{"id":"https://openalex.org/W7155182434","doi":"https://doi.org/10.48550/arxiv.2604.19287","title":"Stitching Arrowhead Curves: Extending the Sierpinski Arrowhead Curve to Higher Dimensions","display_name":"Stitching Arrowhead Curves: Extending the Sierpinski Arrowhead Curve to Higher Dimensions","publication_year":2026,"publication_date":"2026-04-21","ids":{"openalex":"https://openalex.org/W7155182434","doi":"https://doi.org/10.48550/arxiv.2604.19287"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.19287","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19287","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.19287","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104092656","display_name":"Eric Zimmermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zimmermann, Eric","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5063965880","display_name":"Stefan Br\u00fcckner","orcid":"https://orcid.org/0000-0002-0885-8402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruckner, Stefan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.1770000010728836,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.1770000010728836,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.10369999706745148,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.06859999895095825,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/image-stitching","display_name":"Image stitching","score":0.654699981212616},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6305000185966492},{"id":"https://openalex.org/keywords/sierpinski-triangle","display_name":"Sierpinski triangle","score":0.504800021648407},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4927000105381012},{"id":"https://openalex.org/keywords/sierpinski-carpet","display_name":"Sierpinski carpet","score":0.4528000056743622},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.3714999854564667}],"concepts":[{"id":"https://openalex.org/C29081049","wikidata":"https://www.wikidata.org/wiki/Q1364242","display_name":"Image stitching","level":2,"score":0.654699981212616},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6305000185966492},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6018000245094299},{"id":"https://openalex.org/C27176706","wikidata":"https://www.wikidata.org/wiki/Q663365","display_name":"Sierpinski triangle","level":3,"score":0.504800021648407},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4927000105381012},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.46959999203681946},{"id":"https://openalex.org/C116006050","wikidata":"https://www.wikidata.org/wiki/Q280081","display_name":"Sierpinski carpet","level":4,"score":0.4528000056743622},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34040001034736633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3057999908924103},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C53622353","wikidata":"https://www.wikidata.org/wiki/Q1518913","display_name":"Family of curves","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27219998836517334},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2590000033378601},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C70251129","wikidata":"https://www.wikidata.org/wiki/Q260928","display_name":"Jordan curve theorem","level":2,"score":0.25220000743865967},{"id":"https://openalex.org/C7305733","wikidata":"https://www.wikidata.org/wiki/Q207961","display_name":"Geometric shape","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.19287","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19287","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.19287","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.19287","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.7045649290084839}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"Sierpinski":[1,5,54],"triangle":[2],"and":[3,14,97],"the":[4,20,28,39,49,52,95,110],"arrowhead":[6,55],"curve":[7,40,56],"are":[8],"both":[9],"defined":[10],"in":[11,80,94,99,106,109],"dimension":[12],"2":[13],"can":[15],"be":[16],"used":[17],"to":[18,31,57,61,76],"model":[19],"same":[21],"fractal.":[22],"While":[23],"a":[24,74,81,91,113],"natural":[25],"extension":[26,37,60],"of":[27,38,51,112],"triangular":[29],"construction":[30],"arbitrary":[32,62],"dimensions":[33,63],"exists,":[34],"an":[35,59],"analogous":[36],"representation":[41],"does":[42],"not.":[43],"In":[44],"this":[45,70,103],"article,":[46],"we":[47,72,101],"analyze":[48],"properties":[50],"two-dimensional":[53],"formulate":[58],"based":[64],"on":[65,69],"reproduction":[66],"rules.":[67],"Building":[68],"formulation,":[71],"demonstrate":[73],"way":[75],"visualize":[77],"such":[78],"curves":[79],"comparative":[82],"manner":[83],"across":[84],"levels.":[85],"Finally,":[86],"as":[87],"geometric":[88],"patterns":[89],"have":[90],"long":[92],"history":[93],"arts,":[96],"especially":[98],"fashion,":[100],"exemplify":[102],"visualization":[104],"approach":[105],"knitwear,":[107],"specifically":[108],"yoke":[111],"sweater.":[114]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-23T00:00:00"}
