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fractint-digest          Monday, May 31 1999          Volume 01 : Number 394




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

Date: Wed, 26 May 1999 20:03:13 -0400
From: "Phil DiGiorgi" <[e-mail]>
Subject: (fractint) Nifty freeware

Sorry, no fractal content, but I thought this little program might be of
interest to the subscribers to this list.

If you like to use your fractal images on your windows desktop, this program
will get rid of the little rectangles of solid color under your icons.   It
makes the background of the icon text transparent.   Honest, that's all it
does!   I know it ain't much, but it it thrills me to pieces.   I don't know
any other way to do this.

Hope it's useful to somebody.   Here's the URL:
www.pobox.com/~jayguerette/transparent

Phil D.


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Date: Thu, 27 May 1999 11:45:06 +0800
From: [e-mail]
Subject: (fractint) Receipt of 1999/5/10 PM 01:44 message

Re:Re: (fractint) fractal art short course


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Date: Thu, 27 May 1999 11:47:24 +0800
From: [e-mail]
Subject: (fractint) Receipt of 1999/5/7 AM 10:16 message

Re:(fractint) Purely Mathematical


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Date: Thu, 27 May 1999 11:47:57 +0800
From: [e-mail]
Subject: (fractint) Receipt of 1999/5/7 AM 10:00 message

Re:Re: (fractint) Purely mathematical


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Date: 26 May 99 23:22:34 MDT
From: Paul Derbyshire <[e-mail]>
Subject: Re: [(fractint) Receipt of 1999/5/7 AM 10:00 message]

[e-mail] wrote:
> Re:Re: (fractint) Purely mathematical =



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Whuh? What are these messages for?

____________________________________________________________________
Get free e-mail and a permanent address at http://www.netaddress.com/?N=3D=
1

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Date: Thu, 27 May 1999 07:44:42 +0200
From: "Pascal DUCLAUD-LACOSTE" <[e-mail]>
Subject: (fractint) Topology of the MandelBrot

This is a multi-part message in MIME format.

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Bonjour=20

Hi !

1 or 2 years ago I found (on the Web) a map pointing at nice locations =
where to zoom in a Mand.=20

Some area are poor of beautifull things, other have plenty !!! Spendig =
zooming time in a poor area is frustrating ..=20

Is there such a map somewhere ?=20

Many thanks

Pascal=20

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<!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN">
<HTML>
<HEAD>

<META content=3Dtext/html;charset=3Diso-8859-1 =
http-equiv=3DContent-Type>
<META content=3D'"MSHTML 4.72.3110.7"' name=3DGENERATOR>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT color=3D#000000 size=3D2>Bonjour </FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>Hi !</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>1 or 2 years ago I found (on the =
Web) a map=20
pointing at nice locations where to zoom in a Mand. </FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>Some area are poor of beautifull =
things, other=20
have plenty !!! Spendig zooming time in a poor area is frustrating ..=20
</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>Is there such a map somewhere ? =
</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>Many thanks</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2></FONT> </DIV>
<DIV><FONT color=3D#000000 size=3D2>Pascal </FONT></DIV></BODY></HTML>

- ------=_NextPart_000_001C_01BEA814.C8831A40--


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Date: Thu, 27 May 1999 11:09:25 +0200
From: Jan Schaefer <[e-mail]>
Subject: Re: (fractint) Topology of the MandelBrot

Hi,

try this:

http://eulero.ing.unibo.it/~strumia/MappeMandJulia.html

sorry, but only a few zooming areas...

I looked at altavista after: +map +mandelbrot

maybe there are some more in the web

> Pascal DUCLAUD-LACOSTE schrieb:
> Is there such a map somewhere ?

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Date: Thu, 27 May 1999 08:50:24 EDT
From: [e-mail]
Subject: Re: (fractint) Colormaps

In a message dated 5/26/99 7:42:44 AM Eastern Daylight Time, [e-mail]
writes:

<< You probably handcraft your own palettes, but if you or anyone would
 like to try the palette making programs, please let me know.   >>

I'd like to give them a try.

Thank you.

