More about the L-System Machine

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.

L-System basics

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:


von Koch curve

Axiom: F
Rule: F→F+F−−F+F

  • 0: F
  • 1: F+F−−F+F
  • 2: F+F−−F+F+F+F−−F+F−−F+F−−F+F+F+F−−F+F
  • 3: ...

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

 Symbol   Description Symbol   Description


move forward one base length without painting

 F, G

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


Basic signs F, G and additional symbols

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.


Math & Art Gallery


Galerie Cosch


© 2007 Ulrich Schwebinghaus