Christoph Hormann <chr### [at] gmxde> wrote:
: Looks good, i did not yet have time to read it, but the background color
: of the code is disgusting :-)

  Thanks :)

  (Any better suggestion?)

-- 
char*i="b[7FK@`3NB6>B:b3O6>:B:b3O6><`3:;8:6f733:>::b?7B>:>^B>C73;S1";
main(_,c,m){for(m=32;c=*i++-49;c&m?puts(""):m)for(_=(
c/4)&7;putchar(m),_--?m:(_=(1<<(c&3))-1,(m^=3)&3););}    /*- Warp -*/

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In article <3a6db8fe@news.povray.org>, war### [at] tagpovrayorg says...
>   I made a page explaining a bit the Mandelbrot set:
> http://iki.fi/warp/Mandelbrot/
> 
>   Perhaps I should put a link to it in the povVFAQ?
> 
I was wondering whether the inner part of what you call the Mandelbrot 
set /is/ part of the set. Isn't the Mandelbrot set just an infinitely 
large set of points forming an infinitely large (continuous?) line; the 
outline as it were? So anything outside or inside this set of points (or 
line of infinite length) would not be part of it?

-- 
Regards,  Sander

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"Sander Stols" <san### [at] stolscom> wrote in message
news:MPG### [at] NEWSPOVRAYORG...

> I was wondering whether the inner part of what you call the Mandelbrot
> set /is/ part of the set. Isn't the Mandelbrot set just an infinitely
> large set of points forming an infinitely large (continuous?) line; the
> outline as it were? So anything outside or inside this set of points (or
> line of infinite length) would not be part of it?
>
> --
> Regards,  Sander

IMHO, no. Each point is either inside or outside the set. The boundary has
no special significance in that sense. The only point about the boundary is
that it represents the area of least certainty - you can never be sure if,
with one more iteration, a point might suddenly turn out to be outside the
set.

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"Warp" <war### [at] tagpovrayorg> wrote in message
news:3a6ec2ea@news.povray.org...
>
>   You are making Z=Z^2 here, not Z=Z^2+c.
>

Doh! Many thanks - fixed it now.

The final code is:
#declare XStart = -1.5;

#declare XEnd = 5;

#declare YStart = -3/2;

#declare YEnd = 5;

#declare Iterations = 50;

#declare Imaginary = -YStart;

#while(Imaginary >= -YEnd)

    #declare Real = XStart;

    #while(Real <= XEnd)

        #declare Inside = true;

        #declare TReal = Real;

        #declare TImaginary = Imaginary;

        #declare Counter = 1;

        #while(Counter <= Iterations)

            #declare T2Real = TReal;

            #declare TReal = ((TReal * TReal) - (TImaginary * TImaginary));

            #declare TImaginary = (2 * T2Real * TImaginary);

            #if(((TReal * TReal) + (TImaginary * TImaginary)) > 4)

                #declare Inside = false;

                #declare Counter = Iterations;

            #end

            #declare TReal = TReal + Real;

            #declare TImaginary = TImaginary + Imaginary;

            #declare Counter = Counter + 1;

        #end

        #if(Inside)

            #debug "X"

        #else

            #debug " "

        #end

        #declare Real = Real + ((XEnd - XStart)/130);

    #end

    #debug "\n"

    #declare Imaginary = Imaginary - ((YEnd - YStart)/80);

#end

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In article <3a6edafc$1@news.povray.org>, tom### [at] tomandlucouk says...
> IMHO, no. Each point is either inside or outside the set. The boundary has
> no special significance in that sense. The only point about the boundary is
> that it represents the area of least certainty - you can never be sure if,
> with one more iteration, a point might suddenly turn out to be outside the
> set.
Hm, it seems I will have to read more about this subject. The only 
somewhat thorough and also difficult book I have is the one by Peitgen 
and Richter :-))
-- 
Regards,  Sander

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Tom Melly <tom### [at] tomandlucouk> wrote:
: Doh! Many thanks - fixed it now.

:             #declare TReal = ((TReal * TReal) - (TImaginary * TImaginary));
:             #declare TImaginary = (2 * T2Real * TImaginary);
:             #if(((TReal * TReal) + (TImaginary * TImaginary)) > 4)
                 ...
:             #end
:             #declare TReal = TReal + Real;
:             #declare TImaginary = TImaginary + Imaginary;

  You are here actually calculating first Z=Z^2, then looking if |Z| > 2
and then calculating Z=Z+c.
  Now, this is interesting. Does this work? In theory you should calculate
Z=Z^2+c first and then see if |Z| > 2.

-- 
char*i="b[7FK@`3NB6>B:b3O6>:B:b3O6><`3:;8:6f733:>::b?7B>:>^B>C73;S1";
main(_,c,m){for(m=32;c=*i++-49;c&m?puts(""):m)for(_=(
c/4)&7;putchar(m),_--?m:(_=(1<<(c&3))-1,(m^=3)&3););}    /*- Warp -*/

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Tom Melly <tom### [at] tomandlucouk> wrote:
: IMHO, no.

  Remove that "IMHO" because you are right.
  Every point painted in "black" is part of the set. The set is defined as
each complex number that fullfills the formula. All the points painted in
black fullfill the formula, thus they belong to the set.

-- 
char*i="b[7FK@`3NB6>B:b3O6>:B:b3O6><`3:;8:6f733:>::b?7B>:>^B>C73;S1";
main(_,c,m){for(m=32;c=*i++-49;c&m?puts(""):m)for(_=(
c/4)&7;putchar(m),_--?m:(_=(1<<(c&3))-1,(m^=3)&3););}    /*- Warp -*/

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BTW, why not use the complex numbers feature in MegaPOV ?

Fabien.

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Fabien Mosen <fab### [at] skynetbe> wrote:
: BTW, why not use the complex numbers feature in MegaPOV ?

  Why not, indeed.
  If the programming language used supports directly complex numbers, then
the code can be simplified a bit.

  For an example, see:
http://iki.fi/warp/MandScripts/matlab.html

-- 
char*i="b[7FK@`3NB6>B:b3O6>:B:b3O6><`3:;8:6f733:>::b?7B>:>^B>C73;S1";
main(_,c,m){for(m=32;c=*i++-49;c&m?puts(""):m)for(_=(
c/4)&7;putchar(m),_--?m:(_=(1<<(c&3))-1,(m^=3)&3););}    /*- Warp -*/

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I think the pov code for making Mandel patterns is very cool, I like doing
multiple-OoM zooms on it.

Q's:
1. Can you zoom on that ASCII code?

2. Programs like Tierazon are really cool in that they let you plug in your
own equations.  How close is Tom's code to making one's own *pattern*  for
one's own original complex math?

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