A Survey of Mathematics Related Topics: Pg. 482, Figure 9.70

This activity allows the user to step through the process of building the Sierpinski's Carpet.

This activity is meant to show how changing the shape but using the same idea for a generator in a geometric fractal can yield a predictable final product. This activity should be tried after the Sierpinski's Triangle Activity for comparison purposes.

To build the Sierpinski's Carpet, start with a square with side length 1 unit, completely shaded. (Iteration 0, or the initiator)

Divide each square into nine equal squares and cut out the middle one. (the generator)

Repeat this process on all shaded squares. Stage 2 is shown below.

The limiting figure for this process is called the Sierpinski's Carpet.