- --Bob Carr--

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Date: Thu, 27 May 1999 09:09:53 -0400
From: Barry N Merenoff <[e-mail]>
Subject: (fractint) Re: 1/f scaling noise

A while ago I sent in two questions about 1/f scaling noise. Does anybody=

have answers?

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Date: Thu, 27 May 1999 19:00:41 +0100
From: "Les St Clair" <[e-mail]>
Subject: Re: (fractint) Topology of the MandelBrot

Hi Pascal

> 1 or 2 years ago I found (on the Web) a map pointing at nice locations where
to zoom in a Mand.
> Is there such a map somewhere ?

In between making complaints about Fractint Paul Derbyshire managed to put this
useful guide together...

"PGD's Quick Guide to the Mandelbrot Set", it can be found at
http://www.globalserve.net/~derbyshire/manguide.html


(just kidding Paul <g>)

cheers, Les



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

Date: Thu, 27 May 1999 21:56:58 -0500
From: Bob Margolis <[e-mail]>
Subject: (fractint) Beginner's Tips

Greetings Budding Fractalartisans:

Here's what Juan Luis Mart=EDnez has to say at his  Web site
( Doing Fractals http://home.coqui.net/storjorn/Opinion/My_fractals.html =
) about creating fractal art:

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

I don't think of myself as an expert fractal artist (there's a lot to be =
learn before that), but I can
state some basic "principles" about fractal creation I have realized so f=
ar:=20

Patience is the keyword. Producing a fractal is a complex process even to=
 a fast computer. Each figure
requires a lot of calculations, and those take time. The deeper you go, t=
he slowest the process will be.

Keep the image relatively small (between 300x300 and 600x600, but not sma=
ller or you won't discern the
details) while searching for the area that attracks your creative self. O=
nce you finish working with it,
change to a big resolution for the final file.

Regularly it will take just a few minutes to calculate a fractal, but som=
etimes it could take as long as
several hours or even days (and even a lot more). That depends on the com=
plexity of the fractal and the
number of iterations you choose.

A small change in the parameters - the values of each variable - will res=
ult in an entirely different image.
Once you find something interesting, save it or write the values on paper=
 or to a text file (using
NOTEPAD, for example). Otherwise, you won't probably be able to return to=
 that same spot again. You
could end up with two dozen fractals before finishing a single image, but=
 you won't regret it if suddenly
an unexpected and unwelcome error happens.

Most of the fractal generators I know produce a parameter's file whenever=
 they save a bitmap (that's
the case with all of Ferguson's generators). Some others (FractInt among =
them) store that information in
the same image's file; thus, be sure to keep an unadulterated copy of the=
 original file if you plan to alter
the fractal in a graphics editor later. INFI and Kaos Rhei won't do any o=
f that automatically, so get used
to do it manually. For INFI, create a new bookmark for every image you co=
me up with; for Kaos Rhei,
choose "Save Parameters" from the FILE menu item.

It's also practically impossible to produce two identical images except w=
hen using the same, and only
the same, parameters. So keep those files in a save place. They are the t=
he only way you have to
reproduce an image (if need be) and could be a proof of authorship.

It is absolutely probable that you won't know what an image will look lik=
e beforehand. You'll be
exploring an imaginary and never-ending world, searching for new vistas t=
o bring to the real one.

There are certain basic features that are easy to remember and recognize,=
 but while you "travel" along
the Mandelbrot regions, for example, new patterns never seeing before wil=
l come into view. That's part
of the thrill that attracts us to fractal art.

If you have been zooming in a region for a while, chances are that you ha=
ve noticed that several
features look whashed out, with dark patches and without any detail. It's=
 just that you are too deep into
the figure at "low resolution". Adjust the number of iterations to a high=
er value and the small
Mandelbrots, ridges, spirals, smoothness and spikes will return to view.

It's not possible to explore the whole Mandelbrot set in a lifetime, let =
along all other fractal types out
there. Although you can see many fractal images in a lot of publications,=
 web sites and other products
(including nature), the chances of getting an original composition are hi=
gh.

Most fractal generators are capable of applying filters such as stalks, a=
tan, strands and bubbles, to an
image. Those are also mathematical expressions that enhance or adds featu=
res to these intriguing
shapes.

