论文标题
培养伊甸园
Cultivating the Garden of Eden
论文作者
论文摘要
细胞自动机中的伊甸园（GOE）状态是没有前体的网格配置，也就是说，它们只能作为初始条件发生。找到可以最大程度地减少或最大化某些感兴趣标准（例如网格大小，密度等）的个人配置一直是娱乐性数学中的一种流行运动，但是对蜂窝自动机的一组Goes的系统研究很少见。本文介绍了Conway生命游戏（GOL）蜂窝自动机中GOE配置正在进行的计算研究的当前结果。具体而言，我们描述了密度/尺寸空间中的dov和nongoes布局图的当前状态，表征了前体数量的密度依赖性结构如何随着网格大小的增加而变化，因为我们接近开始发生的点，提供了所有已知的goe配置的目录，并为11x11的网格尺寸提供了一个构成voe的网络，并构成了一个构成的结构。
Garden of Eden (GOE) states in cellular automata are grid configurations which have no precursors, that is, they can only occur as initial conditions. Finding individual configurations that minimize or maximize some criterion of interest (e.g., grid size, density, etc.) has been a popular sport in recreational mathematics, but systematic studies of the set of GOEs for a cellular automaton have been rare. This paper presents the current results of an ongoing computational study of GOE configurations in Conway's Game of Life (GoL) cellular automaton. Specifically, we describe the current status of a map of the layout of GOEs and nonGOEs in density/size space, characterize how the density-dependent structure of the number of precursors varies with increasing grid size as we approach the point where GOEs begin to occur, provide a catalog of all known GOE configurations up to a grid size of 11x11, and initiate a study of the structure of the network of constraints that characterize GOE vs. nonGOE configurations.
