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Abstract: We consider the problem of computing a response curve for binary cellularautomata - that is, the curve describing the dependence of the density of onesafter many iterations of the rule on the initial density of ones. Wedemonstrate how this problem could be approached using rule 130 as an example.For this rule, preimage sets of finite strings exhibit recognizable patterns,and it is therefore possible to compute both cardinalities of preimages ofcertain finite strings and probabilities of occurrence of these strings in aconfiguration obtained by iterating a random initial configuration $n$ times.Response curves can be rigorously calculated in both one- and two-dimensionalversions of CA rule 130. We also discuss a special case of totally disorderedinitial configurations, that is, random configurations where the density ofones and zeros are equal to 1-2.



Author: Henryk Fukś

Source: https://arxiv.org/







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