The dynamics of fuzzy cellular automata: rule 30

Authors:
Angelo B. Mingarelli;Elzbieta Beres
Affiliations:
School of Mathematics, Carleton University, Ottawa, Ontario, Canada;Department of Electrical Engineering, Carleton University, Ottawa, Ontario, Canada
Venue:
ISTASC'04 Proceedings of the 4th WSEAS International Conference on Systems Theory and Scientific Computation
Year:
2004

Citing 3
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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 [3] and continued for Rule 110 in [5]. We present new results regarding the dynamics of fuzzy Rule 30 whose Boolean evolution is known to be chaotic [[7], p. 871]. In particular, we show that in the fuzzy case with a finite support configuration all temporal sequences are aperiodic, and their convergence is strongly dependent upon their positions along key diagonals. It follows that fuzzy Rule 30 is neither chaotic nor random. It turns out that the evolution and dynamics in this case differ radically from those in fuzzy Rule 90.