Fundamental clusters in spatial 2×2 games

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Abstract
The notion of fundamental clusters is introduced, serving as a rule of thumb to characterize the statistical properties of the complex behaviour of cellular automata such as spatial 2×2 games. They represent the smallest cluster size determining the fate of the entire system. Checking simple growth criteria allows us to decide whether the cluster–individuals, e.g. some mutant family, are capable of surviving and invading a resident population. In biology, spatial 2×2 games have a broad spectrum of applications ranging from the evolution of cooperation and intraspecies competition to disease spread. This methodological study allows simple classifications and long–term predictions in various biological and social models to be made.

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