This example was created with the help of Robert M. Dickau's Mathematica code for L-systems, available on his homepage.

Space filling curves are also discussed in Stan Wagon's book "Mathematica in Action".

This graphic was constructed by replacing each of the lines of the first step by several smaller lines.

The curve "covers" a greater volume after each step. In the limit of infinitely many steps of replacements the curve in fact becomes "space-filling". (This is clearly impossible, if all curves are considered to be one-dimensional.)