Unidimensional games, propitious environments, and maximum diversity

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Abstract
Cellular automata have been extensively used in the modeling of complexity. In biological phenomena complexity is directly related to the intuitive concept of diversity, which manifests itself in several forms. Particularly, the game Life [E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays (Academic, New York, 1982), Vol. 2] may be viewed as a picture of nonlinear open biological systems acting cooperatively. However, it has been shown that, in Life, diversity (defined in terms of different clusters) decreases with time. We derive an alternative game introducing the concept of a propitious environment which confers longevity to live sites in time evolution. It is shown that the game self-organizes in a configuration of maximum diversity exhibiting a high geometrical complexity. This game is considered in one dimension and has some connections with the unidimensional Life.

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