Theory of edges of leaves
Center for Nonlinear Dynamics and Department of Physics
The University of Texas at Austin, Austin TX 78712, USA
Accepted: 10 March 2003
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.
PACS: 45.70.Qj – Pattern formation / 46.32.+x – Static buckling and instability / 46.70.Hg – Membranes, rods and strings
© EDP Sciences, 2003