Artificial morphogenesis of curved surface structures inspired by differential growth in biology.

Abstract

From the elegant petals of flowers to advanced aerospace designs, curved surfaces are fundamental to both natural and engineered systems, playing critical roles in structural and functional performance. In biology, these surfaces frequently arise from differential growth processes, where spatially varying growth rates orchestrate the transformation of flat tissues into intricate three-dimensional forms, exemplified by leaf curling or organ development. Engineering such surfaces, however, remains challenging, as current methods are energy-intensive, material-heavy, and lack the efficiency and adaptability seen in natural systems. Here, we demonstrate an artificial morphogenesis methodology that fabricates curved surfaces from planar materials by programming area change rates calculated through conformal mapping. Using heat-shrink film, we three-dimensionally-printed precisely patterned non-shrinking elements to implement calculated area change rate distributions, ensuring precision and reproducibility. This method enables the design and production of diverse target shapes using adaptable materials that maintain their shape even in dry environments. Compared with conventional techniques, this approach reduces material waste, eliminates the need for moulds and offers high adaptability. This bioinspired framework bridges biological principles with modern fabrication techniques, advancing curved surface design. Potential applications include adaptive medical implants for minimally invasive surgeries, lightweight aerospace structures and soft robotic skins with real-time adaptability.