Random threshold growth dynamics

A site in Z becomes occupied with a certain probability as soon as it sees at least a threshold number of already occupied sites in its neighborhood. Such randomly growing sets have the following regularity property: a large fully occupied set exists within a fixed distance (which does not increase with time) of every occupied point. This property suffices to prove convergence to an asymptotic shape. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15: 93–111, 1999