electric circuits - Resistance between any 2 nodes on an infinite square grid

This question is motivated by this xkcd comic strip
.

The problem is indeed interesting, and my first recollection upon reading this was a similar problem in the book Problems in General Physics by I.E.Irodov(which, in my humble opinion,is a masterpiece).

The question I wanted to ask is, are there any generalizations of the problem known? Can be find the resistance between any two nodes of the grid as a function of the distance between the nodes?

Many thanks in advance!

Answer

Yes, it is possible. For example Kevin Brown did here and here including this table.

so for the xkcd problem the answer is $-\frac{1}{2}+\frac{4}{\pi} \approx 0.773$.