Sughimura, Noritsugu, Reiji Suzuki, and Takaya Arita. “Non-uniform Cellular Automata based on Open-ended Rule Evolution.” Artificial Life and Robotics 19, no. 2 (2014): 120-126.
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Cellular automata (CAs) are mathematical models of spatially and temporally discrete mathematical systems. Non-uniform CAs are the cellular automata in which each cell may contain a different transition rule and change it with time, while all cells share the same transition rule in regular CAs. Little is still known about the dynamics of open-ended evolution of rules in non-uniform CAs. The purpose of our study is to construct and investigate a model of non-uniform CAs capable of open-ended rule evolution exhibiting a wide variety of behavior across all Wolfram’s classes. For this purpose, we construct 1-dimensional 2-state 3 neighborhood non-uniform CAs with evolving transition rules. In the model, we found an interesting dynamics that Class II (periodical behavior) and III (chaotic behavior) patterns emerged alternately, between which Class IV patterns sometimes emerged.