caa a22 4500 44539160X CHVBK 20180317143048.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10955-010-0103-9 doi (NATIONALLICENCE)springer-10.1007/s10955-010-0103-9 The One-Dimensional Exactly 1 Cellular Automaton: Replication, Periodicity, and Chaos from Finite Seeds [Elektronische Daten] [Janko Gravner, David Griffeath] In the Exactly 1 cellular automaton (also known as Rule 22), every site of the one-dimensional lattice is either in state 0 or in state 1, and a synchronous update rule dictates that a site is in state 1 next time if and only if it sees a single 1 in its three-site neighborhood at the current time. We analyze this rule started from finite seeds, i.e., those initial configurations that have only finitely many 1's. Three qualitatively different types of evolution are observed: replication, periodicity, and chaos. We focus on rigorous results, assisted by algorithmic searches, for the first two behaviors. In particular, we explain why replication is observed so frequently and present a method for collecting the smallest periodic seeds. Some empirical observations about chaotic seeds are also presented. The Author(s), 2010 Additive dynamics nationallicence Cellular automaton nationallicence Chaos nationallicence Entropy nationallicence Periodic attractor nationallicence Replicator nationallicence Gravner Janko Mathematics Department, University of California, 95616, Davis, CA, USA aut Griffeath David Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA aut Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/1(2011-01-01), 168-200 0022-4715 142:1<168 2011 142 10955 https://doi.org/10.1007/s10955-010-0103-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-010-0103-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gravner Janko Mathematics Department, University of California, 95616, Davis, CA, USA aut NATIONALLICENCE 700 1- Griffeath David Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 142/1(2011-01-01), 168-200 0022-4715 142:1<168 2011 142 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer