The leaf venation as formed in a tensorial field
@article{Couder2002TheLV,
title={The leaf venation as formed in a tensorial field},
author={Yves Couder and Ludovic Pauchard and Catherine Allain and M Adda-Bedia and St{\'e}phane Douady},
journal={The European Physical Journal B - Condensed Matter and Complex Systems},
year={2002},
volume={28},
pages={135-138}
}Abstract:The veins of plant leaves exhibit a large variety of morphologies. They are often thought to result from their growth in a concentration scalar field. It is shown here that the topology of these patterns rather corresponds to what is expected from growth in a tensorial stress field. This is demonstrated by analogic experiments performed on crack formation in gel films where many characteristic venation patterns, of both dicotyledons and monocotyledons, were reproduced. This suggests… Expand
78 Citations
The Role of Elastic Stresses on Leaf Venation Morphogenesis
- Biology, Physics
- PLoS Comput. Biol.
- 2008
It is argued that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development. Expand
Hierarchical layout model for reinforcement inspired by Mechanics in leaf venation morphogenesis
- Biology
- 2011 International Conference on Remote Sensing, Environment and Transportation Engineering
- 2011
Hierarchy optimization model is proposed for reinforcement distribution of plant venation, where energy criterion, shear stress and areoles division is responsible for three ranks of veins respectively. Expand
Morphogenetic processes: from leaves to embryos
- Materials Science
- 2020
The present manuscript is devoted to two works related to the spontaneous formation of patterns in Nature: venation in leaves and evolution of embryos. Morphogenetic processes and growth-induced… Expand
Petal shapes of sympetalous flowers: the interplay between growth, geometry and elasticity
- Physics
- 2012
The growth of a thin elastic sheet imposes constraints on its geometry such as its Gaussian curvature KG. In this paper, we construct the shapes of sympetalous bell-shaped flowers with a constant… Expand
In silico leaf venation networks: growth and reorganization driven by mechanical forces.
- Biology, Medicine
- Journal of theoretical biology
- 2009
The results suggest that the local structure of venation networks results from a reorganization driven by mechanical forces, independently of how veins form, supported by recent observations of vein development in young leaves and by the good quantitative agreement between simulations and data from mature leaves. Expand
A constant production hypothesis guides leaf venation patterning.
- Biology, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 2006
The consequences of the hypothesis that auxin is produced at a constant rate in every cell are determined and the model further implies the Sachs Canalization Hypothesis and resolves a dilemma regarding the role of auxin in cell growth. Expand
Modeling and visualization of leaf venation patterns
- Mathematics
- SIGGRAPH 2005
- 2005
We introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards… Expand
Modeling and visualization of leaf venation patterns
- Computer Science
- SIGGRAPH '05
- 2005
A class of biologically-motivated algorithms for generating leaf venation patterns that simulate the interplay between three processes, including development of veins towards hormone (auxin) sources embedded in the leaf blade, and modification of both the vein pattern and source distribution by leaf growth. Expand
The origin of the diversity of leaf venation pattern
- Biology, Medicine
- Developmental dynamics : an official publication of the American Association of Anatomists
- 2006
A mathematical model based on the positive feedback regulation between plant hormone auxin and its efflux carrier can produce diverse leaf venation patterns with spatial regularity under similar conditions to those of leaf development, that is, in the presence of leaf expansion and auxin sink. Expand
The Mechanics of Leaf Growth on Large Scales
- Materials Science
- 2018
Leaf growth is a process during which the leaf expands by many orders of magnitude, while maintaining a proper shape. Complex mechanisms which are not fully understood regulate the local, individual… Expand
References
SHOWING 1-7 OF 7 REFERENCES
Pattern Formation in Plant Tissues
- Biology
- 1991
This chapter discusses the interactions of developing organs and Hormones as correlative agents with respect to pattern formation, and some of the findings are surprising. Expand
Couder in: Branching in Nature
- 2001
in: Branching in Nature, edited by V
- Fleury et al. (Springer-EDP Sciences,
- 2001
Perspectives in Fluid Dynamics, edited by G.K
- 2000
in: Positional controls in plant development, edited by W
- Barlow, D.J. Carr (Cambridge University Press,
- 1984
Proc
- Nat. Acad. Sci. 98,