Modeling and visualization of leaf venation patterns

@article{Runions2005ModelingAV,
  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.},
  year={2005},
  volume={24},
  pages={702-711}
}
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… 

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References

SHOWING 1-10 OF 57 REFERENCES

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

CLASSIFICATION OF THE ARCHITECTURE OF DICOTYLEDONOUS LEAVES

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.
...