Influence of Local Interaction and Fluctuation in a Cellular Automaton Simulations

Abstract

Cellular automaton simulations are interesting to investigate space-time patterns of systems consisting of various inter-component interactions. One of the typical simulations is the one based on the "Game of Life" algorithm (GLA) which was proposed by Conway. In the present paper, GLA is mathematically formulated and is generalized as a simulation tool for studying dependence of patterns by revising the algorithm for time evolution, changing the initial distribution ratio of the "ON" state (corresponding to "a life" at a cell), extending the range of the interaction, and taking into account the effect of fluctuation as a model for a realistic open system. In the present study, we monitor the number of the "ON" state, a number of steps to reach an equilibrium, and chemical potential in the simulated pattern by considering the interaction energy. In most cases, the number of the "ON" state cells decreases as the simulation step proceeds. Interestingly, we observed that, in some conditions, the number of the "ON" state increases. A variety of simulated patterns will be discussed and analyzed to understand a general trend in pattern formation in cellular automaton simulations.