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Последний выпуск: 19.06.2015

L-Systems

The following is based on L-Systems as described in "Lecture Notes in Biomathematics" by Przemyslaw Prusinkiewcz and James Hanan. A brief description of an 0L system will be presented here but for a more complete description the user should consult the literature.
Simpleminded example of 0L system

A string of characters (symbols) is rewritten on each iteration according to some replacement rules. Consider an initial string (axiom)

F+F+F+F

and a rewriting rule

F --> F+F-F-FF+F+F-F

After one iteration the following string would result

F+F-F-FF+F+F-F + F+F-F-FF+F+F-F + F+F-F-FF+F+F-F + F+F-F-FF+F+F-F

For the next iteration the same rule is applied but now to the string resulting from the last iteration

F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-FF+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F+ F+ F-F-FF+ F+ F-F-F+ F-F-FF+ F+ F-F

Some symbols are now given a graphical meaning, for example, F means move forward drawing a line, + means turn right by some predefined angle (90 degrees in this case), - means turn left. Using these symbols the initial string F+F+F+F is just a rectangle (? = 90). The replacement rule F --> F+F-F-FF+F+F-F replaces each forward movement by the following figure

The first iteration interpreted graphically is

The next iteration interpreted graphically is:

The following characters have a geometric interpretation.

Recent usage of L-Systems is for the creation of realistic looking objects that occur in nature and in particular the branching structure of plants. One of the important characteristics of L systems is that only a small amount of information is required to represent very complex objects. So while the bushes in figure 9 contain many thousands of lines they can be described in a database by only a few bytes of data, the actual bushes are only "grown" when required for visual presentation. Using suitably designed L-System algorithms it is possible to design the L-System production rules that will create a particular class of plant.

Further examples:


















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