Since this torus-like object rendering seems to be in fashion nowadays,
I decided to try for myself, and here is the result:

Post a reply to this message

Attachments:
Download 'GlassTorus.jpg' (69 KB)

Preview of image 'GlassTorus.jpg'

Look, it's a teething ring

Post a reply to this message

Yeah, rotate it 360 degrees in an animation and see what chaos is really
like! (j/k)
Cool render. It reminds me of all those glass renders I left unfinished. :)

Grim

Post a reply to this message

Warp wrote:

>   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.

Mmmh.  I don't think that the Mandelbrot set is chaotic.  It's a
fractal,
but not all fractals are chaotic.  Most chaotic phenomenas shows
fractals
properties when graphically transcribed (Lorenz equations,...), but
there
are as many deterministic (algorithmic) fractals as chaotic fractals.
Chaos is characterized by it's sensitivity to initial conditions, so
maybe your "pattern" is chaotic...

Though, yes, these things are marvellous and amazing.  The pattern you
found has certainly the 2 properties shared by all fractals : it comes
from an iterative process (the rays, refracted, reflected,
photonized(!)),
and must be self-similar (I suppose that, if you zoom, you will find
that
each part ressembles the whole, even at smallest scales).

Fabien.

Post a reply to this message

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 -*/

Post a reply to this message

> Cool render. It reminds me of all those glass renders I left
unfinished. :)
Uhhh ... I know so much what you mean ...

--

 ,',    Jan Walzer      \V/  http://wa.lzer.net     ,',
',','   student of      >|<  mailto:jan### [at] lzernet ',','
  '   ComputerScience   /A\  +49-177-7403863         '

Post a reply to this message

<snip>
> Mmmh.  I don't think that the Mandelbrot set is chaotic.
<snip>
> Chaos is characterized by it's sensitivity to initial conditions,
<snip>

As I understand it, the Mandelbrot set is not chaotic because it is a static
entity and chaos is a property of dynamic systems.  However the system that
generates the Mandelbrot set is chaotic (sensitive to initial conditions).
People often omit the word 'set' and use 'Mandelbrot' to refer to both the
set and the system that generates it, so 'the Mandelbrot' can be thought of
as chaotic.

Post a reply to this message

>   Now, this is interesting. For no apparent reason a quite chaotic pattern
> (with greenish-yellow coloration) has appeared seemingly from nowhere on
the
> sphere at the right of the central sphere.

I assume the sky is, as it appears, just a plain gradient without patterns
or turbulence.  What happens when you change the ground to just a flat,
plain colour?  If the pattern is still there, could you post a close-up?

Post a reply to this message

"Edward Coffey" <e.c### [at] ugradunimelbeduau> wrote in message
news:3967e406@news.povray.org...
| >   Now, this is interesting. For no apparent reason a quite chaotic pattern
| > (with greenish-yellow coloration) has appeared seemingly from nowhere
|
| I assume the sky is, as it appears, just a plain gradient without patterns
| or turbulence.  What happens when you change the ground to just a flat,
| plain colour?  If the pattern is still there, could you post a close-up?

It's pretty obvious to me that it's the caustic on the textured ground, more
or less directly in line with the light source and sphere segment, showing up
as a magnified refraction.  That's has to be the explanation.

Bob

Post a reply to this message

Warp wrote:
> 
>   Since this torus-like object rendering seems to be in fashion nowadays,
> I decided to try for myself, and here is the result:
> 

I like this one, simple and elegant. Definitely wallpaper material.

As for the 'chaotic' pattern; my first guess would be sampling inaccuratcies (in
the transmitted rays) increased by the complex internal reflections. It's even
more probable if the torus doesn't have ignore_photons; internally reflected
photons can give weird results.
Of course, I don't understand a thing about complex planes or chaos theory, so
my scope is limited.

-- 
Margus Ramst

Personal e-mail: mar### [at] peakeduee
TAG (Team Assistance Group) e-mail: mar### [at] tagpovrayorg

Post a reply to this message