Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 12, Iss. 4, October, 2008, pp. 371-395
@2008 Society for Chaos Theory in Psychology & Life Sciences


The Emergence of Dynamic Form Through Phase Relations in Dynamical Systems

Thomas E. Malloy, University of Utah
Jonathan Butner, University of Utah
Gary C. Jensen, University of Utah

Abstract: Theories of visual form have been plagued with the problem of the correspondence between aspects of the form across time and across spatial location. Following Bateson”s idea that knowledge emerges from the relations among multiple flows of difference, our computational model illustrates how visual form can emerge from the phase relations between two such flows in a way that eliminates the correspondence problem. Computationally, the first flow of process in a Boolean network falls into one among many different attractor cycles each of which cycles at a given fundamental frequency. A second cyclic systemic flow, with its own frequency, is computationally necessary before a person can experience the patterns (transients, attractors) of the first flow on a computer monitor; and the frequency of this second flow is a control variable. Dynamic visual form, in this computational logic, emerges from the phase relations between the frequencies of the two flows. These dynamic forms exhibit, simultaneously, many kinds of apparent motion suggesting that the processes generating apparent motion are not merely illusions but are in the service of dynamic form perception. This model of perceptual organization and moving form is discussed in relation to other approaches.

Keywords: Dynamic form perception, perceptual organization, correspondence problem, dynamical systems, phase relations, Boolean simulations, emergence