wfl> On 11/15/08, rwg@sdf.lonestar.org <rwg@sdf.lonestar.org> wrote:
rwg> DanA>What I wrote was misunderstood.
Sorry about that, Dan! ...
So SW's intial assessment was correct: trivial.
Do I need a smiley here?
wfl> The property of "locality" seems to have been overlooked in the
current discussion. As far as I recall, no-one had denied that Peano-like curves are relatively easy to construct.
Indeed. There are 2^8 variations on my Treano function, corresponding to reflecting each of the eight subcubes about a diagonal plane. E.g., I probably should have 0, Treano[t8, a1[[{3,2,1}]]/2, a0][[{3,1,2}]]/2, instead of 0, Treano[t8, a1[[{1,3,2}]]/2, a0][[{1,3,2}]]/2, to get a more consistent texture.
[Nor unfortunately, has anyone else attempted to discuss exactly what exactly constitutes a Hilbert-like curve in dimension > 2.] WFL
For dimension D, presumably a finite state machine converting D bit bytes of t into vectors of D one bit bytes of x1,...,x_D, with corner connectivity. Once you build one, you can fairly easily build the inverse, which produces a vector of possibly several inverse images. rwg>Oops, I used the long awaited mouse tumble feature to find a
much nicer pose, but the Export command captured the original one.
If you have Mma, I highly recommend, e.g., mouse-wobbling Graphics3D[Table[Stick[Treano[(k+1/3)/512],Treano[(k+4/3)/512]],{k,0,510}]] and Graphics3D[Table[Stick[Treano[(k+0/3)/511],Treano[(k+3/3)/511]],{k,0,510}]] Looking at stills of these is like trying to parse protein molecules. --rwg TRIANGULATED ADULTERATING BATHYTHERM BETA RHYTHM PORTATIVE VAPORETTI PASSENGER LINER ??