Grammar-Based Models and Fractals

  • Winfried KurthEmail author
  • Dirk Lanwert


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”).


Search Pattern Tree Crown Graph Transformation Photosynthetic Performance Graph Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Functional-structural plant model


Growth-grammar related interactive modelling platform


Relational growth grammar


Extended L-system language

Further Readings

  1. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department for Computer Science, Chair for Computer Graphics and Ecological InformaticsGeorg-August University of GöttingenGöttingenGermany

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