Simple form of the stationary distribution for 3D cellular automata in a special case

Alexandru Agapie

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 13, 2495-2499

Abstract: 3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all ones. Otherwise–and this is the case we tackle–the chain is ergodic, thus allowing for the search of stationary distributions. This proves cumbersome in the general case, still, under detailed balance equation, the stationary distribution can be derived in closed form. The probability of a particular state is found to be exponential in the number of zero–one borders within the configuration.

Keywords: Finite homogeneous Markov chain; Cellular automata; Ising model; Interacting particle system; Voter model (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:13:p:2495-2499

DOI: 10.1016/j.physa.2010.03.011

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