Extending Conways Game of Life

Abstract

Wayne M Getz and Richard Salter

We introduce an n-state Game of Life (GoL) on a cellular array (cells indexed by (i, j)), where each state σ = 0, ..., n − 1 has a nominal values vσ ≥ 0. The game involves computing the sum of the state values of the eight cells that surround cell (i, j) and using this sum to determine whether cell (i, j) stays in state σ, progress to state σ + 1, or reverts at state 0. We illustrate examples of this game, identifying still-life, oscillator, glider, and replicator patterns, as well as the long term behavior arising from random and regular starting configurations. Importantly, we provide two freely downloadable application programs that can be used to explore the behavior of the three and four state GoLs discussed in this paper.

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