Environmental Engineering Reference
In-Depth Information
Chapter 11
Grammar-Based Models and Fractals
Winfried Kurth and Dirk Lanwert
Abstract 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”).
Abbreviations
FSPM Functional-structural plant model
GroIMP Growth-grammar related interactive modelling platform
RGG
Relational growth grammar
XL
Extended L-system language
