Auxiliary Materials for Cyclic Cellular Automata in 3D
Cyclic cellular automata are known to self-organize into periodic structures. We illustrate this in three dimensions using four types of "neighborhood". Von Neuman (face neighbors), Mixed (Moore in two dimensions, Von Neuman in other), Edge (neighbors have at least an edge in common), Moore (at least a vertex in common). Movies and selected frames may be found below. Images show four states in a 3D view and all states of the top plane. A preprint is available [Preprint] See also: Medley of spirals from cyclic cellular automata. Note: if your browser does not support this type of *.mov file, save the file and load it with quicktime.
Von Neuman, N=38 states
Mixed, N=56 states
Edge, N=86 states
Moore, N=128 states
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Von Neuman, N=38 states
Mixed, N=56 states
Edge, N=86 states
Moore, N=128 states
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Von Neuman, N=38 states
Mixed, N=56 states
Edge, N=86 states
Moore, N=128 states