From Fractal Geometry to Fractal Cognition: Experimental Tools and Future Directions for Studying Recursive Hierarchical Embedding
Abstract
1. Introduction
2. Conceptual Foundations
2.1. Defining Recursive Hierarchical Embedding (RHE)
2.2. From Fractals to Bounded Cognition
3. Experimental Paradigms for Studying RHE
3.1. Behavioral Methods
3.2. Interference, Neuropsychological, and Transfer Paradigms
3.3. Neuroimaging Applications
4. Empirical Findings on RHE Across Domains
4.1. Behavioral Evidence—In What Domains Is RHE Represented?
4.2. Evidence from Lesions, Interference, and Atypical Development
4.3. Neural Bases of Recursion Across Domains
4.4. Insights from Artificial Grammar Learning and Computational Approaches
5. Open Questions and Future Directions
5.1. Challenges in Studying RHE
5.2. Towards Mechanistic Modeling
5.3. Expanding the Empirical Program
5.4. Toward a Unified Science of Fractal Cognition
6. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Eke, A.; Herman, P.; Kocsis, L.; Kozak, L. Fractal Characterization of Complexity in Temporal Physiological Signals. Physiol. Meas. 2002, 23, R1. [Google Scholar] [CrossRef]
- Halsey, T.C.; Jensen, M.H.; Kadanoff, L.P.; Procaccia, I.; Shraiman, B.I. Fractal Measures and Their Singularities: The Characterization of Strange Sets. Phys. Rev. A 1986, 33, 1141. [Google Scholar] [CrossRef]
- Mandelbrot, B.B. Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2013; ISBN 1-4757-2763-1. [Google Scholar]
- Mandelbrott, B.B. The Fractal Geometry of Nature; Freeman: New York, NY, USA, 1982. [Google Scholar]
- Fisher, Y. Fractal Image Compression. Fractals 1994, 2, 347–361. [Google Scholar] [CrossRef]
- Turcotte, D.L. Fractals and Chaos in Geology and Geophysics; Cambridge University Press: Cambridge, UK, 1997; ISBN 0-521-56733-5. [Google Scholar]
- Martins, M.D. Distinctive Signatures of Recursion. Philos. Trans. R. Soc. B Biol. Sci. 2012, 367, 2055–2064. [Google Scholar] [CrossRef] [PubMed]
- Martins, M.D. Cognitive and Neural Representations of Fractals in Vision, Music, and Action. In The Fractal Geometry of the Brain; Di Ieva, A., Ed.; Advances in Neurobiology; Springer International Publishing: Cham, Switzerland, 2024; pp. 935–951. ISBN 978-3-031-47606-8. [Google Scholar]
- Chomsky, N. Interfaces + Recursion = Language?: Chomsky’s Minimalism and the View from Syntax-Semantics; De Gruyter Mouton: Berlin, Germany, 2007; ISBN 978-3-11-020755-2. [Google Scholar]
- Hulst, H. van der Recursion and Human Language. In Recursion and Human Language; De Gruyter Mouton: Berlin, Germany, 2010; ISBN 978-3-11-021925-8. [Google Scholar]
- Jackendoff, R.; Lerdahl, F. The Capacity for Music: What Is It, and What’s Special about It? Cognition 2006, 100, 33–72. [Google Scholar] [CrossRef]
- Lerdahl, F.; Jackendoff, R.S. A Generative Theory of Tonal Music, Reissue, with a New Preface; MIT Press: Boston, MA, USA, 1996; ISBN 0-262-26091-3. [Google Scholar]
- Martins, M.D.; Martins, I.P.; Fitch, W.T. A Novel Approach to Investigate Recursion and Iteration in Visual Hierarchical Processing. Behav. Res. 2016, 48, 1421–1442. [Google Scholar] [CrossRef] [PubMed]
- Jackendoff, R. Précis of foundations of language: Brain, meaning, grammar, evolution. Behav. Brain Sci. 2003, 26, 651–665. [Google Scholar] [CrossRef] [PubMed]
- Martins, M.D.; Bianco, R.; Sammler, D.; Villringer, A. Recursion in Action: An fMRI Study on the Generation of New Hierarchical Levels in Motor Sequences. Hum. Brain Mapp. 2019, 40, 2623–2638. [Google Scholar] [CrossRef]
