On the limit sets of cellular automata
SIAM Journal on Computing
Classifying circular cellular automata
Physica D
Hierarchy of fuzzy cellular automata
Fuzzy Sets and Systems
Cellular automata in fuzzy backgrounds
Physica D
Theoretical Computer Science
Chaotic subshifts and related languages applications to one-dimensional cellular automata
Fundamenta Informaticae - Special issue on cellular automata
Fuzzy Cellular Automata for Modeling Pattern Classifier
IEICE - Transactions on Information and Systems
RBFFCA: A Hybrid Pattern Classifier Using Radial Basis Function and Fuzzy Cellular Automata
Fundamenta Informaticae - Special issue on DLT'04
Radial View of Continuous Cellular Automata
Fundamenta Informaticae - Membrane Computing
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Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the ''fuzzification'' of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper we consider circular FCA; their asymptotic behavior has been observed through simulations and FCA have been empirically classified accordingly. No analytical study exists so far to support those observations. We now start the analytical study of circular FCA's dynamics by considering a particular set of FCA (Weighted Average rules) which includes rules displaying most of the observed dynamics, and we precisely derive their behavior. We confirm the empirical observations proving that all weighted average rules are periodic in time and space, and we derive their periods.