{"id":"https://openalex.org/W2117740782","doi":"https://doi.org/10.1142/s0218127405014775","title":"A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART V: FRACTALS EVERYWHERE","display_name":"A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART V: FRACTALS EVERYWHERE","publication_year":2005,"publication_date":"2005-12-01","ids":{"openalex":"https://openalex.org/W2117740782","doi":"https://doi.org/10.1142/s0218127405014775","mag":"2117740782"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127405014775","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014775","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/A5090657067","display_name":"Leon O. Chua","orcid":"https://orcid.org/0000-0002-1652-5464"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"LEON O. CHUA","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079651154","display_name":"Valeriy I. Sbitnev","orcid":"https://orcid.org/0000-0001-6006-0214"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"VALERY I. SBITNEV","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108108861","display_name":"Sook Yoon","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"SOOK YOON","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA 94720, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090657067"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":1.7568,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.84644721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"12","first_page":"3701","last_page":"3849"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9970999956130981,"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":0.9970999956130981,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9139000177383423,"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/T10244","display_name":"Chaos control and synchronization","score":0.9057999849319458,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7289851903915405},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.549075186252594},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49310943484306335},{"id":"https://openalex.org/keywords/symmetrization","display_name":"Symmetrization","score":0.459126353263855},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.44433000683784485},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.4412984251976013},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4026726186275482},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37146925926208496},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.26587265729904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7289851903915405},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.549075186252594},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49310943484306335},{"id":"https://openalex.org/C64999384","wikidata":"https://www.wikidata.org/wiki/Q3507967","display_name":"Symmetrization","level":2,"score":0.459126353263855},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.44433000683784485},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.4412984251976013},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4026726186275482},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37146925926208496},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26587265729904175},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127405014775","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127405014775","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1535419201","https://openalex.org/W2037830802","https://openalex.org/W2087874897","https://openalex.org/W2146531915","https://openalex.org/W2147856686","https://openalex.org/W2339378878","https://openalex.org/W4298054937"],"related_works":["https://openalex.org/W2074849352","https://openalex.org/W2029780455","https://openalex.org/W2964072642","https://openalex.org/W4300193992","https://openalex.org/W148042662","https://openalex.org/W2920386017","https://openalex.org/W2336702490","https://openalex.org/W2795454383","https://openalex.org/W2964013457","https://openalex.org/W2027287659"],"abstract_inverted_index":{"This":[0],"fifth":[1],"installment":[2],"is":[3,96,132,151,200],"devoted":[4],"to":[5,77,135,154,187],"an":[6,38,90],"in-depth":[7],"study":[8],"of":[9,43,68,81,93,117,215,223,227,234,276,296],"CA":[10],"Characteristic":[11],"Functions,":[12],"a":[13,54,78,109],"unified":[14],"global":[15,33],"representation":[16],"for":[17,26,85,98],"all":[18,50,86],"256":[19,87],"one-dimensional":[20],"Cellular":[21],"Automata":[22],"local":[23,30,88,127,146,229,258],"rules.":[24],"Except":[25],"eight":[27],"rather":[28],"special":[29],"rules":[31,259],"whose":[32],"dynamics":[34],"are":[35,185,217,260,272,292],"described":[36],"by":[37],"affine":[39],"(mod":[40],"1)":[41,72],"function":[42,171,226],"only":[44,191,248,267],"one":[45],"binary":[46,105,236,263],"cell":[47,207],"state":[48],"variable,":[49],"characteristic":[51,83,101,170,183,225,278],"functions":[52,84,102,184],"exhibit":[53],"fractal":[55],"geometry":[56],"where":[57,197],"self-similar":[58],"two-dimensional":[59],"substructures":[60],"manifest":[61],"themselves,":[62],"ad":[63],"infinitum,":[64],"as":[65,107],"the":[66,114,125,136,144,155,201,206,220,224,249,252,277],"number":[67],"cells":[69],"(I":[70],"+":[71],"\u2192":[73],"\u221e.":[74],"In":[75,175],"addition":[76],"complete":[79],"gallery":[80],"time-1":[82],"rules,":[89],"accompanying":[91],"table":[92],"explicit":[94],"formulas":[95],"given":[97],"generating":[99],"these":[100,118,235],"directly":[103],"from":[104,168,219],"bit-strings,":[106],"in":[108,181,211],"digital-to-analog":[110],"converter.":[111],"To":[112,280],"illustrate":[113],"potential":[115],"applications":[116],"fundamental":[119],"formulas,":[120],"we":[121,142],"prove":[122,143],"rigorously":[123],"that":[124,282],"\"right-copycat\"":[126],"rule":[128,147,230],"[Formula:":[129,148],"see":[130,149],"text]":[131,150],"equivalent":[133,152],"globally":[134,153],"classic":[137],"\"left-shift\"":[138],"Bernoulli":[139,158],"map.":[140,159],"Similarly,":[141],"\"left-copycat\"":[145],"\"right-shift\"":[156],"inverse":[157],"Various":[160],"geometrical":[161],"and":[162,172,190,231,242,251,288,303],"analytical":[163],"properties":[164],"have":[165,268,285,300],"been":[166,301],"identified":[167,302],"each":[169,228],"explained":[173],"rigorously.":[174],"particular,":[176],"two-level":[177],"stratified":[178],"subpatterns":[179],"found":[180],"most":[182],"shown":[186],"emerge":[188],"if,":[189,192],"b":[193,198],"1":[194,199],"\u2260":[195],"0,":[196],"\"synaptic":[202],"coefficient\"":[203],"associated":[204],"with":[205,262],"differential":[208],"equation":[209],"developed":[210],"Part":[212],"I.":[213],"Gardens":[214],"Eden":[216],"derived":[218],"decimal":[221],"range":[222],"tabulated.":[232,304],"Each":[233],"strings":[237],"has":[238,243],"no":[239,245,269,286,289],"predecessors":[240],"(pre-image)":[241],"therefore":[244],"past,":[246,287],"but":[247,271],"present":[250],"future.":[253],"Even":[254],"more":[255],"fascinating,":[256],"many":[257],"endowed":[261],"configurations":[264],"which":[265],"not":[266],"predecessors,":[270],"also":[273],"fixed":[274],"points":[275,284],"functions.":[279],"dramatize":[281],"such":[283],"future,":[290],"they":[291],"henceforth":[293],"christened":[294],"\"Isles":[295],"Eden\".":[297],"They":[298],"too":[299]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"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"}