After getting the figure concentrate on coloring it. That will make the d=
ifference between a regular
image and an artwork. The coloring method will depend on the fractal gene=
rator you are using. Some
use palettes in which you are free to select the colors to be used; other=
s use color controls, and you
just have to move the sliders up or down, left to right, until you get th=
e combination that fits your
taste; some use algorithms to give the tones to each pixel; while others =
are based on predefined color
maps which colors can be rotated in order to change their hues.

Feel free to apply post-processing techniques to the resulting images. Wh=
ile some purists will say they
hurt the natural figure (what certainly is true), they will add to the cr=
eative process, increasing the
artistic outcome.

Study, at least briefly, the mathematics behind the images. You will disc=
over you don't need to be a
genius to understand the basic concepts. The sole process of generating a=
 figure will help you to get
some clues that could later turn into wonders.

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

Now go create some fractal art.

Bob "When Will This Zoom-in End?" Margolis
                                                                         =
                 .

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

Date: 28 May 99 09:19:31 MDT
From: Paul Derbyshire <[e-mail]>
Subject: Re: [(fractint) Topology of the MandelBrot]

"Pascal DUCLAUD-LACOSTE" <[e-mail]> wrote:=


> Hi !

> 1 or 2 years ago I found (on the Web) a map pointing at nice locations =
>
where to zoom in a Mand. =


It moved. The new address is
http://www.globalserve.net/~derbyshire/manguin1.html   ;-)

> Some area are poor of beautifull things, other have plenty !!! Spendig =
>
zooming time in a poor area is frustrating .. =


You seem to have gotten a strange or corrupt copy of the Mandelbrot set..=
=2Emine
has no "poor areas" :-) Sometimes you need to dig a bit, but almost anywh=
ere
has something of interest... after all, everywhere has mini Mandelbrots a=
nd
embellished versions of any area can be found near any mini Mandelbrot.


____________________________________________________________________
Get free e-mail and a permanent address at http://www.netaddress.com/?N=3D=
1

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Date: Fri, 28 May 1999 11:21:46 -0600
From: Phil McRevis <[e-mail]>
Subject: (fractint) double messages

I asked XMission about this -- apparently it is an interaction between
mail user agents and the list software.  It is spurious and (so far)
unrepeatable, which makes it difficult to debug.  Apparently there is
some mail software out there that receives the mail, but makes the
sender think that the mail hasn't been received.  Thus the sender
retransmits the message.  At least the problem results in duplicate
messages, rather than messages lost!
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
          <http://www.eden.com/~thewho>

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

Date: Fri, 28 May 1999 18:54:28 -0700
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) Topology of the MandelBrot

At 07:44 AM 5/27/99 +0200, Pascal wrote:
>1 or 2 years ago I found (on the Web) a map pointing at nice locations
>where to zoom in a Mand.
>...
>Is there such a map somewhere ?

My favorite way to find hot spots is to poke around the set using
attractor plots.  In Fractint, this is accomplished using the "orbits"
function ("o" key).  After you M-set is done generating, press "o"
and move the cursor around until you start seeing interesting shapes
in the orbit window, then zoom in on those coordinates.  As the
shampoo bottle says, "lather, rinse, repeat".  In this case, feel free
to do so ad infinitum!


Psychoholically yours,
        Bud


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

Date: Fri, 28 May 1999 23:11:54 -1000
From: "David Jones" <[e-mail]>
Subject: Re: (fractint) Topology of the MandelBrot

On 28 May 99 at 18:54, Mark Christenson wrote:

> At 07:44 AM 5/27/99 +0200, Pascal wrote:
> >1 or 2 years ago I found (on the Web) a map pointing at nice locations
> >where to zoom in a Mand.
> >...
> >Is there such a map somewhere ?
>
> My favorite way to find hot spots is to poke around the
> set using attractor plots.  In Fractint, this is
> accomplished using the "orbits" function ("o" key).
> After you M-set is done generating, press "o" and move
> the cursor around until you start seeing interesting
> shapes in the orbit window, then zoom in on those
> coordinates.  As the shampoo bottle says, "lather,
> rinse, repeat".  In this case, feel free to do so ad
> infinitum!