- Vicari, G.; Adenzato, M. Is Recursion Language-Specific? Evidence of Recursive Mechanisms in the Structure of Intentional Action. Conscious. Cogn. 2014, 26, 169–188. [Google Scholar] [CrossRef]
- Christiansen, M.H.; Chater, N. The Now-or-Never Bottleneck: A Fundamental Constraint on Language. Behav. Brain Sci. 2016, 39, e62. [Google Scholar] [CrossRef]
- Cowan, N. The Magical Mystery Four: How Is Working Memory Capacity Limited, and Why? Curr. Dir. Psychol. Sci. 2010, 19, 51–57. [Google Scholar] [CrossRef]
- Fitch, W.T.; Friederici, A.D. Artificial Grammar Learning Meets Formal Language Theory: An Overview. Philos. Trans. R. Soc. B Biol. Sci. 2012, 367, 1933–1955. [Google Scholar] [CrossRef]
- Martins, M.D.; Fischmeister, F.P.; Puig-Waldmüller, E.; Oh, J.; Geißler, A.; Robinson, S.; Fitch, W.T.; Beisteiner, R. Fractal Image Perception Provides Novel Insights into Hierarchical Cognition. NeuroImage 2014, 96, 300–308. [Google Scholar] [CrossRef]
- Martins, M.D.; Gingras, B.; Puig-Waldmueller, E.; Fitch, W.T. Cognitive Representation of “Musical Fractals”: Processing Hierarchy and Recursion in the Auditory Domain. Cognition 2017, 161, 31–45. [Google Scholar] [CrossRef] [PubMed]
- Martins, M.D.; Fischmeister, F.P.S.; Gingras, B.; Bianco, R.; Puig-Waldmueller, E.; Villringer, A.; Fitch, W.T.; Beisteiner, R. Recursive Music Elucidates Neural Mechanisms Supporting the Generation and Detection of Melodic Hierarchies. Brain Struct. Funct. 2020, 225, 1997–2015. [Google Scholar] [CrossRef] [PubMed]
- Martins, M.D.; Laaha, S.; Freiberger, E.M.E.M.; Choi, S.; Fitch, W.T. How Children Perceive Fractals: Hierarchical Self-Similarity and Cognitive Development. Cognition 2014, 133, 10–24. [Google Scholar] [CrossRef] [PubMed]
- Martins, M.D.; Muršič, Z.; Oh, J.; Fitch, W.T. Representing Visual Recursion Does Not Require Verbal or Motor Resources. Cogn. Psychol. 2015, 77, 20–41. [Google Scholar] [CrossRef]
- Martins, M.D.; Krause, C.; Neville, D.A.; Pino, D.; Villringer, A.; Obrig, H. Recursive Hierarchical Embedding in Vision Is Impaired by Posterior Middle Temporal Gyrus Lesions. Brain 2019, 142, 3217–3229. [Google Scholar] [CrossRef]
- Rosselló, J.; Celma-Miralles, A.; Martins, M.D. Visual Recursion without Recursive Language? A Case Study of a Minimally Verbal Autistic Child. Front. Psychiatry 2025, 16, 1540985. [Google Scholar] [CrossRef]
- Fitch, W.T. Three Meanings of “Recursion”: Key Distinctions for Biolinguistics. In The Evolution of Human Language; Larson, R.K., Déprez, V., Yamakido, H., Eds.; Cambridge University Press: Edinburgh, UK, 2010; pp. 73–90. ISBN 978-0-521-51645-7. [Google Scholar]
- Hauser, M.D.; Chomsky, N.; Fitch, W.T. The Faculty of Language: What Is It, Who Has It, and How Did It Evolve? Science 2002, 298, 1569–1579. [Google Scholar] [CrossRef]
- Lobina, D.J. Recursion and the Competence/Performance Distinction in AGL Tasks. Lang. Cogn. Process. 2011, 26, 1563–1586. [Google Scholar] [CrossRef]
- Roeper, T. The Acquisition of Recursion: How Formalism Articulates the Child’s Path. Biolinguistics 2011, 5, 057–086. [Google Scholar] [CrossRef]
- Carnie, A. Syntax: A Generative Introduction; John Wiley & Sons: Hoboken, NJ, USA, 2021; ISBN 1-119-56931-1. [Google Scholar]
- Chomsky, N. Syntactic Structures; Mouton de Gruyter: Berlin, Geramny, 2002; ISBN 3-11-017279-8. [Google Scholar]
- Jackendoff, R. The Architecture of the Language Faculty; MIT Press: New York, NY, USA, 1997; ISBN 0-262-60025-0. [Google Scholar]
