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PDF 1.2 MB
DOI: http://dx.doi.org/10.7551/978-0-262-32621-6-ch119
Pages 744-749
First published 30 July 2014

Self-Organizing Process and Cluster Network in the Game of Life

Yoshihiko Kayama and Yasumasa Imamura

Abstract (Excerpt)

Conway's Game of Life, which is one of the most studied cellular automata, contains a self-organized rest state with residual clusters of live cells including the well-known patterns like Block and Beehive. The present article aims to discuss the self-organizing process from the viewpoint of a network representation of the Game of Life. Scale-free property of the network associated with the rest state is resilient against consecutive removals of a hub node. Of the two types of residual clusters, whose links continue to grow or not over time, the type of clusters accompanied by growing links is essential in the self-organizing process. Mixing the two types of clusters, which diversifies scales of branch graphs that correspond to avalanches caused by one-cell perturbations in the rest state, contributes to the scale-free property of the rest state. Furthermore, a network of clusters can be obtained from the rest-state network by regarding the clusters as composites of live cells.