{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T10:48:52Z","timestamp":1753872532928,"version":"3.41.2"},"reference-count":52,"publisher":"AIP Publishing","issue":"2","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2007,6,1]]},"abstract":"<jats:p>We study the dynamics of patterns exhibited by rule 52, a totalistic cellular automaton displaying intricate behaviors and wide regions of active\/inactive synchronization patches. Systematic computer simulations involving 230 initial configurations reveal that all complexity in this automaton originates from random juxtaposition of a very small number of interfaces delimiting active\/inactive patches. Such interfaces are studied with a sidewise spatial updating algorithm. This novel tool allows us to prove that the interfaces found empirically are the only interfaces possible for these periods, independently of the size of the automata. The spatial updating algorithm provides an alternative way to determine the dynamics of automata of arbitrary size, a way of taking into account the complexity of the connections in the lattice.<\/jats:p>","DOI":"10.1063\/1.2732896","type":"journal-article","created":{"date-parts":[[2007,6,28]],"date-time":"2007-06-28T22:09:32Z","timestamp":1183068572000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Spatial updating, spatial transients, and regularities of a complex automaton with nonperiodic architecture"],"prefix":"10.1063","volume":"17","author":[{"given":"Joana G.","family":"Freire","sequence":"first","affiliation":[{"name":"Universidade de Lisboa Departamento de F\u00edsica, Faculdade de Ci\u00eancias, , Lisboa, Portugal and"},{"name":"Universidade Federal do Rio Grande do Sul Instituto de F\u00edsica, , 91501-970 Porto Alegre, Brazil"}]},{"given":"Owen J.","family":"Brison","sequence":"additional","affiliation":[{"name":"Universidade de Lisboa Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, , Lisboa, Portugal"}]},{"given":"Jason A. C.","family":"Gallas","sequence":"additional","affiliation":[{"name":"Universidade Federal do Rio Grande do Sul Instituto de F\u00edsica, , 91501-970 Porto Alegre, Brazil"}]}],"member":"317","published-online":{"date-parts":[[2007,6,28]]},"reference":[{"volume-title":"Small Worlds","year":"1999","key":"2023080123455424700_c1"},{"volume-title":"Dynamical Systems","year":"2005","key":"2023080123455424700_c2"},{"volume-title":"The Structure and Dynamics of Networks","year":"2006","key":"2023080123455424700_c3"},{"volume-title":"Linked","year":"2003","key":"2023080123455424700_c4"},{"volume-title":"Nexus: Small World and the Ground-Breaking Theory of Networks","year":"2002","key":"2023080123455424700_c5"},{"volume-title":"Essays on Cellular Automata","year":"1970","author":"Burks","key":"2023080123455424700_c6"},{"volume-title":"A New Kind of Science","year":"2002","key":"2023080123455424700_c7"},{"volume-title":"Cellular Automata Modeling of Physical Systems","year":"1998","key":"2023080123455424700_c8a"},{"volume-title":"Modeling Chemical Systems using Cellular Automata","year":"2005","key":"2023080123455424700_c8b"},{"volume-title":"Cellular Automata","year":"2001","key":"2023080123455424700_c9"},{"volume-title":"Complexity: Hierarchical Structures and Scaling in Physics","year":"1997","key":"2023080123455424700_c10"},{"volume-title":"An Introduction to Kolmogorov Complexity and its Applications","year":"1993","key":"2023080123455424700_c11"},{"key":"2023080123455424700_c12","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-0623-9","volume-title":"Measures of Complexity and Chaos","author":"Abraham","year":"1989"},{"volume-title":"Discourses","year":"1637","key":"2023080123455424700_c13a"},{"volume-title":"De Homines","year":"1662","key":"2023080123455424700_c13b"},{"volume-title":"Living Dolls: A Magical History Of The Quest For Mechanical Life","year":"2002","key":"2023080123455424700_c14a"},{"volume-title":"Le r\u00eave de l\u2019Homme-Machine: De l\u2019Automate \u00e0 l\u2019Andro\u00efde","year":"2005","key":"2023080123455424700_c14b"},{"key":"2023080123455424700_c15","doi-asserted-by":"crossref","DOI":"10.1007\/11861201","volume-title":"Cellular Automata","author":"El Yacoubi","year":"2006"},{"volume-title":"Cellular Automata","year":"2005","author":"Sloot","key":"2023080123455424700_c16"},{"key":"2023080123455424700_c17","doi-asserted-by":"publisher","first-page":"066112","DOI":"10.1103\/PhysRevE.71.066112","volume":"71","year":"2005","journal-title":"Phys. Rev. E"},{"key":"2023080123455424700_c18","doi-asserted-by":"publisher","first-page":"036130","DOI":"10.1103\/PhysRevE.73.036130","volume":"73","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023080123455424700_c19","doi-asserted-by":"publisher","first-page":"011907","DOI":"10.1103\/PhysRevE.73.011907","volume":"73","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023080123455424700_c20","doi-asserted-by":"publisher","first-page":"016208","DOI":"10.1103\/PhysRevE.74.016208","volume":"74","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023080123455424700_c21","doi-asserted-by":"publisher","first-page":"031110","DOI":"10.1103\/PhysRevE.74.031110","volume":"74","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023080123455424700_c22","doi-asserted-by":"publisher","first-page":"036102","DOI":"10.1103\/PhysRevE.74.036102","volume":"74","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2023080123455424700_c23","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.physleta.2005.08.016","volume":"346","year":"2005","journal-title":"Phys. Lett. A"},{"key":"2023080123455424700_c24","doi-asserted-by":"publisher","first-page":"036707","DOI":"10.1103\/PhysRevE.68.036707","volume":"68","year":"2003","journal-title":"Phys. Rev. E"},{"key":"2023080123455424700_c25","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1103\/RevModPhys.55.601","volume":"55","year":"1983","journal-title":"Rev. Mod. Phys."