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