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fractint-digest       Saturday, January 10 1998       Volume 01 : Number 068




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

Date: Sat, 10 Jan 1998 06:41:12 -0800
From: cindy mitchell <[e-mail]>
Subject: (fractint) Re: Dick Amerman

Hi Dick,
I would appreciate it if you would send me the Dec97 .par and .frm files.
This last week I have also been going thru the list and sorting frms and pars.
I am still in this year. Next step (nearly impossibe ) to go thru all the
snippets
I have collected in 1997, and save them in  appropriate files.
  Thank You,
  Cindy
>
>Up to December 31, 1997, I saved them in Dec97.par and Dec97.frm.  All the pars
>are  cleaned up and all draw.  For many of the images, I've modified the
comment
>lines in the parameter sets by adding the time it takes to draw on my
equipment.
>If there were formulas without pars to call them, I have only spotchecked.
Some of
>the formulas, like the vector and dmj-pub formulas, I've saved in their own frm
>files, again with spotchecking on how they run.
>
>There's an exception to haveing all the par/frm sets!  Somewhere along the
line, I
>lost track of the formula, xmasseahorse.  Maybe somebody could repost that
one to
>me at my personal mailbox.
>
>Now, I'm working on Jan98.par and Jan98.frm.
>
>I have not taken the time to cross reference the example pars to the formulas
>because the formula names appear in the pars and can be searched out with
PFE32 or
>by visual scanning in an editor.  This should not be much of a problem if I
stay
>with the month-sized files.
>
>Dec97.par is about 58K and Dec97.frm is about 20K in size.
>
>I don't have much experience in posting except as attachments, which I
understand
>some of you have difficulty with.  If anyone wants one or both of the above
>collections, the vector frms or the djm-pub frms, let me know, tell me how
you want
>them posted to you, and I'll give it a try.  If the number of people
wanting them
>is small, it will probably be best for me to send such postings to your
personal
>mailboxes.
>
>I'm not committing to anything for the future!  I have to travel in my
work, and
>may even eventually decide to withdraw from this list because of the volume of
>traffic -- 60 to 80 messages in one 24-hour period is a bit much!  Sure
have been
>learning a lot, though and getting many good images and formulas.  So, I'll
stick
>with it as long as I can.
>
>Dick Amerman
>
>
>-
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>


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

Date: Fri, 9 Jan 1998 18:47:01 -0800
From: "Jay Hill"<[e-mail]>
Subject: (fractint) Re: Archiving pars/frms

Hi,
Dick Amerman wrote:
> There's an exception to haveing all the par/frm sets!  Somewhere along
the line, I
> lost track of the formula, xmasseahorse.  Maybe somebody could repost
that one to
> me at my personal mailbox.

Done and...  Look for it here in a day or so...

http://home.san.rr.com/jayrhill/CARLSON.PAR

> My save format is  something like this:
> ; Date
> ; From
> ; or Comment { ... } if there is a comment  or part of a comment I want
to save
> formulas or image parameters

One needs be careful that the part of the comments needed to use
the frm are visible from in Fractint, the part about the parameters.
I notice Carlson's comments use 3 lines for fancy ******* boxes.
This can cut into info space we need to see when working
with the parameters, especially in more complicated frm. I
recommend against such, at least at the top of the frm file.

Here is a quote from one of Paul's frm:

>    ;****************************************************
>    ; Always use floating point math and outside=summ.
>    ;
>    ; Parameters:

Now there are 3 lines which are not needed. They can push lines like this:

>    ; Note that the equation variable is w, not z.  Always
>    ; initialize z to zero.

right off the bottom of the little window!!!  Not to pick on Paul, but...


