## 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 | Fractint | 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:

Minkowski

The Dragon:

Archipel (Mandelbrot):