We conceptualize personality and individual variation from the perspective of dynamical systems. People's thoughts, feelings, and predispositions for action are inherently dynamic, displaying constant change due to internal mechanisms and external forces, but over time the flow of thought and action converges on a narrow range of states--a fixed-point attractor--that provides cognitive, affective, and behavioral stability. An attractor for personal dynamics develops through two mechanisms: the synchronization of individuals' internal states in social interaction, and the self-organization of thoughts and feelings with respect to a higher-order property (e.g., goal, self-concept). We present formal models of both processes and instantiate each in computer simulations. Discussion centers on the implications of interpersonal synchronization and self-organization dynamics for issues in personality psychology, including shared vs. non-shared environmental influences on personality development, the expression of personality in social interaction, personal stability vs. change, personal vs. situational causation, and the emergence of self-concept.