Characterization of architectural tree models using L-systems and Petri nets

We propose a symbolic notation inspired by L−systems and a graphical representation based on Petri nets to formally describe architectural tree models introduced by Hallé and Oldeman (HO models). The two formalisms are related, but lead to visually different model presentations and are preferable in different applications. Specifically, L−systems are useful as an input for simulation programs, whereas Petri net graphs lend themselves to more intuitive comprehension of some aspects of the models. We focus on the developmental fate of the apices, configuration of the branching points, and plagiotropy and orthotropy of tree axes as the key characteristics of HO models. Contrary to the original HO classification, we do not consider the distinction between continuous and rhythmic growth. With this limitation, in this paper we are able to characterize most HO models using L−systems and Petri nets.