Universal Veins

Despite the stunning diversity of leaf shapes from one plant variety to another, a universal formula may guide the vein patterns in all leaves. Researchers at the Laboratorie de Physique Statistique (S. Bohn, 33-1-4432-3447, bohn@lps.ens.fr) and the Museum National d'Historie Naturalle, both in Paris, recently studied the networks of veins in leaves from several plant types.

An analysis of leaf vein networks revealed simple relationships between the angles that veins form when they intersect and the thickness of the veins at the intersections. At a three-way junction of similarly sized veins, the angles between the veins are all roughly 120 degrees (see image). At locations where a small vein joins a large vein, however, the angles between the small vein and the larger one approach 90 degrees.

Imagine, for example, the angles formed by pulling on a light thread tied to a taut rope. The similarity between a network of threads and ropes exerting forces on each other and the patterns in leaf veins suggested to the researchers that there is an underlying mechanism in leaf formation that is reminiscent of simple mechanics problems.

The model breaks with theories of leaf networks related to soap froths (which require all intersection angles to equal 120 degrees), crack propagation (with 90 degree intersections where new cracks meet old cracks), and Turing diffusion (which leads to patterns that resemble spreading tree branches, rather than the net-like patterns found in leaf veins). Some botanists had considered leaf veins as potential tools for categorizing plants.

The universal similarity of vein structure from one plant to another suggests that the patterns provide insight to leaf mechanics, but are of little help in distinguishing or cataloging plants. (S. Bohn et al., Phys. Rev. E, June 2002.)