In the mammalian primary visual cortex, neural tuning to stimulus orientation is organized in either columnar or salt- and-pepper patterns across species. For decades, this sharp contrast has spawned fundamental questions about the origin of functional architectures in visual cortex. However, it is unknown whether these patterns reflect disparate developmental mechanisms across mammalian taxa or simply originate from variation of biological parameters under a universal development process. In this work, after the analysis of data from eight mammalian species, we show that cortical organization is predictable by a single factor, the retino-cortical mapping ratio. Groups of species with or without columnar clustering are distinguished by the feedforward sampling ratio, and model simulations with controlled mapping conditions reproduce both types of organization. Prediction from the Nyquist theorem explains this parametric division of the patterns with high accuracy. Our results imply that evolutionary variation of physical parameters may induce development of distinct functional circuitry.