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Fractal polyhedra in Stella

 
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robertw
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Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Sun Apr 13, 2008 4:00 pm    Post subject: Fractal polyhedra in Stella Reply with quote

I mentioned elsewhere George Hart's class assignment using Great Stella to create fractal polyhedra.

Well I thought I'd start a thread about making fractal polyhedra in Stella. Here are some examples, starting with George's and then some of my own:



So I encourage others to post their own images of fractal polyhedra created in Stella, and discuss techniques for their construction.

Rob.
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polymorphic



Joined: 17 Feb 2008
Posts: 26

PostPosted: Mon Apr 14, 2008 4:02 pm    Post subject: Reply with quote

Hi Rob,

I don't know that this is truly fractal. I got this idea while working with Jim's Molybi polyhedra

http://www.orchidpalms.com/polyhedra/rhombic/molybi/molybi.htm

Take any antiprism (or prism for that matter) and shrink one of the major polygons on one side, but keep it regular. Attach that to the faces of any polyhedron with matching faces. Then attach them again to the smaller faces canonically.

Regularity of the major faces doesn't matter, as long as the one major face is the same shape as the the other and a minature of it. The connecting triangles or squares can be distorted and would alter the appearance of the finished fractal polyhedron making it perhaps gnarled.

This concept could be extended beyond prismatics but I think ultimately some kind of symmetry needs to be maintained.

I will attempt to attach an image. Here is Ti with pentagons and hexgons treated in this manor.


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Roger Kaufman
http://www.interocitors.com/polyhedra/
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Ulrich



Joined: 29 Jan 2008
Posts: 87
Location: Germany

PostPosted: Tue Apr 15, 2008 6:17 am    Post subject: Reply with quote

Roger,

some time ago, I made lots of such structures:



see:

http://www.polyedergarten.de/polyhedrix/e_augintro.htm


In a similar way, you can produce pretty spirals:




http://www.polyedergarten.de/polyhedrix/ico_octa/ico_octa_spiral_leo_2.html

Ulrich
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polymorphic



Joined: 17 Feb 2008
Posts: 26

PostPosted: Wed Apr 16, 2008 1:22 am    Post subject: Reply with quote

Ulrich,

These are very nice. The second one, upon opening, I find is actually a 2D spiral like a snail shell. Interesting. Stella is downsizing each icosahedron as it goes.

These all probably have some fractal properties. What the actual fractional dimension is would be a math problem. I would say that since we are starting with 3D objects then the fractional dimention must be between 3 and 4.

Roger
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Roger Kaufman
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