{"id":"https://openalex.org/W2788453866","doi":"https://doi.org/10.1155/2018/7315695","title":"The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group","display_name":"The Visualization of Spherical Patterns with Symmetries of the Wallpaper Group","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2788453866","doi":"https://doi.org/10.1155/2018/7315695","mag":"2788453866"},"language":"en","primary_location":{"id":"doi:10.1155/2018/7315695","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/7315695","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/7315695.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/complexity/2018/7315695.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103109597","display_name":"Shihuan Liu","orcid":"https://orcid.org/0000-0003-3003-1919"},"institutions":[{"id":"https://openalex.org/I14748160","display_name":"Jinggangshan University","ror":"https://ror.org/04exd0a76","country_code":"CN","type":"education","lineage":["https://openalex.org/I14748160"]},{"id":"https://openalex.org/I4800084","display_name":"Southwest Jiaotong University","ror":"https://ror.org/00hn7w693","country_code":"CN","type":"education","lineage":["https://openalex.org/I4800084"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shihuan Liu","raw_affiliation_strings":["School of Mathematics & Physics, Jinggangshan University, Ji' an 343009, China","Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 611756, China","Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 611756","School of Mathematics & Physics, Jinggangshan University, Ji'an 343009"],"raw_orcid":"https://orcid.org/0000-0003-3003-1919","affiliations":[{"raw_affiliation_string":"School of Mathematics & Physics, Jinggangshan University, Ji' an 343009, China","institution_ids":["https://openalex.org/I14748160"]},{"raw_affiliation_string":"Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 611756, China","institution_ids":["https://openalex.org/I4800084"]},{"raw_affiliation_string":"Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 611756","institution_ids":["https://openalex.org/I4800084"]},{"raw_affiliation_string":"School of Mathematics & Physics, Jinggangshan University, Ji'an 343009","institution_ids":["https://openalex.org/I14748160"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071836942","display_name":"Ming Leng","orcid":null},"institutions":[{"id":"https://openalex.org/I14748160","display_name":"Jinggangshan University","ror":"https://ror.org/04exd0a76","country_code":"CN","type":"education","lineage":["https://openalex.org/I14748160"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming Leng","raw_affiliation_strings":["School of Mathematics & Physics, Jinggangshan University, Ji' an 343009, China","School of Mathematics & Physics, Jinggangshan University, Ji'an 343009"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics & Physics, Jinggangshan University, Ji' an 343009, China","institution_ids":["https://openalex.org/I14748160"]},{"raw_affiliation_string":"School of Mathematics & Physics, Jinggangshan University, Ji'an 343009","institution_ids":["https://openalex.org/I14748160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058224525","display_name":"Peichang Ouyang","orcid":"https://orcid.org/0000-0003-0447-3190"},"institutions":[{"id":"https://openalex.org/I14748160","display_name":"Jinggangshan University","ror":"https://ror.org/04exd0a76","country_code":"CN","type":"education","lineage":["https://openalex.org/I14748160"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Peichang Ouyang","raw_affiliation_strings":["School of Mathematics & Physics, Jinggangshan University, Ji' an 343009, China","School of Mathematics & Physics, Jinggangshan University, Ji'an 343009"],"raw_orcid":"https://orcid.org/0000-0003-0447-3190","affiliations":[{"raw_affiliation_string":"School of Mathematics & Physics, Jinggangshan University, Ji' an 343009, China","institution_ids":["https://openalex.org/I14748160"]},{"raw_affiliation_string":"School of Mathematics & Physics, Jinggangshan University, Ji'an 343009","institution_ids":["https://openalex.org/I14748160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058224525"],"corresponding_institution_ids":["https://openalex.org/I14748160"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.198,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.44273209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2018","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9283000230789185,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9283000230789185,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/wallpaper","display_name":"Wallpaper","score":0.9457417726516724},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.7301393747329712},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6660236716270447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5233646631240845},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5053690075874329},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.46851348876953125},