Consensus formation and the cellular automata

Abstract The decision making process in a society is studied in the context of two-dimensional cellular automata. We obtained the critical value of the order parameter below which this artificial society never reaches a consensus. It is found that a phase transition occurs at a certain value of the order parameter that represents the strength of interaction between agents, just as temperature in the phase transition in the physical systems. The relation between this order parameter and Langton's λ-parameter is studied. Wolfram's totalistic rules are investigated in two dimension with five neighbors.