Thank you, thank you, thank you! Been using Fractint for
years, and just now find out about the delightful Orbits
key!

Another blast of bits from David
http://www.aloha.net/~shauna/   http://www.hawastsoc.org/
For the best Hawaii & Pacific Basin surf forecast:
    http://www.surfreporthawaii.com

Random Thought for this Nanosecond
When push comes to shove, never confuse co-workers with friends.



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

Date: Sat, 29 May 1999 16:33:48 +0100
From: "gwydion" <[e-mail]>
Subject: (fractint) Fractal Symphonies

This is a multi-part message in MIME format.

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    charset="iso-8859-1"
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Musings from Fractal Land
Every shape and every colour that we see ,fires a combination of cones
 and rods {notes}in the eye, sending a signal to the brain.Certain =
combinations of shape and colour, fire signals that are sent to specific =
areas of the brain, {{chords}like the 93rd Stellation of the =
Icosidodecahedron}.Fractals allow this process to reach the next level =
and could be called the gift of Fractal Land{symphonies}.
Due to the infinite nature of fractals, as we look at a fractal  chords =
play together in unique combinations, forming a symphony in the resonant =
chamber of the skull.Fractal explorers experience the new music and are =
changed therin.When VR comes of age these symphonies become Evolutionary =
helpers in a more major way .This is  one of the many gifts of programs =
like Fractint, Ultrafractal, Fractal Extreme and others whom i have not =
met and the explorations you undertake.You are all finding the way =
points for future grand adventures.
Let the music play on.=20
Gwydion

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    charset="iso-8859-1"
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META content=3D"text/html; charset=3Diso-8859-1" =
http-equiv=3DContent-Type>
<META content=3D"MSHTML 5.00.2614.3401" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT size=3D2>Musings from Fractal Land<BR>Every shape and every =
colour that=20
we see ,fires a combination of cones<BR> and rods {notes}in the =
eye,=20
sending a signal to the brain.Certain combinations of shape and colour, =
fire=20
signals that are sent to specific areas of the brain, {{chords}like the =
93rd=20
Stellation of the Icosidodecahedron}.Fractals allow this process to =
reach the=20
next level and could be called the gift of Fractal =
Land{symphonies}.<BR>Due to=20
the infinite nature of fractals, as we look at a fractal  chords =
play=20
together in unique combinations, forming a symphony in the resonant =
chamber of=20
the skull.Fractal explorers experience the new music and are changed =
therin.When=20
VR comes of age these symphonies become Evolutionary helpers in a more =
major way=20
.This is  one of the many gifts of programs like Fractint, =
Ultrafractal,=20
Fractal Extreme and others whom i have not met and the explorations you=20
undertake.You are all finding the way points for future grand =
adventures.<BR>Let=20
the music play on. <BR>Gwydion</FONT></DIV></BODY></HTML>

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Date: Sat, 29 May 1999 10:56:53 -0700
From: Mark Christenson <[e-mail]>
Subject: (fractint) feature request

Yeah, I know I should use the Spanky wish list interface, but
I also know you developers are on this list and 20.0 is just
around the corner.  I figured this idea would get lost in the
wash on the wish list, and so chose to break protocol and
post it here:

Would it be possible to implement the Decomposition coloring
method in *multiples* of two rather than *powers* of two?  Or
what about *any* number (less than 257 :-) )?  It would make
life easier by allowing one to apply palettes with different "periods"
to a fractal.  I have often had to create a stretched version of
an existing palette for this reason.


Thanks, Bud


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Date: Sat, 29 May 1999 15:26:16 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) feature request

In article <[e-mail]>,
    Mark Christenson <[e-mail]>  writes:

> I figured this idea would get lost in the
> wash on the wish list, and so chose to break protocol and
> post it here:

Its actually the other way around.  If you submit your idea/request
via the wish list its much less likely to get lost.  That, after all,
is the whole point of the wish list.  So.... submit your idea again
through the wish list.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
[e-mail]    <http://www.eden.com/~thewho>

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Date: Sat, 29 May 1999 20:50:53 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) Topology of the MandelBrot

Mark wrote:

> My favorite way to find hot spots is to poke around the set using
> attractor plots.  In Fractint, this is accomplished using the "orbits"
> function ("o" key).  After you M-set is done generating, press "o"
> and move the cursor around until you start seeing interesting shapes
> in the orbit window, then zoom in on those coordinates.

