rwg>that (self redefining) exact rational Treano function is Mathematica,
not Macsyma! It maps 0 to (0,0,0) and 1 to (1,0,1), and all connections are corner to corner. I (incorrectly) thought my ViewPoint trajectory included a good view of this. Sorry. The problem is, to avoid self-contact, the plot images [1/1536,1-2/1536], not [0,1], so it never actually hits a corner.
Amazingly, Treano[1/28] = Treano[27/28] = {1/2,0,1/2} = Treano[1/2]. I.e., it revisits the midpoint when 93% through! More important, Treano[11/14] = {1,1,1}, so Graphics3D[Table[Stick[Treano[11/14/8^3 + (k)/8/8], Treano[11/14/8^3 + (k + 1)/8/8]], {k, 0, 8^2-2}]] produces http://gosper.org/treano64.SWF, connecting the centers of the subcubes. (This bounding box < [0,1]^3.) --rwg INTERPOLATED LATENT PERIOD ACTINOMETRIES REACTION TIMES