- Odifreddi, P. Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers; Elsevier: Amsterdam, The Netherlands, 1992; Volume 125, ISBN 0-08-088659-0. [Google Scholar]
- Koch, H.V. Sur Une Courbe Continue sans Tangente, Obtenue Par Une Construction Géométrique Élémentaire. Ark. Mat. Astron. Och Fys. 1904, 1, 681–704. [Google Scholar]
- Mandelbrot, B.B. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science 1967, 156, 636–638. [Google Scholar] [CrossRef] [PubMed]
- Matsuyama, T.; Matsushita, M. Fractal Morphogenesis by a Bacterial Cell Population. Crit. Rev. Microbiol. 1993, 19, 117–135. [Google Scholar] [CrossRef]
- Meinhardt, H. Models of Biological Pattern Formation: From Elementary Steps to the Organization of Embryonic Axes. In Current Topics in Developmental Biology; Schnell, S., Maini, P.K., Newman, S.A., Newman, T.J., Eds.; Multiscale Modeling of Developmental Systems; Academic Press: Cambridge, MA, USA, 2008; Volume 81, pp. 1–63. [Google Scholar]
- Udden, J.; Martins, M.D.; Zuidema, W.; Fitch, W.T. Hierarchical Structure in Sequence Processing: How Do We Measure It and What’s the Neural Implementation? Top. Cogn. Sci. 2019, 12, 910–924. [Google Scholar] [CrossRef]
- Dedhe, A.M.; Clatterbuck, H.; Piantadosi, S.T.; Cantlon, J.F. Origins of Hierarchical Logical Reasoning. Cogn. Sci. 2023, 47, 13250. [Google Scholar] [CrossRef]
- Dedhe, A.M.; Piantadosi, S.T.; Cantlon, J.F. Cognitive Mechanisms Underlying Recursive Pattern Processing in Human Adults. Cogn. Sci. 2023, 47, e13273. [Google Scholar] [CrossRef]
- Martins, M.D.; Bergmann, Z.V.; Bianco, R.; Sammler, D.; Villringer, A. Acquisition and Utilization of Recursive Rules in Motor Sequence Generation. Cogn. Sci. 2025, 49, e70108. [Google Scholar] [CrossRef]
- Fischmeister, F.P.; Martins, M.D.; Beisteiner, R.; Fitch, W.T. Self-Similarity and Recursion as Default Modes in Human Cognition. Cortex 2017, 97, 183–201. [Google Scholar] [CrossRef] [PubMed]
- Ravignani, A.; Westphal-Fitch, G.; Aust, U.; Schlumpp, M.M.; Fitch, W.T. More than One Way to See It: Individual Heuristics in Avian Visual Computation. Cognition 2015, 143, 13–24. [Google Scholar] [CrossRef]
- Brown, J. Some Tests of the Decay Theory of Immediate Memory. Q. J. Exp. Psychol. 1958, 10, 12–21. [Google Scholar] [CrossRef]
- Frank, M.C.; Fedorenko, E.; Lai, P.; Saxe, R.; Gibson, E. Verbal Interference Suppresses Exact Numerical Representation. Cogn. Psychol. 2012, 64, 74–92. [Google Scholar] [CrossRef] [PubMed]
- Peterson, L.; Peterson, M.J. Short-Term Retention of Individual Verbal Items. J. Exp. Psychol. 1959, 58, 193. [Google Scholar] [CrossRef] [PubMed]
- Bates, E.; Wilson, S.M.; Saygin, A.P.; Dick, F.; Sereno, M.I.; Knight, R.T.; Dronkers, N.F. Voxel-Based Lesion-Symptom Mapping. Nat. Neurosci. 2003, 6, 448–450. [Google Scholar] [CrossRef]
- Rorden, C.; Karnath, H.-O.; Bonilha, L. Improving Lesion-Symptom Mapping. J. Cogn. Neurosci. 2007, 19, 1081–1088. [Google Scholar] [CrossRef]
- Shallice, T. From Neuropsychology to Mental Structure; From Neuropsychology to Mental Structure; Cambridge University Press: New York, NY, USA, 1988; pp. xv, 462. ISBN 978-0-521-30874-8. [Google Scholar]
- Caramazza, A. On Drawing Inferences about the Structure of Normal Cognitive Systems from the Analysis of Patterns of Impaired Performance: The Case for Single-Patient Studies. Brain Cogn. 1986, 5, 41–66. [Google Scholar] [CrossRef]
- Gentner, D. Bootstrapping the Mind: Analogical Processes and Symbol Systems. Cogn. Sci. 2010, 34, 752–775. [Google Scholar] [CrossRef]
