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.

[1]  Maurice Goursat,et al.  The dynamic equations of the tree morphogenesis GreenLab model , 2003 .

[2]  A. Bell,et al.  Plant Form: An Illustrated Guide to Flowering Plant Morphology , 1991 .

[3]  Alvy Ray Smith,et al.  Plants, fractals, and formal languages , 1984, SIGGRAPH.

[4]  Paul-Henry Cournède,et al.  Structural Factorization of Plants to Compute Their Functional and Architectural Growth , 2006, Simul..

[5]  D. Barthélémy,et al.  Plant architecture: a dynamic, multilevel and comprehensive approach to plant form, structure and ontogeny. , 2007, Annals of botany.

[6]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[7]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[8]  Winfried Kurth,et al.  Growth grammars simulating trees - an extension of L-systems incorporating local variables and sensitivity , 1997 .

[9]  Y. Guédon,et al.  Pattern analysis in branching and axillary flowering sequences. , 2001, Journal of theoretical biology.

[10]  Oliver Deussen,et al.  Digital Design of Nature - Computer Generated Plants and Organics , 2010, X.media.publishing.

[11]  H. Jones,et al.  Plants and Microclimate. , 1985 .

[12]  P. de Reffye,et al.  A dynamic, architectural plant model simulating resource-dependent growth. , 2004, Annals of botany.

[13]  Veva Elwell,et al.  Toxicity and Anti-Inflammatory Activity of Phenolic-Rich Extract from Nopalea cochenillifera (Cactaceae): A Preclinical Study on the Prevention of Inflammatory Bowel Diseases , 2023, Plants.

[14]  A. Lindenmayer,et al.  Developmental models of herbaceous plants , 1990 .

[15]  Bao-Gang Hu,et al.  Interactive simulation of plant architecture based on a dual-scale automaton model , 2003 .

[16]  A. Lindenmayer.  Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[17]  P. de Reffye,et al.  Parameter optimization and field validation of the functional-structural model GREENLAB for maize. , 2006, Annals of botany.

[18]  Marc Jaeger,et al.  Plant models faithful to botanical structure and development , 1988, SIGGRAPH.

[19]  Aristid Lindenmayer,et al.  Mathematical Models for Cellular Interactions in Development , 1968 .

[20]  Paul-Henry Cournède,et al.  Analytical study of a stochastic plant growth model: Application to the GreenLab model , 2008, Math. Comput. Simul..