  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.
