In 1968 Aristid Lindenmayer, a biologist, introduced a formal method for modelling the development of plants. Now called L-systems, Lindenmayer's method is a type of rewriting system, a general tool for constructing complex objects by starting with a simple object and recursively replacing parts according to instructions provided by a set of rewriting rules. Although the basic ideas of rewriting systems have been known since the beginning of this century, they were not much used until the 1950s when Noam Chomsky applied them to describe the syntax of natural languages. A key difference between Lindenmayer's and Chomsky's uses of rewriting systems, illustrating the effectiveness of L-systems for fractals, is that Chomsky applied the rules sequentially while Lindenmayer applied them simultaneously.
Graphical representations of L-Systems were first published in 1974 by Frijters and Lindenmayer, and by Hogeweg and Hosper. The potential of L-systems for producing realistic images of plants was demonstrated in 1978 by Smith.
In 1979 Szilard and Quinton showed L-systems can generate fractal curves. In 1983 Siromoney and Subramanian used L-systems to space-filling curves. In 1982 Dekking found the dimension fo some curves generated by L-systems. In 1986 Prusinkiewicz produced more examples of fractals and plants generated by L-systems, using turtle graphics for the output. Also, he obtained 3-dimensional versions of L-systems.
Good references are Prusinkiewicz and Hanan, and Prusinkiewicz and Lindenmayer.
Return to L-Systems.