Links in the text refer to the lower part of the page

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:

Hilbert's curve: Axioma X, Rules: X => -YF+XFX+FY- and Y=> +XF-YFY-FX+ . This type of curves have the
remarkable property that they can fill a 2 (or more) dimensional space.
The curves below were drawn by increasing the order (1,2,3,4,5 and 6) and decreasing the line length (32,16,8,4,2,1).
The number of points inside the square that are covered by the curve increases with each step.
In fact there is no limit to the number of points that can be covered by the curve as you proceed in this way.
This means that the curve is "space filling".