Cristian Ilies Vasile has created the coolest visualization of Pi I've seen. First he divided a circle in 10 segments, from 0 to 9. Then he traced a path going from the third segment to the first segment. From 1, the path jumps to 4, then back to 1, then 5 and so on. After a while, π appears in front of your eyes. The final illustration is beautiful.
This is the animation:
Another visualization also reveals the number of times a pairs repeat using bubbles. The bigger the bubble, the more frequent the pair.