Alan Turing, in “The Chemical Basis of Morphogenesis” [Turing AM (1952) Philos Trans R Soc Lond 237(641):37–72], described how, in circular arrays of identical biological cells, diffusion can interact with chemical reactions to generate up to six periodic spatiotemporal chemical structures. Turing proposed that one of these structures, a stationary pattern with a chemically determined wavelength, is responsible for differentiation. We quantitatively test Turing’s ideas in a cellular chemical system consisting of an emulsion of aqueous droplets containing the Belousov–Zhabotinsky oscillatory chemical reactants, dispersed in oil, and demonstrate that reaction-diffusion processes lead to chemical differentiation, which drives physical morphogenesis in chemical cells. We observe five of the six structures predicted by Turing. In 2D hexagonal arrays, a seventh structure emerges, incompatible with Turing’s original model, which we explain by modifying the theory to include heterogeneity.