same formula are technically the same
fractal.

Sincerely,
        Collin

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

Date: Fri, 3 Nov 2000 19:35:25 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) Classic FOTD 04-11-00 (Fractally Exciting [8])

Classic FOTD -- November 04, 2000 (Rating 8)

Fractal visionaries and enthusiasts:

There's a lot of fractal in today's classic fractal, so much
fractal in fact that I found the image fractally exciting.  I
named the picture accordingly, and rated it an outstanding 8.

Once again I unwrapped the MandelbrotMix4 formula to search for
my CFOTD.  The exact fractal formula that was iterated to
produce the rather spectacular midget is 0.1Z^(-1000)+Z^2+(1/C).
The escape radius is 100.

As do all fractals, the image has detail beyond limit.  But this
fractal exceeds even the expected detail.  Rarely have I seen
such a variety of color and detail in a fractal, especially a
one-layer image rendered with the usual flat equal-iteration
bands and inside=0.  Of course, I revved up the colors a small
amount in a graphic program, but the processed color palette has
been incorporated into the parameter file, so regardless of
whether one downloads the GIF image from:

          alt.binaries.pictures.fractals

or from:

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

or renders it directly from the attached parameter file, the
image will display the full range of colors.

Since the parameter file takes almost 18 minutes to render on a
200mhz Pentium, the download is the wiser choice.

The fractal weather today was once again perfect.  The high
temperature reached 73F (23C), which made both the cats and me
happy.  The philosophy is still stagnated, waiting until my muse
returns.

Regardless of whether the muse returns tomorrow, I shall return
with another fractal and a few words to go along with the
fractal.  For now, the day's work is done, and it's time to
settle down for a relaxing evening in front of the TV,
especially with a junky old movie or two showing.

Until tomorrow, take care, and don't count your fractals until
they're rendered.


Jim Muth
[e-mail]


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

Fractally_Exciting { ; time=0:17:51.43 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=-177.609990921166/+0.03714106316788/2.283\
  007e+008/1/-127.499/0.004 params=0.1/-1000/1/2/0/0
  float=y maxiter=2000 inside=0 logmap=329 periodicity=9
  colors=000pgzwnzzuzwrurprmnngmkbif_gbVf_PdXKaR<2>7XH\
  CRGGMEKJCOEBRB9VEBXGCYJE_KGaMHdPJfRKgTMiXOkYPm_RnVXp\
  PapMdrHisCns9rp6nm4mi2kf1ib0g_0d<2>P0_M0YK0XJ0TH2RGB\
  PGHOEPMCXKBdJBkH9fG7bE7_C6XC4TB4P92M72J74O66R66V47_4\
  7b49f2Bi2Bn1Cr1Cu1Ey0Gz0<2>Hz0Mz1Pz2Tu6Xp7_i9bdCf_Ei\
  TGmOJpHK<2>z1Rz0Tz0Yy0au1fs2ir4mn6rm7ui9zgBzfCziJsmP\
  fpXTrdHn`EkYBgT9fR6bP4_N1XL0VJ0RH0OG0KD0JB0G90C60D50\
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  X9fK0aO0YR0TV2PY4Ma7Hd9EgCBkE6nH2rJ0sKya7pXCgRG_MJTH\
  MKCRC7V42Y00a24d79f<2>KPmPVpTar<2>fpy_spTwgMy_GzRBzK\
  EyJHsHKnGOiGRfEVaCYXBaRByM9BJ7gE6n96r44u02y02nM1dk0X\
  z0dz2ky6rsBymEzgJzbMzYP<2>zX6yX0yYCyYOy__y_kyawyazya\
  zpbz<3>OizHkz9mz2nz0nyYMzz0zr7zbJuOXp7gk0uf0zb0zYGuV\
  YpR_uXay_<3>gzrkzknzfpzaszVwzPyzKzzGzz9zz4zz0<2>zz0T\
  zzYzzdzzkzz
  }

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, 3 Nov 2000 20:02:51 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Fractal Geometry Summer Workshop

On  3 Nov 00 at 14:19, Barry N. Merenoff wrote:

> Message text written by
> INTERNET:[e-mail]
> >The book "Turbulent Mirror" has a very good discussion
> and explanation of fractals that would be very good for
> newbies to fractals. <
>
> I thought "Turbulent Mirror" was too philosophical.
> "Fractals Everywhere" sticks more to the subject.

