"What is this?" the viewer may wonder. John's interesting discovery is that one can fill all space by placing ever-smaller shapes at random without overlap (the areas of the shapes must follow a prescribed sequence). In the limit where one places an infinite number of shapes, they completely fill the space in fractal fashion. The evidence is that any shape will work. It may seem surprising, but all of these varied images are *examples of the same algorithm*. The rules only apply to the shapes -- the color scheme can be chosen arbitrarily.

These low-resolution images give a nice overview, but one can ask "Do they *really* fill space?" The best answer to that is to go to the 1 million circles page. The statistical geometry described file (warning, it has equations) contains a complete mathematical account of the algorithm used. Those interested in trinkets and curios (mugs, prints) can visit John's Zazzle store.