The same happens, in fact, for space-filling curves. Sure, in _most_ of the area covered by the curve, closeness of points means closeness on the curve. But in

The same happens, in fact, for space-filling curves. Sure, in _most_ of the area covered by the curve, closeness of points means closeness on the curve. But in this Hilbert curve: https://upload.wikimedia.org/wikipedia/commons/7/7c/Hilbert-curve_rounded-gradient-animated.gif https://upload.wikimedia.org/wikipedia/commons/7/7c/Hilbert-... Consider the two points on the curve straddling the middle of the top edge of the square. They are very close together, but their 1D addresses on the curve are very far apart (one close-ish to the beginning, and one close-ish to the end)! There ain't no free lunch.