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• W2068775135 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." @default.
• W2068775135 created "2016-06-24" @default.
• W2068775135 creator A5047801859 @default.
• W2068775135 date "2010-07-01" @default.
• W2068775135 modified "2023-10-17" @default.
• W2068775135 title "Simple form of the stationary distribution for 3D cellular automata in a special case" @default.
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• W2068775135 doi "https://doi.org/10.1016/j.physa.2010.03.011" @default.
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