L-Py: An L-System Simulation Framework for Modeling Plant Architecture Development Based on a Dynamic Language

The study of plant development requires increasingly powerful modeling tools to help understand and simulate the growth and functioning of plants. In the last decade, the formalism of L-systems has emerged as a major paradigm for modeling plant development. Previous implementations of this formalism were made based on static languages, i.e., languages that require explicit definition of variable types before using them. These languages are often efficient but involve quite a lot of syntactic overhead, thus restricting the flexibility of use for modelers. In this work, we present an adaptation of L-systems to the Python language, a popular and powerful open-license dynamic language. We show that the use of dynamic language properties makes it possible to enhance the development of plant growth models: (i) by keeping a simple syntax while allowing for high-level programming constructs, (ii) by making code execution easy and avoiding compilation overhead, (iii) by allowing a high-level of model reusability and the building of complex modular models, and (iv) by providing powerful solutions to integrate MTG data-structures (that are a common way to represent plants at several scales) into L-systems and thus enabling to use a wide spectrum of computer tools based on MTGs developed for plant architecture. We then illustrate the use of L-Py in real applications to build complex models or to teach plant modeling in the classroom

Phyllotaxis without symmetry - what can we learn from flower heads?

A survey and model of fasciated flower heads separate fundamental and derived characteristics of phyllotactic patterns and highlight open problems in phyllotaxis research. Phyllotaxis is commonly considered in the context of circular meristems or receptacles, yet non-circular (fasciated) structures also give rise to new primordia and organs. Here we investigate phyllotactic patterns in fasciated flower heads in the Asteraceae plant family. We begin by surveying the phenomenon of fasciation. We then show that phyllotactic patterns in fasciated heads can be generated by removing the inessential assumption of circularity from the previously published model of gerbera heads. To characterize these patterns, we revisit the conceptual framework in which phyllotactic patterns are commonly described. We note that some notions, in particular parastichies and parastichy numbers, maintain their significance in non-circular phyllotaxis, whereas others, in particular the divergence angle, need to be extended or lose their role. These observations highlight a number of open problems related to phyllotaxis in general, which may be elucidated by studies of fasciated heads.Peer reviewe

L-systems in Geometric Modeling

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Une méthode structurelle pour évaluer les propriétés d autosimilarité des plantes

National audienceContexte : L'architecture d'une plante est une notion fondamentale utilisée en botanique depuis une trentaine d'années pour parler de l'organisation des structures végétales. Cette notion fait référence à deux types principaux d'information sur la plante considérés dans l'espace et le temps: la géométrie (forme) de ses composants d'une part, et leur topologie (type et adjacence de ces mêmes composants) d'autre part. De nombreux travaux botaniques se sont intéressés à la caractérisation ces deux types d'information pour différentes espèces, variétés de plantes et conditions de développement. Pourtant, il n'existe pas à ce jour de méthode générale permettant de quantifier deux aspects fondamentaux et étroitement liés de l'étude de l'architecture des plantes : - La caractérisation de l'irrégularité (parfois très prononcée) de la forme d'une plante (de sa distribution de feuilles dans l'espace par exemple). - Le degré de similarité à toutes les échelles des systèmes ramifiés contenus dans une plante

Phyllotactic patterning of gerbera flower heads

Phyllotaxis, the distribution of organs such as leaves and flowers on their support, is a key attribute of plant architecture. The geometric regularity of phyllotaxis has attracted multidisciplinary interest for centuries, resulting in an understanding of the patterns in the model plants Arabidopsis and tomato down to the molecular level. Nevertheless, the iconic example of phyllotaxis, the arrangement of individual florets into spirals in the heads of the daisy family of plants (Asteraceae), has not been fully explained. We integrate experimental data and computational models to explain phyllotaxis in Gerbera hybrida. We show that phyllotactic patterning in gerbera is governed by changes in the size of the morphogenetically active zone coordinated with the growth of the head. The dynamics of these changes divides the patterning process into three phases: the development of an approximately circular pattern with a Fibonacci number of primordia near the head rim, its gradual transition to a zigzag pattern, and the development of a spiral pattern that fills the head on the template of this zigzag pattern. Fibonacci spiral numbers arise due to the intercalary insertion and lateral displacement of incipient primordia in the first phase. Our results demonstrate the essential role of the growth and active zone dynamics in the patterning of flower heads.Peer reviewe

Mechanical Stress Induces Remodeling of Vascular Networks in Growing Leaves

International audienceDifferentiation into well-defined patterns and tissue growth are recognized as key processes in organismal development. However, it is unclear whether patterns are passively, homogeneously dilated by growth or whether they remodel during tissue expansion. Leaf vascu-lar networks are well-fitted to investigate this issue, since leaves are approximately two-dimensional and grow manyfold in size. Here we study experimentally and computationally how vein patterns affect growth. We first model the growing vasculature as a network of viscoelastic rods and consider its response to external mechanical stress. We use the so-called texture tensor to quantify the local network geometry and reveal that growth is heterogeneous , resembling non-affine deformations in composite materials. We then apply mechanical forces to growing leaves after veins have differentiated, which respond by anisotropic growth and reorientation of the network in the direction of external stress. External mechanical stress appears to make growth more homogeneous, in contrast with the model with viscoelastic rods. However, we reconcile the model with experimental data by incorporating randomness in rod thickness and a threshold in the rod growth law, making the rods viscoelastoplastic. Altogether, we show that the higher stiffness of veins leads to their reorientation along external forces, along with a reduction in growth heterogeneity. This process may lead to the reinforcement of leaves against mechanical stress. More generally , our work contributes to a framework whereby growth and patterns are coordinated through the differences in mechanical properties between cell types

In search of the right abstraction: the synergy between art, science, and information technology in the modeling of natural phenomena

in the modeling of natural phenomen