Simon Wacker
Published 2016-03-21Version 1
We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; vertex-transitive graphs, in particular, Cayley graphs, acted on by automorphisms; groups acting on themselves by multiplication; and integer lattices acted on by translations.
The Garden of Eden Theorem for Cellular Automata on Group Sets
Universal groups of cellular automata
Bounding the minimal number of generators of groups of cellular automata
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