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Antichaos in a class of random Boolean cellular automata

By James F. Lynch


A variant of Kauffman’s model of cellular metabolism is presented. It is a randomly generated network of boolean gates, identical to Kauffman’s except for a small bias in favor of boolean gates that depend on at most one input. The bias is asymptotic to 0 as the number of gates increases. Upper bounds on the time until the network reaches a state cycle and the size of the state cycle, as functions of the number of gates n, are derived. If the bias approaches 0 slowly enough, the state cycles will be smaller than n c for some c < 1. This lends support to Kauffman’s claim that in his version of random network the average size of the state cycles is approximately n 1/2

Topics: Proposed running head, Antichaos in Random Boolean Nets Keywords, cellular automata, random graphs, stability
Year: 1993
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