It'd be cool to learn how one could reduce this resistances in this grid to an equivalent resistance. Perhaps you could share some insights?
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Stallman's (or Sussman?) thesis back in the 70s dealt with something similar. Basically an "AI system" that solves circuits by transforming them to simpler circuits using heuristics. It even solves BJTs by assuming the state its run and then seeing if the circuit is self consistent.
It looks possible for finite circuits. I doubt there is a general method for infinite systems, because the details of the infinite network are difficult to automate.
(For example, cut all the resistance that connect (x,0) and (x+1,0) when x is a prime number. The solution posted in the comments here assume a very even network, and adding some "random" cuts would break the symmetry.
I think there are numerical solutions possible for any network. Worst case solving KVL KCL to find the equivalent resistance between two nodes is an option. In a real circuit netlist the number of nodes is finite and often you can just ignore dangling resistances.