{"title":"Cultivating the Garden of Eden","authors":"R. Beer","doi":"10.25088/complexsystems.32.1.1","DOIUrl":null,"url":null,"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.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":"64 1","pages":"1-17"},"PeriodicalIF":0.7000,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Complex Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.25088/complexsystems.32.1.1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
