Generation and visualization of root-like structures in a three-dimensional space

In his Notebooks Leonardo da Vinci describes his diameter squared rule for the branching of above-ground tree parts. We now apply this branching-rule to the study of root-branching. Repeated application of this rule in a recursive computer program (ArtRoot) produces the diameters of the branches. An algorithm in this recursive program calculates the orientation of the branches in a three-dimensional space. From these data three-dimensional root-like structures are visualized by a computer program (PLUTON) designed to draw three-dimensional molecular structures. The visualization shows that starting from a relatively simple, symmetrical structure of dichotomous branching, more complex, asymmetrical root-like structures arise even if only a few parameter values are changed. The introduction of randomness into parameter values produces structures that differ considerably in their architecture. An extra force has been added in order to influence the orientation of new branches in space and to increase the flexibility of the structure formation.