- Ruiz, F.J.; Luciano, C. Cross-domain Analogies as Relating Derived Relations among Two Separate Relational Networks. J. Exp. Anal. Behav. 2011, 95, 369–385. [Google Scholar] [CrossRef]
- Singley, M.K.; Anderson, J.R. The Transfer of Cognitive Skill; Harvard University Press: Cambridge, MA, USA, 1989; ISBN 0-674-90340-4. [Google Scholar]
- Bouvet, L.; Rousset, S.; Valdois, S.; Donnadieu, S. Global Precedence Effect in Audition and Vision: Evidence for Similar Cognitive Styles across Modalities. Acta Psychol. 2011, 138, 329–335. [Google Scholar] [CrossRef]
- Fitch, W.T.; Hauser, M.D.; Chomsky, N. The Evolution of the Language Faculty: Clarifications and Implications. Cognition 2005, 97, 179–210. [Google Scholar] [CrossRef]
- Roeper, T. The Prism of Grammar: How Child Language Illuminates Humanism; A Bradford Book: Cambridge, MA, USA, 2007; ISBN 978-0-262-18252-2. [Google Scholar]
- Fedorenko, E.; Shain, C. Similarity of Computations Across Domains Does Not Imply Shared Implementation: The Case of Language Comprehension. Curr. Dir. Psychol. Sci. 2021, 30, 526–534. [Google Scholar] [CrossRef] [PubMed]
- Fedorenko, E.; Patel, A.; Casasanto, D.; Winawer, J.; Gibson, E. Structural Integration in Language and Music: Evidence for a Shared System. Mem. Cogn. 2009, 37, 1–9. [Google Scholar] [CrossRef]
- Fadiga, L.; Craighero, L.; D’Ausilio, A. Broca’s Area in Language, Action, and Music. Ann. N. Y. Acad. Sci. 2009, 1169, 448–458. [Google Scholar] [CrossRef]
- Martins, M.; Cook, D.; Villringer, A. Recursion Beyond Language: Lexical and Arithmetic Interference in Visual Hierarchical Embedding. 2025. Available online: https://osf.io/preprints/psyarxiv/rg9hw_v1 (accessed on 6 October 2025).
- Scholz, R.; Villringer, A.; Martins, M.D. Distinct Hippocampal and Cortical Contributions in the Representation of Hierarchies. eLife 2023, 12, e87075. [Google Scholar] [CrossRef]
- Friederici, A.D. Hierarchy Processing in Human Neurobiology: How Specific Is It? Phil. Trans. R. Soc. B 2020, 375, 20180391. [Google Scholar] [CrossRef] [PubMed]
- Friederici, A.D. Evolutionary Neuroanatomical Expansion of Broca’s Region Serving a Human-Specific Function. Trends Neurosci. 2023, 46, 786–796. [Google Scholar] [CrossRef] [PubMed]
- Skeide, M.A.; Friederici, A.D. The Ontogeny of the Cortical Language Network. Nat. Rev. Neurosci. 2016, 17, 323–332. [Google Scholar] [CrossRef]
- Fitch, W.T.; Hauser, M.D. Computational Constraints on Syntactic Processing in a Nonhuman Primate. Science 2004, 303, 377–380. [Google Scholar] [CrossRef]
- Uddén, J.; Ingvar, M.; Hagoort, P.; Petersson, K.M. Implicit Acquisition of Grammars with Crossed and Nested Non-adjacent Dependencies: Investigating the Push-down Stack Model. Cogn. Sci. 2012, 36, 1078–1101. [Google Scholar] [CrossRef]
- Ferrigno, S.; Cheyette, S.J.; Carey, S. Do Humans Use Push-Down Stacks When Learning or Producing Center-Embedded Sequences? Cogn. Sci. 2025, 49, e70112. [Google Scholar] [CrossRef]
- Perfors, A.; Tenenbaum, J.B.; Regier, T. The Learnability of Abstract Syntactic Principles. Cognition 2011, 118, 306–338. [Google Scholar] [CrossRef]
- Christiansen, M.H.; Chater, N. Toward a Connectionist Model of Recursion in Human Linguistic Performance. Cogn. Sci. 1999, 23, 157–205. [Google Scholar] [CrossRef]
- Christiansen, M.H.; Chater, N. Language as Shaped by the Brain. Behav. Brain Sci. 2008, 31, 489–509. [Google Scholar] [CrossRef]
- Lakretz, Y.; Dehaene, S. Recursive Processing of Nested Structures in Monkeys? Two Alternative Accounts. 2021. Available online: https://osf.io/preprints/psyarxiv/k8vws_v1 (accessed on 6 October 2025).