It is, particularly later on. But the explanation of
who a fractal is and how they are made is very
accessible.

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
Welfare is a class for Liberal Arts majors. (D.Jones)



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

Date: Sat, 04 Nov 2000 01:55:46 EST
From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Re:

>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!

I suggest downloading Fractint
(http://spanky.triumf.ca/www/fractint/fractint/html IIRC) and browsing its
online help.
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------------------------------

Date: Fri, 3 Nov 2000 22:14:56 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Fractal Geometry Summer Workshop

On  3 Nov 00 at 20:02, David Jones wrote:

> It is, particularly later on. But the explanation of who
> a fractal is and how they are made is very accessible.

Oh, dear! Now I have to wonder if fractal sets are
complex enough to develop intelligence! #-)


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

Date: Sat, 04 Nov 2000 21:47:39 +1300
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

At 14:13 03/11/2000 -0500, you wrote:
>Message text written by INTERNET:[e-mail]
> >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.<
>
>Not quite. A dust has a "topological dimension" of zero. A connected Julia
>has a topological dimension of one, and a fractal with a decorated interior
>has a topological dimension of two. Note that the topological dimension is
>always an integer, and is not the quantity usually referred to as
>dimension. That usual quantity is the Hausdorff dimension, which is always
>greater than the topological dimension, and may be fractional. The measure
>of a fractal is in units of length to the power of the Hausdorff dimension.

If you're using a Hausdorff measure, that is - Lebesgue measure was what I
had in mind. Whether it was appropriate could be debated, but what I was
emphasising was that the Julia dusts themselves are never actually seen in
any rendering (the connected components of which always being to small to
be drawn), only their surroundings. So topological dimension was more
relevant than Hausdorff.

I shouldn't have said "isolated", it is true - I should have said
"disconnected".

>The Mandelbrot Set, with a solid-color fill,

Just say "the boundary of the Mandelbrot set" :-)

>has a topological dimension of 1 and a Hausdorff dimension of 2...

>This means that the boundary forms structures that
>appear to be filled in with a boundary-only area, but which when magnified
>are always seen to be merely a curve.

But still appears to fill an entire area even when magnified.

Morgan
"My rust is flaking"


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

Date: Sat, 4 Nov 2000 11:22:50 -0200
From: "Fernando Bresslau" <[e-mail]>
Subject: Re: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

Look at today┤s FotD. If you watch the formula, you┤ll see that something is
done to z before it is used in the formua. that┤s the initialization, and if
I understood it correctly, it ensures that the midgets found in the fractal
aren┤t distorted..
Fernando Bresslau

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
}


- ----- Original Message -----
From: "Barry N. Merenoff" <[e-mail]>
To: <[e-mail]>
Sent: Friday, November 03, 2000 4:38 PM
Subject: Midgets - Re: (fractint) FOTD 29-10-00 (The Green Goblet [5])


Message text written by INTERNET:[e-mail]
>I think that the iteration should be trapped with some starting values<

That's an interesting idea. Could you please elaborate on it? Or maybe send
a sample Par?

Sincerely,
        Collin

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

Date: Sat, 4 Nov 2000 09:37:50 -0500
From: "Barry N. Merenoff" <[e-mail]>
Subject: Re: Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

Message text written by INTERNET:[e-mail]
>that=B4s the initialization, and if
I understood it correctly, it ensures that the midgets found in the fract=
al
aren=B4t distorted..<

That's something I've never understood about MandelMix4. I thought that t=
he
best initialization is one which makes the derivative of the iteration
zero. The initialization in MandelMix4 makes the derivative of the
iteration
z*k*(a*b*z^b+d*f*z^f)
I don't understand the significance of this value.

