Extended mean-field study of a stochastic cellular automaton
György Szabó, Géza Ódor · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1994
Extended mean-field theory is used for studying the one-dimensional stochastic cellular automaton with Rule 18 defined by Wolfram [Rev. Mod. Phys. 55, 601 (1983)]. The analysis is carried out at different levels taking n-point and n-pair correlations explicitly into consideration. The pair approximations reproduce the exact results in the deterministic limit. The critical behavior is studied by the Pad\'e approximant method and the predicted critical probability and exponent agree with previous data within a few percent.