I seem to recall that pretty good solutions to the "Travelling Salesman" problem can be gotten by visiting the cities in the order traced out by certain space-filling curves. I don't know if this works for the sphere or not, but perhaps postal codes could be so chosen this way. On the other hand, phone area codes seem to have been chosen with some sort of "coding theory" algorithm, so that points close to one another would have area codes as different as possible. At 04:08 PM 7/22/2004, Mike Stay wrote:
To specify a point in a two-dimensional space, we use two coordinates. I can't find any reference on how to specify a point in a fractional-dimensional space. Do any funsters know?
http://www.cut-the-knot.org/do_you_know/dimension.shtml gives an example of a fractal with rational Hausdorff dimension, 3/2. Apparently, one can specify three points on the curve with two coordinates. I've no idea how one would approach the Koch curve.
-- Mike Stay staym@clear.net.nz http://www.cs.auckland.ac.nz/~msta039