Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!swrinde!zaphod.mps.ohio-state.edu!samsung!munnari.oz.au!uniwa!tim From: tim@maths.uwa.oz.au (Tim Boykett) Newsgroups: comp.theory.cell-automata Subject: Re: Spherical CA Message-ID: <1990Oct5.064458.26401@uniwa.uwa.oz> Date: 5 Oct 90 06:44:58 GMT References: <90277.175712HFIHC@CUNYVM.BITNET> Sender: usenet@uniwa.uwa.oz (USENET News System) Organization: University of Western Australia Lines: 39 HFIHC@CUNYVM writes: >Has anyone ever designed and/or implemented a CA for a spherical surface? >If so, how do you tile a spherical surface so that no cell is larger, or >differently shaped than another? >Any ideas? >-Hoss >------- >H. Y. Firooznia >HFIHC@CUNYVM.CUNY.EDU I have never implemented one, but a number of cell-shapes and sizes could be used. My first guess was the pattern used on a soccer ball, but I seem to remember that has a mixture of hexagons and pentagons on it. You will need to use shapes that are polyhedra, ie they are topologically isomorphic to a sphere, but they have flat surfaces. There is a technical name for this process, but I can't remember it. You will need a shape for the faces of your polyhedra. The patterns to use would have to be triangles, squares or pentagons, presuming yoy want regular polygons for the faces. This is because 3 hexagons make a flat tiling. with triangles, you could have 3,4 or 5 around each vertex. 3 would give tetrahedral shape, 4 would give a pair of square-based pyramids joined at the base, and 5 would give a 20-faced object. You can see what these look like in any role-playing game shop, the are dice with 4,8,20 sides resp. With square faces, you can only get a cube shape, with pentagons you can only get a 12-sided shape. I don't think there are anyother regular polyhedra that can be made though have a weak memory of someone shoing me a 100-sided dice that was regular. I hope this semi-mathematical diatribe answers your question, otherwise don't hesitate to ask again. Tim. tim@madvax.maths.uwa.oz.au