Phase transition between reactive and predictive eye movements is confirmed with nonlinear forecasting and surrogates

We previously demonstrated that there is an abrupt (rather than smooth) transition between reactive and predictive modes of eye-movement tracking of target lights (a phase transition). We also found evidence that the sequence of eye movements in the reactive mode was independent, while those in the predictive mode were correlated and possibly formed a random fractal sequence. Here, we confirm this finding by quantifying the rate of decay of nonlinear forecasting when applied to these data, and develop an extension to small data sets using surrogate data. Verification of these statistical properties in small data sets will be of great use in situations, such as the clinical testing of neurological patients, in which testing time is limited due to subject discomfort or other considerations.