},{"key":"2023080123455424700_c26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0167-2789(97)84209-1","volume":"10","year":"1984","journal-title":"Physica D"},{"key":"2023080123455424700_c27","doi-asserted-by":"publisher","first-page":"L393","DOI":"10.1088\/0305-4470\/22\/9\/007","volume":"22","year":"1989","journal-title":"J. Phys. A"},{"key":"2023080123455424700_c28","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/0167-2789(90)90177-Q","volume":"45","year":"1990","journal-title":"Physica D"},{"key":"2023080123455424700_c29","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/0167-2789(84)90251-3","volume":"10","year":"1984","journal-title":"Physica D"},{"key":"2023080123455424700_c30","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1142\/S0129183190000098","volume":"1","year":"1990","journal-title":"Int. J. Mod. Phys. C"},{"key":"2023080123455424700_c31","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/0378-4371(92)90106-Z","volume":"180","year":"1992","journal-title":"Physica A"},{"key":"2023080123455424700_c32","doi-asserted-by":"publisher","first-page":"R7881","DOI":"10.1103\/PhysRevA.44.R7881","volume":"44","year":"1991","journal-title":"Phys. Rev. A"},{"key":"2023080123455424700_c33","first-page":"355","volume":"166","year":"1992","journal-title":"Phys. Lett. A"},{"key":"2023080123455424700_c34","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1016\/S0370-1573(01)00025-4","volume":"356","year":"2002","journal-title":"Phys. Rep."},{"key":"2023080123455424700_c35","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.physa.2005.05.016","volume":"356","year":"2005","journal-title":"Physica A"},{"key":"2023080123455424700_c36"},{"key":"2023080123455424700_c37","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.physleta.2007.01.071","volume":"366","year":"2007","journal-title":"Phys. Lett. A"},{"key":"2023080123455424700_c38","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1103\/PhysRevLett.78.444","volume":"78","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"2023080123455424700_c39","doi-asserted-by":"publisher","first-page":"028105","DOI":"10.1103\/PhysRevLett.94.028105","volume":"94","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"2023080123455424700_c40"},{"key":"2023080123455424700_c41","first-page":"128","volume-title":"Complex Systems, Organization and Networks of Automata","author":"Peliti","year":"1987"},{"key":"2023080123455424700_c42","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1038\/35065725","volume":"410","year":"2001","journal-title":"Nature (London)"},{"key":"2023080123455424700_c43","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1140\/epjb\/e2004-00110-5","volume":"38","year":"2004","journal-title":"Eur. Phys. J. B"},{"volume-title":"A Different Universe: Reinventing Physics from the Bottom Down","year":"2005","key":"2023080123455424700_c44"},{"key":"2023080123455424700_c45","doi-asserted-by":"publisher","first-page":"017102","DOI":"10.1103\/PhysRevE.74.017102","volume":"74","year":"2006","journal-title":"Phys. Rev. E"},{"volume-title":"Defining and Detecting Emergence in Complex Networks","year":"2005","key":"2023080123455424700_c46"},{"key":"2023080123455424700_c47","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/0167-2789(94)90273-9","volume":"75","year":"1994","journal-title":"Physica D"},{"key":"2023080123455424700_c48","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0167-2789(94)90272-0","article-title":"Constructive complexity and artificial reality","volume":"75","author":"Kaneko","year":"1994","journal-title":"Physica D"},{"key":"2023080123455424700_c49","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.physd.2005.06.031","volume":"210","year":"2005","journal-title":"Physica D"}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/1.2732896\/13556952\/026113_1_online.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/1.2732896\/13556952\/026113_1_online.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T23:46:08Z","timestamp":1690933568000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/17\/2\/026113\/934600\/Spatial-updating-spatial-transients-and"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6,1]]},"references-count":52,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,6,1]]}},"URL":"https:\/\/doi.org\/10.1063\/1.2732896","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"type":"print","value":"1054-1500"},{"type":"electronic","value":"1089-7682"}],"subject":[],"published-other":{"date-parts":[[2007,6]]},"published":{"date-parts":[[2007,6,1]]},"article-number":"026113"}}