Publication: Response curves for cellular automata in one and two dimensions - an example of rigorous calculations

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Title	Response curves for cellular automata in one and two dimensions - an example of rigorous calculations
Authors/Editors*	H. FukÅ and A. Skelton
Where published*	Journal of Natural Computing Research
How published*	Journal
Year*	2010
Volume	1
Number	3
Pages	85â99
Publisher
Keywords
Link	http://www.igi-global.com/Bookstore/Article.aspx?TitleId=49127
Abstract	We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate 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 of certain finite strings and probabilities of occurrence of these strings in a configuration obtained by iterating a random initial configuration $n$ times. Response curves can be rigorously calculated in both one- and two-dimensional versions of CA rule 130. We also discuss a special case of totally disordered initial configurations, t hat is, random configurations where the density of ones and zeros are equal to 1/2.