Modeling and visualization of leaf venation patterns

  title={Modeling and visualization of leaf venation patterns},
  author={Adam Runions and Martin Fuhrer and Brendan Lane and Pavol Federl and Anne-Ga{\"e}lle Rolland-Lagan and Przemyslaw Prusinkiewicz},
  journal={ACM Trans. Graph.},
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 hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of… 

Simulation and visualization of adapting venation patterns

A procedural biologically motivated method to simulate the development of leaf contours and the generation of different levels of leaf venation systems, which simulates leaf forms ranging from simple shapes to lobed leaves.

Procedural techniques for simulating the growth of plant leaves and adapting venation patterns

This paper presents biologically-motivated a procedural method for the simulation of leaf contour growth and venation development that consists of a Voronoi-Diagram that is discretised along the vein structures.

Procedural modeling and visualization of multiple leaves

An effective method of easy and intuitive modeling of various types of multiple leaves from plants, including flowering plants and trees, and of naturally visualizing them is proposed, and a color model based on convolution sums of divisor functions to naturally simulate the color patterns of leaf surfaces is introduced.


In most cases, closed venation structures deflect less than open structures, which is in line with proposals that the formation of loops in leaves relates to structural performance.

In silico leaf venation networks: growth and reorganization driven by mechanical forces.

The Role of Elastic Stresses on Leaf Venation Morphogenesis

It is argued that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development.

Modeling Plant Tissue Growth and Cell Division

This chapter introduces computational approaches for studying patterning processes driven by molecular regulatory and signaling networks on spatial, multicellular domains, including mass-spring, finite element, and Hamiltonian-based approaches.

Quantitative analysis of venation patterns of Arabidopsis leaves by supervised image analysis.

The results show the evolution of vascular traits during leaf development, suggest a self-organizing mechanism for leaf venation patterning, and reveal a tight balance between the number of end-points and branching points within the leaf vascular network that does not depend on the Leaf developmental stage and cellular content, but on the leaf position on the rosette.

Leaf Extraction and Analysis Framework Graphical User Interface: Segmenting and Analyzing the Structure of Leaf Veins and Areoles1[W][OA]

The Leaf Extraction and Analysis Framework Graphical User Interface (LEAF GUI), a user-assisted software tool that facilitates improved empirical understanding of leaf network structure, is introduced.

Reviewing models of auxin canalization in the context of leaf vein pattern formation in Arabidopsis.

Three canalization models can account for an acropetal development of the midvein if vein formation is sink-driven and are in agreement with venation patterns resulting from inhibited auxin transport, and loops and discontinuous venations patterns can be obtained assuming proper spacing of discrete auxin sources.



A model for vein formation in higher plants

  • G. Mitchison
  • Computer Science
    Proceedings of the Royal Society of London. Series B. Biological Sciences
  • 1980
A mathematical model is formulated based on evidence that the capacity of a given pathway to transport this signal increases with the flux it carries, and it is shown that this model can simulate Sachs’s experiments on vein formation.

Evolution and Function of Leaf Venation Architecture: A Review

This review summarizes current knowledge of interrelationships between the form and function of leaf venation and the evolution of Leaf venation patterns and refers to the topic of individual and intraspecific variation.

The leaf venation as formed in a tensorial field

It is shown here that the topology of these patterns rather corresponds to what is expected from growth in a tensorial stress field, and suggests a set of hypotheses which is new but supported by known physiological data.

Growth dynamics underlying petal shape and asymmetry

A model is developed and used to show that a key aspect of shape—petal asymmetry—in the petal lobe of Antirrhinum depends on the direction of growth rather than regional differences in growth rate, implying that long-range signals orient growth along the petals as a whole.

The genetics of geometry.

Although much progress has been made in understanding how gene expression patterns are established during development, much less is known about how these patterns are related to the growth of

Morphogenesis of lines and nets.

  • H. Meinhardt
  • Biology
    Differentiation; research in biological diversity
  • 1976
A model is proposed in which a few simple coupled biochemical reactions are able to generate complex linear appearing structures and networks that show self-regulating properties and other features found in the leaf vascular system, the pattern of tracheae in insect epidermis, and other biological networks.

Reviewing models of auxin canalisation in the context of vein pattern formation in Arabidopsis leaves

Several hypotheses have been formed to explain vein pattern formation. Sachs proposed that veins develop as a result of the gradual canalisation of auxin: the auxin transport capacity of some cell


A rigorous method of describing the features of leaves is of immediate usefulness in both modern and fossil taxonomic studies, and it is anticipated that leaves will play an increasingly important part in phylogenetic and ecological studies.

Models and Hypotheses

A model is proposed in which a few simple coupled biochemical reactions are able to generate complex linear appearing structures and networks that show self-regulating properties and other features found in the leaf vascular system, the pattern of tracheae in insect epidermis, and other biological networks.

Physically-based simulation of plant leaf growth: Research Articles

Numerical simulations indicate that different portions of the leaf expand at different rates, which is consistent with the biological observations in the growth of a plant leaf.