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.

康威的生命游戏是最著名的元胞自动机。它是一个经典的涌现和自组织模型，图灵完备，可以模拟一个通用的构造函数。生命游戏属于具有 262,144 个成员的半完全元胞自动机系列。这些自动机中的许多可能值得像生命游戏一样受到关注，如果不是更多的话。我们在这里解决的挑战是为组织这个大家庭提供一个结构，以便更容易找到有趣的自动机，并理解自动机之间的关系。Packard 和 Wolfram (1985) 根据观察到的规则行为将家庭分为四类。Eppstein (2010) 基于规则的形式提出了一种替代的四类系统。而不是基于阶级的组织，我们提出了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。这个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。空间中最近的邻居具有相似的行为。这个空间应该让研究人员更容易看到半全盘规则家族的结构，并找到家族中隐藏的宝石。