2swirl             { ; Copyright (c) Jay Hill, 1998
  reset=1960 type=formula formulafile=astroid.par
  formulaname=astroid_mset
  center-mag=-0.75346568113634480/+0.04710531541637864/5751.935/1/-90
  params=0.005/0.3/8/30 float=y maxiter=3000 inside=253 outside=summ
  colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40zz0<28>aG00zR<28>0C40z\
  z<28>0CCGGz<28>00O000<10>000z88000000
  }

Jay



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

Date: Thu, 8 Jan 1998 21:41:59 +1100
From: "B Michie" <[e-mail]>
Subject: (fractint) centre-mag

I am getting a message - oops, couldn't understand argument center-mag=etc.
on virtually every par I try to use. Can someone please tell me what the
problem might be?
Beth

Plant real trees. Don't give me rubbish like, "I'd like
 a tall tree, but it mustn't grow above the gutters!
Oh- and the colour of the flowers mustn't clash
with the brickwork -- Spare me !@#$%^&***!

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

Date: Fri, 9 Jan 1998 21:43:48 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) centre-mag

Beth asked:

> I am getting a message - oops, couldn't understand argument center-mag=etc.
> on virtually every par I try to use. Can someone please tell me what the
> problem might be?

Are you using winfract? If not, what fractint version?

Tim

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

Date: Fri, 9 Jan 1998 22:46:07 -0500
From: "Jason Hine" <[e-mail]>
Subject: Re: (fractint) centre-mag

>I am getting a message - oops, couldn't understand argument center-mag=etc.
>on virtually every par I try to use. Can someone please tell me what the
>problem might be?
>Beth


I'm going to guess that you're using an older version of Fractint; the
center-mag coord method wasn't implemented until relatively recently.  You can
link to a site to download the most recent version at http://spanky.triumf.ca
Hope that helps,
Jason


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

Date: Sat, 10 Jan 1998 14:55:41 +1100
From: "B Michie" <[e-mail]>
Subject: (fractint) Why won't center-mag compute

Why does Winfract consistently tell me that "Oops, can't understand
argument: center-mag =etc"
It is doing it every time, and the next screen says can't open "filename"
.frm
I should be giving up at this stage, but I'm a tenacious little thing, and
I'm not going to let it beat me!
Advice welcome. A double Scotch would likewise help
Beth



Plant real trees. Don't give me rubbish like, "I'd like
 a tall tree, but it mustn't grow above the gutters!
Oh- and the colour of the flowers mustn't clash
with the brickwork -- Spare me !@#$%^&***!

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

Date: Sat, 10 Jan 1998 05:04:33 +0100
From: [e-mail] (Guy Marson)
Subject: Re: (fractint) centre-mag

Hi Beth,

Try Fractint ver. 19.6..  it will work fine..


Cheers,

Guy

>I am getting a message - oops, couldn't understand argument center-mag=etc.
>on virtually every par I try to use. Can someone please tell me what the
>problem might be?
>Beth
>
>Plant real trees. Don't give me rubbish like, "I'd like
> a tall tree, but it mustn't grow above the gutters!
>Oh- and the colour of the flowers mustn't clash
>with the brickwork -- Spare me !@#$%^&***!
>
>-
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>


Fungi for fun = FunGUY... @:-]

(Guy Marson, 45b, rue de Bettembourg, L-5810 Hesperange)
(Tel./Fax : [phone])  e-mail: [e-mail]


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

Date: Fri, 9 Jan 1998 23:03:34 -0600
From: "Tim Wegner" <[e-mail]>
Subject: (fractint) Simplgif update

I'd like to ask folks on the list who are interested to do some
testing for me.

Fractint's save-to-GIF feature has been reliable for many years.
However, a few years ago, Jon Noring started running into problems
with very large images. Some of the pieces of his giant images
wouldn't save properly, and in other cases simplgif failed to combine
the images made with the divide and conquor method. We studied the
code but could not find the problem. LZW algorithms are not easy to
understand or debug.

