{"id":"https://openalex.org/W4200325250","doi":"https://doi.org/10.3390/fractalfract5040272","title":"Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations","display_name":"Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations","publication_year":2021,"publication_date":"2021-12-14","ids":{"openalex":"https://openalex.org/W4200325250","doi":"https://doi.org/10.3390/fractalfract5040272"},"language":"en","primary_location":{"id":"doi:10.3390/fractalfract5040272","doi":"https://doi.org/10.3390/fractalfract5040272","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract5040272","pdf_url":"https://www.mdpi.com/2504-3110/5/4/272/pdf?version=1639581257","source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2504-3110/5/4/272/pdf?version=1639581257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082416493","display_name":"Swati Antal","orcid":"https://orcid.org/0000-0001-5517-0021","observed_orcids":["https://orcid.org/0000-0001-5517-0021"]},"institutions":[{"id":"https://openalex.org/I185052938","display_name":"Hemwati Nandan Bahuguna Garhwal University","ror":"https://ror.org/00mvp1q86","country_code":"IN","type":"education","lineage":["https://openalex.org/I185052938"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Swati Antal","raw_affiliation_strings":["BGR Campus, Hemavati Nandan Bahuguna Garhwal University, Pauri Garhwal 246001, India"],"raw_orcid":"https://orcid.org/0000-0001-5517-0021","affiliations":[{"raw_affiliation_string":"BGR Campus, Hemavati Nandan Bahuguna Garhwal University, Pauri Garhwal 246001, India","institution_ids":["https://openalex.org/I185052938"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077282941","display_name":"Anita Tomar","orcid":"https://orcid.org/0000-0001-8033-856X","observed_orcids":["https://orcid.org/0000-0001-8033-856X"]},"institutions":[{"id":"https://openalex.org/I4405256247","display_name":"Sri Dev Suman Uttarakhand University","ror":"https://ror.org/03yx73m48","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405256247"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Anita Tomar","raw_affiliation_strings":["Pt. L.M.S. Campus, Sri Dev Suman Uttrakhand University, Rishikesh 249201, India"],"raw_orcid":"https://orcid.org/0000-0001-8033-856X","affiliations":[{"raw_affiliation_string":"Pt. L.M.S. Campus, Sri Dev Suman Uttrakhand University, Rishikesh 249201, India","institution_ids":["https://openalex.org/I4405256247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085133098","display_name":"Darshana J. Prajapati","orcid":"https://orcid.org/0000-0001-8527-0007","observed_orcids":["https://orcid.org/0000-0001-8527-0007"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Darshana J. Prajapati","raw_affiliation_strings":["M.B. Patel Institute of Technology, New Vallabh Vidyanagar 388121, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"M.B. Patel Institute of Technology, New Vallabh Vidyanagar 388121, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087489129","display_name":"Mohammad Sajid","orcid":"https://orcid.org/0000-0002-9921-787X","observed_orcids":["https://orcid.org/0000-0002-9921-787X","https://orcid.org/0009-0005-6858-7324"]},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Mohammad Sajid","raw_affiliation_strings":["Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-9921-787X","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087489129"],"corresponding_institution_ids":["https://openalex.org/I156216236"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1728},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1728},"fwci":4.2653,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.9602355,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"5","issue":"4","first_page":"272","last_page":"272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9940999746322632,"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":0.9940999746322632,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T14002","display_name":"Art, Technology, and Culture","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/1213","display_name":"Visual Arts and Performing Arts"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/julia-sets","display_name":"Julia sets","score":0.984000027179718},{"id":"https://openalex.org/keywords/fixed-point-iteration","display_name":"fixed point iteration","score":0.7649999856948853},{"id":"https://openalex.org/keywords/complex-dynamics","display_name":"complex dynamics","score":0.6460000276565552},{"id":"https://openalex.org/keywords/fractal-art","display_name":"fractal art","score":0.6209999918937683},{"id":"https://openalex.org/keywords/hibiscus","display_name":"Hibiscus","score":0.7210000157356262},{"id":"https://openalex.org/keywords/catharanthus-roseus","display_name":"Catharanthus