Phase transitions near the "game of Life"

Abstract

Whether or not the cellular automaton (CA) "game of Life" is an example of self-organized criticality has been a controversial question. Here we view the problem from a different perspective by introducing probabilities into the rules. Thereby we extend the discrete space of deterministic CA to a hypercubic space of stochastic CA, where each corner represents a deterministic CA. We examine the scaling structure near the "game of Life" corner and identify a phase-transition line separating "Life" and "Death." The transition line ends very close to but not in the "game of Life."