For those unfamiliar with this feature, Fractint can make large
images by piecing together smaller images. See the bottom of the <b>
screen. If you set x multiples and y multiples to values such as 3
or 4, a batch file called makemig.bat is created. If you run this,
result is to create a number of small images and combine them in a
multiple image GIF. The simplgif utility combines a multiple image
GIF into a single image. There's a commented out line that does this
at the bottom of makemig.bat, or you can type the command in by hand.

Recently I received an email of a case where simplegif failed
horribly for a very ordinary case. Try the default mandelbrot
using "divide and conquor" parameters of 7x7 at 800x600 pixels,
resulting in an image of 5600x4200. The image is bad halfway through.
(You can view large images in Fractint at lower resolutions - just
select a viewable video mode).

I have added a new (well, new to simplgif) GIF encoding algorithm. It
is based on the Unix compress algorithm. Simplgif now works fine with
the above example. The new simplgif still has the old encoding built
in. Just add a third argument like this:

   simplgif source.gif target.gif anything_here

and the old "pdgif" algorithm is used. Without the third argument,
the new "compress" algorithm is used. As a bonus, the new algorithm
compresses a lot better!

You can get this test version of simplgif via ftp from:

ftp://ftp.phoenix.net/pub/USERS/twegner/simplgif.zip

Please don't upload this anywhere. When we're through testing we'll
release it.

Be warned that simplgif does not save fractal data. Also make sure
you have lots of disk space. Simplgif warns you how much it needs.

I'd appreciate folks trying to find images that don't work with
simplgif. The best way to do this is to make large fractint images.
However, you can copy any GIF image with simplgif.

I'm especially interested is cases that break with the old algorithm
that work with the new, or ANY case that fails with the new
algorithm. You can report back to the list. Or if these test reports
get too numerous and tedious for the list, just email me directly.

If the new simplgif works OK I'll replace Fractint's native encoding
with the same code as well as release the fixed simplgif.

Thanks very much!!!

Tim


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

Date: Fri, 9 Jan 1998 23:41:37 -0600
From: "Debora A Henderson" <[e-mail]>
Subject: (fractint) Dalem@???????

Hi Dale,
     Please email me at [e-mail].  Obviously my news reader
doesn't keep mail for long, so I lost your e-mail and web site address.
Thanks


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

Date: Sat, 10 Jan 1998 01:19:41 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) terrible oversight

wizzle wrote:

>BTW...my computer scientist son was babbling about a mathematical proof that
>computers are limited....can't remember quite how...but we were discussing
>the fractal art conundrum.

That's not babbling, that's Godel's Incompleteness Theorem!


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Fri, 9 Jan 1998 23:17:41 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: Re: Archiving pars/frms (was: Re: (fractint) Petals_Julia)

Anyone archiving these things might want to look at George Martin's
ORGFRM program, which can be found at Spanky:

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

George's program offers a way to catalog formulas and to skip duplicate
entries.  The tally is now up to 4500 entries!  Unfortunately, there's not
a similar program (of which I'm aware) for par files.  Dan Goldwater has a
page for his Fracxtr compilation, but it hasn't been updated in nearly 3
years.  Anyone feel ambitious?  :-)

- -------------------------------------------------------------------------------
Kerry Mitchell
[e-mail]
- -------------------------------------------------------------------------------


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Date: Sat, 10 Jan 1998 01:29:37 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) Liouville Julia set

I was browsing my copy of TBOF the other day, and noted that the section
on which Mandelbrot points produce what kinds of Julia sets, it mentions
for the edges of components, ones with rational internal angle produce
parabolic Julias, but the section on Siegel disks indicates these only
occur for "sufficiently irrational" internal angles. Later it says the
angle must be "badly approximated by rational numbers" and provides two
criteria, one a convergent/divergent series, the other a Diophantic
equation. Later still, irrational numbers not "badly approximated by
rational numbers" are described as, or as a superset of, Liouville
numbers, and an example of such a number is provided: 1/2+1/4+...+1/2^(n!)
where n! is n factorial. The first four terms in the number are 1/2, 1/4,
1/64, and 1/16777216. Those four terms give the number to the limits of double
precision arithmetic! Note how it is very closely approximated by the
rational numbers that are the partial sums of the terms.

