Nature’s forms are frilly, flexible, and functional

A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This seen leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from perspective non-Euclidean plate theory. identify novel type defect, branch-point normal map, that allows for generation such complex wrinkling patterns elastic hyperbolic surfaces, even absence stretching. argue branch points are natural defects sheets, they carry topological charge which gives them degree robustness, can influence overall surface without concentrating energy. develop theory their role determining mechanical response sheets to weak external forces.