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Author Topic: Generalized Apollonius: random ellipsoid packings  (Read 1554 times)
Description: a numerical experiment resulting in a random fractal
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hobold
Fractal Bachius
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Posts: 573


« on: February 04, 2013, 12:18:10 PM »

I was reading up on collision tests for ellipsoids, and found out that this is a surprisingly tricky task. There are no closed formulas even for low dimensional cases (such as our familiar three dimensional space). But numerical approximation works reasonably well.

To put my newly gained knowledge to the test, I decided to generalize Apollonius' sphere packings a bit:



This lump of sticky pebbles (100000 random ellipsoids packed on the surface of another random ellipsoid) has no further significance other than being a pretty picture. Technically it should be a random fractal (if I have done everything mostly right), but it does not really lead to new fractal worlds.

Before I link to an animation of the thing, I want to extend a preemptive apology to lycium: this is not a lighting model. These are just formulas that were, pardon the rude pun, "pulled from where the light don't shine" smiley. I know this with certainty, because I programmed the raytracer myself. (Even PoV-Ray has better lighting, but my code can render an antialiased frame of the animation in 1.3 seconds ... after 15 minutes of building an acceleration structure for all frames, though.)

That being said, here is the animation for those who want to look at the object from all sides:

http://vectorizer.org/boar/elliFoam007.mp4
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knighty
Fractal Iambus
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Posts: 819


« Reply #1 on: February 04, 2013, 04:02:17 PM »

Looks good! Its fractal nature could be emphasized by rendering it's intersection with the first ("the other") ellipsoid or just rendering the ellipsoids which size is under some thresold.
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hobold
Fractal Bachius
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Posts: 573


« Reply #2 on: February 04, 2013, 06:36:55 PM »

To me, the more "correct" visualization styles seemed more boring. But judge for yourself:
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knighty
Fractal Iambus
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Posts: 819


« Reply #3 on: February 04, 2013, 07:28:29 PM »

IMHO there is not any correct visualization style.

You are right, the first picture looks better but in the second, The fractal nature of the object (the limit set) is obvious. (Of course, one have to prove it mathematically.  cheesy)
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