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6 Responses:

  1. You know the facade is a Penrose tiling, right? Not the good one, though.

    • jwz says:

      I didn't notice that -- it looked periodic to me. And yeah, there are more interesting choices. Maybe it's the line weight that I'm not so fond of.

      Found the press release:

      • It's P3, the fat & thin rhombuses. P2 is the more famous kites & darts. I can't tell whether it's periodic or not - I think all the Penrose tilings can be done periodic if you want to.

        • Nick Lamb says:

          None of the Penrose proto tile sets can make a periodic tiling. That's sort of the point.

          Does San Francisco do Open House? I know New York does. Personally I'm an infrastructure person, so I like to see sewers and waste processing plants, but fancy architecture is fun too.

          • The tilings are obligate aperiodic iff you obey the matching rules. Hard to say if this facade does so.

            • Nick Lamb says:

              The matching rules are how Penrose got here, but they're equivalent to a slight modification of the tiles themselves (basically imagine making them jigsaw pieces with tiny lugs, so they only fit together on some edges) and it turns out that for a bunch of the mathematics that follows that's a more helpful perspective. The simple colored geometric shapes look cooler on a secondary school classroom wall though.

              This facade is indeed a Penrose tiling to the extent I'm able to examine it in this photograph. The mounting points confuse things a little bit, in a normal periodic tiling you'd arrange for them to always be at a vertex, or always in the middle of a tile, with the aperiodic tiling of course you can't choose either. I'm not going to examine it minutely to ensure there's no fudging anywhere, but the larger mounted elements aren't identical and you can verify _that_ with a very brief visual inspection, so if they _have_ fudged it somewhere it clearly didn't save them any money making the thing.