I have an idea that this procedure might lead to self similar areas,
which might not be desirable.

After first implementig arbitrary precision, I tried to "fish" for a
fractal in very deep water (e.g. high magnification). I did it by using
viewwindows mode and letting just a few pixels develop in solid
guessing mode. Where pixels had different colors, I figured it was
safe to zoom. What I was trying to avoid was a solid area with no
structure. The problem was that arbitrary precision is slow, so I
was trying to see where to zoom by generating very few pixels.

When I was done, I let the whole fractal calculate. I wondered if I
had set some kind of a record, since the magnification was
something like 10^900, and the fracta;l looked quite interesting.

But alas, something looked wrong. The fractal looked familiar. In
fact the fractal was identical (except for rotation) to a fractal
generated at the same place but with a very modest magnification.

From my very limited experience, it seems to me that most
strategies from zooming in to very deep magnifications are liekely
to fall into "whirlpools of self similarity" where nothing new is found.
One strategy to avoid this is to follow a descreasing sequence of
migit Mandelbrots. I don't know how to prove this, but it seems
apparent from experimentation that midgits are not self-similar,
quite the contrary: as one zooms deeper, the patters surrounding
the midgits change.

Questions:

1. Is it true that zooms following sequences of smaller and smaller
midgits never fall into self-similarity

2. Are there other strategies for zooming to great depths that result
in different images as one goes deeper.

Tim


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Date: 29 May 99 21:29:05 MDT
From: Paul Derbyshire <[e-mail]>
Subject: Re: [Re: (fractint) Topology of the MandelBrot]

"Tim Wegner" <[e-mail]> wrote:
Mark wrote:

> I have an idea that this procedure might lead to self similar areas, =

> which might not be desirable. =


I would expect that it would not, if you take care to choose based on see=
ing
*new* shapes in the orbits.

> After first implementig arbitrary precision, I tried to "fish" for a =

> fractal in very deep water (e.g. high magnification). I did it by using=
 =

> viewwindows mode and letting just a few pixels develop in solid =

> guessing mode. Where pixels had different colors, I figured it was =

> safe to zoom. What I was trying to avoid was a solid area with no =

> structure. The problem was that arbitrary precision is slow, so I =

> was trying to see where to zoom by generating very few pixels.

> When I was done, I let the whole fractal calculate. I wondered if I =

> had set some kind of a record, since the magnification was =

> something like 10^900, and the fracta;l looked quite interesting. =


> But alas, something looked wrong. The fractal looked familiar. In =

> fact the fractal was identical (except for rotation) to a fractal =

> generated at the same place but with a very modest magnification.

> From my very limited experience, it seems to me that most =

> strategies from zooming in to very deep magnifications are liekely =

> to fall into "whirlpools of self similarity" where nothing new is
> found...

In a sense, all whirlpools are illusory. The M-set is *never* quite
self-similar. Example: Start with a seahorse and generate an image of the=

spiral. Save this in a par file. Zoom the outer curve of the spiral and f=
ind a
double spiral which hides a midget.

Now from the original spiral, zoom the center of the spiral two or three
times. Whirlpool? Maybe not. Zoom a part of spiral arm and find a double
spiral. The double spiral is not the same! It has many more turns.

But to see anything interesting deep in the spiral you couldn't find near=
 the
surface, you need to move away from the middle eventually and aim for whe=
re
there is a midget.

The moral of this story is, the stuff around midgets in a "whirlpool" cha=
nges
the deeper you go, usually by wrapping around more times in some way.

> One strategy to avoid this is to follow a descreasing sequence of =

> migit Mandelbrots.

> I don't know how to prove this, but it seems apparent from
> experimentation that midgits are not self-similar, quite the contrary:
> as one zooms deeper, the patters surrounding the midgits change.

