POV-Ray : Newsgroups : povray.binaries.images : My version of the (semi)photorealistic torus thingie : Re: My version of the (semi)photorealistic torus thingie Server Time
1 Oct 2024 22:27:49 EDT (-0400)
  Re: My version of the (semi)photorealistic torus thingie  
From: Moon47
Date: 8 Jul 2000 17:57:09
Message: <3966553E.37CA38AE@earthlink.net>
I would ask you to explain... But a sample scene/code of the math described would
be nice to learn from... Maybe a little explanation... My math is not that
extensive...

Warp wrote:

>   Chaos seems to emerge when one less expects. Just think about the following
> case:
>   Take a complex number (a+bi). Now raise it to the power 2 and add the
> original value to it. Do this again and again a certain number of times.
> If the absolute value of the resulting number doesn't seem to go to infinite,
> draw that point as black in the complex plane, else color that point according
> to the number of iterations you made to decide that it goes to infinite
> (you can decide it by looking if the absolute value goes bigger than a
> big enough number).
>   Now do this with all the complex numbers within a certain area, say, from
> -2-2i to 2+2i.
>   What image do you expect to appear? Well, one could imagine that perhaps
> a black-filled circle surrounded by concentric colored circles. Perhaps even
> a more complex image, but still quite simple and predictable. Or perhaps
> you just get completely random-colored pixels.
>   But no. Chaos kicks in. The resulting image is chaotic.
>   Not random. Randomness is chaotic in a way, but this chaos is different.
> There are quite well-defined visible patterns that form quite beautiful
> shapes. The variety of different shapes is amazing.
>   Now, a similar phenomenon happened here. Contrary to all logic a quite
> simple formula resulted in a chaotic pattern which make more or less
> beautiful shapes, a bit like clouds. What a wonderfully fractalic detail.
>   Chaos never stops marveling me when it kicks in when it's less expected.
> </boring mumbo-jumbo>
>
> --
> main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
> ):5;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/


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