I generated a Julia set from the 'lambda' type using it as internal angle
on the main component (for the lambda type this is the unit disk, greatly
simplifying things, as using L for the Liouville number the Julia
parameters are just the cosine + i times the sine of 2*pi*L). I also
generated one for a known Siegel disk, whose internal angle is the golden
mean, (sqrt(5)-1)/2.

Attached below is the PAR. The Liouville one is fascinating to study using
the orbits window. Generate it and hit o, and look at the assorted orbits
for points in the interior. If that is a Siegel disk it's a damned weird
one. If it is not... what is it?


Liouville          {
  reset=1960 type=lambda passes=1 center-mag=0.5/0/0.6666667
  params=0.09801751303322832/-0.9951846899640191 float=y
  maxiter=1048576 inside=0 logmap=yes
  colors=000F0K<59>T0bU0cU0cV1cV2d<60>zzzzzzzzy<60>zz1zz0zy0yx0<58>G2JF0KF\
  0KF0KF0K
  }

Siegel             {
  reset=1960 type=lambda passes=1 center-mag=0.5/0/0.6666667
  params=-0.7373688780783196/-0.675490294261524 float=y
  maxiter=1048576 inside=0 logmap=yes
  colors=000F0K<59>T0bU0cU0cV1cV2d<60>zzzzzzzzy<60>zz1zz0zy0yx0<58>G2JF0KF\
  0KF0KF0K
  }


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Sat, 10 Jan 1998 01:58:45 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) RE: fractint-digest V1 #62

You found that interesting? Well read Penrose's _Shadows of the Mind_. A
possible explanation is posited there, namely that the brain contains
structures that operate as quantum computers not subject to the
limitations of classical mechanics, nor to the Turing machine's limits of
finite states and finite speed. (Yes, a quantum computer is capable not of
infinite speed, but almost as good, of infinite parallel computation. Some
extended computations that never halt in a normal Turing machine might
stop in finite time run infinitely parallel... who knows?)

Also, one should not overlook an instance of a Turing halting problem and
indecidability situation that is quite familiar and relevant to this
group. Namely, the question of whether a given 'c' is in or out of the
M-set! Periodicity checking or direct mathematical computation of the
components of M (all described by various inequalities involving
polynomials p(c) and |p(c)|<=1) can determine more and more points as
belonging to M, and direct iteration more and more as being outside M, as
time goes on, but only in the infinite limit are all points in and all
points out identified.


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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

Date: Sat, 10 Jan 1998 00:01:08 -0800
From: "Jay Hill" <[e-mail]>
Subject: Re: (fractint) Liouville Julia set

Hi Paul,

>The Liouville one is fascinating to study using the orbits window.
> Generate it and hit o, and look at the assorted orbits for points
> in the interior.

Very interesting. The orbit on a P200 gave the impression of a beating heart.

I reproduce your par here with slight zoom in and color change so
I can see the edge a little better. I also toss out two others...these are
really chunky fractals! If we use passes=g we don't see correct valleys.

As for your remarks in the other thread...
> namely that the brain contains structures that operate as quantum
> computers not subject to the limitations of classical mechanics, nor
> to the Turing machine's limits of finite states and finite speed.

I have the other day teased one of the computer science types I know
about the stopping problem applied to the brain. I suggested it might be
fear of such that drives some at the office to drink so much coffee!
(Would not want that up stairs computer to stop while contemplating
one of your Siegel disks.)  On the other hand,  I pointed out to him that
quantum effects might allow the brain to restart.

I can only hope that .....zzzzzzzzzzzz.... oops, got to be careful, almost
halted again....     :-)

As for
> the question of whether a given 'c' is in or out of the M-set [...]
> only in the infinite limit are all points in and all points out identified.

