Environmental Engineering Reference
In-Depth Information
11.1
Introduction
Grammar-based or rule-based modelling tries to capture the morphological develop-
ment of organisms in three-dimensional space. For example, in plants we can often
observe that they are composed of structural units (internodes, root segments, buds,
leaves, flowers), which are repeated in space and which grow and develop according
to clear botanical rules (e.g. laws of phyllotaxis or inflorescence architecture). Thus,
a seemingly complex tree crown can be described by quite a small number of
geometrical units and rules. All simulations of ecological situations where a precise
description of three-dimensional arrangements is needed can profit from such a rule-
based description e.g. for tree crowns competing for light and space, and for root
systems competing for soil resources.
The Hungarian biologist Aristid Lindenmayer (1925-1989) was the first to use a
grammar-based formalism to simulate the growth of organisms, namely, of filamen-
tous algae (Lindenmayer 1968). His rule systems were later denoted Lindenmayer
systems or L-systems. For a while, the applications of this new formalism remained
restricted to morphological studies of small herbaceous plants (e.g. Frijters and
Lindenmayer 1974) or to the free exploration of forms which can be obtained by
parameter variations in the rule systems (Hogeweg and Hesper 1974). Later, Smith
(1984) and Prusinkiewicz (1987) combined L-systems with a powerful description
code for static branching structures, turtle geometry, and used this approach for plant
models in computer graphics. A book with numerous illustrations (Prusinkiewicz and
Lindenmayer 1990) inspired further work of this sort. L-systems were also used for
other organisms forming branched structures, such as fungi (Tunbridge and Jones
1995) and corals (NVIDIA 2006). However, Herman and Schiff (1975) already had a
more ambitious aim: “
...
a general purpose simulator in which all kinds of different
biological ideas can be tested with ease.” To accomplish this, the purely structural
representations which can be obtained with simple L-systems were not sufficient. The
guiding idea was to extend the L-system approach to a formal calculus which could
play a role in biology which is analogous, e.g., to that of differential equations in
physics or group theory in crystallography. The first steps were already done by
Prusinkiewicz and by Lindenmayer himself when they introduced numerical para-
meters in their L-systems. Later, a combination of the rule-based approach with
process-oriented models of biological systems was realized in various forms. Room
and Hanan (1995) coined the term “virtual plants” for the resulting simulated organ-
isms, and in the preface to Siev
anen et al. (1997), the notion of “functional-structural
tree model” was used, which was later generalized to “functional-structural plant
model” (FSPM). To provide flexible tools for creating FSPMs, several authors
extended the concept of an L-system. For instance, in the language XL (which will
be used below for some “virtual plant” examples), L-systems are extended to graph
grammars and rule application is combined with classical imperative and object-
oriented programming in order to capture the process-related aspects of plant growth
in an adequate way in a model. Such an extended grammar approach is quite
powerful: Recently, Courn
`
de (2009) has also shown that the basic algorithms of
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