The leaf venation as formed in a tensorial field

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.