Constitutive property of the local organization of leaf venation networks

Institut de Syste ´matique, Museum National d’Histoire Naturelle, Laboratoire de Phanerogamie, 16 rue Buffon, 75005 Paris, France~Received 22 December 2001; published 28 June 2002!The leaf venation of dicotyledons forms complex patterns. In spite of their large variety of morphologiesthese patterns have common features. They are formed of a hierarchy of structures, which are connected toform a reticulum. Excellent images of these patterns can be obtained from leaves from which the soft tissueshave been removed. A numerical image processing has been developed, specially designed for a quantitativeanalysis of this type of network. It provides a precise characterization of its geometry. The resulting datareveals a surprising property of reticula’s nodes: the angles between vein segments are very well defined andit is shown that they are directly related by the radii of the segments. The relation between radii and angles canbe expressed very simply using a phenomenological analogy to mechanics. This local organization principle isuniversal; all leaf venation patterns studied show the same behavior. The results are compared with physicalnetworks such as fracture arrays or soap froth in terms of hierarchy and reorganization.DOI: 10.1103/PhysRevE.65.061914 PACS number~s!: 87.90.1y, 05.65.1b, 89.75.FbI. INTRODUCTION