{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T13:43:07Z","timestamp":1792590187519,"version":"4.5.0"},"reference-count":67,"publisher":"AIP Publishing","issue":"10","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,1]]},"abstract":"<jats:p>Live-streaming platforms generate high-frequency records of collective human activity in which many loosely coordinated users react in real time to shared external stimuli and to one another. We investigate whether the temporal organization of Twitch chat messages exhibits multifractal signatures characteristic of complex dynamical systems. Selected high-activity chats were converted into time series by measuring the length of each consecutive message in words, with platform emotes treated as individual tokens. The resulting signals display heterogeneous fluctuations, bursty organization, and heavy-tailed distributions that, in several cases, are better captured by q-Weibull forms than by conventional light-tailed models. Autocorrelation analysis reveals persistent temporal dependence over broad ranges of message lags, indicating that the variability is not produced by independent message generation alone. Multifractal Detrended Fluctuation Analysis shows that some chats possess well-developed multifractal spectra and generalized Hurst exponents strongly dependent on moment order, whereas others exhibit weak scaling, approximately monofractal behavior, or no well-defined scaling regime. Surrogate tests indicate that temporal correlations are essential for the observed multifractality, while heavy tails enhance its apparent strength. Under particular dynamical conditions, Twitch chat may, therefore, form an emergent collective signal whose fragmented, reactive, associative, and multiscale organization is structurally reminiscent of stream-of-consciousness narrative. This expression is used strictly as a structural and dynamical analogy, not as a claim of a unified collective mind or of semantic, cognitive, or phenomenological equivalence with literary stream-of-consciousness writing. The results position live-stream chat dynamics within the broader physics of complex, intermittent, human-generated signals.<\/jats:p>","DOI":"10.1063\/5.0355584","type":"journal-article","created":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T13:06:08Z","timestamp":1792587968000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Some Twitch chats exhibit multifractal characteristics resembling stream-of-consciousness narrative"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-9259-3526","authenticated-orcid":false,"given":"Marcin","family":"B\u00f3l","sequence":"first","affiliation":[{"name":"Faculty of Computer Science and Mathematics, Cracow University of Technology 1 , ul. Warszawska 24, 31-155 Krak\u00f3w,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1613-6175","authenticated-orcid":false,"given":"Stanis\u0142aw","family":"Dro\u017cd\u017c","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science and Mathematics, Cracow University of Technology 1 , ul. Warszawska 24, 31-155 Krak\u00f3w,","place":["Poland"]},{"name":"Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences 2 , ul. Radzikowskiego 152, 31-342 Krak\u00f3w,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-4244-317X","authenticated-orcid":false,"given":"Robert","family":"Kluszczy\u0144ski","sequence":"additional","affiliation":[{"name":"Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences 2 , ul. Radzikowskiego 152, 31-342 Krak\u00f3w,","place":["Poland"]},{"name":"Faculty of Mathematics and Computer Science, Jagiellonian University 3 , ul. \u0141ojasiewicza 6, 30-348 Krak\u00f3w,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8813-9637","authenticated-orcid":false,"given":"Jaros\u0142aw","family":"Kwapie\u0144","sequence":"additional","affiliation":[{"name":"Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences 2 , ul. Radzikowskiego 152, 31-342 Krak\u00f3w,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2131-7440","authenticated-orcid":false,"given":"Marcin","family":"W\u0105torek","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science and Mathematics, Cracow University of Technology 1 , ul. Warszawska 24, 31-155 