To have this you would need every patch of a tiling to be unique, right? I think then if you had this you would be guaranteed to be an aperiodic tiling: since no two patches are alike, there’s no way to translate it. Conversely, my gut says that aperiodic tilings have this property at *some level*.
Also, if you allow for tesselations where each tile is unique, there’s probably something cool that could be done with fractal edges to encode position
