Start from a given point, which in this case is (0,0)

Pick one of eight directions (up, down, left, right, and the diagonals) at random. The algorithm I used has these choices equally weighted, but one could generalise that.

Draw a line of length one in that direction.

Loop

These are simple random walks that allow crossings, visiting the same point more than once and allows loops.

May I ask which algorithm you used to produce these runs?

Thanks!

Cheers,
Chris