Krak\u00f3w,","place":["Poland"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,21]]},"reference":[{"issue":"5915","key":"2026102109060386300_c1","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1126\/science.1167742","article-title":"Computational social science","volume":"323","year":"2009","journal-title":"Science"},{"key":"2026102109060386300_c2","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1038\/s41586-019-1138-y","article-title":"Machine behaviour","volume":"568","year":"2019","journal-title":"Nature"},{"key":"2026102109060386300_c3","volume-title":"The Platform Society: Public Values in a Connective World","year":"2018","edition":"1st"},{"key":"2026102109060386300_c4","volume-title":"Social Big Data Analytics: Practices, Techniques, and Applications","year":"2021","edition":"1st"},{"key":"2026102109060386300_c5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2021.10.005","article-title":"Social physics","volume":"948","year":"2022","journal-title":"Phys. Rep."},{"key":"2026102109060386300_c6","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1177\/0163443718818363","article-title":"The impacts of live streaming and Twitch.tv on the video game industry","volume":"41","year":"2019","journal-title":"Media, Cult. Soc."},{"key":"2026102109060386300_c7","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.chb.2018.02.013","article-title":"Social motivations of live-streaming viewer engagement on twitch","volume":"84","year":"2018","journal-title":"Comput. Hum. Behav."},{"key":"2026102109060386300_c8","doi-asserted-by":"publisher","first-page":"1969","DOI":"10.1080\/1369118X.2021.1913211","article-title":"Building viewer engagement through interaction rituals on Twitch.tv","volume":"25","year":"2022","journal-title":"Inf., Commun. Soc."},{"key":"2026102109060386300_c9","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.pragma.2017.01.013","article-title":"Toward a transcription and analysis of live streaming on twitch","volume":"115","year":"2017","journal-title":"J. Pragmat."},{"key":"2026102109060386300_c10","doi-asserted-by":"publisher","first-page":"2441","DOI":"10.1038\/s41562-025-02373-5","article-title":"Higher-order interactions shape collective human behaviour","volume":"9","year":"2025","journal-title":"Nat. Hum. Behav."},{"key":"2026102109060386300_c11","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.physrep.2012.01.007","article-title":"Physical approach to complex systems","volume":"515","year":"2012","journal-title":"Phys. Rep."},{"key":"2026102109060386300_c12","volume-title":"Stream in Consciousness in the Modern Novel","year":"1958","edition":"3rd"},{"key":"2026102109060386300_c13","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.ins.2015.10.023","article-title":"Quantifying origin and character of long-range correlations in narrative texts","volume":"331","year":"2016","journal-title":"Inf. Sci."},{"key":"2026102109060386300_c14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2023.12.002","article-title":"Complex systems approach to natural language","volume":"1053","year":"2024","journal-title":"Phys. Rep."},{"key":"2026102109060386300_c15","doi-asserted-by":"publisher","first-page":"023155","DOI":"10.1063\/5.0248520","article-title":"Quantifying patterns of punctuation in modern Chinese prose","volume":"35","year":"2025","journal-title":"Chaos"},{"key":"2026102109060386300_c16","doi-asserted-by":"publisher","first-page":"083124","DOI":"10.1063\/5.0203530","article-title":"Statistics of punctuation in experimental literature\u2014The remarkable case of Finnegans Wake by James Joyce","volume":"34","year":"2024","journal-title":"Chaos"},{"key":"2026102109060386300_c17","doi-asserted-by":"publisher","first-page":"177","DOI":"10.3390\/e27020177","article-title":"Punctuation patterns in Finnegans Wake by James Joyce are largely translation-invariant","volume":"27","year":"2025","journal-title":"Entropy"},{"key":"2026102109060386300_c18","first-page":"1","article-title":"Storychat: Designing a narrative-based viewer participation tool for live streaming chatrooms","year":"2023"},{"key":"2026102109060386300_c19","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1089\/cyber.2009.0411","article-title":"Mirror, mirror on my facebook wall: Effects of exposure to facebook on self-esteem","volume":"14","year":"2011","journal-title":"Cyberpsychol., Behav., Soc. Netw."