{"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":true},"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","School of Mathematics & Physics, Jinggangshan University, Ji'an 343009","Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 611756"],"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":"School of Mathematics & Physics, Jinggangshan University, Ji'an 343009","institution_ids":["https://openalex.org/I14748160"]},{"raw_affiliation_string":"Sichuan Province Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu 611756","institution_ids":["https://openalex.org/I4800084"]}]},{"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"],"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"],"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":0.44256408,"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":true,"landing_page_url":"https://doaj.org/article/6639602dbb87449cb1f7c8cd66a66d8c","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":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":[{"score":0.7799999713897705,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"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/G2087396116","display_name":null,"funder_award_id":"China","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/G2802911279","display_name":null,"funder_award_id":"Young","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4009049029","display_name":null,"funder_award_id":"Startup","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4671531071","display_name":null,"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"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"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":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}