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Nucleation parameters for discrete threshold growth on \(\mathbb{Z}^2\). (English) Zbl 0899.60085

Summary: 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.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
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References:

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