[7373737373]

minor correction: 2^(NxN) squares per row, right?

[pontifier]

Yeah, what was I thinking?? I really need to slow down sometimes. This should contain every finite pattern, right?

[7373737373]

Yes, sounds like it! Though I'm thinking that the relative arrangement of patterns would also make a difference. I wonder if such a thing as "all (infinitely many) possible arrangements of all patterns" can exist