Evil Mad Scientist Laboratories has an ingenious how-to on creating a clay model of a fractal known as a Sierpinski triangle.
One of our favorite shapes is the Sierpinski triangle. In one sense, a mere mathematical abstraction, on the other, a pattern that naturally emerges in real life from several different simple algorithms. On paper, one can play the Chaos Game to generate the shape (or cheat and just use the java applet).
You can also generate a Sierpinski triangle in what is perhaps a more obvious way: by exploiting its fractal self-similarity.