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Author Topic: Sphere Inversion Fractals  (Read 3150 times)
Description: Mobius inversions etc.
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fractalrebel
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« on: November 20, 2009, 09:25:44 PM »

Let's not forget there is another large group of 3D type fractals out there which use sphere inversions. Here is an example that uses Mobius Transforms.


* OtherWorlds.jpg (75.27 KB, 800x640 - viewed 534 times.)
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fractalrebel
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« Reply #1 on: November 20, 2009, 09:47:46 PM »

Here is another example, this time straight sphere inversions starting with a tetrahedral arrangement of tangent spheres, and yes, it is a fractal. The top has been lopped off so you can see some of the details of interior.


* PuzzleInBlue.jpg (170.6 KB, 800x800 - viewed 602 times.)
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fractalrebel
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« Reply #2 on: November 20, 2009, 10:10:09 PM »

Both the Mobius inversions and the straight 3D inversions use the "Plane and Sphere Raytracing" formula in the Ultrafractal database (reb5.ucl). It in turn calls a raytrace library called RaytraceSphere in reb.ulb. Anyone who own UF 5 has access to the database and can see the code used. The tetrahedral sphere inversions and the Mobius inversions are plugins to RaytraceSphere.
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cKleinhuis
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« Reply #3 on: November 21, 2009, 01:55:27 AM »

i recently read the book from "indra's pearls " which was dealing with the moebius transform, nice to see those images!
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lycium
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« Reply #4 on: November 21, 2009, 04:57:57 AM »

i also have that book, it's such a joy smiley

here are some sphere inversion fractals i rendered in 2005:

http://imgur.com/hQ7WG.jpg
http://imgur.com/3jzgU.jpg
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fractalrebel
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« Reply #5 on: November 21, 2009, 06:13:16 AM »

Nice,

Looks like these were mapped onto a Riemann sphere.
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