You are hereLsystems: a turtle draws plantsClick to choose your language: Lindenmayer systems – or Lsystems for short – find an increasing number of applications in computer graphics, especially in fractals and realistic modelling of plants. More exotic applications, ranging from the reproduction of a traditional East Indian art form to graphically motivated algorithms for music composition, are also known. Lsystems base on productions – rules represented by strings. These rules define graphical structures. Let us consider strings built of two letters a and b (they may occur many times in a string). For each letter we specify a rewriting rule. The rule a: ab means that the letter a is to be replaced by the string ab, and the rule b: a means that the letter b is to be replaced by a. The rewriting process starts from a distinguished string called the axiom. Let us assume that it consists of a single letter b. In the first derivation step (the first step of rewriting) the axiom b is replaced by a using production b: a. In the second step a is replaced by ab using production a: ab. The word ab consists of two letters, both of which are simultaneously replaced in the next derivation step. Thus, a is replaced by ab, b is replaced by a, and the string aba results. In a similar way (by the simultaneous replacement of all letters), the string aba yields abaab which in turn yields abaababa, then abaababaabaab, and so on (Figure 1). Figure 1. Example of a derivation in an Lsystem Many fractals are thought of as sequence of primtive elements – line segments. The lengths of segments and the angles between them play a crucial role. To produce fractals, strings generated by Lsystems must contain the necessary information about figure geometry. LOGOstyle helps at defining graphical structures. Now you are ready to read about threedimensional Lsystems!
