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,
email@example.com) and the Museum National d'Historie Naturalle, both
in Paris, recently studied the networks of veins in leaves from several
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.)