Avoiding yourself, it turns out, is a hard problem.
In a two dimensions lattice, the random walker is
Certain to walk back to the origin.

Since the origin can be placed wherever,
He is certain to cross his path
Everywhere.

Unless he randomly walks
In higher dimensions,
A hopeful man should prepare

Himself to meet himself
As a reminder of how he didn’t get lost
And it was just a matter of time.

Credit image : Nicolas Cage in the Weatherman