The complex behaviors in cellular automata have been widely developed in recent years to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic background. This type of automata has been frequently found either by conducting an exhaustive search or through a meticulous construction of the evolution rule. In this study, the specification of cellular automata with complex behaviors was obtained by utilizing randomly generated specimens. In particular, it was proposed that a cellular automaton of n states should be specified at random and then extended to another automaton with a higher number of states so that the original automaton operates as a periodic background where the additional states serve to define the gliders. Moreover, this study presents an explanation of this method. Furthermore, the random way of defining complex cellular automata was studied by using mean-field approximations for various states and local entropy measures. This specification was refined with a genetic algorithm to obtain specimens of a higher degree of complexity. By adopting this methodology, it was possible to generate complex automata with hundreds of states, demonstrating the fact that randomly defined local interactions with multiple states can construct complexity.

近年来，细胞自动机中的复杂行为得到了广泛发展，以生成和分析自动机，该自动机产生在周期性背景下相互作用的空间移动模式或滑翔机。这种类型的自动机经常通过进行详尽的搜索或通过细化构建进化规则来找到。在这项研究中，通过利用随机生成的标本获得具有复杂行为的细胞自动机的规范。特别是，有人提出n为元的自动机应该随机指定状态，然后将其扩展到具有更多状态的另一个自动机，以便原始自动机作为周期性背景运行，在此背景下，其他状态用于定义滑翔机。此外，这项研究提出了这种方法的解释。此外，通过使用各种状态的均值场近似和局部熵测度，研究了定义复杂细胞自动机的随机方法。使用遗传算法对该规范进行完善，以获得更高复杂度的标本。通过采用这种方法，可以生成具有数百个状态的复杂自动机，这说明了以下事实：随机定义的具有多个状态的局部交互会构成复杂性。