Alfaro Gaspar, Sanjuán Miguel A F
Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles, 28933 Madrid, Spain.
Chaos. 2024 Aug 1;34(8). doi: 10.1063/5.0227349.
Elementary cellular automata are the simplest form of cellular automata, studied extensively by Wolfram in the 1980s. He discovered complex behavior in some of these automata and developed a classification for all cellular automata based on their phenomenology. In this paper, we present an algorithm to classify them more effectively by measuring difference patterns using the Hamming distance. Our classification aligns with Wolfram's and further categorizes them into additional subclasses. Finally, we have found a heuristic reasoning providing and explanation about why some rules evolve into fractal patterns.
初等元胞自动机是元胞自动机的最简单形式，20世纪80年代由沃尔夫勒姆进行了广泛研究。他在其中一些自动机中发现了复杂行为，并基于其现象学对所有元胞自动机进行了分类。在本文中，我们提出了一种算法，通过使用汉明距离测量差异模式来更有效地对它们进行分类。我们的分类与沃尔夫勒姆的分类一致，并进一步将它们细分为更多子类。最后，我们找到了一种启发式推理，对一些规则为何演变成分形图案给出了解释。
