How do animals visually guide their activities in a cluttered environment? Gibson (1979) proposed that they perceive what environmental objects offer or afford for action. An analysis of affordances in terms of the dynamics of an animal-environment system is presented. Critical points, corresponding to phase transitions in behavior, and optimal points, corresponding to stable, preferred regions of minimum energy expenditure, emerge from variation in the animal-environment fit. It is hypothesized that these points are constants across physically similar systems and that they provide a natural basis for perceptual categories and preferences. In three experiments these hypotheses are examined for the activity of human stair climbing, by varying riser height with respect to leg length. The perceptual category boundary between "climbable" and "unclimbable" stairs is predicted by a biomechanical model, and visually preferred riser height is predicted from measurements of minimum energy expenditure during climbing. It is concluded that perception for the control of action reflects the underlying dynamics of the animal-environment system.