- Ferrigno, S.; Cheyette, S.J.; Piantadosi, S.T.; Cantlon, J.F. Recursive Sequence Generation in Monkeys, Children, U.S. Adults, and Native Amazonians. Sci. Adv. 2020, 6, eaaz1002. [Google Scholar] [CrossRef]
- Liao, D.A.; Brecht, K.F.; Johnston, M.; Nieder, A. Recursive Sequence Generation in Crows. Sci. Adv. 2022, 8, eabq3356. [Google Scholar] [CrossRef]
- Rey, A.; Fagot, J. Associative Learning Accounts for Recursive-Structure Generation in Crows. Learn. Behav. 2023, 51, 347–348. [Google Scholar] [CrossRef]
- Rey, A.; Perruchet, P.; Fagot, J. Centre-Embedded Structures Are a by-Product of Associative Learning and Working Memory Constraints: Evidence from Baboons (Papio Papio). Cognition 2012, 123, 180–184. [Google Scholar] [CrossRef]
- Berwick, R.C.; Friederici, A.D.; Chomsky, N.; Bolhuis, J.J. Evolution, Brain, and the Nature of Language. Trends Cogn. Sci. 2013, 17, 89–98. [Google Scholar] [CrossRef]
- Hagoort, P. On Broca, Brain, and Binding: A New Framework. Trends Cogn. Sci. 2005, 9, 416–423. [Google Scholar] [CrossRef]
- Friederici, A.D.; Chomsky, N.; Berwick, R.C.; Moro, A.; Bolhuis, J.J. Language, Mind and Brain. Nat. Hum. Behav. 2017, 1, 713–722. [Google Scholar] [CrossRef]
- Jeon, H.-A.; Friederici, A.D. Degree of Automaticity and the Prefrontal Cortex. Trends Cogn. Sci. 2015, 19, 244–250. [Google Scholar] [CrossRef]
- Jeon, H.-A.; Friederici, A.D. Two Principles of Organization in the Prefrontal Cortex Are Cognitive Hierarchy and Degree of Automaticity. Nat. Commun. 2013, 4, 2041. [Google Scholar] [CrossRef] [PubMed]
- Matchin, W.; Hammerly, C.; Lau, E. The Role of the IFG and pSTS in Syntactic Prediction: Evidence from a Parametric Study of Hierarchical Structure in fMRI. Cortex 2017, 88, 106–123. [Google Scholar] [CrossRef] [PubMed]
- Margulies, D.S.; Ghosh, S.S.; Goulas, A.; Falkiewicz, M.; Huntenburg, J.M.; Langs, G.; Bezgin, G.; Eickhoff, S.B.; Castellanos, F.X.; Petrides, M.; et al. Situating the Default-Mode Network along a Principal Gradient of Macroscale Cortical Organization. Proc. Natl. Acad. Sci. USA 2016, 113, 12574–12579. [Google Scholar] [CrossRef]
Paradigm Type | Domains Applied | Input/Output Structure | Dependent Measures | Advantages/Constraints |
---|---|---|---|---|
Discrimination tasks | Vision, Music, Motor | Participants choose the correct continuation versus foil alternatives | Accuracy, RT, foil-type sensitivity | Requires carefully matched controls (iteration, foils) for low-level heuristics |
Production tasks | Motor, Language | Participants extend a sequence beyond the given input without external cues | Accuracy, temporal patterns | Stronger test of internal generativity; reduces reliance on perceptual heuristics |
Interference/Dual-task | Vision | RHE combined with secondary task taxing working memory, verbal resources, etc. | ΔAcc/RT degradation under load | Identifies shared versus independent cognitive resources |
Neuropsychological/Lesion | Vision, Language | RHE with brain damage or neurodevelopmental differences | Presence/absence of RHE, domain dissociations | Reveals necessity of systems |
