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