On Thu, Aug 28, 2008 at 4:52 PM, Fred lunnon <fred.lunnon@gmail.com> wrote:
I've been spending quality time with Hilbert walks (finite approximations to Hilbert curves) in d-space lately (don't tell RWG), my ruminations somewhat inconvenienced by inability to locate a definition of what might actually constitute a Hilbert walk/curve in any dimension d > 2.
Previous authors seem to cheerfully ignore the difficulty; or perhaps they just implicitly define a walk as being whatever convoluted Hmaitonian path their proposed algorithm happens to construct.
While I have some ideas about an appropriate general definition, it's still not very clear to me exactly what properties --- combinatorial or possibly staistical --- of such a path might be significant in applications --- such as multiple-key database, and equation solving in many variables.
Can anybody out there cast light on these matters? Fred Lunnon
Gray codes! The nth approximation to a Hilbert curve in d-dimensional space is an (nd)-bit Gray code. http://en.wikipedia.org/wiki/Gray_code -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com