Neuroimaging paradigms | Vision | Discrimination/production tasks adapted for fMRI/EEG, focusing on recursive step transitions | BOLD/ERP responses during rule application | Identifies shared/distinct neural resources; Must isolate generative processing from perceptual input |
Domain-Population | Paradigm | RHE/ITE (Mean Acc) | Performance Patterns |
---|---|---|---|
Vision—Adults [13] | Discrimination | R: 82%, I: 92% | RHE: ↑ learning curves; slow strategies more accurate; correlated with ToH; ITE correlated with SpWM. |
Vision—Children [23] | Discrimination | 7–8 yrs: R: 59%, I: 62% 9–10 yrs: R: 80%, I: 78% Order I→R (ΔR: ↑24%) | RHE: ↑ learning curves; scaffolded by ITE. RHE & ITE correlated with 1-level linguistic embedding (controlling for IQ). |
Auditory— Non-musicians & Musicians [21] | Discrimination | Non-mus: R: 71%, I: 70% Musicians: R: 84% | RHE: ↑ learning curves; strong expertise effect; correlated with visual RHE and ToH. |
Motor—Adults [42] | Discrimination & production (2-day training) | Disc (d2): R: 86%, I: 85% Prod (d2): R: 59%, I: 70% Prod I→R (ΔR: ↑22%) Prod d1→d2 (ΔR: ↑17%) | RHE: ↑ learning curves; Production scaffolded by ITE & boosted by sleep (d2); clustered temporal pattern. |
Vision— Lesion patients [25] | Discrimination; Lesion-symptom mapping; Drift diffusion model | R: 80%, I: 82% Order I→R (ΔR: ↑20%) | RHE (v ITE): correlated with 2-level linguistic embedding; Scaffolded by ITE; posterior lesions ↓ drift; frontal lesions ↓ boundary. |
Vision—Minimally verbal autistic child [26] | Discrimination | R: 72.2%, I: 64.8% (both pass) | RHE intact despite no linguistic syntax. ITE more fragile. |
Vision—Adults [24,61] | Discrimination dual task: - VerbalWM [24] - VisualWM [61] - Lexical retrieval [61] - Serial arithmetic [61] | Baseline [61]: R: 83%, I: 87% verbalWM [24]: R: 86% visWM [61]: R: 85%, I: 83% Lexical [61]: R: 75%, I: 70% Arith. [61]: R: 78%, I: 70% | lexical/arithmetic interference ↓ drift and boundary. RHE less affected than ITE; no verbal or visual WM interference. |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2025 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Martins, M.J.D. From Fractal Geometry to Fractal Cognition: Experimental Tools and Future Directions for Studying Recursive Hierarchical Embedding. Fractal Fract. 2025, 9, 654. https://doi.org/10.3390/fractalfract9100654
Martins MJD. From Fractal Geometry to Fractal Cognition: Experimental Tools and Future Directions for Studying Recursive Hierarchical Embedding. Fractal and Fractional. 2025; 9(10):654. https://doi.org/10.3390/fractalfract9100654
Chicago/Turabian StyleMartins, Mauricio J. D. 2025. "From Fractal Geometry to Fractal Cognition: Experimental Tools and Future Directions for Studying Recursive Hierarchical Embedding" Fractal and Fractional 9, no. 10: 654. https://doi.org/10.3390/fractalfract9100654
APA StyleMartins, M. J. D. (2025). From Fractal Geometry to Fractal Cognition: Experimental Tools and Future Directions for Studying Recursive Hierarchical Embedding. Fractal and Fractional, 9(10), 654. https://doi.org/10.3390/fractalfract9100654