roseus","score":0.9359999895095825}],"concepts":[{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.8764277696609497},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.7513877749443054},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.6888977885246277},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.6289190053939819},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5592582821846008},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5592576265335083},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5549368858337402},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4601041078567505},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.45902663469314575},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3675254285335541},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28250327706336975},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2593287229537964},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1854267418384552},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/fractalfract5040272","doi":"https://doi.org/10.3390/fractalfract5040272","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract5040272","pdf_url":"https://www.mdpi.com/2504-3110/5/4/272/pdf?version=1639581257","source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e62f1a5692834f5796e903f444630e8d","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/e62f1a5692834f5796e903f444630e8d","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,"listed_in":[],"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":"Fractal and Fractional, Vol 5, Iss 4, p 272 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/fractalfract5040272","doi":"https://doi.org/10.3390/fractalfract5040272","is_oa":true,"landing_page_url":"https://doi.org/10.3390/fractalfract5040272","pdf_url":"https://www.mdpi.com/2504-3110/5/4/272/pdf?version=1639581257","source":{"id":"https://openalex.org/S4210227020","display_name":"Fractal and Fractional","issn_l":"2504-3110","issn":["2504-3110"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-20","russia-white-list-1"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fractal and Fractional","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200325250.pdf","grobid_xml":"https://content.openalex.org/works/W4200325250.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1579586326","https://openalex.org/W1950518118","https://openalex.org/W1995946054","https://openalex.org/W1996239470","https://openalex.org/W2023358569","https://openalex.org/W2051914037","https://openalex.org/W2056966260","https://openalex.org/W2056986815","https://openalex.org/W2069435104","https://openalex.org/W2079711316","https://openalex.org/W2088536270","https://openalex.org/W2261545930","https://openalex.org/W2492617191","https://openalex.org/W2529003330","https://openalex.org/W2767011351","https://openalex.org/W2902765692","https://openalex.org/W2910668859","https://openalex.org/W2922108273","https://openalex.org/W2947234601","https://openalex.org/W2983930617","https://openalex.org/W3017811005","https://openalex.org/W3104062444","https://openalex.org/W3135416777","https://openalex.org/W4213078570","https://openalex.org/W4252709697","https://openalex.org/W6722858508","https://openalex.org/W6745533756"],"related_works":["https://openalex.org/W4404423246","https://openalex.org/W7204760169","https://openalex.org/W4404993805","https://openalex.org/W3081318753","https://openalex.org/W4403903213","https://openalex.org/W4226087465","https://openalex.org/W7133310930","https://openalex.org/W4320492621","https://openalex.org/W4280534765","https://openalex.org/W7112520930"],"abstract_inverted_index":{"We":[0],"explore":[1],"some":[2],"new":[3],"variants":[4],"of":[5,39,44,49,52,67],"the":[6,11,37,42,56,71],"Julia":[7],"set":[8],"by":[9],"developing":[10],"escape":[12],"criteria":[13],"for":[14],"a":[15,24],"function":[16],"sin(zn)+az+c,":[17],"where":[18],"a,c\u2208C,":[19],"n\u22652,":[20],"and":[21,47,61,97,100],"z":[22],"is":[23],"complex":[25],"variable,":[26],"utilizing":[27],"four":[28],"distinct":[29],"fixed":[30],"point":[31],"iterative":[32],"methods.":[33],"Furthermore,":[34],"we":[35],"examine":[36],"impact":[38],"parameters":[40],"on":[41,59],"deviation":[43],"dynamics,":[45],"color,":[46],"appearance":[48],"fractals.":[50],"Some":[51,80],"these":[53],"fractals":[54,81],"represent":[55],"stunning":[57],"art":[58],"glass,":[60],"Rangoli":[62],"(made":[63],"in":[64,77,88],"different":[65],"parts":[66],"India,":[68],"especially":[69],"during":[70],"festive":[72],"season)":[73],"which":[74],"are":[75,82],"useful":[76],"interior":[78],"decoration.":[79],"similar":[83],"to":[84],"beautiful":[85],"objects":[86],"found":[87],"our":[89],"surroundings":[90],"like":[91],"flowers":[92],"(to":[93],"be":[94],"specific":[95],"Hibiscus":[96],"Catharanthus":[98],"Roseus),":[99],"ants.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6}],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2021-12-31T00:00:00"}