Yep. Every mini Mandelbrot has a characteristic filament that attaches to=
 it.
As you zoom up mini Mandelbrots you accrete more filament types.

> 1. Is it true that zooms following sequences of smaller and smaller =

> midgits never fall into self-similarity

Yep. Although things can just keep getting hairy.

> 2. Are there other strategies for zooming to great depths that result =

> in different images as one goes deeper.

Yep. There are two basic strategies. One is to zoom and generally hang ar=
ound
mini Mandelbrots; the other is to zoom into clefts between buds, where yo=
u can
accumulate more kinds of spirals or seahorse arms or scepters.

There's a third, more advanced strategy, which is to mix the two abopve
strategies.

As for strategy 1, I must elaborate. You can zoom to the actual mini
Mandelbrot and explore its clefts and primary dendrites. You can zoom ver=
y
near it and explore attached filaments for their mini Julias. There are
infinitely many variations here. For instance you can zoom at a midget an=
d
then a midget of the first's primary dendrites, then find an interesting =
area
of the micro Mandelbrot. Find a dendrite, which will have filaments assoc=
iated
with the micro. Zoom one of the filaments. It has mini Julias and more
filaments, these associated with the mini. Zoom this tertiary filament an=
d
there are more embedded Julias... which are associated with the mini, not=
 the
micro. These mini Julias have, embedded in them ... mini Julias of a diff=
erent
type, those characteristic of the micro. Yikes!

Instead, you can stop far out from the mini, where there are only two or =
four
or eight or sixteen repeated filaments. Then attack one of these. You get=

"dumbbells" or other shapes. Zoom a 3-armed spiral for instance. One arm =
goes
to the mother set, two terminate in bulbs. Zoom an arm and find a doubled=

spiral. Instead of aiming for the central, probably still invisibly small=

mini, attack one of the double spiral's arms. Pick one that terminates. F=
ind a
doubling, and you'll see that each spiral in the doubled spiral has one a=
rm to
the central join where a mini lurks and one arm that terminates and a thi=
rd
arm that passes through another joining on the way to the mother set. Now=

attack the remaining terminating arm...
As for locating the mini, it makes a difference where it is on a filament=
, or
how deep in a whirlpool.

When exploring a mini Julia, you can find a mini in the center, but you c=
an
also attack the mini Julia's other structures... spirals, seahorse eyes,
dendrites, or whatever.




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Date: Sun, 30 May 1999 18:10:42 EDT
From: [e-mail]
Subject: (fractint) A Julia type...

Hi Everybody,

Below is the FRM and PAR for a Julia type that I really liked.

- --Bob Carr--

Carr3534(YAXIS){;Modified Sylvie Gallet frm.1996
;passes=1 needs to be used with this PHC formula
pixel=-abs(real(pixel))+flip(imag(pixel))
b3a=(0.1+|0.018/pixel|)
b1=(|0.026/pixel|)-conj(|0.025/pixel|)-real(0.025/pixel)
b1a=flip(conj(0.1+pixel))*(pixel)-(conj(0.1/pixel))+sqr(flip(0.1/pixel))
b3=((b1a^1.5)/((|0.2/pixel|)))-conj(b3a)/pixel
b5=(|pixel/2|)*b3-flip(flip(0.046/pixel))^3.9+0.0015/pixel-0.066824
z=whitesq*b5-(whitesq==0)*b5
c1=1.5*z^1.2,c2=2.25*z,c3=3.375*z,c4=5.0625*z
l1=real(p1),l2=imag(p1),l3=real(p2),l4=imag(p2)
bailout=16,iter=0:
t1=(iter==l1),t2=(iter==l2),t3=(iter==l3),t4=(iter==l4)
t=1-(t1||t2||t3||t4),z=z*t,c=c*t+c1*t1+c2*t2+c3*t3+c4*t4
z=z^2+(-0.748800289672,-0.1350036189)-0.0000230
iter=iter+1
(conj(|z|))<=bailout
}

