Based on this image created by Matt Henderson, I decided to write something for myself that would explore other possible random walks, although mine are generated in a slightly different way than what Matt did.
Each of these images (which will only appear in Chrome, Safari or Firefox, sorry people still using Internet Explorer) is a visual representation of the first 100, 000 digits of the number where each digit of the number corresponds to a different rotation. They may take a while to calculate, depending on the speed of your computer.
Note that for the last "random walk", I increased the scale significantly over the other random walks so that it made the pattern more obvious.