The amazing dynamics of stochastic pattern formation and growth models inspired by the Conway's Game of Life

Abstract

Several modifications of the famous mathematical Game of Life are introduced by making Game of Life rules stochastic and mutual influence of cells in their 8-neighborhood on a rectangular lattice spatially non-uniform. Results are reported of experimental investigation of evolutionary dynamics of the introduced models. A number of new phenomena in the evolutionary dynamics of the models and collective behavior of patterns they generate are revealed, described and illustrated: formation of maze-like patterns as fixed points of the models, "self-controlled growth", "eternal life" in a bounded space and "coherent shrinkage".