Publication: Orbits of the Bernoulli measure in single-transition asynchronous cellular automata

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Title	Orbits of the Bernoulli measure in single-transition asynchronous cellular automata
Authors/Editors*	H. FukÅ and A. Skelton
Where published*	Proceedings of AUTOMATA 2011, Santiago, Chile
How published*	Proceedings
Year*	2011
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Abstract	We study iterations of the Bernoulli measure under nearest-neighbour asynchronou s binary cellular automata (CA) with a single transition. For these CA, we show that a coarse-level description of the orbit of the Bernoulli measure can be obtained, that is, one can explicit ly compute measures of short cylinder sets after arbitrary number of iterations of the CA. In particular, we give expressions for probabilities of ones for all three minimal single-transition rules, as well as expressions for probabilities of blocks of length 3 for some of them. These expressions can be interpreted as ``response curves'', that is, curves describing the dependence of the final density of ones on the initial density of ones.