Carr3534            { ; "Heraldic" Julia.
  reset=1960 type=formula formulafile=43kCarr.frm formulaname=Carr3534
  passes=1 center-mag=0.0010622/0.0133912/0.7950156
  params=200/300/400/550 float=y maxiter=647 periodicity=0
  colors=000<6>00043C<12>OHz<12>000<10>zpa<6>_SMWPKTKNPGPMBSI7U<10>1020000\
  00<14>wo`<15>`00<15>000WOG<13>zo`<15>UMFWLE<13>`Ft`Fw_Et<12>L7UK7SH7UGBV\
  FFW<14>1hz011<12>AFHBGM<15>zzzxxx000ttt<11>WWWUUUTTT<9>AAA
  }


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Date: Sun, 30 May 1999 16:21:23 -0600
From: Phil McRevis <[e-mail]>
Subject: Re: (fractint) Topology of the MandelBrot

In article <[e-mail]>,
    "Tim Wegner" <[e-mail]>  writes:

> apparent from experimentation that midgits are not self-similar,
> quite the contrary: as one zooms deeper, the patters surrounding
> the midgits change.

I think what you're seeing here is the period doubling phenomenon that
one would observe by following the midgets that are centered on the
real line.  The dynamics of M on the real line are the same as the
dynamics of the bifurcation plots.  A colleague once wrote a program
that superimposed the two and you can see that the bifurcation plot
goes through its first bifurcation at the point where the circle joins
the main cardiod.  The next bifurcation happens at the place where the
midget centered on the real line touches the circle, and so-on.  If
one used this as a zooming strategy, you'd find that the midgets keep
reappearing, but that the number of tendrils leading into the midgets
follow a period doubling progression.  Aliasing soon takes over after
several zooms :-), preventing you from seeing all the tendrils.
- --
<http://www.xmission.com/~legalize/>    Legalize Adulthood!
    ``Ain't it funny that they all fire the pistol,
      at the wrong end of the race?''--PDBT
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Date: Mon, 31 May 1999 09:29:21 -0300
From: "Ricardo M. Forno" <[e-mail]>
Subject: RE: (fractint) Topology of the MandelBrot

My English is somewhat poor. What is a midgit? The Babylon translator does
not know it.
- ----- Original Message -----
From: Tim Wegner <[e-mail]>
To: <[e-mail]>
Sent: Saturday, May 29, 1999 11:50 PM
Subject: Re: (fractint) Topology of the MandelBrot


> Mark wrote:
>
> > My favorite way to find hot spots is to poke around the set using
> > attractor plots.  In Fractint, this is accomplished using the "orbits"
> > function ("o" key).  After you M-set is done generating, press "o"
> > and move the cursor around until you start seeing interesting shapes
> > in the orbit window, then zoom in on those coordinates.
>
> I have an idea that this procedure might lead to self similar areas,
> which might not be desirable.
>
> After first implementig arbitrary precision, I tried to "fish" for a
> fractal in very deep water (e.g. high magnification). I did it by using
> viewwindows mode and letting just a few pixels develop in solid
> guessing mode. Where pixels had different colors, I figured it was
> safe to zoom. What I was trying to avoid was a solid area with no
> structure. The problem was that arbitrary precision is slow, so I
> was trying to see where to zoom by generating very few pixels.
>
> When I was done, I let the whole fractal calculate. I wondered if I
> had set some kind of a record, since the magnification was
> something like 10^900, and the fracta;l looked quite interesting.
>
> But alas, something looked wrong. The fractal looked familiar. In
> fact the fractal was identical (except for rotation) to a fractal
> generated at the same place but with a very modest magnification.
>
> From my very limited experience, it seems to me that most
> strategies from zooming in to very deep magnifications are liekely
> to fall into "whirlpools of self similarity" where nothing new is found.
> One strategy to avoid this is to follow a descreasing sequence of
> migit Mandelbrots. I don't know how to prove this, but it seems
> apparent from experimentation that midgits are not self-similar,
> quite the contrary: as one zooms deeper, the patters surrounding
> the midgits change.
>
> Questions:
>
> 1. Is it true that zooms following sequences of smaller and smaller
> midgits never fall into self-similarity
>
> 2. Are there other strategies for zooming to great depths that result
> in different images as one goes deeper.
>
> Tim
>
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
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End of fractint-digest V1 #394
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