Abstract: The paper introduces a two-step method of quantifying eye movement transitions between Areas of Interests (AOIs). First, individuals' gaze switching patterns, represented by fixated AOI sequences, are modeled as Markov chains. Second, Shannon's entropy coefficient of the fit Markov model is computed to quantify the complexity of individual switching patterns. To determine the overall distribution of attention over AOIs, the entropy coefficient of individuals' stationary distribution of fixations is calculated. The novelty of the method is that it captures the variability of individual differences in eye movement characteristics, which are then summarized statistically. The method is demonstrated on gaze data collected during free viewing of classical art paintings. Shannon's coefficient derived from individual transition matrices is significantly related to participants' individual differences as well as to their aesthetic experience of art pieces.