Continuous phase transitions in the perception of multistable visual patterns.

The phenomenon of stroboscopic alternative motion exhibits five different percepts that are seen with an increase in the frequency of presentation: (a) succession, (b) fluttering motion, (c) reversible clockwise and counter-clockwise turning motion, (d) oppositional motion and (e) simultaneity. From a synergetic point of view the increase in frequency is a control parameter and the different percepts are order parameters with phase transitions in between. The neural network model of Carmesin and Arndt is applied to receive predictions about hysteresis and phase transitions between these order parameters. Empirical data show the different motion percepts (b), (c) and (e) have lognormal distributions. Following the theoretical model, it is argued that there are three different phases, (a), (c) and (e), with two continuous phase transitions, (b) and (d), between them. The experimental data substantially match the theoretical assumptions.

A neural network model for stroboscopic alternative motion.

A neural network which models multistable perception is presented. The network consists of sensor and inner neurons. The dynamics is established by a stochastic neuronal dynamics, a formal Hebb-type coupling dynamics and a resource mechanism that corresponds to saturation effects in perception. From this a system of coupled differential equations is derived and analyzed Single stimuli are bound to exactly one percept, even in ambiguous situations where multistability occurs. The network exhibits discontinuous as well as continuous phase transitions and models various empirical findings, including the percepts of succession, alternative motion and simultaneity, the percept of oscillation is explained by oscillating percepts of a continuous phase transition.