Simple form of the stationary distribution for 3D cellular automata in a special case

3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all o...

Full description

Saved in:
Bibliographic Details
Published in:Physica A 2010-07, Vol.389 (13), p.2495-2499
Main Author: Agapie, Alexandru
Format: Article
Language:English
Subjects:
Borders
Cellular automata
Chains
Exact solutions
Finite homogeneous Markov chain
Interacting particle system
Ising model
Markov chains
Mathematical analysis
Statistical mechanics
Three dimensional
Voter model
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c335t-18f4458b7e7af06a85a04442e4512c3a1ba6158845f06dbf5dd34cfc9d16d4ad3
cites cdi_FETCH-LOGICAL-c335t-18f4458b7e7af06a85a04442e4512c3a1ba6158845f06dbf5dd34cfc9d16d4ad3
container_end_page 2499
container_issue 13
container_start_page 2495
container_title Physica A
container_volume 389
creator Agapie, Alexandru
description 3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all ones. Otherwise–and this is the case we tackle–the chain is ergodic, thus allowing for the search of stationary distributions. This proves cumbersome in the general case, still, under detailed balance equation, the stationary distribution can be derived in closed form. The probability of a particular state is found to be exponential in the number of zero–one borders within the configuration.
doi_str_mv 10.1016/j.physa.2010.03.011
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_901672294</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0378437110002153</els_id><sourcerecordid>901672294</sourcerecordid><originalsourceid>FETCH-LOGICAL-c335t-18f4458b7e7af06a85a04442e4512c3a1ba6158845f06dbf5dd34cfc9d16d4ad3</originalsourceid><addsrcrecordid>eNp9kLtOxDAQRS0EEsvCF9C4o0qwY-dVUKDlKa1EAVtbEz-0XiVxsB0k_h6HpaYazcy9o7kHoWtKckpodXvIp_13gLwgaUJYTig9QSva1CwrKG1P0Yqwusk4q-k5ugjhQAihNStWaPduh6nX2Dg_YGdw3GscIkTrRvDfWNkQve3mpV80mD1gqft-7sFjmKMbIAK2IwYcJi0t9FhC0JfozEAf9NVfXaPd0-PH5iXbvj2_bu63mWSsjBltDOdl09W6BkMqaEognPNC85IWkgHtoKJl0_AybVVnSqUYl0a2ilaKg2JrdHO8O3n3OesQxWDD8h-M2s1BtAlOXRQtT0p2VErvQvDaiMnbIUUUlIiFoTiIX4ZiYSgIE4lhct0dXTqF-LLaiyCtHqVW1msZhXL2X_8PA0p72g</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>901672294</pqid></control><display><type>article</type><title>Simple form of the stationary distribution for 3D cellular automata in a special case</title><source>ScienceDirect Freedom Collection</source><creator>Agapie, Alexandru</creator><creatorcontrib>Agapie, Alexandru</creatorcontrib><description>3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all ones. Otherwise–and this is the case we tackle–the chain is ergodic, thus allowing for the search of stationary distributions. This proves cumbersome in the general case, still, under detailed balance equation, the stationary distribution can be derived in closed form. The probability of a particular state is found to be exponential in the number of zero–one borders within the configuration.</description><identifier>ISSN: 0378-4371</identifier><identifier>EISSN: 1873-2119</identifier><identifier>DOI: 10.1016/j.physa.2010.03.011</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Borders ; Cellular automata ; Chains ; Exact solutions ; Finite homogeneous Markov chain ; Interacting particle system ; Ising model ; Markov chains ; Mathematical analysis ; Statistical mechanics ; Three dimensional ; Voter model</subject><ispartof>Physica A, 2010-07, Vol.389 (13), p.2495-2499</ispartof><rights>2010 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c335t-18f4458b7e7af06a85a04442e4512c3a1ba6158845f06dbf5dd34cfc9d16d4ad3</citedby><cites>FETCH-LOGICAL-c335t-18f4458b7e7af06a85a04442e4512c3a1ba6158845f06dbf5dd34cfc9d16d4ad3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Agapie, Alexandru</creatorcontrib><title>Simple form of the stationary distribution for 3D cellular automata in a special case</title><title>Physica A</title><description>3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all ones. Otherwise–and this is the case we tackle–the chain is ergodic, thus allowing for the search of stationary distributions. This proves cumbersome in the general case, still, under detailed balance equation, the stationary distribution can be derived in closed form. The probability of a particular state is found to be exponential in the number of zero–one borders within the configuration.