FINITE SIZE SCALING BEHAVIOR OF A BIASED MAJORITY-RULE CELLULAR AUTOMATON

We consider the biased majority rule cellular automaton, in which the sites take the majority of the states (0 or 1) of their neighbors to update their states, with a bias towards 1 in case of ties. We observe that in any dimension for any initial density of 1's the probability of final complete occupancy by 1's converges to 1 as the lattice grows. In two dimensions the value p(L, α) of the initial density for which the probability of eventual complete occupancy of a lattice L × L is α ∈ (0, 1), is shown to satisfy for fixed α the bounds A logL< p(L, α) < B logL for large L, where A and B are positive and finite constants. © 1990.