On Thu, 10 Apr 2008, Bill Gosper wrote: ...
To spacefill a blob, find one with a self similar dissection and order the n subblobs in a Hamiltonian path (the path suggested by your polygonal squiggles). Chop the unit interval into n pieces of which the subblobs are the images. Recurse. ...
I've been thinking of making a mosaic out of wood or tile using this technique. Use 4 different colors or shades of square tiles A,B,C,D, perhaps sorting from light to dark, and use them to represent 00, 01, 10, 11. Hilbert: BADC CDAB BCDC ADAB It would be amusing to tile a floor that way and see if anybody noticed. You could even use hilbert tiles: http://www.designbiz.com/Biz/bizProfile.asp?CompanyID=79983 I doubt the cycling pattern would be very elucidating; the rainbow effect works better but would require unique tiles: http://mathforum.org/advanced/robertd/hilbert2.gif It makes me wonder if there are other ways to illuminate the path from 0-1.