{"id":"https://openalex.org/W2155858955","doi":"https://doi.org/10.1142/s0218127411029240","title":"ON THE STRUCTURE OF REAL-VALUED ONE-DIMENSIONAL CELLULAR AUTOMATA","display_name":"ON THE STRUCTURE OF REAL-VALUED ONE-DIMENSIONAL CELLULAR AUTOMATA","publication_year":2011,"publication_date":"2011-05-01","ids":{"openalex":"https://openalex.org/W2155858955","doi":"https://doi.org/10.1142/s0218127411029240","mag":"2155858955"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411029240","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411029240","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100340420","display_name":"Xu Xu","orcid":"https://orcid.org/0000-0002-9721-9054"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"XU XU","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108195447","display_name":"Stephen P. Banks","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"STEPHEN P. BANKS","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069916821","display_name":"Mahdi Mahfouf","orcid":"https://orcid.org/0000-0002-7349-5396"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"MAHDI MAHFOUF","raw_affiliation_strings":["Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK"],"affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100340420"],"corresponding_institution_ids":["https://openalex.org/I91136226"],"apc_list":null,"apc_paid":null,"fwci":0.3138,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62575183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"05","first_page":"1265","last_page":"1279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cellular-automaton","display_name":"Cellular automaton","score":0.9231162071228027},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7286902070045471},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.6721596121788025},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6243664026260376},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.6226105690002441},{"id":"https://openalex.org/keywords/reversible-cellular-automaton","display_name":"Reversible cellular automaton","score":0.6063727736473083},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5959973335266113},{"id":"https://openalex.org/keywords/stochastic-cellular-automaton","display_name":"Stochastic cellular automaton","score":0.5946951508522034},{"id":"https://openalex.org/keywords/block-cellular-automaton","display_name":"Block cellular automaton","score":0.5677177906036377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5129201412200928},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.5048509240150452},{"id":"https://openalex.org/keywords/elementary-cellular-automaton","display_name":"Elementary cellular automaton","score":0.4695960283279419},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4644147753715515},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4604969024658203},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4517514109611511},{"id":"https://openalex.org/keywords/asynchronous-cellular-automaton","display_name":"Asynchronous cellular automaton","score":0.42975515127182007},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41103675961494446},{"id":"https://openalex.org/keywords/mobile-automaton","display_name":"Mobile automaton","score":0.35646504163742065},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32099753618240356},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.1934744119644165},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16249877214431763},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.0746999979019165},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06502330303192139}],"concepts":[{"id":"https://openalex.org/C35527583","wikidata":"https://www.wikidata.org/wiki/Q189156","display_name":"Cellular automaton","level":2,"score":0.9231162071228027},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7286902070045471},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.6721596121788025},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6243664026260376},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.6226105690002441},{"id":"https://openalex.org/C181266644","wikidata":"https://www.wikidata.org/wiki/Q7318293","display_name":"Reversible cellular automaton","level":5,"score":0.6063727736473083},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5959973335266113},{"id":"https://openalex.org/C192499940","wikidata":"https://www.wikidata.org/wiki/Q17022326","display_name":"Stochastic cellular automaton","level":3,"score":0.5946951508522034},{"id":"https://openalex.org/C63497236","wikidata":"https://www.wikidata.org/wiki/Q4927188","display_name":"Block cellular automaton","level":5,"score":0.5677177906036377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5129201412200928},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.5048509240150452},{"id":"https://openalex.org/C193261270","wikidata":"https://www.wikidata.org/wiki/Q1875447","display_name":"Elementary cellular automaton","level":5,"score":0.4695960283279419},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4644147753715515},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4604969024658203},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4517514109611511},{"id":"https://openalex.org/C13743347","wikidata":"https://www.wikidata.org/wiki/Q4812203","display_name":"Asynchronous cellular automaton","level":5,"score":0.42975515127182007},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41103675961494446},{"id":"https://openalex.org/C50348692","wikidata":"https://www.wikidata.org/wiki/Q6887056","display_name":"Mobile automaton","level":4,"score":0.35646504163742065},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32099753618240356},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.1934744119644165},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16249877214431763},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0746999979019165},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06502330303192139},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127411029240","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411029240","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:shura.shu.ac.uk:17030","is_oa":false,"landing_page_url":"http://shura.shu.ac.uk/17030/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401600","display_name":"SHURA (Sheffield Hallam University Research Archive) (Sheffield Hallam University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71422933","host_organization_name":"Sheffield Hallam University","host_organization_lineage":["https://openalex.org/I71422933"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7560132423","display_name":null,"funder_award_id":"EP/F023464/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W379230650","https://openalex.org/W626893493","https://openalex.org/W2001109406","https://openalex.org/W2036919025","https://openalex.org/W2124261671","https://openalex.org/W2146531915","https://openalex.org/W4244242344"],"related_works":["https://openalex.org/W1985126997","https://openalex.org/W2082165113","https://openalex.org/W4230368856","https://openalex.org/W4226197978","https://openalex.org/W2057143978","https://openalex.org/W1483948757","https://openalex.org/W2079399661","https://openalex.org/W1975368934","https://openalex.org/W3124593645","https://openalex.org/W3005591624"],"abstract_inverted_index":{"It":[0],"is":[1],"well-known":[2],"that":[3],"binary-valued":[4],"cellular":[5,37,64],"automata,":[6],"which":[7,43,66],"are":[8],"defined":[9],"by":[10],"simple":[11],"local":[12],"rules,":[13],"have":[14,67],"the":[15],"amazing":[16],"feature":[17],"of":[18,36,49],"generating":[19],"very":[20],"complex":[21],"patterns":[22],"and":[23,56,70],"having":[24],"complicated":[25],"dynamical":[26],"behaviors.":[27],"In":[28],"this":[29],"paper,":[30],"we":[31],"present":[32],"a":[33],"new":[34],"type":[35],"automaton":[38],"based":[39],"on":[40],"real-valued":[41,63],"states":[42],"produce":[44],"an":[45],"even":[46],"greater":[47],"amount":[48],"interesting":[50],"structures":[51],"such":[52],"as":[53],"fractal,":[54],"chaotic":[55],"hypercyclic.":[57],"We":[58],"also":[59],"give":[60],"proofs":[61],"to":[62],"systems":[65],"fixed":[68],"points":[69],"periodic":[71],"solutions.":[72]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}