Ronin Institute.
Artif Life. 2021 Jun 11;27(1):62-71. doi: 10.1162/artl_a_00337.
Conway's Game of Life is the best-known cellular automaton. It is a classic model of emergence and self-organization, it is Turing-complete, and it can simulate a universal constructor. The Game of Life belongs to the set of semi-totalistic cellular automata, a family with 262,144 members. Many of these automata may deserve as much attention as the Game of Life, if not more. The challenge we address here is to provide a structure for organizing this large family, to make it easier to find interesting automata, and to understand the relations between automata. Packard and Wolfram (1985) divided the family into four classes, based on the observed behaviors of the rules. Eppstein (2010) proposed an alternative four-class system, based on the forms of the rules. Instead of a class-based organization, we propose a continuous high-dimensional vector space, where each automaton is represented by a point in the space. The distance between two automata in this space corresponds to the differences in their behavioral characteristics. Nearest neighbors in the space have similar behaviors. This space should make it easier for researchers to see the structure of the family of semi-totalistic rules and to find the hidden gems in the family.
康威生命游戏是最著名的细胞自动机。它是一个著名的涌现和自组织模型，它是图灵完备的，可以模拟通用构造器。生命游戏属于半整体细胞自动机的集合，这个集合有 262144 个成员。如果不是更多的话，其中许多自动机可能值得像生命游戏一样受到关注。我们在这里面临的挑战是提供一个组织这个大家庭的结构，使找到有趣的自动机变得更容易，并理解自动机之间的关系。Packard 和 Wolfram（1985）根据规则的观察行为将这个家族分为四类。Eppstein（2010）提出了一个替代的四分类系统，基于规则的形式。我们不是基于类的组织，而是提出一个连续的高维向量空间，其中每个自动机由空间中的一个点表示。该空间中两个自动机之间的距离对应于它们行为特征的差异。空间中的最近邻具有相似的行为。这个空间应该使研究人员更容易看到半整体规则家族的结构，并找到家族中的隐藏瑰宝。
