{"id":"https://openalex.org/W4236598182","doi":"https://doi.org/10.3389/fphys.2012.00127","title":"Measuring Fractality","display_name":"Measuring Fractality","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W4236598182","doi":"https://doi.org/10.3389/fphys.2012.00127","pmid":"https://pubmed.ncbi.nlm.nih.gov/22586408","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/3345945"},"language":"en","primary_location":{"id":"doi:10.3389/fphys.2012.00127","doi":"https://doi.org/10.3389/fphys.2012.00127","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fphys.2012.00127","pdf_url":"https://www.frontiersin.org/articles/10.3389/fphys.2012.00127/pdf","source":{"id":"https://openalex.org/S52732750","display_name":"Frontiers in Physiology","issn_l":"1664-042X","issn":["1664-042X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Physiology","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/articles/10.3389/fphys.2012.00127/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034975618","display_name":"Tatjana Stadnitski","orcid":"https://orcid.org/0000-0002-5794-6011","observed_orcids":["https://orcid.org/0000-0002-5794-6011"]},"institutions":[{"id":"https://openalex.org/I196349391","display_name":"Universit\u00e4t Ulm","ror":"https://ror.org/032000t02","country_code":"DE","type":"education","lineage":["https://openalex.org/I196349391"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Tatjana Stadnitski","raw_affiliation_strings":["Psychological Methods, Institute of Psychology and Education, University of Ulm Ulm, Germany","University of Ulm, Institute of Psychology and Education, Ulm, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Psychological Methods, Institute of Psychology and Education, University of Ulm Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]},{"raw_affiliation_string":"University of Ulm, Institute of Psychology and Education, Ulm, Germany","institution_ids":["https://openalex.org/I196349391"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034975618"],"corresponding_institution_ids":["https://openalex.org/I196349391"],"apc_list":{"value":3150,"currency":"CHF","value_usd":3801},"apc_paid":{"value":3150,"currency":"CHF","value_usd":3801},"fwci":9.9476,"has_fulltext":true,"cited_by_count":74,"citation_normalized_percentile":{"value":0.97695117,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"3","issue":null,"first_page":"127","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fractality","display_name":"fractality","score":0.722000002861023},{"id":"https://openalex.org/keywords/1-f-noise","display_name":"1/f noise","score":0.9679999947547913},{"id":"https://openalex.org/keywords/self-similarity","display_name":"self-similarity","score":0.8429999947547913},{"id":"https://openalex.org/keywords/long-range-dependence","display_name":"long-range dependence","score":0.9100000262260437},{"id":"https://openalex.org/keywords/power-law","display_name":"power law","score":0.8019999861717224},{"id":"https://openalex.org/keywords/hurst-exponent","display_name":"Hurst exponent","score":0.8560000061988831},{"id":"https://openalex.org/keywords/scaling-exponents","display_name":"scaling exponents","score":0.9729999899864197},{"id":"https://openalex.org/keywords/fractional-integration","display_name":"fractional integration","score":0.9200000166893005},{"id":"https://openalex.org/keywords/arfima","display_name":"ARFIMA","score":0.675000011920929},{"id":"https://openalex.org/keywords/power-spectral-density","display_name":"power spectral density","score":0.8920000195503235},{"id":"https://openalex.org/keywords/detrended-fluctuation-analysis","display_name":"detrended fluctuation analysis","score":0.9980000257492065},{"id":"https://openalex.org/keywords/stationarity-tests","display_name":"stationarity testing","score":0.6439999938011169},{"id":"https://openalex.org/keywords/short-memory-processes","display_name":"short memory processes","score":0.7459999918937683},{"id":"https://openalex.org/keywords/time-series-analysis","display_name":"time series analysis","score":0.8180000185966492}],"concepts":[{"id":"https://openalex.org/C96835011","wikidata":"https://www.wikidata.org/wiki/Q1638718","display_name":"Hurst exponent","level":2,"score":0.8250499963760376},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.8140178918838501},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7003020644187927},{"id":"https://openalex.org/C21689155","wikidata":"https://www.wikidata.org/wiki/Q2451452","display_name":"Detrended fluctuation analysis","level":3,"score":0.6712372303009033},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.6101536154747009},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5537654757499695},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5464552640914917},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5183785557746887},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.4864335060119629},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.473283976316452},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.4338442087173462},{"id":"https://openalex.org/C1297061","wikidata":"https://www.wikidata.org/wiki/Q4826945","display_name":"Autoregressive fractionally integrated moving average","level":4,"score":0.4263659119606018},{"id":"https://openalex.org/C119453123","wikidata":"https://www.wikidata.org/wiki/Q262372","display_name":"Self-similarity","level":2,"score":0.41339483857154846},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3949432075023651},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.38343071937561035},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.3322099447250366},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2901463508605957},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20299562811851501},{"id":"https://openalex.org/C2986394398","wikidata":"https://www.wikidata.org/wiki/Q1805477","display_name":"Long