Elementary Cellular Automata with Memory

Paul-Jean Letourneau

University of Calgary

A simple modification of an elementary cellular automaton will be presented, in which the center cell of the three-cell neighborhood is referenced from a number of time steps in the past. Two different emulations in terms of range-1 CAs will be described. Analytical results for the bounds on finite growth rates and diffusion constants will also be given. Exact results and mean-field approximations will be presented for statistical mechanical behavior, in particular discrete dynamical density maps, correlation functions, the growth of perturbations, and phase transitions.

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