In the year 1968 the german biologist Aristid Lindenmayer developed a model, demonstrating plant's growth with the use of some "construction rules", today named L-System.
The basic principle is simple: Starting with the axiom as the first element, the construction rules form complex expressions which have to be drawn. We only need line elements of a fixed basic length (F, G). In addition there are rotations by a standard angle.
The growing machine is controlled by up to two construction rules. These rules induce the exchange of single symbols by longer expressions and form a more detailed construction. The new expression contains the same symbols, so the following step has to replace them again. The number of steps is called the level (order). The final expression forms the drawing with line elements, rotations and unvisible jumps. Watch the example:
Every F is replaced by F+F−−F+F, the other symbols remain unchanged.
Download lsystem.js (watch the HTML source code of the previous page). KineticJS is used for the movable point.
List of the most important symbols
move forward one base length without painting
move forward one base length with painting
rotate left by the standard angle
rotate right by the standard angle
save position and direction, multiply the base length by the standard factor
restore position and direction, divide the base length by the standard factor
save position and direction
restore position and direction
multiply the base length by the standard factor
divide the base length by the standard factor
The essay "Wachstumssimulationen" describes the background of the L-System in a more precise manner. Perhaps you'll be able to transform the terms for using them with my machine. Sorry, the essay is only available in german.