The Global Evolution of General Fuzzy Cellular Automata
Angelo B. Mingarelli
We present new techniques for detecting the evolution and dynamics of general cellular automata where the methods can be applied to show that all except possibly 6 of the 255 fuzzy rules considered in [4] have asymptotic limits that are continuous functions of the initial string and so chaos cannot occur, i.e., no sensitive dependence on a finite initial string is possible for this class of fuzzy CA’s. It follows that there is a lack of complexity when considering these continuous CA’s. This answers, in particular, a question posed in [4]. We apply the general theory so developed to fuzzy Rules 30, 110, considered in earlier papers and the new rules 18, 45, and 184, each one of which has a boolean counterpart with interesting features. This produces a road-map for an almost complete investigation into the dynamics and evolution of such fuzzy cellular automata (CA), obtained by the fuzzification of the disjunctive normal form, initiated for fuzzy rule 90 in [4], for fuzzy rule 110 in [7], and for fuzzy rule 30 in [8].