Cultivating the Garden of Eden

IF 0.7 4区数学 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Advances in Complex Systems Pub Date : 2022-06-15 DOI:10.25088/complexsystems.32.1.1

R. Beer

引用次数: 0

Abstract

Garden of Eden (GOE) states in cellular automata are grid configurations that 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 non-GOEs in 1-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 11×11, and initiate a study of the structure of the network of constraints that characterize GOE versus non-GOE configurations.

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培育伊甸园

元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出现。寻找最小化或最大化某些感兴趣的标准(例如，网格大小，密度等)的单个配置一直是休闲数学中的流行运动，但对元胞自动机的go集的系统研究很少。本文介绍了在Conway的生命游戏(GoL)元胞自动机中正在进行的GOE配置计算研究的当前结果。具体地说,我们描述的当前状态的地图去non-GOEs 1-density /大小的布局空间,描述如何前体的数量的密度制约的结构随增加网格大小随着我们方法的地方开始出现,提供了一个目录的所有已知的通用配置11×11的网格大小,并发起一项研究的约束网络的结构描述横过和non-GOE配置。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Complex Systems 综合性期刊-数学跨学科应用

CiteScore

1.40

自引率

0.00%

发文量

121

审稿时长

6-12 weeks

期刊介绍： Advances in Complex Systems aims to provide a unique medium of communication for multidisciplinary approaches, either empirical or theoretical, to the study of complex systems. The latter are seen as systems comprised of multiple interacting components, or agents. Nonlinear feedback processes, stochastic influences, specific conditions for the supply of energy, matter, or information may lead to the emergence of new system qualities on the macroscopic scale that cannot be reduced to the dynamics of the agents. Quantitative approaches to the dynamics of complex systems have to consider a broad range of concepts, from analytical tools, statistical methods and computer simulations to distributed problem solving, learning and adaptation. This is an interdisciplinary enterprise.