Periodic patterns are pervasive in nature, so how are they are formed during development? Almost seventy years ago, Alan Turing described how periodicity could arise simply from the interaction of two diffusing morphogens [in so-called reaction-diffusion (RD) systems]. RD morphogen pairs have since been identified in numerous contexts, but many developmental patterning systems involve more than just two morphogens. Now, Andrew Economou, Nicholas Monk and Jeremy Green explore how FGF, Hedgehog, Wnt and BMP morphogens contribute to the striped pattern of mouse rugae (ridges on the roof of the mouth). Chemical inhibition of any one of these pathways alters the striped pattern, and direct transcriptional targets of the pathways are also expressed periodically. The observed inhibition patterns cannot be explained by pairs of morphogens acting in classical two-component systems. Thousands of potential networks made up of three or more components were then constrained by accounting for the periodicity, phase and perturbation responses of the pattern in vivo. An additional level of constraint was provided by a time series of in situ hybridisations, which revealed the temporal dynamics of the four pathways. Out of an original 39,755 network topologies, 154 are consistent with the observed dynamics, and all of them contain the same core interactions. Multi-morphogen RD networks can thus be effectively constrained with inputs from experimental perturbation and temporal dynamics.