On the Manhattan-distance between points on space-filling mesh-indexings

Indexing schemes based on space filling curves like the Hilbert
curve are a powerful tool for building efficient parallel
algorithms on mesh-connected computers. The main reason is that
they are locality-preserving, i.e., the Manhattan-distance between
processors grows only slowly with increasing index differences.
We present a simple and easy-to-verify proof that the Manhattan-
distance of any indices i and j is bounded by 3*sqrt{