</description><subject>Borders</subject><subject>Cellular automata</subject><subject>Chains</subject><subject>Exact solutions</subject><subject>Finite homogeneous Markov chain</subject><subject>Interacting particle system</subject><subject>Ising model</subject><subject>Markov chains</subject><subject>Mathematical analysis</subject><subject>Statistical mechanics</subject><subject>Three dimensional</subject><subject>Voter model</subject><issn>0378-4371</issn><issn>1873-2119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kLtOxDAQRS0EEsvCF9C4o0qwY-dVUKDlKa1EAVtbEz-0XiVxsB0k_h6HpaYazcy9o7kHoWtKckpodXvIp_13gLwgaUJYTig9QSva1CwrKG1P0Yqwusk4q-k5ugjhQAihNStWaPduh6nX2Dg_YGdw3GscIkTrRvDfWNkQve3mpV80mD1gqft-7sFjmKMbIAK2IwYcJi0t9FhC0JfozEAf9NVfXaPd0-PH5iXbvj2_bu63mWSsjBltDOdl09W6BkMqaEognPNC85IWkgHtoKJl0_AybVVnSqUYl0a2ilaKg2JrdHO8O3n3OesQxWDD8h-M2s1BtAlOXRQtT0p2VErvQvDaiMnbIUUUlIiFoTiIX4ZiYSgIE4lhct0dXTqF-LLaiyCtHqVW1msZhXL2X_8PA0p72g</recordid><startdate>20100701</startdate><enddate>20100701</enddate><creator>Agapie, Alexandru</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20100701</creationdate><title>Simple form of the stationary distribution for 3D cellular automata in a special case</title><author>Agapie, Alexandru</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c335t-18f4458b7e7af06a85a04442e4512c3a1ba6158845f06dbf5dd34cfc9d16d4ad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Borders</topic><topic>Cellular automata</topic><topic>Chains</topic><topic>Exact solutions</topic><topic>Finite homogeneous Markov chain</topic><topic>Interacting particle system</topic><topic>Ising model</topic><topic>Markov chains</topic><topic>Mathematical analysis</topic><topic>Statistical mechanics</topic><topic>Three dimensional</topic><topic>Voter model</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Agapie, Alexandru</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physica A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Agapie, Alexandru</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Simple form of the stationary distribution for 3D cellular automata in a special case</atitle><jtitle>Physica A</jtitle><date>2010-07-01</date><risdate>2010</risdate><volume>389</volume><issue>13</issue><spage>2495</spage><epage>2499</epage><pages>2495-2499</pages><issn>0378-4371</issn><eissn>1873-2119</eissn><abstract>3D cellular automata can be analyzed by means of finite homogeneous Markov chains. If the automaton is allowed to change only one cell per iteration, and the transition probability depends linearly on the number of ones in the neighborhood, the Markov chain has two attractors at all zeroes and all ones. Otherwise–and this is the case we tackle–the chain is ergodic, thus allowing for the search of stationary distributions. This proves cumbersome in the general case, still, under detailed balance equation, the stationary distribution can be derived in closed form. The probability of a particular state is found to be exponential in the number of zero–one borders within the configuration.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physa.2010.03.011</doi><tpages>5</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0378-4371
ispartof Physica A, 2010-07, Vol.389 (13), p.2495-2499
issn 0378-4371
1873-2119
language eng
recordid cdi_proquest_miscellaneous_901672294
source ScienceDirect Freedom Collection
subjects Borders
Cellular automata
Chains
Exact solutions
Finite homogeneous Markov chain
Interacting particle system
Ising model
Markov chains
Mathematical analysis
Statistical mechanics
Three dimensional
Voter model
title Simple form of the stationary distribution for 3D cellular automata in a special case
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T18%3A36%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Simple%20form%20of%20the%20stationary%20distribution%20for%203D%20cellular%20automata%20in%20a%20special%20case&rft.jtitle=Physica%20A&rft.au=Agapie,%20Alexandru&rft.date=2010-07-01&rft.volume=389&rft.issue=13&rft.spage=2495&rft.epage=2499&rft.pages=2495-2499&rft.issn=0378-4371&rft.eissn=1873-2119&rft_id=info:doi/10.1016/j.physa.2010.03.011&rft_dat=%3Cproquest_cross%3E901672294%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c335t-18f4458b7e7af06a85a04442e4512c3a1ba6158845f06dbf5dd34cfc9d16d4ad3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=901672294&rft_id=info:pmid/&rfr_iscdi=true