ON BEHAVIORS OF CELLULAR AUTOMATA WITH RULE 156

This paper deals with one-dimensional finite cellular automata with a triplet local transition rule 156 and fixed boundary conditions. The author observed behaviors of CA-156 000 (m) by computer, and found formulae of number of limit cycles and transient length from observation. And the author got proof of them. 1 Introduction J. von Neumann introduced cellular automata capable of self-reproduction and universal computation. While cellular automata have simple structure, their global behaviors caused by interactions between cells are very complicated. Their global behaviors are similar to behaviors of complex systems as fractals, chaotic phenomenon and so on. S. Wolfram and other researchers rerealized important roles of cellular automata as theoretical models of complex systems. Cellular automata have wide applications in biology, physics, computer science, mathematics and so on. Recently various cellular automata are investigated and applied by many researchers. S. Wolfram classifie...

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