Inspired by Martin Gardner's book "aha! Gotcha: Paradoxes to puzzle and delight", in the section on statistical clumping:
A striking experiment in clumping was discovered by A. D. Moore, an engineer at the University of Michigan. Moore calls it the "nonpareil mosaic" because it uses large quantities of nonpareils, a sugar candy manufactured in the shape of tiny colored spheres. Obtain enough red and green nonpareils so that you can fill a glass bottle with equal amounts of each. Shake the bottle until the two colors are thoroughly mixed.
Inspect the sides of the bottle. You would expect to a see a homogenous mix of colors, but instead you see a beautiful mosaic made up of irregular large red clumps interspersed with equally large green clumps. The pattern is so unexpected that even mathematicians, when they first see it, believe that some sort of electrostatic effect is causing spheres of like color to stick to one another. Actually, nothing but chance is operating. The mosaic is the normal result of random clumping.
If this seems hard to believe, try this simple experiment. On a sheet of graph paper, outline a 20-by-20 square. Take each cell in turn and color it red or green, choosing the color by flipping a coin. When the 400-cell square is fully colored, you will see the same kind of mosaic that appeared on the sides of the bottle.
Click to try different settings. How much of the effect do you think you see?