Constitutive property of the local organization of leaf venation networks

The leaf venation of dicotyledons forms complex patterns. In spite of their large variety of morphologies these patterns have common features. They are formed of a hierarchy of structures, which are connected to form a reticulum. Excellent images of these patterns can be obtained from leaves from which the soft tissues have been removed. A numerical image processing has been developed, specially designed for a quantitative analysis of this type of network. It provides a precise characterization of its geometry. The resulting data reveals a surprising property of reticula's nodes: the angles between vein segments are very well defined and it is shown that they are directly related by the radii of the segments. The relation between radii and angles can be expressed very simply using a phenomenological analogy to mechanics. This local organization principle is universal; all leaf venation patterns studied show the same behavior. The results are compared with physical networks such as fracture arrays or soap froth in terms of hierarchy and reorganization.