Leaves and ramification

Abstract

Leaf veins have two main functions: they constitute the mechanical reinforcement system and the transport system. To analyse the vein pattern it is necessary to have a - as far as possible - quantitative description of the vein system of real leaves. Quantities used in modern plant anatomy have to be completed by measurements of the fractality of the ramification system (as grid dimension and as exponent of scaling) and by a measure for the partition of the leaf area and the complexity of the patch pattern which we call the supply coefficient. The leaf venation pattern is a result of the evolutionary process. To find out criteria of a relative optimization during this process, we used simple models of the ramification of leaves. By computer methods such models were tested regarding their quality as a reinforcement system. In real leaves. there must be compromises between reinforcement and transport functions. The quantities used to describe the leaf vein systems can be applied to other reticulate sytems. We selected street nets of towns , and some comparisons between the ramification systems of leaves and of towns show similarities and differences which are discussed.