A Classification Scheme for Fuzzy Cellular Automata with Applications to ECA

Abstract

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.