Lindenmayer systems

Lindenmayer systems

Lindenmayer systems (L-systems, turtle graphics) are used to generate Fractal curves (Koch, Sierpinski, Levy, Dragon), Space filling curves (Hilbert, Peano-Gosper), Growth patterns in plants, etc. It is an iterative string rewriting method. Starting from the Axioma a new string is formed by replacing the string symbols according to a few given Rules. The final string contains instructions telling the turtle where to go, or how to draw the path. The list contains a number of well known examples. Choose one of them and push the Draw button to draw it in the graphical window. You may construct your own examples and add them to the list.

More information on Lindenmayer systems: Some history | Mathforum | Ridldle | Wikipedia | Mathworld | Algorithmic botany

Lindenmayer systems – Fractal curves

Koch curve for order 1 to 4. The line length is adjusted (27, 9, 3,1; see the Demonstration)

Koch’s snowflake:

Sierpinski Gasket:

Sierpinski Carpet:


The Dragon:

Archipel (Mandelbrot):