Many natural fruits and vegetables adopt an approximately spheroidal shape and are characterized by their distinct undulating topologies. We demonstrate that various global pattern features can be reproduced by anisotropic stress-driven buckles on spheroidal core/shell systems, which implies that the relevant mechanical forces might provide a template underpinning the topological conformation in some fruits and plants. Three dimensionless parameters, the ratio of effective size/thickness, the ratio of equatorial/polar radii, and the ratio of core/shell moduli, primarily govern the initiation and formation of the patterns. A distinct morphological feature occurs only when these parameters fall within certain ranges: In a prolate spheroid, reticular buckles take over longitudinal ridged patterns when one or more parameters become large. Our results demonstrate that some universal features of fruit/vegetable patterns (e.g., those observed in Korean melons, silk gourds, ribbed pumpkins, striped cavern tomatoes, and cantaloupes, etc.) may be related to the spontaneous buckling from mechanical perspectives, although the more complex biological or biochemical processes are involved at deep levels. morphogenesis ͉ nonlinear mechanics ͉ pattern formation ͉ physical geometry S pontaneous buckling of thin films on compliant substrates can achieve numerous highly ordered patterns due to mismatched deformation (1-6), which can be manipulated in different ways (1, 7-9). Buckling may also play an important role in the morphogenesis of some plant parts, including phyllotactic pattern in compressed tunica (10, 11), primordium initiation in sunflower capitulum (12), and Fibonacci patterns resembling those in some flowering cactus and pine cones (2), among others, in a way that is similar to the energy-minimizing buckling of a compressed shell on an elastic foundation (10).Many natural fruits and vegetables can be approximated as spheroidal stiff exocarp (shell)/compliant sarcocarp (core) systems, which exhibit intriguing buckle-like profiles. For example, the Korean melon (yellow melon) and ridged gourd (or silk gourd, luffa acutangula) are distinguishable by 10 equidistant longitudinal ridges that run from stem to tip. Small pumpkins, acorn squashes, and carnival squashes often have ϳ10 uniformly spaced ribs, whereas the large pumpkins often have ϳ20 or more ridges. Similar undulating morphologies found in varieties of cucumis melons, gourds, striped cavern tomatoes, bell peppers, and other fruits and vegetables underpin their distinctive appearances. Although pattern formation in plants usually involves various complex biological and biochemical processes (11,13,14), such distinctive yet simple features make one wonder whether there exist other relatively simpler mechanisms contributing to the morphogenesis at the macroscopic scale, and the possibility of stress-driven buckling is explored in this study.Consider a model spheroidal core/shell system where the shell is characterized by (x 2 ϩ y 2 )/a 2 ϩ z 2 /b 2 ϭ 1 with equator...
