Deborah J. Aks, University of Wisconsin–Whitewater, Whitewater, WI
Gregory J. Zelinsky, State University of New York, Stony Brook, NY
Julien C. Sprott, University ofWisconsin – Madison, Madison, WI

Abstract: 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.

Keywords: visual search, eye-movements, attention, Fourier analysis, pink noise, self-organized criticality