Parametric L-systems and Their Application To the Modelling and Visualization of Plants

James Hanan


In this dissertation, parametric L-systems are presented as the foundation of a computer graphics tool for simulating and visualizing the development of plants.

L-systems were introduced in 1968 by Aristid Lindenmayer as a mathematical model of multicellular organisms. They employ a parallel string-rewriting mechanism to describe the development of branching structures. The resulting strings can be interpreted geometrically and visualized using computer graphics techniques to create both realistic and schematic images of the modelled structures. The formalism can be applied for a variety of scientific, educational, and commercial purposes.

Parametric L-systems extend the original concept of L-systems by associating numerical parameters with the symbols representing plant components. This allows easy quantification of geometric attributes of a model, and provides a simple means for the expression of continuous processes, such as diffusion of hormones and the resulting distribution of concentrations. Formal definitions are proposed for contextfree and context-sensitive parametric L-systems with either deterministic or stochastic application of production rules.

The practical value of parametric L-systems is demonstrated in this dissertation by examples that include models of plants ranging from algae to trees. Model development is controlled by lineage mechanisms, with information passed from parent to child module. This mechanism is combined in some models with endogenous interaction, where information flows through a growing structure. Selected models are suitable for simulating time-lapse photography through computer animation.

Extensions to the formalism of parametric L-systems incorporate useful features of other programming languages and provide techniques for creating hierarchical models.


James Hanan. Parametric L-systems and Their Application To the Modelling and Visualization of Plants. Ph.D. dissertation, University of Regina, June 1992.

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