{"id":"https://openalex.org/W1963496695","doi":"https://doi.org/10.1007/s00454-012-9431-7","title":"Mandelbrot Set + Symmetry Groups \u2217 Higher Dimensions = ?","display_name":"Mandelbrot Set + Symmetry Groups \u2217 Higher Dimensions = ?","publication_year":2012,"publication_date":"2012-07-26","ids":{"openalex":"https://openalex.org/W1963496695","doi":"https://doi.org/10.1007/s00454-012-9431-7","mag":"1963496695"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-012-9431-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9431-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9431-7.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9431-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050959995","display_name":"Elizabeth R. Chen","orcid":"https://orcid.org/0000-0002-8904-7977"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Elizabeth R. Chen","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA","Department of Mathematics, University of Michigan, Ann Arbor, USA 48109"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, USA 48109","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050959995"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05252901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9983999729156494,"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":0.9983999729156494,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mandelbrot-set","display_name":"Mandelbrot set","score":0.9732337594032288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8098701238632202},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.7361185550689697},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.6328790783882141},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5909205079078674},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5770976543426514},{"id":"https://openalex.org/keywords/generating-set-of-a-group","display_name":"Generating set of a group","score":0.5545486807823181},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5210925340652466},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4885633885860443},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.4700074791908264},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4393472671508789},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20067179203033447},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17438551783561707},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.164061039686203},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07651382684707642}],"concepts":[{"id":"https://openalex.org/C97519476","wikidata":"https://www.wikidata.org/wiki/Q257","display_name":"Mandelbrot set","level":3,"score":0.9732337594032288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8098701238632202},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.7361185550689697},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.6328790783882141},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5909205079078674},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5770976543426514},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.5545486807823181},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5210925340652466},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4885633885860443},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.4700074791908264},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4393472671508789},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20067179203033447},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17438551783561707},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.164061039686203},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07651382684707642},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/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},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-012-9431-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9431-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9431-7.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-012-9431-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-012-9431-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9431-7.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1963496695.pdf","grobid_xml":"https://content.openalex.org/works/W1963496695.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W113908933","https://openalex.org/W390053422","https://openalex.org/W1494214320","https://openalex.org/W1533967041","https://openalex.org/W1628935478","https://openalex.org/W2000902737","https://openalex.org/W2004190107","https://openalex.org/W2050881950","https://openalex.org/W2082013839","https://openalex.org/W2092812553","https://openalex.org/W2112887636","https://openalex.org/W2135234236","https://openalex.org/W2315104614","https://openalex.org/W2321232269","https://openalex.org/W2340951675","https://openalex.org/W2481452710","https://openalex.org/W4244010489"],"related_works":["https://openalex.org/W2903687319","https://openalex.org/W2021918652","https://openalex.org/W2907112423","https://openalex.org/W1963496695","https://openalex.org/W2467723682","https://openalex.org/W4287325179","https://openalex.org/W2165709755","https://openalex.org/W2145815337","https://openalex.org/W3165734106","https://openalex.org/W2069602920"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}