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When visual input has conflicting interpretations, conscious perception can alternate spontaneously between competing interpretations [1]. There is a large amount of unexplained variability between individuals in the rate of such spontaneous alternations in perception [2–5]. We hypothesized that variability in perceptual rivalry might be reflected in individual differences in brain structure, because brain structure can exhibit systematic relationships with an individual's cognitive experiences and skills [6–9]. To test this notion, we examined in a large group of individuals how cortical thickness, local gray-matter density, and local white-matter integrity correlate with individuals' alternation rate for a bistable, rotating structure-from-motion stimulus [10]. All of these macroscopic measures of brain structure consistently revealed that the structure of bilateral superior parietal lobes (SPL) could account for interindividual …