The shape of a rose petal

The rose petal has a distinctive set of sharp bends along the edges of its outer petals. To understand the origin of this growth pattern, we dissect rose petals to show that the their Gaussian curvature changes from positive to negative toward the outer edges. Using scaling and stability analysis, we show that a curved “sonic" line controls the shape and location of edge buckling, which is itself driven by in-plane growth. We verify our results by numerically solving the nonlinear elastic equations associated with the growing surface. Our analysis suggests a method of designing buckled edge structures with controlled in-plane growth.