Self-controlled growth, coherent shrinkage, eternal life in a self-bounded space and other amazing evolutionary dynamics of stochastic pattern formation and growth models inspired by Conways Game of Life

Abstract

Results of experimental investigation are presented of evolutionary dynamics of several stochastic pattern formation and growth models designed by modifications of the famous mathematical Game of Life. The modifications are two-fold: Game of Life rules are made stochastic and mutual influence of neighboring cells is made non-uniform. The results reveal a number of new phenomena in the evolutionary dynamics of the models: - Ordering of chaos to maze-like patterns: evolutionary formation, from arbitrary seed patterns, of stable maze-like patterns with chaotic dislocations that resemble natural patterns frequently found in the nature, such as skin patterns of some animals. The remarkable property of these patterns is their capability of unlimited growth, self-healing and transplantation. - Self-controlled growth of chaotic live formations into communities bounded, depending on the model, by a square, hexagon or octagon, until they reach a certain critical size, after which the growth stops. - Coherent shrinkage of mature, after reaching a certain size, communities into one of stable or oscillating patterns preserving in this process isomorphism of their bounding shapes until the very end. - Eternal life in a self-bounded space of communities: seemingly permanent birth/death activity of communities after they reach a certain size and shape.