Eur. Phys. J. B 28, 135-138 (2002)
https://doi.org/10.1140/epjb/e2002-00211-1

The leaf venation as formed in a tensorial field

¹ Laboratoire de Physique Statistique (Associé au CNRS et aux Universités Paris VI et Paris VII) , École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
² Laboratoire FAST (Unité mixte de Recherche Paris VI, Paris XI et CNRS, bâtiment 502) , Campus Universitaire, 91405 Orsay Cedex, France

Corresponding author: ^a couder@physique.ens.fr

Received: 11 March 2002
Published online: 19 July 2002

Abstract

The veins of plant leaves exhibit a large variety of morphologies. They are often thought to result from their growth in a concentration scalar field. It is shown here that the topology of these patterns rather corresponds to what is expected from growth in a tensorial stress field. This is demonstrated by analogic experiments performed on crack formation in gel films where many characteristic venation patterns, of both dicotyledons and monocotyledons, were reproduced. This suggests, for the origin of the veins formation, a set of hypotheses which is new but supported by known physiological data.