Cellular Automata, Dynamics and Complexity
In this paper we study some dynamical aspects of Cellular Automata. Essentially we characterize the steady state behavior for a class of local rules in the context of Potts and Bounded Threshold Automata. For Potts automata we exhibit a class that has a complex dynamics, i.e. the automaton simulates any logical function by coding binary information as gliders in a one-dimensional cellular space. On the other hand, we characterize another class which has a simple dynamical behavior: fixed points or two-cycles in the steady state. In the context of Bounded Threshold Automata with arbitrary interactions (not necessarily symmetric) we characterize its dynamics for one-dimensional cellular arrays: the only admissible cycles have period T ≤ 4. Furthermore, we give sufficient conditions to obtain a period-2 behavior in high dimensional lattices.
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