Complex behavior in perceptual line length

There is ample evidence to show that nonlinear dynamical or chaotical properties underlie aspects of physiology, neurology, and even behavior. This paper presents a psychophysical "cascading" experiment in which the response is passed on to the next trial as the new stimulus. The time series of response is modeled by a nonlinear psychophysical model based on an existing recursive cubic polynomial function called the "Γ recursion" originated by Robert Gregson. The responses in the cascading experiment are found to be classified into three categories, and some show the trace of chaos. However, the attempt to model the time series with the new model or the original Γ recursion resulted only in coarse approximations to the data. In spite of its inadequacy at simulating the time series itself, the new model managed to simulate the autocorrelation functions of the original data. These results suggest that the model we propose is in some sense within the same family of dynamical systems as the psychophysical dynamical system generating the observed data although it is necessary to develop more subtle nonlinear dynamical models.