When a different pattern is presented to each eye, the perceived image spontaneously alternates between the two patterns (binocular rivalry); the dynamics of these bistable alternations are known to be stochastic. Examining multistable binocular rivalry (involving four dominant percepts), we demonstrated path dependence and on-line adaptation, which were equivalent whether perceived patterns were formed by single-eye dominance or by mixed-eye dominance. The spontaneous perceptual transitions tended to get trapped within a pair of related global patterns (e.g., opponent shapes and symmetric patterns), and during such trapping, the probability of returning to the repeatedly experienced patterns gradually decreased (postselection pattern adaptation). These results suggest that the structure of global shape coding and its adaptation play a critical role in directing spontaneous alternations of visual awareness in perceptual multistability.