It is in fact, none other than that famous mathematical constant Pi. The image is a "walk" made out of the first 100 billion digits of pi, in base 4.
Starting at the origin, each digit forced a point to move in one of four directions: a 0 made the point move right, a 1 made the point move up, a 2 left, and 3 down. What you see is the route that 100 billion digits traced out. The result is beautiful—if chaotic. [Gigapan via Flowing Data]