Affiliations: School of Information Technology and Engineering,
University of Ottawa, 800 King Edward, Ottawa, Ontario, K1N 6N5, Canada.
[email protected]; [email protected]
Note: [] Address for correspondence: School of Information Technology and Engineering, University of Ottawa, 800 King Edward,
Ottawa, Ontario, K1N 6N5, Canada
Abstract: 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).
