The mechanics behind the beauty of roses

Abstract

Nature’s artistry in shaping living forms often arises from the delicate interplay between growth and geometry. From the undulating margins of lotus leaves to rippled edges of lily petals, intricate three-dimensional configurations emerge as biological tissues grow unevenly from the initial two-dimensional geometry. For decades, Gauss’s Theorema Egregium—a geometrical theory that links intrinsic curvature of a surface to measurements of its distance and angle—has served as the cornerstone for understanding such morphogenesis (1, 2). On page 520 of this issue, Zhang et al. (3) report a distinct mechanism underlying the formation of sharp cusps of rose petals that deviates from this classical incompatibility. This discovery reframes understanding of how geometrical constraints sculpt biological forms and opens new avenues for engineering shape-shifting materials.