Abstract
The list of psychological processes thought to exhibit fractal behavior is growing. Although some might argue that the seeming ubiquity of fractal patterns illustrates their significance, unchecked growth of that list jeopardizes their relevance. It is important to identify when a single behavior is and is not fractal in order to make meaningful conclusions about the processes underlying those patterns. The hypothesis tested in the present experiment is that fractal patterns reflect the enactment of control. Participants performed two steering tasks: steering on a straight track and steering on a circular track. Although each task could be accomplished by holding the steering wheel at a constant angle, steering around a curve may require more constant control, at least from a psychological standpoint. Results showed that evidence for fractal behavior was strongest for the circular track; straight tracks showed evidence of two scaling regions. We argue from those results that, going forward, the goal of the fractal literature should be to bring scaling behavior under experimental control.
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Abney DH, Warlaumont AS, Haussman A, Ross JM, Wallot S (2014) Using nonlinear methods to quantify changes in infant limb movements and vocalizations. Front Psychol 5:1–15
Aks DJ, Zelinsky G, Sprott JC (2002) Memory across eye-movements: 1/f dynamics in visual search. Nonlinear Dyn Psychol Life Sci 6:1–25
Anastas JR, Stephen DG, Dixon JA (2011) The scaling behavior of hand motions reveals self-organization during an executive function task. Phys A 390:1539–1545
Anderson CM, Lowen SB, Renshaw PF (2006) Emotional task-dependent low-frequency fluctuations and methylphenidate: wavelet scaling analysis of 1/f-type fluctuations in fMRI of the cerebellar vermis. J Neurosci Methods 151(1):52–61
Bak P (1997) How nature works. Oxford University Press, Oxford
Collins JJ, DeLuca CJ (1993) Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp Brain Res 95:308–318
Delignières D, Torre K (2009) Fractal dynamics of human gait: a reassessment of the 1996 data of Hausdorff et al. J Appl Physiol 106(4):1272–1279
Delignieres D, Ramdani S, Lemoine L, Torre K, Fortes M, Ninot G (2006) Fractal analyses for ‘short’ time series: a re-assessment of classical methods. J Math Psychol 50(6):525–544
Delignières D, Torre K, Lemoine L (2008) Fractal models for event-based and dynamical timers. Acta Psychol 127:382–397
Dingwell JB, Cusumano JP (2010) Re-interpreting detrended fluctuation analyses of stride-to-stride variability in human walking. Gait Posture 32(3):348–353
Eke A, Herman P, Bassingthwaighte JB, Raymond GM, Percival DB, Cannon M, Balla L, Ikrenyi C (2000) Physiological time series: distinguishing fractal noises from motions. Eur J Physiol 439:403–415
Eke A, Herman P, Kocsis I, Kozak LR (2002) Fractal characterization of complexity in temporal physiological signals. Physiol Meas 23:R1–R38
Fine JM, Likens AD, Amazeen EL, Amazeen PG (2015) Emergent coordination in complexity matching: local dynamics and global variability. J Exp Psychol Hum Percept Perform 41(3):723–737
Gates DH, Dingwell JB (2007) Peripheral neuropathy does not alter the fractal dynamics of stride intervals of gait. J Appl Physiol 102(3):965–971
Gilden DL (2001) Cognitive emissions of 1/f noise. Psychol Rev 108(1):33–56
Gilden DL (2009) Global model analysis of cognitive variability. Cogn Sci 33(8):1441–1467
Gilden DL, Hancock H (2007) Response variability in attention-deficit disorders. Psychol Sci 18(9):796–802
Gilden DL, Thornton T, Mallon MW (1995) 1/f noise in human cognition. Science 267:1834–1839
Goldberger AL, Amaral LAN, Hausdorff JM, Ivanov PCh, Peng C-K, Stanley HE (2002) Fractal dynamics in physiology: alterations with disease and aging. Proc Natl Acad Sci USA 99(1):2466–2472
Gorman JC, Amazeen PG, Cooke NJ (2010) Team coordination dynamics. Nonlinear Dyn Psychol Life Sci 14(3):265–289
Hausdorff JM (2009) Gait dynamics in Parkinson’s disease: common and distinct behavior among stride length, gait variability, and fractal-like scaling. Chaos Interdiscip J Nonlinear Sci 19(2):026113-1–026113-14
Hausdorff JM, Mitchell SL, Firtion R, Peng CK, Cudkowicz ME, Wei JY, Goldberger AL (1997) Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington’s disease. J Appl Physiol 82(1):262–269
Hausdorff JM, Ashkenazy Y, Peng C-K, Ivanov PCh, Stanley HE, Goldberger AL (2001) When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations. Phys A 302(1):138–147
Holden JG, Choi I, Amazeen PG, Van Orden G (2011) Fractal 1/ƒ dynamics suggest entanglement of measurement and human performance. J Exp Psychol Hum Percept Perform 37(3):935–948
Ihlen EAF, Vereijken B (2010) Interaction-dominant dynamics in human cognition: beyond 1/ƒ α fluctuation. J Exp Psychol Gen 139(3):436–463
Ivanov PC, Amaral LAN, Goldberger AL, Havlin S, Rosenblum MG, Stanley HE, Struzik ZR (2001) From 1/f noise to multifractal cascades in heartbeat dynamics. Chaos Interdiscip J Nonlinear Sci 11(3):641–652
Kello CT, Beltz BC, Holden JG, Van Orden GC (2007) The emergent coordination of cognitive function. J Exp Psychol Gen 136(4):551–568
