{"id":"https://openalex.org/W2939922837","doi":"https://doi.org/10.3390/sym11040577","title":"The Symmetry in the Noise-Perturbed Mandelbrot Set","display_name":"The Symmetry in the Noise-Perturbed Mandelbrot Set","publication_year":2019,"publication_date":"2019-04-21","ids":{"openalex":"https://openalex.org/W2939922837","doi":"https://doi.org/10.3390/sym11040577","mag":"2939922837"},"language":"en","primary_location":{"id":"doi:10.3390/sym11040577","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040577","pdf_url":"https://www.mdpi.com/2073-8994/11/4/577/pdf?version=1556158402","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/4/577/pdf?version=1556158402","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030724640","display_name":"Tian-Wen Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianwen Sun","raw_affiliation_strings":["Research Center of Dynamics System and Control Science, Shandong Normal University, Jinan 250014, China"],"affiliations":[{"raw_affiliation_string":"Research Center of Dynamics System and Control Science, Shandong Normal University, Jinan 250014, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039762053","display_name":"Da Wang","orcid":"https://orcid.org/0000-0003-4404-901X"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Da Wang","raw_affiliation_strings":["Research Center of Dynamics System and Control Science, Shandong Normal University, Jinan 250014, China"],"affiliations":[{"raw_affiliation_string":"Research Center of Dynamics System and Control Science, Shandong Normal University, Jinan 250014, China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039762053"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2475,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.53383867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"11","issue":"4","first_page":"577","last_page":"577"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10427","display_name":"Visual perception and processing mechanisms","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10427","display_name":"Visual perception and processing mechanisms","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10691","display_name":"Retinal Development and Disorders","score":0.9621999859809875,"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/T10971","display_name":"Olfactory and Sensory Function Studies","score":0.9351000189781189,"subfield":{"id":"https://openalex.org/subfields/2809","display_name":"Sensory Systems"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mandelbrot-set","display_name":"Mandelbrot set","score":0.979033350944519},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6909237504005432},{"id":"https://openalex.org/keywords/asymmetry","display_name":"Asymmetry","score":0.6780245304107666},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6351072788238525},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49819016456604004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4793330132961273},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4644109904766083},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4462684690952301},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.4433622360229492},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.43896862864494324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3303709924221039},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2987218499183655},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2575531005859375},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2324562966823578},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.2068823277950287},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1699979305267334},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.11735594272613525},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07687690854072571},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.0739109218120575}],"concepts":[{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.979033350944519},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6909237504005432},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.6780245304107666},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6351072788238525},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49819016456604004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4793330132961273},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4644109904766083},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4462684690952301},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.4433622360229492},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.43896862864494324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3303709924221039},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2987218499183655},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2575531005859375},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2324562966823578},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.2068823277950287},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1699979305267334},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.11735594272613525},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07687690854072571},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0739109218120575},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.0},{"id":"https://openalex.org/C131021393","wikidata":"https://www.wikidata.org/wiki/Q7512759","display_name":"Signal transfer function","level":4,"score":0.0},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"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/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym11040577","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040577","pdf_url":"https://www.mdpi.com/2073-8994/11/4/577/pdf?version=1556158402","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f8ab9215b0d148988f4358b898a129e5","is_oa":true,"landing_page_url":"https://doaj.org/article/f8ab9215b0d148988f4358b898a129e5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 4, p 577 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/11/4/577/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym11040577","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym11040577","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040577","pdf_url":"https://www.mdpi.com/2073-8994/11/4/577/pdf?version=1556158402","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4699999988079071}],"awards":[{"id":"https://openalex.org/G1923071379","display_name":null,"funder_award_id":"61703251","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4534319367","display_name":null,"funder_award_id":"2017M612337","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2939922837.pdf","grobid_xml":"https://content.openalex.org/works/W2939922837.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1462036404","https://openalex.org/W1533967041","https://openalex.org/W1968808817","https://openalex.org/W2009389445","https://openalex.org/W2010397987","https://openalex.org/W2020003671","https://openalex.org/W2031879246","https://openalex.org/W2032727615","https://openalex.org/W2034278904","https://openalex.org/W2051446272","https://openalex.org/W2054520167","https://openalex.org/W2058841755","https://openalex.org/W2073556564","https://openalex.org/W2075190036","https://openalex.org/W2083642281","https://openalex.org/W2088720515","https://openalex.org/W2101542661","https://openalex.org/W2156821812","https://openalex.org/W2266138283","https://openalex.org/W2292728498","https://openalex.org/W2337437238","https://openalex.org/W2346430432","https://openalex.org/W2352978371","https://openalex.org/W2361616357","https://openalex.org/W2529003330","https://openalex.org/W2593020849","https://openalex.org/W2595902612","https://openalex.org/W2808720755","https://openalex.org/W2889306452","https://openalex.org/W2963119846","https://openalex.org/W6705513857","https://openalex.org/W6728004239"],"related_works":["https://openalex.org/W1975469967","https://openalex.org/W1973236628","https://openalex.org/W4287812451","https://openalex.org/W3022718941","https://openalex.org/W2150219835","https://openalex.org/W2346565650","https://openalex.org/W2067853971","https://openalex.org/W2084965710","https://openalex.org/W1996414039","https://openalex.org/W2506602630"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,6,10,17,24,27,30,42,46,50,54,58,65,85],"destruction":[4],"of":[5,9,29,41,53,87],"symmetrical":[7],"structure":[8],"noise-perturbed":[11,31,55],"Mandelbrot":[12,32,56],"set":[13,33],"(M-set).":[14],"By":[15],"applying":[16],"\u201csymmetry":[18],"criterion\u201d":[19,78],"method,":[20],"we":[21,72],"quantitatively":[22],"compare":[23],"damages":[25],"to":[26],"symmetry":[28,77],"resulting":[34],"from":[35],"additive":[36],"and":[37,49,68],"multiplicative":[38],"noises.":[39],"Because":[40],"uneven":[43],"distribution":[44],"between":[45,64],"core":[47],"positions":[48,52],"edge":[51],"set,":[57],"comparison":[59],"results":[60],"reveal":[61],"a":[62,74],"paradox":[63],"visual":[66,88],"sense":[67],"quantified":[69],"result.":[70],"Thus,":[71],"propose":[73],"new":[75],"\u201cvisual":[76],"method":[79],"that":[80],"is":[81],"more":[82],"suitable":[83],"for":[84],"measurement":[86],"asymmetry.":[89]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}