15.1 Formal definition

A L-System is a formal grammar with :

  1. An alphabet V : The set of the variables of the L-System. V * stands for the set of the “words” we could generate with any symbols taken from alphabet V , and V + the set of “words” with at least one symbol.
  2. A set of constant values S. Some of this symbol are common to all L-System. (in particular with the turtle!).
  3. A start awiom ω taken from V + , it is the initial state.
  4. A set of prodution rules P of the V symbols.

Such a L-System is defined as a tuple {V,S,ω,P}.

Let’s consider the following L-system:

The two production rules are rewriting rules. On each step, the symbol A is replaced by the séequence AB, and the symbol B is replaced by A. Here are the first iterations of this Lindemayer system:


Ok, ok but concretely? Let’s read next section!