Walking with Pi

Below are the walks generated by using Pi (in base 4) as a random number generator and then performing a random walk in an infinite grid.

Each image represents intervals of 500,000 (base 4) digits of Pi.

So far, no instructions have been found, but I will keep looking!

Walks

500,000

500,000 digit random walk of Pi

1,000,000

1,000,000 digit random walk of Pi

1,500,000

1,500,000 digit random walk of Pi

2,000,000

2,000,000 digit random walk of Pi

2,500,000

2,500,000 digit random walk of Pi

3,000,000

3,000,000 digit random walk of Pi