},{"key":"2026102109060386300_c20","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1080\/1369118X.2012.678878","article-title":"Critical questions for big data: Provocations for a cultural, technological, and scholarly phenomenon","volume":"15","year":"2012","journal-title":"Inf., Commun. Soc."},{"key":"2026102109060386300_c21","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1038\/335405a0","article-title":"Multifractal phenomena in physics and chemistry","volume":"335","year":"1988","journal-title":"Nature"},{"key":"2026102109060386300_c22","doi-asserted-by":"publisher","first-page":"125901","DOI":"10.1088\/1361-6633\/ab42fb","article-title":"Multifractal analysis of financial markets: A review","volume":"82","year":"2019","journal-title":"Rep. Prog. Phys."},{"key":"2026102109060386300_c23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2020.10.005","article-title":"Multiscale characteristics of the emerging global cryptocurrency market","volume":"901","year":"2021","journal-title":"Phys. Rep."},{"key":"2026102109060386300_c24","doi-asserted-by":"publisher","first-page":"112663","DOI":"10.1016\/j.chaos.2022.112663","article-title":"Do the global grain spot markets exhibit multifractal nature?","volume":"164","year":"2022","journal-title":"Chaos, Solitons Fractals"},{"key":"2026102109060386300_c25","doi-asserted-by":"publisher","first-page":"2350090","DOI":"10.1142\/S0218348X23500901","article-title":"Testing for intrinsic multifractality in the global grain spot market indices: A multifractal detrended fluctuation analysis","volume":"31","year":"2023","journal-title":"Fractals"},{"key":"2026102109060386300_c26","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1038\/20924","article-title":"Multifractality in human heartbeat dynamics","volume":"399","year":"1999","journal-title":"Nature"},{"key":"2026102109060386300_c27","doi-asserted-by":"publisher","first-page":"105916","DOI":"10.1016\/j.bspc.2023.105916","article-title":"Multifractal organization of EEG signals in multiple sclerosis","volume":"91","year":"2024","journal-title":"Biomed. Signal Process. Control"},{"key":"2026102109060386300_c28","doi-asserted-by":"publisher","first-page":"2146","DOI":"10.1029\/2003GL018099","article-title":"Nonlinearity and multifractality of climate change in the past 420\u2009000 years","volume":"30","year":"2003","journal-title":"Geophys. Res. Lett."},{"key":"2026102109060386300_c29","doi-asserted-by":"publisher","first-page":"062130","DOI":"10.1103\/PhysRevE.92.062130","article-title":"Multifractal to monofractal evolution of the London street network","volume":"92","year":"2015","journal-title":"Phys. Rev. E"},{"key":"2026102109060386300_c30","doi-asserted-by":"publisher","first-page":"1141","DOI":"10.1103\/PhysRevA.33.1141","article-title":"Fractal measures and their singularities: The characterization of strange sets","volume":"33","year":"1986","journal-title":"Phys. Rev. A"},{"key":"2026102109060386300_c31","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1016\/j.humov.2013.01.008","article-title":"Multifractal formalisms of human behavior","volume":"32","year":"2013","journal-title":"Hum. Mov. Sci."},{"key":"2026102109060386300_c32","doi-asserted-by":"publisher","first-page":"622","DOI":"10.1177\/00315125221149147","article-title":"Multifractal nonlinearity moderates feedforward and feedback responses to suprapostural perturbations","volume":"130","year":"2023","journal-title":"Percept. Mot. Ski."},{"key":"2026102109060386300_c33","doi-asserted-by":"publisher","first-page":"1956","DOI":"10.1098\/rsif.2011.0846","article-title":"Culturomics meets random fractal theory: Insights into long-range correlations of social and natural phenomena over the past two centuries","volume":"9","year":"2012","journal-title":"J. R. Soc. Interface"},{"key":"2026102109060386300_c34","doi-asserted-by":"publisher","first-page":"036108","DOI":"10.1103\/PhysRevE.78.036108","article-title":"A model for interevent times with long tails and multifractality in human communications: An application to financial trading","volume":"78","year":"2008","journal-title":"Phys. Rev. E"},{"key":"2026102109060386300_c35","doi-asserted-by":"publisher","first-page":"125633","DOI":"10.1016\/j.physa.2020.125633","article-title":"Long-term correlations and multifractality of toll-free calls in China","volume":"567","year":"2021","journal-title":"Physica A"},{"key":"2026102109060386300_c36","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1007\/s40042-022-00448-4","article-title":"Multifractal analysis of social media use in financial markets","volume":"80","year":"2022","journal-title":"J. Korean Phys. Soc."