I agree. A few years ago I posted to sci.fractals an article titled
The Mandelbrot Chaosometer where I describe some aspects
of this problem.

Jay

Liouville-1    { ; Paul Derbyshire
                 ; zoom in and color change by Jay Hill
  reset=1960 type=lambda passes=1
  center-mag=0.5/4.44089e-016/0.8912656
  params=0.09801751303322832/-0.9951846899640191 float=y
  maxiter=1048576 inside=0 logmap=yes
  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
  savename=Liouvill
  }

Siegel-1       { ; Paul Derbyshire
                 ; zoom in and color change by Jay Hill
                 ; params=exp(2*i*pi*a), a=(sqrt(5.)-1.)/2.
  reset=1960 type=lambda center-mag=0.5/6.66134e-016/0.9861933
  params=-0.7373688780783196/-0.675490294261524 float=y
  maxiter=1048576 inside=0 logmap=yes passes=1
  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
  savename=Siegel
  }

Siegel-2 { ; Jay Hill
           ; params=exp(2*i*pi*a), a=(sqrt(3.)-1.)/2.
  reset=1960 type=lambda center-mag=0.5/6.66134e-016/0.9861933
  params=-0.666130923602528/0.745834829315743 float=y
  maxiter=1048576 inside=0 logmap=yes passes=1
  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
  savename=Siegel2
  }

Siegel-3 { ; Jay Hill
           ; params=exp(2*i*pi*a), a=(sqrt(7.)-1.)/2.
  reset=1960 type=lambda center-mag=0.5/6.66134e-016/0.9861933
  params=0.442057568870217/-0.896986680951592 float=y
  maxiter=1048576 inside=0 logmap=yes passes=1
  colors=000F0K<29>i0xk0zj0z<29>20z01z01z<30>0Uz1Vz3Wz<28>xxzzzzzzx<59>zz1\
  zz0zy0yx0<56>I4IH3JG2JF0KF0KF0KF0K
  savename=Siegel3
  }


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Date: Sat, 10 Jan 1998 03:27:21 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Client-server Fractint

>
>I was thinking about the forthcoming rewrite of Fractint for version 20,
>and wondered: why not use a client-server model for fractal drawing?
>
>The client sends a message to the server, saying "here is the formula to
>use, please give me the value of the pixels in the rectangle (0,0) to
>(100,100)", and the server sends back the pixels.


Son of a b...   Clever idea! Rather like how the game Quake works. I think
I may keep that in mind also for ProtoMatter.


- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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Date: Sat, 10 Jan 1998 03:32:40 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Client-server Fractint

>There are several client-server distributed M-set programs out there,
>I can dig up references.  Portability is a real problem, although its
>significantly easier now that winsock has become popularized on
>Windows.  However, that still leaves a socket implementation for DOS.
>The technology is there, but interoperability and portability of code
>is a problem for fractint's limited operating environment as a 16-bit
>dos app.

There is a socket library for DJGPP (Gnu C++ for DOS). It allows a DOS app
on a W95 system to access the Windows socket interface. Dunno how easy to
use/stable it is though.

If Fractint 20 is to have any of these really great features, it *must*
migrate to DJGPP or something similar. It is running out of room in its
640K, even with overlays, and even if you make it into "Fractdouble".


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Date: Sat, 10 Jan 1998 03:38:23 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) =3D disease

>I asked Compuserve if there was a way of switching the quoted-printable
>encoding off (as you know, it affects my outgoing posts too). After several
>days I received this reply...
>
>[sarcastic] Very helpful!!


Compu$werve's admin is clueless. Did you know they are blackholing spam
and net abuse complaints? It is rapidly turning into the Internet's
low-rent district...I suggest everyone still on it seriously consider moving.


