During limb development, digits emerge from the undifferentiated mesenchymal tissue that constitutes the limb bud. It has been proposed that this process is controlled by a self-organizing Turing mechanism, whereby diffusible molecules interact to produce a periodic pattern of digital and interdigital fates. However, the identities of the molecules remain unknown. By combining experiments and modeling, we reveal evidence that a Turing network implemented by Bmp, Sox9, and Wnt drives digit specification. We develop a realistic two-dimensional simulation of digit patterning and show that this network, when modulated by morphogen gradients, recapitulates the expression patterns of Sox9 in the wild type and in perturbation experiments. Our systems biology approach reveals how a combination of growth, morphogen gradients, and a self-organizing Turing network can achieve robust and reproducible pattern formation.