2D Cellular Automaton on a Triangulated Surface
2D triangular cellular automata can be applied on any triangulated surface. The given surface has an irregular shape and holes. The pattern spreads over the surface in an "organic" way. Two rules (32583 and 49054) are used as examples. You can try different views by rotating the surface.
In general, every element triangle of a triangulated 3D surface has exactly three neighbors, with the exception of the elements on the edges, with only one or two neighbors. In a topological sense this is equivalent to the notion of a "regular grid", although triangulation does not look regular at all. Because of this neighborhood condition, cellular automata (CA) seem to be particularly suited for such environment. Since the process of mapping and running a triangular CA on a mesh is expensive, the data for this Demonstration was limited to two rules and cached, so that it runs smoothly.
This Demonstration is based on a project done at NKS Summer School 2009 in Pisa, Italy.