On the metric properties of discrete space-filling curves
Craig Gotsman, Michael Lindenbaum · IEEE Transactions on Image Processing · 1996
A space-filling curve is a linear traversal of a discrete finite multidimensional space. In order for this traversal to be useful in many applications, the curve should preserve "locality". We quantify "locality" and bound the locality of multidimensional space-filling curves. Classic Hilbert space-filling curves come close to achieving optimal locality.