11: Grammar-Based Models and Fractals



MCED Chapter 11

Title

Grammar-Based Models and Fractals

Authors

Winfried Kurth and Dirk Lanwert

Abstract (from the book)

In ecological interactions the three-dimensional structure of organisms can play an important role. We will present an approach for modelling and simulation of the development of geometrical structures in space, which is particularly suitable for representing branching systems as they occur in plants. The related notions of self-similarity and fractality will be briefly discussed. The crucial idea for modelling is to describe the development of a modular structure by rules controlling the replacement of substructures by other substructures. Such replacement systems are also called “grammars”. When the structures are encoded as strings, we speak of L-systems. A more general case are graph grammars, where the transformed structures are networks consisting of nodes and arcs. Loosely following Kurth (2007), we will first show example grammars written down in the programming language XL, which simulate the branching structures of simple plants. The final example, also implemented in XL, is about competition and resulting spatial interaction between plants. All code examples can be tested with the free software GroIMP (“Growth-grammar related Interactive Modelling Platform”).

Additional material

Further Reading

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Links

Several software systems exist which can be used to explore the possibilities of fractals and L-systems and to create virtual plants. One of the oldest tools is

It does not only include a simple L-system interpreter, but also other algorithms for generating fractal structures.

developed by Christoph Streit, was one of the first tools specializing on L-systems and was later used in an agronomical application. A more advanced tool,

was developed by Laurens Lapré.

from P. Prusinkiewicz’s team is one of the most widely used L-system software tools, with numerous applications in functional-structural plant modelling.

contains not only an L-system interpreter, but also several tools for analysing branching systems of trees. Meanwhile, most of its functions are also available in the open-source system

developed by Ole Kniemeyer et al. (2004), which offers an advanced, interactive graphics display and an XL compiler.

by Christophe Pradal, is an open-source system designed to compose submodels and tools from different sources in order to create complex models of plants and ecosystems.

General Webpages on L-systems, fractals and functional-structural plant models
L-systems

Fractals

Functional-structural plant models

Project web pages linked to functional-structural plant modelling