Using methods from the theory of fuzzy cellular automata as formulated over the past dECAde we present an analytic comprehensive derivation of a classification of fuzzy cellular automata (FCA) into four classes (1-4). Since fuzzy cellular automata include the elementary cellular automata in the limit, this classification can be applied to the original boolean ECA as considered by Wolfram and others [26]. When restricted in this way we can derive, in part, the Wolfram classification scheme.

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Journal of Cellular Automata
School of Mathematics and Statistics

Mingarelli, A. (2010). A classification scheme for fuzzy cellular automata with applications to ECA. Journal of Cellular Automata, 5(6), 445–467.