Sincerely,
        Collin

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Date: Sat, 4 Nov 2000 22:24:06 +0100
From: "=?ISO-8859-1?B?UHVza+FzIElzdHbhbiBqci4=?=" <[e-mail]>
Subject: Re: (from Barry N. Merenoff) Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

>>I think that the iteration should be trapped with some starting values

>That's an interesting idea. Could you please elaborate on it? Or maybe send
>a sample Par?


I mean that with some starting values, the value of the iterated variable
should stay 'trapped' below a low value. That appears in the inside part of
the Mandelbrot-set, the inside of a connected Julia-set, the zero area
points of an unconnected Julia-set. In these cases, |Z| never exceeds 4.
That's nothing new.



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Date: Sat, 4 Nov 2000 20:03:22 -0600
From: "Jonathan Osuch" <[e-mail]>
Subject: (fractint) Fractint Version 20.1 patch 2

All,

The executable for patch 2 to version 20.1 is now available as fradev.zip
at:

    http://www.fractint.org/ftp/

Here's what's new:

Removed the changes to the savegraphics() and restoregraphics() routines
made in patch 1.  The changes were causing corrupted images with some
resolutions and video adapters.

Updated Bret Mulvey's email address.

Jonathan



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Date: Sat, 4 Nov 2000 21:45:55 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) Classic FOTD 05-11-00 (The next Fractal [6])

Classic FOTD -- November 05, 2000 (Rating 6)

Fractal visionaries and enthusiasts:

Today's fractal features the next midget in an apparently
endless series of midgets, which is reason enough to name the
picture "The Next Midget".  Yes, I realize that a name such as
"The Final Midget" or "Dancing Midget" would be more poetic, but
I was not trying to be a poet.  I was simply trying to name a
fractal.

The bluish-gray picture, with its metallic appearance and broad,
intricate filaments, rates a 6, which is a little above average.
I gave the image just the slightest boost in a graphic program.
The graphic boost is included in the parameter file.

The expression behind the image, Z^(-14)+2.5Z^(-1.45)+(1/C), is
simple enough, and thanks to the wonder-formula MandelbrotMix4,
it produces a fractal filled with midgets.  BTW, I call the
M-Mix4 a wonder-formula because I wonder why it sometimes works
and other times fails to draw a fractal with midgets.

The MandelbrotMix4 formula has an interesting history, which I
may tell in one of these C-FOTD's.  But today is not the day.
It's Saturday evening and the time is near for my weekly
excursion into the world of junk TV.

With the parameter file having a render time of 1-1/2 minutes,
it's a toss-up whether to run the parameter file or to run to
Usenet at:

          <alt.binaries.pictures.fractals>

or to the Web at:

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

and download the GIF image from there.

The fractal weather today was cloudy with a few tiny drops of
rain.  The temperature of 67F (19.5C) was un-notable.  The cats
failed to note it as they frolicked in the yard.

There's no philosophy today, but it's coming, so keep in touch.
You wouldn't want to miss out on the action when the philosophy
breaks.  Until next time, take care, and enjoy today's image.


Jim Muth
[e-mail]


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

The_Next_Midget    { ; time=0:01:29.75 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip
  center-mag=-1.778683555482173/-0.5422446532818447/23\
  5454.1/1/-49.999 params=1/-14/2.5/-1.45/0/0 float=y
  maxiter=1200 inside=0 logmap=17 periodicity=10
  colors=000RQ_UTaWVdZYe`_gcajedlgfmjhplkrmmshhmeeha`d\
  ZY_VTVRPPOKKKHGHCAD86C99AAC9CG8CI7DL7EO6GQ5GU3HW2I_1\
  Ja1Jd<4>0PZ0QY0RY<3>0WT0YR0ZQ0ZQ5_RA_RH`RL`RRaRYaRaa\
  RgcRleRrgTxjTzkTwoUqrVkuWexW_zYUzZPzZKx`HqcDje9cf5Vh\
  1Ok0Hm09o0Gj3Ke<2>HZRLcI<3>cvegzkkzqgwvepyahz_azWVzU\
  OzQHzO9zK2zI0zH8zHKz<2>GuzGzzKzzOxzTuzWqz<3>lczq_zuW\
  z<2>IJz<2>W1z_0zV0zQ1z<3>7Cz2Ez0Hz0Jz2HzAEzJDzRAz<2>\
  o6z<3>sAzsCzuDz<3>xIzyJzzKzzKz<8>eVzcWz`Yz<2>U`zRazQ\
  `z<2>PZzOYzOWzNWzNVzLUzLUz<3>rTz<3>e_za`z_azWdzUez<3\
  >HkzDmzAoz7pz5qz9oz<7>aezedzhcz<3>wZzaRzHKz0Ez0Lz1Tz\
  <2>8mzAuzCzzJszQkzWczcVzjNzpGzhHzcIzYJzRKzLLzGNz9Oz3\
  Pz0PzEYzVdzkkzzrz<2>zNzzKz<2>zGzETzEQzGPzGNzHKzHJzIH\
  zIGz<2>POz
  }

