Abstract: This article details a two-step method of quantifying eye movement transitions between areas of interest (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 from two studies, during free viewing of classical art paintings. Normalized Shannon's entropy, derived from individual transition matrices, is related to participants' individual differences as well as to either their aesthetic impression or recognition of artwork. Low transition and high stationary entropies suggest greater curiosity mixed with a higher subjective aesthetic affinity toward artwork, possibly indicative of visual scanning of the artwork in a more deliberate way. Meanwhile, both high transition and stationary entropies may be indicative of recognition of familiar artwork.