I’ve always been fascinated by the transcendental number pi, so I thought it was really cool when the first 100,000,000,000 digits of pi were transformed into art via a random walk.

(Click for a larger version)

This image represents pi in base-four notation, and each subsequent digit determines the location of the next pixel. Zero means “move down”, one is right, two is up, and three is left. We start at the point marked start and proceed through a hundred billion digits, eventually coming to finish. Although this is hardly a rigorous mathematic proof of the randomness of pi’s digits, the fact that there’s no discernable pattern here is a pretty strong indicator that the digits are likely random.

Math as art is so cool.