},{"key":"2026102109060386300_c37","doi-asserted-by":"publisher","first-page":"032307","DOI":"10.1103\/PhysRevE.96.032307","article-title":"Mechanisms of self-organized criticality in social processes of knowledge creation","volume":"96","year":"2017","journal-title":"Phys. Rev. E"},{"key":"2026102109060386300_c38","doi-asserted-by":"publisher","first-page":"560","DOI":"10.1038\/srep00560","article-title":"Communication activity in a social network: Relation between long-term correlations and inter-event clustering","volume":"2","year":"2012","journal-title":"Sci. Rep."},{"key":"2026102109060386300_c39","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1038\/nature03459","article-title":"The origin of bursts and heavy tails in human dynamics","volume":"435","year":"2005","journal-title":"Nature"},{"key":"2026102109060386300_c40","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1038\/srep00397","article-title":"Universal features of correlated bursty behaviour","volume":"2","year":"2012","journal-title":"Sci. Rep."},{"key":"2026102109060386300_c41","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1038\/srep00402","article-title":"Emotional persistence in online chatting communities","volume":"2","year":"2012","journal-title":"Sci. Rep."},{"key":"2026102109060386300_c42","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1038\/s44271-024-00112-6","article-title":"Online communities come with real-world consequences for individuals and societies","volume":"2","year":"2024","journal-title":"Commun. Psychol."},{"key":"2026102109060386300_c43","doi-asserted-by":"publisher","first-page":"1210","DOI":"10.1177\/0163443720904587","article-title":"The dimensions of streaming: Toward a typology of an evolving concept","volume":"42","year":"2020","journal-title":"Media, Cult. Soc."},{"key":"2026102109060386300_c44","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1177\/01634437231210439","article-title":"The streaming industry and the platform economy: An analysis","volume":"46","year":"2024","journal-title":"Media, Cult. Soc."},{"key":"2026102109060386300_c45","author":"TwitchDownloader"},{"key":"2026102109060386300_c46","author":"TwitchTopSubcribedStreamers"},{"key":"2026102109060386300_c47"},{"key":"2026102109060386300_c48","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1115\/1.4010337","article-title":"A statistical distribution function of wide applicability","volume":"18","year":"1951","journal-title":"ASME J. Appl. Mech."},{"key":"2026102109060386300_c49","doi-asserted-by":"publisher","first-page":"113183","DOI":"10.1016\/j.chaos.2023.113183","article-title":"Universal versus system-specific features of punctuation usage patterns in major Western languages","volume":"168","year":"2023","journal-title":"Chaos, Solitons Fractals"},{"key":"2026102109060386300_c50","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann\u2013Gibbs statistics","volume":"52","year":"1988","journal-title":"J. Stat. Phys."},{"key":"2026102109060386300_c51","doi-asserted-by":"publisher","first-page":"678","DOI":"10.1016\/S0378-4371(03)00071-2","article-title":"q-exponential, Weibull, and q-Weibull distributions: An empirical analysis","volume":"324","year":"2003","journal-title":"Physica A"},{"key":"2026102109060386300_c52","doi-asserted-by":"publisher","first-page":"912","DOI":"10.1080\/03610920802322474","article-title":"On the q-Weibull distribution and its applications","volume":"38","year":"2009","journal-title":"Commun. Stat. \u2013 Theory Methods"},{"key":"2026102109060386300_c53","doi-asserted-by":"publisher","first-page":"720","DOI":"10.1108\/IJQRM-Oct-2011-0143","article-title":"Generalized q-Weibull model and the bathtub curve","volume":"30","year":"2013","journal-title":"Int. J. Qual. Reliab. Manag."