Morphogenesis as Eigen-Configuration: A Topological Theory of Form

Why do complex systems—from crystals to organisms—settle into stable, recurring forms? This paper presents a mathematical framework in which stable morphologies are understood as eigen- configurations of an underlying relational network, termed the causal graph. We define a Morphogenetic Potential, U(s), which quantifies the degree of internal causal conflict within a system configuration . The local minima of this potential—the eigen-configurations—correspond to attractor states that define discrete, stable forms. This model provides a topological account of morphogenesis: the process of form generation is the relaxation of the system down the gradient of U to a nearby eigen-configuration. We show that this framework naturally explains the discreteness of natural forms, the existence of morphological repertoires, and the convergence properties of developing systems. The model is static and ahistorical, serving as the foundation for a dynamic extension incorporating historical habit (treated in a companion paper).