Arithmetic representations of cellular automata

One- and two-dimensional cellular automata (CA) are described in terms of a rithmetic relations. Interpreted as finite state machines, CA are shown to be equivalent to an updating unit that reads, processes and writes data on the array of cells. For 2D Von Neumann CA dynamics is described as a linear lattice of locally coupled 1D CA. The coupling is between nearest neighbors through a set of subrules, equivalent to the usual rules for Von Neumann neighborhoods. Finally, a measure theoretic entropy for one-dimensional CA is introduced to characterize spatial complexity and some numerical results are presented. © 1993.

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