},{"key":"2026102109060386300_c54","volume-title":"Nonparametric Statistical Methods","year":"2013","edition":"3rd"},{"key":"2026102109060386300_c55","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0378-4371(02)01383-3","article-title":"Multifractal detrended fluctuation analysis of nonstationary time series","volume":"316","year":"2002","journal-title":"Physica A"},{"key":"2026102109060386300_c56","doi-asserted-by":"publisher","first-page":"016103","DOI":"10.1103\/PhysRevE.74.016103","article-title":"Wavelet versus detrended fluctuation analysis of multifractal structures","volume":"74","year":"2006","journal-title":"Phys. Rev. E"},{"key":"2026102109060386300_c57","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/0167-2789(83)90235-X","article-title":"The infinite number of generalized dimensions of fractals and strange attractors","volume":"8","year":"1983","journal-title":"Physica D"},{"key":"2026102109060386300_c58","doi-asserted-by":"publisher","first-page":"2730","DOI":"10.1103\/PhysRevA.44.2730","article-title":"Multifractality of self-affine fractals","volume":"44","year":"1991","journal-title":"Phys. Rev. A"},{"key":"2026102109060386300_c59","doi-asserted-by":"publisher","first-page":"770","DOI":"10.1061\/TACEAT.0006518","article-title":"Long-term storage capacity of reservoirs","volume":"116","year":"1951","journal-title":"Trans. Am. Soc. Civ. Eng."},{"key":"2026102109060386300_c60","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1098\/rsta.1937.0005","article-title":"Outline of a theory of statistical estimation based on the classical theory of probability","volume":"236","year":"1937","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A"},{"key":"2026102109060386300_c61","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1016\/S0375-9601(00)00059-1","article-title":"Multi-scaling properties of truncated Levy flights","volume":"266","year":"2000","journal-title":"Phys. Lett. A"},{"key":"2026102109060386300_c62","doi-asserted-by":"publisher","first-page":"60003","DOI":"10.1209\/0295-5075\/88\/60003","article-title":"Quantitative features of multifractal subtleties in time series","volume":"88","year":"2009","journal-title":"Europhys. Lett."},{"key":"2026102109060386300_c63","doi-asserted-by":"publisher","first-page":"034139","DOI":"10.1103\/PhysRevE.107.034139","article-title":"Genuine multifractality in time series is due to temporal correlations","volume":"107","year":"2023","journal-title":"Phys. Rev. E"},{"key":"2026102109060386300_c64","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/0378-4371(90)90339-T","article-title":"Negative fractal dimensions and multifractals","volume":"163","year":"1990","journal-title":"Physica A"},{"key":"2026102109060386300_c65","doi-asserted-by":"publisher","first-page":"1114","DOI":"10.1103\/PhysRevA.43.1114","article-title":"Negative dimensions: Theory, computation, and experiment","volume":"43","year":"1991","journal-title":"Phys. Rev. A"},{"key":"2026102109060386300_c66","doi-asserted-by":"publisher","first-page":"030902(R)","DOI":"10.1103\/PhysRevE.91.030902","article-title":"Detecting and interpreting distortions in hierarchical organization of complex time series","volume":"91","year":"2015","journal-title":"Phys. Rev. E"},{"key":"2026102109060386300_c67","doi-asserted-by":"publisher","first-page":"205","DOI":"10.3390\/math13020205","article-title":"Disentangling sources of multifractality in time series","volume":"13","year":"2025","journal-title":"Mathematics"}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0355584\/21177122\/103134_1_5.0355584.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0355584\/21177122\/103134_1_5.0355584.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T13:06:10Z","timestamp":1792587970000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/36\/10\/103134\/3406956\/Some-Twitch-chats-exhibit-multifractal"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,1]]},"references-count":67,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2026,10,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0355584","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10]]},"published":{"date-parts":[[2026,10,1]]},"article-number":"103134"}}