Yeah, let me try to be more precise, though maybe it's worth writing down in a more formal setting because comments are awkward. Say we're looking at the Hilbert curve. I claim that for
almost all physical positions, a sufficiently small change in position yields a correspondingly small change in coordinate.
In the purely mathematical sense, this means something like "continuous except at points with at least one rational coordinate".
In the programming sense, where everything must be approximated and you're mapping a 2-d lattice to a 1-d lattice, then it's a bit tricky to formulate, but something like: if you take the maximum distance in 1-d space between a 2-d point and its eight "neighbors", then the probability of this distance being > N should be O(1/sqrt(N)). Concretely,
P(point has an adjacent point whose Hilbert coordinate disagrees past the highest n bits) == P(d > 4^n) < 4*(1/2)^n