memory","level":3,"score":0.16581115126609802},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.14927202463150024},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13346171379089355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10467851161956787},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3389/fphys.2012.00127","doi":"https://doi.org/10.3389/fphys.2012.00127","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fphys.2012.00127","pdf_url":"https://www.frontiersin.org/articles/10.3389/fphys.2012.00127/pdf","source":{"id":"https://openalex.org/S52732750","display_name":"Frontiers in Physiology","issn_l":"1664-042X","issn":["1664-042X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Physiology","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:3345945","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/3345945","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Front Physiol","raw_type":"Text"},{"id":"pmid:22586408","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22586408","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in physiology","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:4cf5a1f7faf54470a6f8b53d3912dff6","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/4cf5a1f7faf54470a6f8b53d3912dff6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Physiology, Vol 3 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fphys.2012.00127","doi":"https://doi.org/10.3389/fphys.2012.00127","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fphys.2012.00127","pdf_url":"https://www.frontiersin.org/articles/10.3389/fphys.2012.00127/pdf","source":{"id":"https://openalex.org/S52732750","display_name":"Frontiers in Physiology","issn_l":"1664-042X","issn":["1664-042X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Physiology","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4236598182.pdf","grobid_xml":"https://content.openalex.org/works/W4236598182.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W74712529","https://openalex.org/W163710380","https://openalex.org/W396422028","https://openalex.org/W985156132","https://openalex.org/W1245598776","https://openalex.org/W1969917201","https://openalex.org/W1992839121","https://openalex.org/W1999909108","https://openalex.org/W2000432778","https://openalex.org/W2005466063","https://openalex.org/W2009831767","https://openalex.org/W2028998303","https://openalex.org/W2029638247","https://openalex.org/W2031753087","https://openalex.org/W2038689382","https://openalex.org/W2040938295","https://openalex.org/W2069506961","https://openalex.org/W2075514521","https://openalex.org/W2077655468","https://openalex.org/W2078824647","https://openalex.org/W2081438405","https://openalex.org/W2088581336","https://openalex.org/W2089821756","https://openalex.org/W2098676624","https://openalex.org/W2112932663","https://openalex.org/W2121684477","https://openalex.org/W2126105264","https://openalex.org/W2143742995","https://openalex.org/W2144024103","https://openalex.org/W2157375814","https://openalex.org/W2167362617","https://openalex.org/W2467218978","https://openalex.org/W2468019504","https://openalex.org/W2522027325","https://openalex.org/W2798056406","https://openalex.org/W4230451775","https://openalex.org/W4234959120","https://openalex.org/W4242671632","https://openalex.org/W4292483811","https://openalex.org/W4299784281","https://openalex.org/W6677096361","https://openalex.org/W6844241875"],"related_works":["https://openalex.org/W7097775129","https://openalex.org/W2480916207","https://openalex.org/W2081438405","https://openalex.org/W2792242725","https://openalex.org/W2468019504","https://openalex.org/W2181918241","https://openalex.org/W1969652662","https://openalex.org/W2073018172","https://openalex.org/W2115258861","https://openalex.org/W2551286629"],"abstract_inverted_index":{"WHEN":[0],"INVESTIGATING":[1],"FRACTAL":[2],"PHENOMENA,":[3],"THE":[4,10],"FOLLOWING":[5],"QUESTIONS":[6],"ARE":[7],"FUNDAMENTAL":[8],"FOR":[9],"APPLIED":[11],"RESEARCHER:":[12],"(1)":[13],"What":[14],"are":[15,25,34,38,101,120,144,179],"essential":[16],"statistical":[17],"properties":[18],"of":[19,43,59,85,97,105,128,152],"1/f":[20],"noise?":[21],"(2)":[22],"Which":[23,31],"estimators":[24,104,131],"available":[26],"for":[27],"measuring":[28],"fractality?":[29],"(3)":[30],"measurement":[32],"instruments":[33],"appropriate":[35],"and":[36,50,68,122,126,160],"how":[37],"they":[39],"applied?":[40],"The":[41],"purpose":[42],"this":[44],"article":[45],"is":[46],"to":[47,53],"give":[48],"clear":[49],"comprehensible":[51],"answers":[52],"these":[54],"questions.":[55],"First,":[56],"theoretical":[57],"characteristics":[58],"a":[60],"fractal":[61,71,106,153,171,174],"pattern":[62],"(self-similarity,":[63],"long":[64],"memory,":[65],"power":[66,94,135],"law)":[67],"the":[69,76,80,86,93,98,129],"related":[70],"parameters":[72,107],"(the":[73],"Hurst":[74],"coefficient,":[75],"scaling":[77],"exponent":[78,95],"\u03b1,":[79],"fractional":[81],"differencing":[82],"parameter":[83],"d":[84],"autoregressive":[87],"fractionally":[88],"integrated":[89],"moving":[90],"average":[91],"methodology,":[92],"\u03b2":[96],"spectral":[99,136,161],"analysis)":[100],"discussed.":[102],"Then,":[103],"from":[108,176],"different":[109],"software":[110],"packages":[111],"commonly":[112],"used":[113],"by":[114,146],"applied":[115],"researchers":[116],"(R,":[117],"SAS,":[118],"SPSS)":[119],"introduced":[121],"evaluated.":[123],"Advantages,":[124],"disadvantages,":[125],"constrains":[127],"popular":[130],"([Formula:":[132],"see":[133],"text]":[134],"density,":[137],"detrended":[138],"fluctuation":[139],"analysis,":[140],"signal":[141],"summation":[142],"conversion)":[143],"illustrated":[145],"elaborate":[147],"examples.":[148],"Finally,":[149],"crucial":[150],"steps":[151],"analysis":[154],"(plotting":[155],"time":[156,183],"series":[157],"data,":[158],"autocorrelation,":[159],"functions;":[162],"performing":[163],"stationarity":[164],"tests;":[165],"choosing":[166],"an":[167],"adequate":[168],"estimator;":[169],"estimating":[170],"parameters;":[172],"distinguishing":[173],"processes":[175],"short-memory":[177],"patterns)":[178],"demonstrated":[180],"with":[181],"empirical":[182],"series.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6}],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2022-05-12T00:00:00"}