Grammar-Based Models and Fractals
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”).
KeywordsSearch Pattern Tree Crown Graph Transformation Photosynthetic Performance Graph Grammar
Functional-structural plant model
Growth-grammar related interactive modelling platform
Relational growth grammar
Extended L-system language
- For further reading on the topic, the book “The Algorithmic Beauty of Plants” (Prusinkiewicz and Lindenmayer 1990) is still an excellent introduction. The original source regarding the recently developed language XL is Kniemeyer (2008), which also contains numerous examples. The use of functional-structural plant models in applications can best be traced by looking into the proceedings of the FSPM conferences and workshops: Bouchon et al. (1997), Sievänen et al. (1997), Kastner-Maresch et al. (1998), Andrieu (1999), LeRoux and Sinoquet (2000), Hu and Jaeger (2003), Godin and Sinoquet (2005), Vos et al. (2007), Fourcaud et al. (2008), Hanan and Prusinkiewicz (2008).Google Scholar