Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing instances of complex cellular automata; however, most of the proposed methods are based on a careful search or a meticulous construction of evolution rules. This paper presents the emergence of complex behaviors based on reversible cellular automata. In particular, this paper shows that reversible cellular automata represent an adequate framework to obtain complex behaviors adding only new random states. Experimental results show that complexity can be obtained from reversible cellular automata appending a proportion of about two times more states at random than the original number of states in the reversible automaton. Thus, it is possible to obtain complex cellular automata with dozens of states. Complexity appears to be commonly obtained from reversible cellular automata, and using other operations such as permutations of states or row and column permutations in the evolution rule. The relevance of this paper is to present that reversibility can be a useful structure to implement complex behaviors in cellular automata.

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来自可逆元胞自动机的复杂动力学

复杂性一直是元胞自动机中反复出现的研究课题，因为它们代表了从简单的局部交互中产生复杂行为的系统。之前已经进行了大量研究，提出了复杂元胞自动机的实例；然而，大多数提出的方法都是基于仔细搜索或精心构建进化规则的。本文介绍了基于可逆元胞自动机的复杂行为的出现。特别是，本文表明可逆元胞自动机代表了一个足够的框架来获得仅添加新随机状态的复杂行为。实验结果表明，复杂性可以从可逆元胞自动机随机附加大约两倍于可逆自动机中原始状态数量的状态的比例中获得。因此，可以获得具有数十种状态的复杂元胞自动机。复杂性似乎通常是从可逆元胞自动机中获得的，并在进化规则中使用其他操作，例如状态排列或行列排列。本文的相关性是提出可逆性可以成为在元胞自动机中实现复杂行为的有用结构。并在进化规则中使用其他操作，例如状态排列或行列排列。本文的相关性是提出可逆性可以成为在元胞自动机中实现复杂行为的有用结构。并在进化规则中使用其他操作，例如状态排列或行列排列。本文的相关性是提出可逆性可以成为在元胞自动机中实现复杂行为的有用结构。