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
Models of massive parallelism: analysis of cellular automata and neural networks
Models of massive parallelism: analysis of cellular automata and neural networks
Cellular automata in fuzzy backgrounds
Physica D
Cellular automata for reaction-diffusion systems
Parallel Computing - Special issue: cellular automata
Fuzzy Cellular Automata for Modeling Pattern Classifier
IEICE - Transactions on Information and Systems
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
RBFFCA: A Hybrid Pattern Classifier Using Radial Basis Function and Fuzzy Cellular Automata
Fundamenta Informaticae - Special issue on DLT'04
On the Relationship Between Boolean and Fuzzy Cellular Automata
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Asymptotic Behavior of Fuzzy Cellular Automata
Electronic Notes in Theoretical Computer Science (ENTCS)
On the relationship between fuzzy and Boolean cellular automata
Theoretical Computer Science
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Continuous cellular automata (or coupled map lattices) are cellular automata where the state of the cells are real values in [0, 1] and the local transition rule is a real function. The classical observation medium for cellular automata, whether Boolean or continuous, is the space-time diagram, where successive rows correspond to successive configurations in time. In this paper we introduce a different way to visualize the evolution of continuous cellular automata called Radial Representation and we employ it to observe a particular class of continuous cellular automata called fuzzy cellular automata (FCA), where the local rule is the "fuzzification" of the disjunctive normal form that describes the local rule of the corresponding Boolean cellular automata. Our new visualization method reveals interesting dynamics that are not easily observable with the space-time diagram. In particular, it allows us to detect the quick emergence of spatial correlations among cells and to observe that all circular FCA from random initial configurations appear to converge towards an asymptotic periodic behavior. We propose an empirical classification of FCA based on the length of the observed periodic behavior: interestingly, all the minimum periods that we observe are of lengths one, two, four, or n (where n is the size of a configuration).