{"id":"https://openalex.org/W3013733793","doi":"https://doi.org/10.1109/access.2020.2983474","title":"CR Iteration in Generation of Antifractals With s-Convexity","display_name":"CR Iteration in Generation of Antifractals With s-Convexity","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3013733793","doi":"https://doi.org/10.1109/access.2020.2983474","mag":"3013733793"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.2983474","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2983474","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2020.2983474","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052630982","display_name":"Dong Li","orcid":"https://orcid.org/0009-0003-4039-434X"},"institutions":[{"id":"https://openalex.org/I4210152160","display_name":"Zhengzhou Railway Vocational & Technical College","ror":"https://ror.org/04zs83x19","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210152160"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong Li","raw_affiliation_strings":["Zhengzhou Railway Vocational and Technical College, Zhengzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhengzhou Railway Vocational and Technical College, Zhengzhou, China","institution_ids":["https://openalex.org/I4210152160"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049770575","display_name":"Abdul Aziz Shahid","orcid":"https://orcid.org/0000-0003-4012-8028"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Abdul Aziz Shahid","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-4012-8028","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I142204992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008596168","display_name":"Asifa Tassaddiq","orcid":"https://orcid.org/0000-0002-6165-8055"},"institutions":[{"id":"https://openalex.org/I195631090","display_name":"Majmaah University","ror":"https://ror.org/01mcrnj60","country_code":"SA","type":"education","lineage":["https://openalex.org/I195631090"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Asifa Tassaddiq","raw_affiliation_strings":["College of Computer and Information Sciences, Majmaah University, Al Majma\u2019ah, Saudi Arabia","College of Computer and Information Sciences, Majmaah University, Al Majma'ah, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-6165-8055","affiliations":[{"raw_affiliation_string":"College of Computer and Information Sciences, Majmaah University, Al Majma\u2019ah, Saudi Arabia","institution_ids":["https://openalex.org/I195631090"]},{"raw_affiliation_string":"College of Computer and Information Sciences, Majmaah University, Al Majma'ah, Saudi Arabia","institution_ids":["https://openalex.org/I195631090"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090173410","display_name":"Arshad Khan","orcid":"https://orcid.org/0000-0003-2858-4653"},"institutions":[{"id":"https://openalex.org/I246743127","display_name":"The University of Agriculture, Peshawar","ror":"https://ror.org/02sp3q482","country_code":"PK","type":"education","lineage":["https://openalex.org/I246743127"]},{"id":"https://openalex.org/I4210127363","display_name":"Institute of Management Sciences Peshawar","ror":"https://ror.org/02m8e1r74","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210127363"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Arshad Khan","raw_affiliation_strings":["Institute of Business and Management Sciences, The University of Agriculture, Peshawar, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Business and Management Sciences, The University of Agriculture, Peshawar, Pakistan","institution_ids":["https://openalex.org/I4210127363","https://openalex.org/I246743127"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100963659","display_name":"Xiaorui Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I23171815","display_name":"Zhengzhou University of Light Industry","ror":"https://ror.org/05fwr8z16","country_code":"CN","type":"education","lineage":["https://openalex.org/I23171815"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaorui Guo","raw_affiliation_strings":["Zhengzhou University of Light Industry, Zhengzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhengzhou University of Light Industry, Zhengzhou, China","institution_ids":["https://openalex.org/I23171815"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043740401","display_name":"Maqbool Ahmad","orcid":"https://orcid.org/0000-0001-8621-4541"},"institutions":[{"id":"https://openalex.org/I142204992","display_name":"University of Lahore","ror":"https://ror.org/051jrjw38","country_code":"PK","type":"education","lineage":["https://openalex.org/I142204992"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Maqbool Ahmad","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0001-8621-4541","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I142204992"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":3.1378,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.91917896,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"8","issue":null,"first_page":"61621","last_page":"61630"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9976999759674072,"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/T11822","display_name":"Analytic and geometric function