A natural programmable metamaterial controls 3D curvature of compound eyes.

Panoramic vision of the convex compound eyes, common to insects and crustaceans, relies on micrometer-scale curvature variations. These variations generate specialized visual zones adapted to specific tasks, including detecting prey, mates, or predators. However, how such fine-scale curvature is encoded during development remains unknown. We find in Drosophila melanogaster that the basal surface of the developing retina is organized as a supracellular triangular mesh where the size of these triangles is distributed in a species-specific 2D pattern. Functional experiments using genetic perturbations, together with computational modeling, support the notion that this pattern guides adult eye local curvature. A similar pattern in the Drosophila mauritania developing retina indicates an evolutionary conservation of this mechanism. Our findings identify a mechanism of morphogenesis where fine-scale 3D curvature is programmed in the 2D patterning of a tissue with metamaterial properties. This mechanism provides a framework for designing shape-programmable 3D biological surfaces, with broad implications from synthetic morphogenesis to clinical applications.