The visual cortex of carnivores, primates and their close relatives processes visual information in an array of functional modules called orientation columns. Orientation columns are presumably formed during postnatal development by dynamical pattern formation mechanisms but the exact nature of the underlying processes is a matter of ongoing controversy. Mammalian species exhibiting orientation columns have been on separate evolutionary paths for more than 65 million years, during which widely varying visual cortical architectures have emerged. Here we show that the layout of orientation columns in three species separated since the basal radiation of placental mammals precisely follows a single universal design. Thus, the statistical structure of orientation column systems in ferret, galago and tree shrew is virtually indistinguishable and the average number of orientation pinwheels per hypercolumn in these species is a universal constant, 3.14 ± 0.03. We demonstrate mathematically that all features of the universal design result robustly from the developmental self-organization of cortical networks dominated by long-ranging neuronal interactions, a developmental regime that explains the apparent insensitivity of the universal design to ongoing evolutionary change. Supporting developmental robustness, the universal design also emerges in animals deprived of visual experience. We conclude that visual system evolution in carnivores and primates has favored the development of robust, self-organizing cortical networks for orientation discrimination that are attracted toward a universal design.