A Markovian framework to formalize stochastic L-systems and application to models of plant development

This document is an extension of the article written by \textit{Loi and Cournède} (DMTCS, 2008). This article shows the relationship between stochastic L-Systems and a simplified GreenLab growth model with only branching and differentiation. By writing the probability generating function corresponding to each phenomenon and by compounding them, we get the expected values of the numbers of metamers of each type in the whole plant. In this report, we recall the main results of this article. In addition, we show how to derive the generating function in the general case when growth units contain a random number of metamers. We also get a recursive equation to compute the variance of the numbers of metamers of each type in the plant. Finally, we illustrate the results throughout Monte-Carlo simulations in four cases