You're probably asking yourself, "What the hell is he talking about? There's nothing mysterious about public bathroom floor tile!" But there is. I'm sure you've seen the floor tile I'm talking about. It ususally comes in two color palettes, blue and brown. It consists of three basic quadrilateral shapes, a large square, a small square, and a rectangle. The rectangle is half the size of the large square, and exactly twice the size of the small square. I've included an artist's rendition below for your convenience. The diagram does not show the way in which they are arranged on the floor.
This is the really mysterious part. Most tile has some kind of pattern of a repeating shape, and usually this pattern is extremely obvious. This floor tile on the other hand, has no obvious repeated pattern. Sometimes, in only the blue variety, one can find a pattern, but I consider this a degenerate case. The only possible solution is that this tile is rolled onto the floor, but its hardness and durability make this hard to believe.
After staring at this tile for so long in bathrooms, I've come up with some little diversions to make that bathroom break seem a little bit shorter. I usually like to pretend the larger squares are rooms, the small squares doors, and the rectangles hallways. Then, I try to navigate about the floor. It kind of reminds me of the old Spy vs. Spy video game. Its also sometimes fun to see what kind of shapes you can find in the specks on the tile, or in the tile itself. Above all, however, see if you can find the pattern!