Theory of edges of leaves

PACS. 46.32.+x – Static buckling and instability. PACS. 46.70.Hg – Membranes, rods and strings. Abstract. – We performed experiments in which tearing pieces of plastic produced a fractal boundary. Similar patterns are commonly observed at the edges of leaves. These patterns can be reproduced by imposing metrics upon thin sheets. We present an energy functional that provides a numerical test-bed for this idea, and derive a continuum theory from it. We find ordinary differential equations that provide minimum energy solutions for long thin strips with linear gradients in metric, and verify both numerically and experimentally the correctness of the solutions. Introduction. – Ifone takes a thin piece ofplastic, such as a garbage bag, and rips it in half, the edge takes on a complicated rippled form. We recently performed a careful experimental study of torn sheets and found the edge can have a fractal character, with waves superimposed upon waves over many generations [1]. Our aim in this letter is to provide some explanations for the waves appearing in these systems.