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 = 2km 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 2m 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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Voorhees, B. (2006). Discrete baker transformation for binary valued cylindrical cellular automata. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4173 LNCS, pp. 182–191). Springer Verlag. https://doi.org/10.1007/11861201_23
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