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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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Attachments:
Download 'kifse38_05.jpg' (99 KB)
Preview of image 'kifse38_05.jpg'
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One of the many "soccer ball" fractals.
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Download 'kifsd14_49.jpg' (86 KB)
Preview of image 'kifsd14_49.jpg'
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Here's one of the objects I made to "proof" the setup. I was a bit
heavy-handed with the shading...
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Download 'kifsd15_42.jpg' (81 KB)
Preview of image 'kifsd15_42.jpg'
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This was an early failed attempt. It's an example of how the
"plug-and-chug" method of not doing your homework can go terribly wrong.
It inspired me to find my own symmetry planes. It's actually not that
bad, might even make a nice alien space station :)
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Download 'kifsd7_43.jpg' (32 KB)
Preview of image 'kifsd7_43.jpg'
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Another icosahedron, this time with a small rotation.
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Download 'kifsd21_05.jpg' (72 KB)
Preview of image 'kifsd21_05.jpg'
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Gorgeous, Sam! All of them.
I like the alien space station.... ;-)
Thomas
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Awesome images. I especially like your 'proof' image of the dodecahedral
fractal. Heavy-handed on the shading? Maybe. Looks better for it? Definitely. :)
I shall check out these links too, that'll be my productivity gone for the day!
Bill
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Wonderful! That really is exciting! I'm constantly amazed at the things I see on
this forum. Thanks for sharing!
Regards,
Dave Blandston
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On 12/7/2010 11:58 PM, Thomas de Groot wrote:
> Gorgeous, Sam! All of them.
>
> I like the alien space station.... ;-)
Thanks, Thomas :) Aliens always build the best stuff <g>
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On 12/8/2010 1:24 AM, Bill Pragnell wrote:
> Awesome images. I especially like your 'proof' image of the dodecahedral
> fractal. Heavy-handed on the shading? Maybe. Looks better for it? Definitely. :)
>
> I shall check out these links too, that'll be my productivity gone for the day!
I think you might have been looking for an excuse ;)
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