{"id":"https://openalex.org/W2952258329","doi":"https://doi.org/10.1002/(sici)1099-0526(199901/02)4:3<41::aid-cplx8>3.0.co;2-3","title":"Order and chaos in Hofstadter'sQ(n) sequence","display_name":"Order and chaos in Hofstadter'sQ(n) sequence","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2952258329","doi":"https://doi.org/10.1002/(sici)1099-0526(199901/02)4:3<41::aid-cplx8>3.0.co;2-3","mag":"2952258329"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-0526(199901/02)4:3<41::aid-cplx8>3.0.co;2-3","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-0526(199901/02)4:3<41::aid-cplx8>3.0.co;2-3","pdf_url":null,"source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"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/A5045687627","display_name":"K. Pinn","orcid":null},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Klaus Pinn","raw_affiliation_strings":["Institut fu\u0308r Theoretische Physik I, Universita\u0308t Mu\u0308nster, Wilhelm-Klemm-Str. 9, D-48149 Mu\u0308nster, Germany","Institut f\u00fcr Theoretische Physik I, Universit\u00e4t M\u00fcnster, Wilhelm-Klemm-Str. 9, D-48149 M\u00fcnster, Germany"],"affiliations":[{"raw_affiliation_string":"Institut fu\u0308r Theoretische Physik I, Universita\u0308t Mu\u0308nster, Wilhelm-Klemm-Str. 9, D-48149 Mu\u0308nster, Germany","institution_ids":["https://openalex.org/I22465464"]},{"raw_affiliation_string":"Institut f\u00fcr Theoretische Physik I, Universit\u00e4t M\u00fcnster, Wilhelm-Klemm-Str. 9, D-48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045687627"],"corresponding_institution_ids":["https://openalex.org/I22465464"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":null,"fwci":0.115,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.45918115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"4","issue":"3","first_page":"41","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9955999851226807,"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"}},"topics":[{"id":"https://openalex.org/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9955999851226807,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11567","display_name":"semigroups and automata theory","score":0.9872000217437744,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.8317408561706543},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6590409278869629},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6545633673667908},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6356770992279053},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5960134267807007},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.5797650218009949},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4948362708091736},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.49129217863082886},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.46318531036376953},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37418508529663086},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18671914935112}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.8317408561706543},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6590409278869629},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6545633673667908},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6356770992279053},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5960134267807007},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5797650218009949},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4948362708091736},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.49129217863082886},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.46318531036376953},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37418508529663086},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18671914935112},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1099-0526(199901/02)4:3<41::aid-cplx8>3.0.co;2-3","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-0526(199901/02)4:3<41::aid-cplx8>3.0.co;2-3","pdf_url":null,"source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1991912396","https://openalex.org/W1994768225","https://openalex.org/W2038915991","https://openalex.org/W2329840944","https://openalex.org/W4205534191","https://openalex.org/W4302383489"],"related_works":["https://openalex.org/W2386746265","https://openalex.org/W3011992704","https://openalex.org/W199458103","https://openalex.org/W3100066189","https://openalex.org/W2375799027","https://openalex.org/W2369612463","https://openalex.org/W4220747489","https://openalex.org/W4389457771","https://openalex.org/W2042172774","https://openalex.org/W2953245366"],"abstract_inverted_index":{"A":[0],"number":[1],"of":[2,55,94,114,141],"observations":[3],"are":[4],"made":[5],"on":[6,88],"Hofstadter's":[7],"integer":[8],"sequence":[9,39,54,84],"defined":[10,125],"by":[11,133,151],"Q(n)":[12,48,97],"=":[13,31,33,96,108,116,118,143,153],"Q(n":[14,16,20,22],"\u2212":[15,17,21,23,70,78,98,145,147],"1))":[18],"+":[19],"2)),":[24],"for":[25,160],"n":[26,120],">":[27],"2,":[28],"and":[29,72,126],"Q(1)":[30],"Q(2)":[32],"1.":[34],"On":[35],"short":[36],"scales,":[37],"the":[38,47,83,134],"looks":[40],"chaotic.":[41],"It":[42],"turns":[43],"out,":[44],"however,":[45],"that":[46,63],"can":[49],"be":[50],"grouped":[51],"into":[52],"a":[53,73,89],"generations.":[56],"The":[57,92,110,138],"k-th":[58],"generation":[59,68,76],"has":[60],"2k":[61],"members":[62],"have":[64],"\u201cparents\u201d":[65],"mostly":[66],"in":[67],"k":[69,77],"1":[71],"few":[74],"from":[75],"2.":[79],"In":[80],"this":[81],"sense,":[82],"becomes":[85],"Fibonacci":[86],"type":[87],"logarithmic":[90],"scale.":[91],"variance":[93],"S(n)":[95],"n/2,":[99],"averaged":[100],"over":[101],"generations,":[102],"is":[103,123,149],"\u22452\u03b1k,":[104],"with":[105,129,156],"exponent":[106],"\u03b1":[107],"0.88(1).":[109],"probability":[111,139],"distribution":[112,140],"p*(x)":[113],"x":[115],"R(n)":[117,144],"S(n)/n\u03b1,":[119],"\u226b":[121],"1,":[122],"well":[124,131],"strongly":[127],"non-Gaussian,":[128],"tails":[130],"described":[132],"error":[135],"function":[136],"erfc.":[137],"xm":[142],"R(n":[146],"m)":[148],"given":[150],"pm(xm)":[152],"\u03bbm":[154,157],"p*(xm/\u03bbm),":[155],"\u2192":[158],"\u221a2":[159],"large":[161],"m.":[162],"\u00a9":[163],"1999":[164],"John":[165],"Wiley":[166],"&":[167],"Sons,":[168],"Inc.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}