I'm sure that many here are familiar with this famous problem that popped up on xkcd one day:
On this infinite grid of ideal one-ohm resistors, what's the equivalent resistance between the two marked nodes?
I am intensely curious, however: what if instead of an infinite grid of ideal one-ohm resistors, we had an infinite lattice? (interestingly, I could not find a single image on google illustrating this) This brings up two interesting questions:
- What is the equivalent resistance between two nodes that lie on the same plane of the lattice?
- What is the equivalent resistance between two nodes that do not lie on the same plane of the lattice?
I've searched the site a fair bit, and this question does not seem to have been asked. I don't know anywhere near enough about electrical engineering and circuit physics to even begin tackling this problem, but I would love to see something akin to a solution.