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 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
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Date: Sat, 10 Jan 1998 04:04:12 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) Client-server Fractint

>   The client-server model is clearly elegant, but definitely introduces
>overhead. Would anyone with a really deep knowledge of communications
>protocols, processor cycles, and fractint's current design care to
>comment on how much overhead we're talking about? I mean, if calculation
>is 80% of fractint's drawing time on a typical Pentium, and drawing is
>20%, would some sort of multithreaded client-server design add on another
>20% of time, or 600%, or what?
>   I suppose 'multithreaded' is something of an assumption; to some
>extent you could separate out the two sets of routines (calculating and
>drawing) without really slowing down the code... hmm. Don't know enough
>about fractint's design, do I.

Simple case: one server thread, calculating one image; one client
(interface) thread. Interface thread starts calculation, then sleeps for 1
second or until a keypress (most cycles go to server, calculating) or
mouse input, redraws, sleeps again...

Using a thread package advanced enough to allow a thread to "sleep" with
no processor usage until there's input or a certain time, this would be a
piece of cake and the overhead would be minimal. Indeed, the drawing
overhead would be much less than in current Fractint.




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    `*'  Send any and all mail with attachments to the hotmail address please.
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Date: Sat, 10 Jan 1998 04:18:12 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) Client-server Fractint times two

First to address a concern about float precision being platform dependent.

The calculation engine can be platform independent easily enough, by a few
means.

If the server may run on a machine with no local client:

  * Server can conditionally compile by platform, using #ifdef and #define
    doublebits=80 (or 64, or 128) in different sections.

It may be easier to design if the server always runs with a client. Then
the client runs the server at startup, and tells it the platform's double
bit length and any other such parameters it needs. The client then
contains all platform-specific code.


Now the double client/server model: this involves one calculation server,
three interface clients for that server, one of which is also a client for
a window server.

* Calculation server: As above. Calculation server communicates two things:
  text streams and rectangular chunks of image data. Text streams are used
  to send it command lines: "let maxiter=2000; let type=mandel;
  complexrect -3 1 -1.5 1.5; calculate 0 0 1048 576"
  It may return info by text stream or (as with 'calculate') in chunks of
  fractal data.

* Simple commandline client: Commands are typed at a prompt, go to server;
  a few specific local commands operate on the data chunk last received from
  the server and manipulate such chunks.

  > let type=mandel; complexrect -3 1 -1.5 1.5; calculate 0 0 1048 576
  >
  * Image complete; 634712 bytes of data received.
  > saveto foo.gif
  * 567121-byte GIF saved

  This might be used for batch jobs.

* Client with Fractint-like interface, for backward compatibility and for
  use on terminals with middling capabilities. (DOS, Linux with curses)

* Client that interfaces also to a windowing server and provides a nice
  graphical interface.

* Server for windowing in win32.

* Pseudo-server to translate windowing client stuff to something X-window
  display servers can understand.

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    `*'  Send any and all mail with attachments to the hotmail address please.
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Date: Sat, 10 Jan 1998 05:05:55 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) Fractal calculation server

What should the server calculate and send back?

The answer: Information enough to color the points, but not require
involving the server for simple enough coloring changes. (Palette, logmap
etc.) Only for more complex ones (changing to potential, distest, stalks,
decomp) would the server become involved.

How should that information be encoded?

The answer: As simply as possible.

Imagine the general fractal at this calculated, pre-render stage, to
contain one or more basins of attraction, each with one or two color
parameters, and some exceptional points.

