Mathematics Colloquia and Seminars

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Assume that a cellular automaton (CA) rule enlarges subsets of the two--dimensional lattice, and does so in such a way that a larger set results in a larger outcome. Such models are called monotone solidification CA. In the critical case, these dynamics cannot cover the lattice starting from any finite set, but are able to do so from any set with finite complement. We assume that the initial set is a product measure with a small density, and address various scaling laws for the first passage time to the origin, emergence of shapes, and the ability of the dynamics toovercome pollution of space.