The brain's visual cortex processes information concerning form, pattern, and motion within functional maps that reflect the layout of neuronal circuits. We analyzed functional maps of orientation preference in the ferret, tree shrew, and galago--three species separated since the basal radiation of placental mammals more than 65 million years ago--and found a common organizing principle. A symmetry-based class of models for the self-organization of cortical networks predicts all essential features of the layout of these neuronal circuits, but only if suppressive long-range interactions dominate development. We show mathematically that orientation-selective long-range connectivity can mediate the required interactions. Our results suggest that self-organization has canalized the evolution of the neuronal circuitry underlying orientation preference maps into a single common design.