ant of Langton

Apply the following rule to a grid of black squares: when you get on a black square, make it white and turn to the right; when you get on a white square, make it black and turn to the left.

Surprisingly, after about 1000 steps, a regular path occurs.

You can download a program (302 kB) to make the path visual.
Then you see some kind of ant, wandering around, and at last marching in a stable direction.