- General concept
- Parallel string rewriting system, namely a variant of a formal grammar, most famously used to model the growth processes of plant development.
L-systems are a mathematical formalism proposed by the the Hungarian theoretical biologist and botanist from the University of Utrecht, Aristid Lindenmayer, in 1968, as a foundation for an axiomatic theory of biological development. More recently, L-systems have found several applications in computer graphics including the generation of fractals and the realistic modelling of plants.
The basic idea is to define complex objects by successively replacing parts of a simple object using a set of rewriting rules or productions. The rewriting can be carried out recursively.
The most extensively studied and the best understood rewriting systems operate on character strings. Chomsky's work on formal grammars spawned a wide interest in rewriting systems. The essential difference between Chomsky grammars and L-systems lies in the method of applying productions. In Chomsky grammars productions are applied sequentially, whereas in L-systems they are applied in parallel, replacing simultaneously all letters in a given word. This difference reflects the biological motivation of L-systems. Productions are intended to capture cell divisions in multicellular organisms, where many divisions may occur at the same time.
Many fractals (or at least their finite approximations) can be thought of as sequences of primitive elements/line segments. To produce fractals, strings generated by L-systems must contain the necessary information about figure geometry, and self-similarity is one of the most important properties of fractals. Because of numerous ways branching can be achieved geometrically, there are several ways of creating models of plants as well.
Fractal plant example, cf. the Wikipedia.
To give geometric life to a string of characters, a character string is interpreted as a sequence of drawing instructions using a scheme that is commonly referred to as "turtle graphics". Otherwise the generated object would be very difficult to describe by standard Euclidean geometry. The Logo programming language is one example of such turtle graphics system.
- Usage details
- In order to use the L-system, a parameter indicating the location of the file that defines the objective geometry has to be passed. Then, the standard output of the program can be redirected into a plain text file, to be then graphically represented with a Logo interpreter such as ucblogo:
./bin/lsystem data/file.def > syst.txt; ucblogo syst.txt
- Version:
- 0.0.1
