In perceptual rivalry such as ambiguous figure perception and binocular rivalry, the conscious percept spontaneously alternates between two stable interpretations of an unchanging stimulus. It is well known that the time intervals of the perceptual alternation follow a gamma distribution (GD), but its implication for the alternation mechanism has not been clarified. We examined quantitatively GDs fitted to alternation intervals, and found that the shape-determining parameter alpha of the GDs took natural numbers. Because a GD determined by a natural number alpha is mathematically obtained from a discrete stochastic process (Poisson process), our result indicates that such a stochastic process underlies perceptual rivalry and that the alpha-time accumulation of the discrete events causes a perceptual alternation.