Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
974208 | Physica A: Statistical Mechanics and its Applications | 2010 | 5 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Alexandru Agapie,