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
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.
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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