Spoken text

In some units of the first learning module, Lindenmayer systems were used by executing the graph grammar contained in the modell.rgg file. In this unit, the principles of them are finally to be explained.
Lindenmayer systems are rule systems to replace character sequences. These are based on the work of the botanist Aristid Lindenmayer, who developed the rewriting rules for modeling the growth of filamentous algae.
Through a parallel replacement of all characters to which a rule is applicable, in each derivation step the modeling of a step of plant growth is made possible. This dynamic structure description is the basis of the structural models generated with GroIMP. A precise mathematical definition of L-systems is available in the literature; a short version is shown here. It is important to know that an L-system consists of a set of characters (the alphabet), an initiator (axiom) and a set of rules. The initiator and both sides of each rule consist of characters of the alphabet. The rules consist of a left-hand and a right-hand side. During a derivation step, the character string of the left-hand side is replaced with the character string on the right-hand side, whereby a derivation chain of strings is created, resulting from repeated applications of the replacement process from the initiator.
To illustrate this point a small example is shown. As initiator, we have A. The alphabet consists of A and B. The rules are: A is replaced by B and B is replaced by AB. The replacement procedures are the following:
After several replacement steps the derivation chain shown here is the result.
In order to use these rule systems to model plant structures and their growth, a geometric interpretation must be made possible. For this purpose, the turtle geometry is used. So the set of all turtle commands becomes a subset of the character set of the L-system.