Self-avoiding walks on infinite grids

Suppose we start at \((0,0)\) on the cartesian grid, and wander about randomly only in North, South, East and West directions, never visiting a vertex more than once. How far will we wander before we come to a point around which there are no unvisited vertices? This is best answered experimentally, and indeed it&rsquo;s already be done - note that this article is behind a paywall, but the result…