{"id":"https://openalex.org/W7128375926","doi":"https://doi.org/10.5281/zenodo.18557189","title":"Entropy-Based Distortion in Hashimoto's fractal in his symbolic Collatz model","display_name":"Entropy-Based Distortion in Hashimoto's fractal in his symbolic Collatz model","publication_year":2026,"publication_date":"2026-02-09","ids":{"openalex":"https://openalex.org/W7128375926","doi":"https://doi.org/10.5281/zenodo.18557189"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.18557189","doi":"https://doi.org/10.5281/zenodo.18557189","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18557189","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.18557189","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125398577","display_name":"Thomas Emile Ouellette","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ouellette, Thomas Emile","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5125398577"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27108488,"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":0.9922000169754028,"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":0.9922000169754028,"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/T13234","display_name":"advanced mathematical theories","score":0.0017999999690800905,"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":0.0010999999940395355,"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/collatz-conjecture","display_name":"Collatz conjecture","score":0.9599999785423279},{"id":"https://openalex.org/keywords/symbolic-dynamics","display_name":"symbolic dynamics","score":0.6420000195503235},{"id":"https://openalex.org/keywords/shannon-entropy","display_name":"Shannon entropy","score":0.9860000014305115},{"id":"https://openalex.org/keywords/distortion-factor","display_name":"distortion factor","score":0.5609999895095825},{"id":"https://openalex.org/keywords/subwords","display_name":"subwords","score":0.45100000500679016}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6876000165939331},{"id":"https://openalex.org/C128814272","wikidata":"https://www.wikidata.org/wiki/Q837314","display_name":"Collatz conjecture","level":3,"score":0.656499981880188},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.5440999865531921},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5368000268936157},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.535099983215332},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5087000131607056},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48910000920295715},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4765999913215637},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.4596000015735626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.423799991607666},{"id":"https://openalex.org/C2779190172","wikidata":"https://www.wikidata.org/wiki/Q4913888","display_name":"Binary data","level":3,"score":0.4059000015258789},{"id":"https://openalex.org/C16101541","wikidata":"https://www.wikidata.org/wiki/Q1350838","display_name":"Symbolic dynamics","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.3240000009536743},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3027999997138977},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25870001316070557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25220000743865967},{"id":"https://openalex.org/C2778095710","wikidata":"https://www.wikidata.org/wiki/Q6031225","display_name":"Information source (mathematics)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5281/zenodo.18557189","doi":"https://doi.org/10.5281/zenodo.18557189","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18557189","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.18557189","doi":"https://doi.org/10.5281/zenodo.18557189","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.18557189","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6582708954811096}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"introduce":[1],"in":[2,17],"an":[3,6],"exploratory":[4],"level":[5],"entropy-based":[7],"symbolic":[8],"model":[9],"motivated":[10],"by":[11],"the":[12,18,41],"binary":[13,27],"representation":[14],"of":[15,45],"preimages":[16],"continuous":[19],"Collatz":[20],"framework.":[21],"Using":[22],"Shannon":[23],"entropy":[24],"on":[25,40],"finite":[26],"words":[28],"and":[29,35],"their":[30],"subwords,":[31],"we":[32],"define":[33],"local":[34],"global":[36],"distortion":[37],"factors":[38],"depending":[39],"empirical":[42],"information":[43],"content":[44],"symbol":[46],"sequences.":[47]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2026-02-10T00:00:00"}