Discrete Baker Transformation for Binary Valued Cylindrical Cellular Automata
Recently, the discrete baker transformation has been defined for linear cellular automata acting on multi-dimensional tori with alphabet of prime cardinality. Here we specialize to binary valued cylindrical cellular automata and generalizing the discrete baker transformation to non-linear rules. We show that for a cellular automaton, defined on a cylinder of size n = 2 k m with m odd, the equivalence classes of rules that map to the same rule under the discrete baker transformation fall into equivalence classes labeled by the set of 2 m cellular automata defined on a cylinder of size m. We also derive the relation between the state transition diagram of a cellular automata rule and that of its baker transformation and discuss cycle periods of the baker transformation for odd n.
KeywordsCellular Automaton Additive Rule State Transition Diagram Bruijn Sequence Rule Component
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