theory","score":0.9743000268936157,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9577999711036682,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8461709022521973},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.5981849431991577},{"id":"https://openalex.org/keywords/julia-set","display_name":"Julia set","score":0.5585718154907227},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.5138571262359619},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49140608310699463},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4592262804508209},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.4500397741794586},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40751785039901733},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.382689893245697},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3769274652004242},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37014245986938477},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15180295705795288}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8461709022521973},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5981849431991577},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.5585718154907227},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.5138571262359619},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49140608310699463},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4592262804508209},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.4500397741794586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40751785039901733},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.382689893245697},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3769274652004242},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37014245986938477},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15180295705795288},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.2983474","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2983474","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8091885521814083b4802161cf3ed18e","is_oa":true,"landing_page_url":"https://doaj.org/article/8091885521814083b4802161cf3ed18e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 61621-61630 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.2983474","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.2983474","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G4867725346","display_name":null,"funder_award_id":"RGP-2019-28","funder_id":"https://openalex.org/F4320324553","funder_display_name":"Majmaah University"}],"funders":[{"id":"https://openalex.org/F4320324553","display_name":"Majmaah University","ror":"https://ror.org/01mcrnj60"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W256753007","https://openalex.org/W1646303234","https://openalex.org/W1968134062","https://openalex.org/W1996239470","https://openalex.org/W2011949838","https://openalex.org/W2056966260","https://openalex.org/W2069994471","https://openalex.org/W2079711316","https://openalex.org/W2088536270","https://openalex.org/W2138622485","https://openalex.org/W2139318592","https://openalex.org/W2293100882","https://openalex.org/W2322987032","https://openalex.org/W2344727310","https://openalex.org/W2597630483","https://openalex.org/W2610577227","https://openalex.org/W2613686847","https://openalex.org/W2910668859","https://openalex.org/W2947027196","https://openalex.org/W2961238587","https://openalex.org/W2964335031","https://openalex.org/W2967345134","https://openalex.org/W4210794487","https://openalex.org/W4254148734","https://openalex.org/W4300059230","https://openalex.org/W6636666929","https://openalex.org/W6704833045"],"related_works":["https://openalex.org/W4225469538","https://openalex.org/W2098998857","https://openalex.org/W4224903371","https://openalex.org/W3039100608","https://openalex.org/W4303424403","https://openalex.org/W2125388741","https://openalex.org/W1983704940","https://openalex.org/W3002199636","https://openalex.org/W2925106282","https://openalex.org/W126481034"],"abstract_inverted_index":{"Complex":[0],"graphics":[1],"of":[2,43,49,57,64,89,106],"nonlinear":[3],"dynamical":[4],"systems":[5],"perform":[6],"vital":[7],"role":[8],"in":[9,34],"many":[10],"fields,":[11],"e.g.,":[12],"image":[13],"compression":[14],"or":[15],"encryption,":[16],"art,":[17],"science,":[18],"and":[19],"so":[20],"on.":[21],"Antifractals":[22],"are":[23,77],"generated":[24],"by":[25],"applying":[26],"a":[27,40],"map":[28],"recursively":[29],"to":[30,53,102],"an":[31],"initial":[32],"point":[33],"complex":[35,90],"plane":[36],"that":[37],"have":[38],"become":[39],"significant":[41],"area":[42],"research":[44],"these":[45],"days.":[46],"The":[47],"purpose":[48],"this":[50],"paper":[51],"is":[52],"investigate":[54],"the":[55,104],"dynamics":[56],"antifractals":[58],"like":[59],"anti-Julia":[60],"sets,":[61],"tricornsand":[62],"multicorns":[63],"antiholomorphic":[65],"polynomials":[66],"via":[67],"CR":[68],"iteration":[69],"scheme":[70],"with":[71],"s-convexity.":[72],"Many":[73],"beautiful":[74],"aesthetic":[75],"patterns":[76],"visualized":[78],"for":[79,98],"antipolynomial":[80],"z":[81,83,92],"\u2192":[82],"<sup":[84,93],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[85,94],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[86,95],"+":[87,96],"c":[88],"polynomial":[91],"c,":[97],"m":[99],"\u2265":[100],"2":[101],"explore":[103],"geometry":[105],"antifractals.":[107]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
