[math-fun] Space-filling fabric
http://credentiality2.blogspot.com/2010/06/space-filling-fabric.html I just got back my Hilbert space-filling fabric from spoonflower, a site that'll print any image onto a variety of fabrics. Space-filling fabric is suitable for completely filling any plain spots on your walls, or for topological application. Spoonflower will sell you some of your own: http://www.spoonflower.com/fabric/246090 (I don't think I get any commission if that happens) It's kind of pretty (if rather garish) as a wall hanging, but beyond that I haven't yet figured out quite what to use it for. Someday if I have time, I think it'd be interesting to try out a more restricted color space that clashes less. I'd also buy a few yards of a Gosper fabric for anyone who will generate the corresponding image and source code. I do find it amusing that the fabric is spun from more-or-less one dimensional thread, although I don't see any options on spoonflower for specifying that the manufacturing process must preserve continuity and come from a single thread.
Awhile ago, there was a thread about putting 1-9 in a grid so that all possible pairs were neighbors, when diagonal connections were allowed. It's a much, much harder problem when diagonal connections are not allowed. If the given square is X'ed out in a 5x6 grid, the solution is unique, except for permutations of the digits. All 45 possible number pairs each occur exactly once within the grid. 679226 123456 483753 46X711 995889 --Ed Pegg Jr www.mathpuzzle.com
participants (2)
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Ed Pegg Jr -
Jason