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, 5 Nov 2000 04:02:19 -0500
From: "Barry N. Merenoff" <[e-mail]>
Subject: Re: (from Barry N. Merenoff) Midgets - Re: (fractint) FOTD  29-10-00  (The Green Goblet [5])

Do you know a procedure for finding the maximum value of |Z| for an
arbitrary formula?

Sincerely,
        Collin

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Date: Sun, 5 Nov 2000 10:51:20 EST
From: [e-mail]
Subject: Re: (fractint) Beta version of new animation utility for Fractint available

Can this utility allow me to convert "color" cycled animations from the real
time Fractint into an AVI file?  I love color cycling and have been spending
my time learning to manipulate 256 color fractals.

Let me know.  Tom

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Date: Sun, 05 Nov 2000 16:26:14 GMT
From: "Rupert Millard" <[e-mail]>
Subject: Re: (fractint) Re: List of fractal programs by P.N.L.

Paul,

>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


This is *very* helpful, there are lots of "exhaustive" / "definitive" lists
of fractal software out there:

http://www.geocities.com/arangas/index.html

http://www.eclectasy.com/fractovia/fractal_generators/fractals_freeware1.html

http://thinks.com/software/fractals.htm

& the ones on http://spanky.triumf.ca, http://www.fractalus.com etc.

but I've not yet seen one quite so "exhaustive" / "definitive" as yours!

Keep up the good work,

From,

Rupert

_________________________________________________________________________
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Date: Sun, 05 Nov 2000 11:56:41 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: Re: (fractint) Re: List of fractal programs by P.N.L.

Rupert Millard wrote:
>
> Paul,
>
> >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
>
> This is *very* helpful,

Thank you so *much*!!  But the above link is not the "exhaustive" list
of software, nor does it claim to be.  The preceding sentence mentions
other areas of fractal concern like galleries, etc., and is also
followed by the following two additional links:

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

The three combined URL, will make up the "exhaustive" list of most
things related to fractals.

>
> there are lots of "exhaustive" / "definitive"
> lists of fractal software out there:
> http://www.eclectasy.com/fractovia/fractal_generators/fractals_freeware1.html
>
> http://thinks.com/software/fractals.htm
>

Where do you think the above two originally got their information
from??  I gave Juan Luis permission back around July 05, 1999 to use
that information for his website.

>
> Keep up the good work,

Thank you again, and I hope to be able to continue doing so.

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

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Date: Sun, 05 Nov 2000 13:14:23 -0600
From: "Paul N. Lee" <[e-mail]>
Subject: (fractint) Fractals in Multimedia

The Institute for Mathematics and Its Applications (located at the
University of Minnesota, Twin Cities Campus, in Vincent Hall) will be
having a "Minisymposium" concerning _Fractals in Multimedia_, scheduled
for January 17-19, 2001.

Some of the people involved are as follows:

    Michael Barnsley
    Steven Demko
    Ken Musgrave
    Heinz-Otto Peitgen
    and about 20 more...

