A Stochastic Language for Plant Topology

The article describes a stochastic formal language adapted to the botanical concepts underlying the GreenLab organogenesis model. It is based on stochastic L-systems (parallel rewriting grammars) and on multi-type branching processes: stochastic processes control bud productions and at each growth cycle, each new growth unit is the result of a random variable. This formalism allows determining inductively the generating functions of the resulting plant structures and of the numbers of organs, which fully characterizes the plant development resulting from the elementary stochastic processes of bud productions. The moments of the stochastic distributions of the numbers of organs are also explicitly deduced.