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

TL;DR

This paper explores stochastic modifications of Conway's Game of Life, revealing new phenomena like maze patterns, self-controlled growth, eternal life, and coherent shrinkage through experimental analysis of their evolutionary dynamics.

Contribution

It introduces stochastic and spatially non-uniform rules to the Game of Life, uncovering novel collective behaviors and pattern formations not seen in the classic version.

Findings

Formation of maze-like fixed point patterns

Discovery of self-controlled growth phenomena

Observation of eternal life and coherent shrinkage behaviors

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".