A Symbolic Method to Analyse Patterns in Plant Structure

Abstract

Formal grammars such as L-systems have long been used to describe plant growth dynamics. In this article, they are used for a new purpose. The aim is to build a symbolic method that enables the computation of the stochastic distribution associated with the number of complex structures in plants whose organogenesis is driven by a multitype branching process. For that purpose, a new combinatorial framework is set in which plant structure is coded by a Dyck word. Moreover, organogenesis is represented by stochastic F0L-systems. In doing so, the problem is equivalent to determining the distribution of patterns in random words generated by a stochastic F0L-system. This method finds interesting applications in the parameter identification of stochastic models of plant development.