Further information may be found at the following:

    http://www.ima.umn.edu/multimedia/winter/ms.html

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

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Date: Mon, 6 Nov 2000 00:12:53 -0500 (EST)
From: Jim Muth <[e-mail]>
Subject: (fractint) Classic FOTD 06-11-00 (Abstraction 01 [7])

Classic FOTD -- November 06, 2000 (Rating 7)

Fractal visionaries and enthusiasts:

I appear to be on a roll.  One above-average fractal after
another keeps turning up.  In keeping with the trend, today's
image, which for lack of a better idea has been named
"Abstraction 01", rates an above-average 7.

The formula of today's scene is Z^1.03-Z^(-1.5)+(1/C).  The
calculation was once again done by the mysterious MandelbrotMix4
formula, which appears strange but produces midgets by the
thousands.

The parameter file finishes in 12-1/2 minutes on a reasonably
fast Pentium.  The image file downloads much faster from:

          alt.binaries.pictures.fractals

or from:

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

The fractal weather today was sunny but with puffy white clouds,
and a temperature of 57F (14C), which was barely warm enough for
the fractal cats.

I wish my philosophizing were doing as well as my fractal
searching.  Once again I failed to find the inspiration to
write.  But I'll try again tomorrow.  Until then, take care, and
what did we do with our idle time before fractals existed?


Jim Muth
[e-mail]


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

Abstraction_01     { ; time=0:12:35.44 -- SF5 on a P200
  reset=2001 type=formula formulafile=critical.frm
  formulaname=MandelbrotMix4 function=recip passes=1
  center-mag=+0.24270803302426930/+4.39028735472479500\
  /265776.6/1/22.5 params=-1/-1.5/1/1.03/0/0 float=y
  maxiter=1800 inside=0 logmap=213 periodicity=10
  colors=000S4zT1z<2>Y0zb0zh0zX0z`0zS0zQ0wN0tM0qJ0nH0k\
  E0hD0eA0b80_50X40T10Q<2>00H00K11N<7>PQhSTkVXnY_q`ctc\
  fufixilz<2>ruzqozokzoezn`znVzlQzkKzkGziAzi5zkEzlNznX\
  zoexqnwut0qq0ln1hk2ch4_e4<2>MY8HVADSA<2>0JE0EB0HE<2>\
  0PJ0SK0TM0XN0_P0`Q<3>0kX0nY0o_<3>0ze<3>0zk0ze0x_2tT7\
  oP<3>PY2T_4X`5`b7cb7fc8keAneAqfBuhDxiEziEzkGzlHzlHzo\
  EtqBkrAbu7Tw4Kx2Bz02z00z00z00z0<3>1o01l02h0<3>8X0AT0\
  0b0EQ0MG0T40`00<2>w00z20z50<2>zE2wH5oK7iNAkQBkTElXGl\
  _JnbKneNohPokQkfT<4>XPhTMkQHn<3>E4z70zB1zG5xJAuNErSJ\
  oVNk_ShcXef`bke_oiVrnSwrPzwMzzJwwK<2>`iKeXJiKKn8HoBK\
  oEMoGPoJQoKSoNVoQXoS_oV`oXbo_eobfociofkohlkikfkkclk_\
  nkXoiSqiNriKtiGuhDwh8xh5zh8zfAzeDzcEzbHz`Jz_MzYNzYPz\
  XSzVTzTXzSYzQ`zPbzNczNfzMhzKkzJlzHozGqzEwzGrzEnzDPzz\
  Qzz
  }

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

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


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Date: Mon, 6 Nov 2000 09:09:16 +0100 (CET)
From: Thore Berntsen <[e-mail]>
Subject: Re: (fractint) Beta version of new animation utility for Fractint available

- [e-mail]
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit

>
> Can this utility allow me to convert "color" cycled animations from the real
> time Fractint into an AVI file?  I love color cycling and have been spending
> my time learning to manipulate 256 color fractals.
>
> Let me know.  Tom
>
> --------------------------------------------------------------
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> Post Message:   [e-mail]
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>
>
> Yes it animates colors.
- [e-mail]--


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End of fractint-digest V1 #506
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