Kello CT, Anderson GG, Holden JG, Van Orden GC (2008) The pervasiveness of 1/f scaling in speech reflects the metastable basis of cognition. Cogn Sci 32(7):1217–1231
Kelso JAS (1995) Dynamic patterns: the self-organization of brain and behavior. The MIT Press, Cambridge
Kloos H, Van Orden GC (2009) Soft-assembled mechanisms for the grand theory. In: Spencer JP, Thomas M, McClelland J (eds) Toward a new grand theory of development? Connectionism and dynamics systems reconsidered. Oxford University Press, New York, pp 253–267
Kugler PN, Turvey MT (1987) Information, natural law, and self assembly of rhythmic movement: resources for ecological psychology. Lawrence Erlbaum Associates Inc, Hillsdale
Likens AD, Amazeen PG, Stevens R, Galloway T, Gorman JC (2014) Neural signatures of team coordination are revealed by multifractal analysis. Soc Neurosci 9(3):219–234
Mandelbrot BB (1983) The fractal geometry of nature. Freeman, New York
Marmelat V, Delignières D (2012) Strong anticipation: complexity matching in interpersonal coordination. Exp Brain Res 222:137–148
Marmelat V, Torre K, Delignières D (2012) Relative roughness: an index for testing the suitability of the monofractal model. Front Physiol 3(208):1–11
Marmelat V, Delignières D, Torre K, Beek PJ, Daffertshofer A (2014) ‘Human paced’ walking: followers adopt stride time dynamics of leaders. Neurosci Lett 564:67–71
Papo D (2013) Time scales in cognitive neuroscience. Front Physiol 4(86):1–10
Peng C-K, Buldyrev SV, Havlin S, Simons S, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49:1685–1689
Peng C-K, Mietus JE, Liu Y, Lee C, Hausdorff JM, Stanley HE, Lipsitz LA (2002) Quantifying fractal dynamics of human respiration: age and gender effects. Ann Biomed Eng 30(5):683–692
Raghavendra BS, Dutt DN, Halahalli HN, John JP (2009) Complexity analysis of EEG in patients with schizophrenia using fractal dimension. Physiol Meas 30(8):795–808
Riley MA, Turvey MT (2002) Variability and determinism in motor behavior. J Mot Behav 34(2):99–125
Solé R, Goodwin B (2000) Signs of life: How complexity pervades biology. Basic Books, New York
Stephen DG, Anastas J (2011) Fractal fluctuations in gaze speed visual search. Atten Percept Psychophys 73(3):666–677
Stephen DG, Mirman D (2010) Interactions dominate the dynamics of visual cognition. Cognition 115(1):154–165
Stevens R, Gorman JC, Amazeen P, Likens A, Galloway T (2013) The organizational neurodynamics of teams. Nonlinear Dyn Psychol Life Sci 17(1):67–86
Torre K, Delignières D (2008) Distinct ways of timing movements in bimanual coordination tasks: contribution of serial correlation analysis and implications for modeling. Acta Psychol 129:284–296
Torre K, Wagenmakers E-J (2009) Theories and models of 1/f β noise in human movement science. Hum Mov Sci 28:297–318
Torre K, Delignières D, Lemoine L (2007) 1/f β fluctuations in bimanual coordination: an additional challenge for modeling. Exp Brain Res 183(2):225–234
Torre K, Balasubramaniam R, Rheaume N, Lemoine L, Zelaznik HN (2011) Long-range correlation properties in motor timing are individual and task specific. Psychon Bull Rev 18(2):339–346
Treffner P, Kelso JAS (1999) Dynamic encounters: long memory during functional stabilization. Ecol Psychol 11(2):103–137
Valdez AB, Amazeen EL (2008) Using 1/f noise to examine planning and control in a discrete aiming task. Exp Brain Res 187:303–319
Valdez AB, Amazeen EL (2009) Target dimension affects 1/f noise in aiming. Nonlinear Dyn Psychol Life Sci 13:369–392
Valdez AB, Amazeen EL (2010) Motor imagery may incorporate trial-to-trial error. J Mot Behav 42:241–256
Van Orden G (2010) Voluntary performance. Medicina 46(9):581–594
Van Orden GC, Stephen DG (2012) Is cognitive science usefully cast as complexity science? Top Cogn Sci 4(1):3–6
Van Orden GC, Holden J, Turvey MT (2003) Self-organization of cognitive performance. J Exp Psychol Gen 132:331–350
Wagenmakers E-J, Farrell S, Ratcliff R (2004) Estimation and interpretation of 1/f α noise in human cognition. Psychon Bull Rev 11(4):579–615
Wagenmakers E-J, van der Maas HL, Farrell S (2012) Abstract concepts require concrete models: why cognitive scientists have not yet embraced nonlinearly coupled, dynamical, self-organized critical, synergistic, scale-free, exquisitely context-sensitive, interaction-dominant, multifractal, interdependent brain–body–niche systems. Top Cogn Sci 4(1):87–93
Woyshville MJ, Calabrese JR (1994) Quantification of occipital EEG changes in Alzheimer’s disease utilizing a new metric: the fractal dimension. Biol Psychiatry 35(6):381–387
Yerkes RM, Dodson JD (1908) The relation of strength of stimulus to rapidity of habit-formation. J Comp Neurol Psychol 18(5):459–482
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Likens, A.D., Fine, J.M., Amazeen, E.L. et al. Experimental control of scaling behavior: what is not fractal?. Exp Brain Res 233, 2813–2821 (2015). https://doi.org/10.1007/s00221-015-4351-4
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DOI: https://doi.org/10.1007/s00221-015-4351-4