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.

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