Memory Across Eye-Movements: 1/f Dynamic in Visual Search

D. J. Aks
Department of Psychology, University of Wisconsin -  Whitewater, Whitewater, WI

G. J. Zelinsky
Department of Psychology, State University of New York, Stony Brook, NY

J. C. Sprott
Department of Physics, University of Wisconsin - Madison, Madison, Wisconsin


The ubiquity of apparently random behavior in visual search (e.g., Horowitz & Wolfe, 1998) has led to our proposal that the human oculomotor system has subtle deterministic properties that underlie its complex behavior. We report the results of one subject's performance in a challenging search task in which 10,215 fixations were accumulated. A number of statistical and spectral tests revealed both fractal and 1/f structure. First, scaling properties emerged in differences across eye positions and their relative dispersion (SD/M)--both decreasing over time. Fractal microstructure also emerged in an iterated function systems test and delay plot. Power spectra obtained from the Fourier analysis of fixations produced brown (1/f2) noise and the spectra of differences across eye positions showed 1/f (pink) noise. Thus, while the sequence of absolute eye positions resembles a random walk, the differences in fixations reflect a longer-term dynamic of 1/f pink noise. These results suggest that memory across eye-movements may serve to facilitate our ability to select out useful information from the environment. The 1/f patterns in relative eye positions together with models of complex systems (e.g., Bak, Tang & Wiesenfeld, 1987) suggest that our oculomotor system may produce a complex and self-organizing search pattern providing maximum coverage with minimal effort.

Ref: D. J. Aks, G. J. Zelinsky, and J. C. Sprott, Nonlinear Dynamics, Psychology, and Life Sciences 6, 1-25 (2002).

The complete paper is available in PDF format.

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