Let each point be returned with a type; 0 is exceptional, 1 is a basin.
Each point also has a subtype; for type 1, this is a number identified
with the basin of attraction, 0 to n-1. For type 0, this depends on both the
formula and certain algorithms e.g. distance estimator. 0 is a generic
point used for uncalculated points; points not yet calculated when
rendering a partly done escape time; points not hit by an orbit type, IFS,
or L-system. Formulas can define additional types with positive integers;
so type 0 subtype 1 might be used by a Julia variant to display the
attractor or the critical points. Methods might define negative ones, so
type 0 subtype -1 might, in distance estimator method, mean filament.
As for basin points, type 1 subtype n, these have two other parameters,
m1 and m2, which are doubles between 0 and 1. These depend on the basin
and method. With distance estimator, m1 might be iter/maxiter or
distance/screen diagonal length. With continuous potential, m1 is the
potential. Decomp, in this case, would change m2 instead. Coloring could
use linear mappings a'la Fractal eXtreme from m1 to RGB space or from m2 to
RGB space, or planar mappings from m1xm2 to RGB space by allowing one to
select various points in a [0,1]x[0,1] square and pick shades for them,
the others being interpolated.

Julia set:

type=0 subtype=1 Trapped pixel
type=1 subtype=1 Pixel blew up (decomp about 0, color by iter, zmag,
                                potential to infinity, distest, etc.)
                                m1 depends: iter/maxiter, atan(zmag)*2/pi,
                                potential, distance etc; m2=decomp theta
                                about 0
type=1 subtype=2 Finite attractor  (decomp about attractor point; logmap
                                    inversely about attractor, etc.)

M-set:

type=1 subtype=1 Escaped pixel same as above
type=1 subtype=2 Set point, m1 depends on choice of zero, bof60, bof61...
                            m2 is period if caught by period checking else 0,
                            normalized using maxit.


Julia variant:

type 1 subtype 0 is A(infinity)
type 1 subtype 1...n attractor, based on attractor phase.


and so forth.


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 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
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Date: Sat, 10 Jan 1998 05:26:13 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: (fractint) Generalized Mandel/Julia types

A generalized Mandelbrot/Julia formula type should work as follows:

The formula specifies an iteration equation, together with initial
conditions, while also specifying *critical points* and attractors:

initial:
iteration variable z;
parameter c;
iterate:
sqr(z)+c;
critical:
0;
attractor:
infinity;

This should be interpreted at runtime as follows: Make an M-set by setting
z to 0 ("critical" and c to pixel, or a Julia setting c to a user
parameter and z to pixel; let the user perturb the M-set by choosing a
value that will be added to z. Iterate z^2+c; for the M-set use
periodicity checking and a user-chooseable bailout since infinity is an
attractor.

The attractor list should allow the keyword "infinity", any number, or any
expression in the parameter(s).
The critical list should allow any number, expression in the parameters,
or the keyword "guess".

Guess means that critical points will be sought by a modified Newton's
method dynamically at run-time, for the calculus-impaired to write these
formulas.

The run-time method is as follows:

Pick 100 random z clustered around 0, with fewer out to larger radii.
For each, iterate:
z->z-f(z)*epsilon/(f(z+epsilon)-f(z))
Note that this is just Newton's method replacing the f'(z) with the
approximation (f(z+epsilon)-f(z))/epsilon. Epsilon should be small, e.g.
1e-13. f(z) means to iterate the formula using a random choice of parameters.
This is repeated with a different random choice and critical points that
'wandered' are weeded out. (Those are beyond my ability to program a
computer to find :-) so they'd have to absolutely be included in the
critical: list manually!)



At run time, the user can choose Julia or Mandel. For Julia they can
choose the parameter values and run. For Mandel, they can choose any of
the critical points, choose a perturbation to add to z_0, and run.
Mandel types periodicity check. Julia types iterate all the (known)
critical points and say 100 random z to find all distinct attractors, and
build an attractor list, then the basins can be varicolored, or solid
colored by user choice.

For all, the basins can be further split by phase (one, some, or all), and
decomp should work around the attractor point detected.

Old formulas supported but fancy colorings depend on using IF and ENDIF
and outside=real and other clunky 19.6 style stuff :-), and then using a
single colormap with the single basin the engine believes exists.


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    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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End of fractint-digest V1 #68
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