Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors

Previous research on anticipatory behaviors has found that the fractal scaling of human behavior may attune to the fractal scaling of an unpredictable signal [Stephen DG, Stepp N, Dixon JA, Turvey MT. Strong anticipation: Sensitivity to long-range correlations in synchronization behavior. Physica A 2008;387:5271–8]. We propose to explain this attunement as a case of multifractal cascade dynamics [Schertzer D, Lovejoy S. Generalised scale invariance in turbulent phenomena. Physico-Chem Hydrodyn J 1985;6:623–5] in which perceptual-motor fluctuations are coordinated across multiple time scales. This account will serve to sharpen the contrast between strong and weak anticipation: whereas the former entails a sensitivity to the intermittent temporal structure of an unpredictable signal, the latter simply predicts sensitivity to an aggregate description of an unpredictable signal irrespective of actual sequence. We pursue this distinction through a reanalysis of Stephen et al.’s data by examining the relationship between the widths of singularity spectra for intertap interval time series and for each corresponding interonset interval time series. We find that the attunement of fractal scaling reported by Stephen et al. was not the trivial result of sensitivity to temporal structure in aggregate but reflected a subtle sensitivity to the coordination across multiple time scales of fluctuation in the unpredictable signal.

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