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Greg M. Johnson <gre### [at] my-dejanews com> wrote:
: How close is Tom's code to making one's own *pattern* for
: one's own original complex math?
Megapov supports function patterns which you can use to create your
own patterns.
However, Mandelbrot-type patterns are not possible with the current
implementation since the functions don't support variables nor loops.
Making a Mandelbrot pattern with a pattern function would require something
like this:
#declare Mandel =
function
{ Zr=x; Zi=y; n=0;
while(n<=30 & sqr(Zr)+sqr(Zi)<4)
{ Zi2=sqr(Zi);
Zi=2*Zr*Zi+x;
Zr=sqr(Zr)-Zi2+y;
}
n/30
}
Until functions support variables and while-loops we are out of luck.
Perhaps shaders are the answer?
--
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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"Warp" <war### [at] tagpovrayorg> wrote in message
news:3a6eeefc@news.povray.org...
> 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.
>
Hmm, well it seems to work - if you run the code in POV it produces what
appears to be a Mandelbrot in ascii wherever debug is ending up.
Swapping them around to:
#declare TReal = ((TReal * TReal) - (TImaginary * TImaginary));
#declare TImaginary = (2 * T2Real * TImaginary);
#declare TReal = TReal + Real;
#declare TImaginary = TImaginary + Imaginary;
#if(((TReal * TReal) + (TImaginary * TImaginary)) > 4)
...
#end
seems to produce the exact same pattern - still, at this resolution who
knows? ... ;).
Thinking about it, it's not that surprising. A tendancy towards infinity
will show up in either case - presumably, my Mandelbrot outline has some
differences from having deferred the re-addition of the original real and
imaginary number, but you'd need much higher res. to see it.
Wee! - I love Mandelbrots. Why? Firstly, you can make them with schoolboy
maths. Secondly, imaginary numbers that turn into real numbers when you
square them are funny.
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"Greg M. Johnson" <gre### [at] my-dejanewscom> wrote in message
news:3A6EF35E.3E2188EA@my-dejanews.com...
> 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?
>
Yes, try changing the opening params to:
#declare XStart = -1.5;
#declare XEnd = -1;
#declare YStart = 0;
#declare YEnd = 0.5;
Also, with my error, at this resolution the mandel is not so good, so change
the code I posted from:
#declare TReal = TReal + Real;
#declare TImaginary = TImaginary + Imaginary;
#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;
to:
#declare TReal = TReal + Real;
#declare TImaginary = TImaginary + Imaginary;
#declare TReal = TReal + Real;
#declare TImaginary = TImaginary + Imaginary;
#if(((TReal * TReal) + (TImaginary * TImaginary)) > 4)
#declare Inside = false;
#declare Counter = Iterations;
#end
#declare Counter = Counter + 1;
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"Tom Melly" <tom### [at] tomandlucouk> wrote in message
news:3a6eff76$1@news.povray.org...
> Also, with my error, at this resolution the mandel is not so good, so
change
Oops - make that
from:
#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;
to:
#declare TReal = ((TReal * TReal) - (TImaginary * TImaginary));
#declare TImaginary = (2 * T2Real * TImaginary);
#declare TReal = TReal + Real;
#declare TImaginary = TImaginary + Imaginary;
#if(((TReal * TReal) + (TImaginary * TImaginary)) > 4)
#declare Inside = false;
#declare Counter = Iterations;
#end
#declare Counter = Counter + 1;
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Tom Melly <tom### [at] tomandlucouk> wrote:
: seems to produce the exact same pattern - still, at this resolution who
: knows? ... ;).
I suppose that the difference would probably be seen in the exterior
coloring if you color according to number of iterations until bailout
(ie. as usual).
Since you are not examining whether |Z|>2 but instead |Z^2|>2 it probably
has a drastical effect in the exterior coloring.
I wouldn't be suprised if the fractal itself was a bit deformed because
of this (mainly because your bailout value of 2 might be too low in this
case). Anyways, I would say that to be sure, make Z=Z^2+c first and then
compare.
: Thinking about it, it's not that surprising. A tendancy towards infinity
: will show up in either case
Right, but I'm only worried about the bailout value. If you used a larger
value (presumably 4^2 = 8) then there may not be any problem (except perhaps
a different exterior coloring).
--
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 -*/
Post a reply to this message
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"Warp" <war### [at] tagpovrayorg> wrote in message
news:3a6f2b24@news.povray.org...
<SNIP>
As you may have gathered I zoomed in using the both the correct and
incorrect code and saw distinct differences. The incorrect one also looked
less complex, but I wouldn't swear on that.
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Warp wrote:
: n/30
What exactly was this doing at the bottom--does it close the while next loop
:Perhaps shaders are the answer?
Did I forget to RFTM, or doesn't povray lack these?
> 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 -*/
Could we have the povray-screen-language- compilable version of this?
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How about:
#FFDDCC
#FFCF66
or something similar.
Christoph
--
Christoph Hormann <chr### [at] gmxde>
IsoWood include, radiosity tutorial, TransSkin and other
things on: http://www.schunter.etc.tu-bs.de/~chris/
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On Wed, 24 Jan 2001 16:26:17 -0500 Greg M. Johnson wrote:
>:Perhaps shaders are the answer?
>Did I forget to RFTM, or doesn't povray lack these?
Hi, Greg. There's an unofficial version called POVMan, written by
Vahur Krouverk that supports Renderman-like shaders at:
http://www.aetec.ee/fv/vkhomep.nsf/pages/povman2
--
Alan - ako### [at] povrayorg - a k o n g <at> p o v r a y <dot> o r g
http://www.povray.org - Home of the Persistence of Vision Ray Tracer
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Greg M. Johnson <gre### [at] my-dejanewscom> wrote:
: : n/30
: What exactly was this doing at the bottom--does it close the while next loop
That's the result of the function. I mean, it's the function itself.
That is, as if we just had wrote:
#declare Mandel = function { n/30 }
Everything before that is just precalculation that is not part of the
function itself.
: Could we have the povray-screen-language- compilable version of this?
Perhaps if I have the time and motivation to "port" it to povray :)
--
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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