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.44897758960723877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3758881390094757},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37131983041763306},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24014407396316528},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17379510402679443},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06862878799438477}],"concepts":[{"id":"https://openalex.org/C83599316","wikidata":"https://www.wikidata.org/wiki/Q1139104","display_name":"Wallpaper","level":2,"score":0.9457417726516724},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7301393747329712},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6660236716270447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5233646631240845},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5053690075874329},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.46851348876953125},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.44897758960723877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3758881390094757},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37131983041763306},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24014407396316528},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17379510402679443},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06862878799438477},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2018/7315695","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/7315695","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/7315695.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:7315695","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2018/7315695.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:6639602dbb87449cb1f7c8cd66a66d8c","is_oa":false,"landing_page_url":"https://doaj.org/article/6639602dbb87449cb1f7c8cd66a66d8c","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2018 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2018/7315695","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/7315695","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/7315695.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.7799999713897705}],"awards":[{"id":"https://openalex.org/G1490064569","display_name":null,"funder_award_id":"11761039","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2589212967","display_name":null,"funder_award_id":"11461035","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4671531071","display_name":"\u9762\u5411\u5c42\u6b21\u5f0fFPGA\u7684\u591a\u76ee\u6807\u5e03\u5c40\u548c\u5e03\u7ebf\u95ee\u9898\u7814\u7a76","funder_award_id":"61363014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5199800786","display_name":null,"funder_award_id":"GJJ160749","funder_id":"https://openalex.org/F4320325626","funder_display_name":"Education Department of Jiangxi Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320325626","display_name":"Education Department of Jiangxi Province","ror":null},{"id":"https://openalex.org/F4320328643","display_name":"Jinggangshan University","ror":"https://ror.org/04exd0a76"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2788453866.pdf","grobid_xml":"https://content.openalex.org/works/W2788453866.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W16416857","https://openalex.org/W1985736473","https://openalex.org/W1996924980","https://openalex.org/W2024603146","https://openalex.org/W2034506745","https://openalex.org/W2048151058","https://openalex.org/W2072750622","https://openalex.org/W2159806637","https://openalex.org/W2318136776","https://openalex.org/W2583900428","https://openalex.org/W4230773447","https://openalex.org/W4292414116"],"related_works":["https://openalex.org/W627623861","https://openalex.org/W3138321446","https://openalex.org/W2364642894","https://openalex.org/W2076703156","https://openalex.org/W1975341022","https://openalex.org/W2766377737","https://openalex.org/W1995820642","https://openalex.org/W3210901769","https://openalex.org/W4226313719","https://openalex.org/W2384722316"],"abstract_inverted_index":{"By":[0],"constructing":[1],"invariant":[2],"mappings":[3,24,42],"associated":[4],"with":[5,33],"wallpaper":[6,19,50,54],"groups,":[7],"this":[8],"paper":[9],"presents":[10],"a":[11,45,76],"simple":[12,26],"and":[13,28],"efficient":[14],"method":[15],"to":[16],"generate":[17],"colorful":[18],"patterns.":[20,51],"Although":[21],"the":[22,34,63,67],"constructed":[23],"have":[25],"form":[27],"only":[29],"two":[30],"parameters,":[31],"combined":[32],"color":[35],"scheme":[36],"of":[37,48],"orbit":[38],"trap":[39],"algorithm,":[40],"such":[41],"can":[43],"create":[44],"great":[46],"variety":[47],"aesthetic":[49],"The":[52],"resulting":[53],"patterns":[55,70],"are":[56],"further":[57],"projected":[58],"by":[59],"central":[60],"projection":[61],"onto":[62],"sphere.":[64],"This":[65],"creates":[66],"interesting":[68],"spherical":[69],"that":[71],"possess":[72],"infinite":[73],"symmetries":[74],"in":[75],"finite":[77],"space.":[78]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2025-10-10T00:00:00"}
