Wikipedia hath written:
Every substitution tiling (up to mild conditions) can be "enforced by matching rules"—that is, there exist a set of marked tiles that can only form exactly the substitution tilings generated by the system. The tilings by these marked tiles are necessarily aperiodic.
If I understand this correctly (and indeed I may not), it means that if you have a way of expanding any tile and then subdividing it into tiles, and your tiles have their edges marked in such a way that the subdivision does not allow any of the tiles to be flipped or rotated, then the resulting tiling will not have any translational symmetries. (For simplicity, I'm limiting this to tilings of the plane.)
I've seen this same idea expressed in pretty much the same way in several places. They seem to take it as intuitively clear that when the tile edges can only be lined up in one way in each subdivision, you can't shift the tiling to be coincident with itself, i.e. the tiling is non-periodic. I'm probably missing the obvious here, but I don't see the connection. Why does the inability to flip or rotate tiles in a subdivision prevent translational symmetry?