Some Mathematics

Plants as Mathematical Objects

In order to generate a mathematical description of branching structures, we need formulations coming from statistics because of the underlying random processes of parameters such as branching frequency, growth direction and/or the lengths of the branches. The same case arises for quantitatively describing plant populations. In this chapter we will discuss these methods, first for single branching structures and later for plant populations.

Firstly, one can divide and organize branching characteristics into different classification systems. For example, such descriptions indicate the frequency of the branching of a plant or a river on a specific branching level. The results serve the quantitative analysis of branching structures as well as the synthetic production of plants.

Secondly, plant geometry can be still more generally described. Here Benoit Mandelbrot laid the groundwork with the definition and application of the term “fractal” . In connection with fractal analysis, abstract branching structures and also real trees are assigned fractal dimensions, which permits us to compare them to other natural objects with fractal characteristics.