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The emergence of complex behaviors in cellular automata is an area that hasbeen widely developed in recent years with the intention to generate andanalyze automata that produce space-moving patterns or gliders that interact ina periodic background. Frequently, this type of automata has been found througheither an exhaustive search or a meticulous construction of the evolution rule.In this study, the specification of cellular automata with complex behaviorswas obtained by utilizing randomly generated specimens. In particular, itproposed that a cellular automaton of $n$ states should be specified at randomand then extended to another automaton with a higher number of states so thatthe original automaton operates as a periodic background where the additionalstates serve to define the gliders. Moreover, this study presented anexplanation of this method. Furthermore, the random way of defining complexcellular automata was studied by using mean-field approximations for variousstates and local entropy measures. This specification was refined with agenetic algorithm to obtain specimens with a higher degree of complexity. Withthis methodology, it was possible to generate complex automata with hundreds ofstates, demonstrating that randomly defined local interactions with multiplestates can construct complexity.

Random Expansion Method for the Generation of Complex Cellular Automata