{"id":"https://openalex.org/W2094409927","doi":"https://doi.org/10.1080/10586458.2005.10128919","title":"Outer Boundaries of Self-Similar Tiles","display_name":"Outer Boundaries of Self-Similar Tiles","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2094409927","doi":"https://doi.org/10.1080/10586458.2005.10128919","mag":"2094409927"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2005.10128919","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128919","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002567806","display_name":"Shawn Drenning","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shawn Drenning","raw_affiliation_strings":["\n Mathematics Department, University of Chicago, Chicago, IL 60637","Mathematics Department, University of Chicago, Chicago, IL 60637"],"affiliations":[{"raw_affiliation_string":"\n Mathematics Department, University of Chicago, Chicago, IL 60637","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"Mathematics Department, University of Chicago, Chicago, IL 60637","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008221231","display_name":"Judith Palagallo","orcid":null},"institutions":[{"id":"https://openalex.org/I110152177","display_name":"University of Akron","ror":"https://ror.org/02kyckx55","country_code":"US","type":"education","lineage":["https://openalex.org/I110152177"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Judith Palagallo","raw_affiliation_strings":["\n Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002","Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002"],"affiliations":[{"raw_affiliation_string":"\n Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002","institution_ids":["https://openalex.org/I110152177"]},{"raw_affiliation_string":"Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002","institution_ids":["https://openalex.org/I110152177","https://openalex.org/I4210131439"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074941542","display_name":"Thomas E. Price","orcid":null},"institutions":[{"id":"https://openalex.org/I110152177","display_name":"University of Akron","ror":"https://ror.org/02kyckx55","country_code":"US","type":"education","lineage":["https://openalex.org/I110152177"]},{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Price","raw_affiliation_strings":["\n Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002","Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002"],"affiliations":[{"raw_affiliation_string":"\n Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002","institution_ids":["https://openalex.org/I110152177"]},{"raw_affiliation_string":"Dept. of Theoretical & Applied Mathematics, University of Akron, Akron, OH 44325\u20134002","institution_ids":["https://openalex.org/I110152177","https://openalex.org/I4210131439"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067488367","display_name":"Robert S. Strichartz","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert S. Strichartz","raw_affiliation_strings":["\n Mathematics Department, Cornell University, Malott Hall, Ithaca, NY 14853","Mathematics Department, Cornell University, Malott Hall, Ithaca, NY 14853"],"affiliations":[{"raw_affiliation_string":"\n Mathematics Department, Cornell University, Malott Hall, Ithaca, NY 14853","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Mathematics Department, Cornell University, Malott Hall, Ithaca, NY 14853","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002567806"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":null,"apc_paid":null,"fwci":0.3366,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.63371089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"199","last_page":"209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9975000023841858,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9925000071525574,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9836999773979187,"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/mathematics","display_name":"Mathematics","score":0.8237665891647339},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.7588552236557007},{"id":"https://openalex.org/keywords/tile","display_name":"Tile","score":0.7020610570907593},{"id":"https://openalex.org/keywords/iterated-function-system","display_name":"Iterated function system","score":0.6134206652641296},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5494288206100464},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5255735516548157},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5165321230888367},{"id":"https://openalex.org/keywords/boundary-representation","display_name":"Boundary representation","score":0.43974804878234863},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4318673014640808},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3230152726173401},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3142601251602173},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24185100197792053},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.14625707268714905}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8237665891647339},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.7588552236557007},{"id":"https://openalex.org/C2780728851","wikidata":"https://www.wikidata.org/wiki/Q468402","display_name":"Tile","level":2,"score":0.7020610570907593},{"id":"https://openalex.org/C168460219","wikidata":"https://www.wikidata.org/wiki/Q1502167","display_name":"Iterated function system","level":3,"score":0.6134206652641296},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5494288206100464},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5255735516548157},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5165321230888367},{"id":"https://openalex.org/C117258860","wikidata":"https://www.wikidata.org/wiki/Q895153","display_name":"Boundary representation","level":3,"score":0.43974804878234863},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4318673014640808},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3230152726173401},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3142601251602173},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24185100197792053},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.14625707268714905},{"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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":2,"locations":[{"id":"doi:10.1080/10586458.2005.10128919","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2005.10128919","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.em/1128100132","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.em/1128100132","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1513702114","https://openalex.org/W2002031800","https://openalex.org/W2024190285","https://openalex.org/W2060189933","https://openalex.org/W2069868484","https://openalex.org/W2080003810","https://openalex.org/W2091470825","https://openalex.org/W2092019061","https://openalex.org/W2113117511","https://openalex.org/W2138958715","https://openalex.org/W2140747446","https://openalex.org/W2144592703","https://openalex.org/W2154163141","https://openalex.org/W2591895333","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1561687547","https://openalex.org/W2369480152","https://openalex.org/W4287710035","https://openalex.org/W2017482687","https://openalex.org/W2368621955","https://openalex.org/W2972725323","https://openalex.org/W3158017144","https://openalex.org/W4383425433","https://openalex.org/W2068677575","https://openalex.org/W2356012241"],"abstract_inverted_index":{"There":[0],"are":[1,8],"many":[2],"examples":[3],"of":[4,23,26,36,43,47,78],"self-similar":[5],"tiles":[6,17],"that":[7,20,97,111,122],"connected,":[9],"but":[10],"whose":[11],"interior":[12,28],"is":[13,51,94,104,119],"disconnected.":[14],"For":[15],"such":[16],"we":[18,125],"show":[19],"the":[21,27,44,48,54,62,71,75,129,138,144],"boundary":[22,46,56,73],"a":[24,33,41,67,79,88,108],"component":[25],"may":[29,140],"be":[30,141],"decomposed":[31],"into":[32],"finite":[34],"union":[35],"pieces,":[37],"each":[38],"similar":[39],"to":[40,69,106],"subset":[42],"outer":[45,55,72],"tile.":[49],"This":[50],"significant":[52],"because":[53],"typically":[57],"has":[58],"lower":[59],"dimension":[60],"than":[61],"full":[63],"boundary.":[64],"We":[65],"describe":[66],"method":[68,85,130],"realize":[70],"as":[74],"invariant":[76],"set":[77],"graph-directed":[80],"iterated":[81],"function":[82],"system.":[83],"The":[84],"works":[86],"under":[87],"certain":[89],"\"finiteness''":[90],"assumption.":[91],"While":[92],"it":[93,103,112,118,123],"not":[95],"clear":[96,132],"this":[98],"assumption":[99],"always":[100],"holds,":[101,124],"and":[102,133],"problematic":[105],"give":[107,126],"rigorous":[109],"proof":[110],"holds":[113],"even":[114],"in":[115],"cases":[116],"where":[117,128],"\"visually":[120],"clear''":[121],"some\\nexamples":[127],"yields":[131],"nontrivial":[134],"results.":[135],"Details":[136],"concerning":[137],"algorithms":[139],"found":[142],"at":[143],"website":[145],"www.math.cornell.edu/~$sld32/Tiles.html.":[146]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
