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Author (up) Goles, E.; Montalva-Medel, M.; Mortveit, H.; Ramirez-Flandes, S. url  openurl
  Title Block Invariance in Elementary Cellular Automata Type Journal Article
  Year 2015 Publication Journal Of Cellular Automata Abbreviated Journal J. Cell. Autom.  
  Volume 10 Issue 1-2 Pages 119-135  
  Keywords Elementary cellular automata; block updates; periodic points; block invariance  
  Abstract Consider an elementary cellular automaton (ECA) under periodic boundary conditions. Given an arbitrary partition of the set of vertices we consider the block updating, i.e. the automaton's local function is applied from the first to the last set of the partition such that vertices belonging to the same set are updated synchronously. The automaton is said block-invariant if the set of periodic configurations is independent of the choice of the block updating. When the sets of the partition are singletons we have the sequential updating: vertices are updated one by one following a permutation pi. In [5] the authors analyzed the pi-invariance of the 2(8) = 256 possible ECA rules (or the 88 non-redundant rules subset). Their main result was that for all n > 3, exactly 41 of these non-redundant rules are pi-invariant. In this paper we determine the subset of these 41 rules that are block invariant. More precisely, for all n > 3, exactly 15 of these rules are block invariant. Moreover, we deduce that block invariance also implies that the attractor structure itself is independent of the choice of the block update.  
  Address [Goles, Eric; Montalva-Medel, Marco; Ramirez-Flandes, Salvador] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Penalolen, Chile, Email: eric.chacc@uai.cl;  
  Corporate Author Thesis  
  Publisher Old City Publishing Inc Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1557-5969 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000350183000006 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 461  
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