Greetings!

Last May, "knighty" of fractalforums.com amazed fractal fans worldwide 
when he presented a new class of escape time fractals he calls 
"Kaleidoscopic IFS." Forum members quickly grasped the concept and 
proceeded to create many interesting variants, many of which you can see 
in this seminal thread: 
http://www.fractalforums.com/3d-fractal-generation/kaleidoscopic-%28escape-time-ifs%29/?PHPSESSID=8fddfae07b02d36cd3c05e028fd6a7d9

Jos Leys then went on to describe these fractals in more detail: 
http://images.math.cnrs.fr/Un-ballon-de-foot-fractal.html I highly 
recommend checking out the rest of his site if you haven't done so 
already; he's done some very cool things.

The theory behind these objects is that all polyhedra have a set of 
symmetry planes about which geometry may be reflected. If an iterated 
function is reflected, scaled off-center and tested against a sphere, 
there will be an emergence of new, often unexpected shapes.

I have managed to make a full implementation of the five Platonic 
solids, along with an ad-hoc cavity shader. You can find the scene file 
here: 
http://news.povray.org/povray.text.scene-files/thread/%3C4cff1d96%40news.povray.org%3E/

Perhaps you'll find these fractals as captivating as I do :)

Happy Raytracing!

-Sam

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