The dynamics of general fuzzy cellular automata

Abstract

We continue the investigation into the dynamics and evolution of fuzzy rules, obtained by the fuzzification of the disjunctive normal form, and initiated for rule 90 in [2], for rule 110 in [10] and for rule 30 in [3]. We present general methods for detecting the evolution and dynamics of any one of the 255 fuzzy rules and apply this theory to fuzzy rules 30, 110, 18, 45, and 184, each of which has a Boolean counterpart with interesting features. Finally, it is deduced that (except for at most nine cases) no fuzzy cellular automaton admits chaotic behavior in the sense that no sensitive dependence on the initial string can occur. © Springer-Verlag Berlin Heidelberg 2005.