L-Systems consist of a series of productions of the form
predecessor -> successor
where each of predecessor or successor is a series of symbols drawn from some alphabet. From a given start symbol or string, these rules are applied in parallel to produce a new string. This process can be repeated indefinitely. Given appropriate initial strings and rules, the resultant strings model various biological structures. This basic system can be augmented with randomness, paramaterized properties and nondeterminism.
Once this machinery is in place, various ways of visualizing the strings can be added. One of the easiest of these is turtle graphics, where the produced string is a program describing the path of a pen drawing an image. Pictures of plants and other recursive structures can be produced this way. A more complex method of visualization is converting the produced string into a three dimensional model of the structure.
For instance, a simple exampe would be the rule
A -> AA
This would draw simply a straight line, which would be subdived multiple times. Two useful operators are + and -, which rotate the angle at which to draw the next segment. These are used in
A -> A+A--A+A
which, at one itereation, draws a line with a triangular bump in it. Iterated multiple times, it draws the Koch curve.
Another pair of useful operators are [ and ]. The first pushes the current settings (angle and length) onto a stack and the second pops the top off the stack and replaces the current settings with it. This allows us to save points to return to in the future. An example using this is
A->BB+[+A-A-A]-[-A+A+A]
After converting our L-Systems into hierarachical models, we may wish to animate them. We do this in a similar manner to a particle system. Each segment lives n its own space with the origin and the end of its parent. Each segment experiences several torques which may cause it to rotate. One of these is a torque back towards the position it belongs. Other forces can be added, such as wind or drag. Using these, we can simulate trees blowing in the wind.