NUCLEATION PARAMETERS FOR DISCRETE THRESHOLD GROWTH ON ℤ^{2}

JANKO GRAVNER AND DAVID GRIFFEATH

Abstract. Threshold Growth is a cellular automaton on an integer lattice in which the occupied set grows according to a simple local rule: a site becomes occupied if and only if it sees at least a threshold number of previously occupied sites in its prescribed neighborhood. We study the minimal number of sites that these dynamics need for persistent growth in two dimensions.