• Is this it? - Phing.
  • No. The error is further down the tile. The kite and dart tiles are arranged to form a rhombus. If that happens, the pattern can be periodic.
  • Ouch! - dmswart

Penrose Tiling

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This is how you know you're in a mathematician's house. The bathroom floor is tiled with a Penrose tiling. (The Penrose tiling has two distinct features--first, that it's aperiodic. Second, that it's made with two basic shapes.)

(There is actually one small error in this tiling. Can you spot the error?)

dmswart, Phing., Jordi Fontich, and 25 other people added this photo to their favorites.

  1. dmswart 79 months ago | reply

    How?
    who?
    Where can I get some?

    (by the way here's my effort: www.flickr.com/photos/dmswart/410908194/

  2. tiwonge 79 months ago | reply

    This is a retired math professor from Boise State.

    He had to have them specially made. And he had to convince them that this tiling would actually work before they would make them. He wanted to do a 10-fold symmetry (because then there would be 10 lines to be used as a guide), but at the time, he couldn't print it with his computer, so he had to do one with 5-fold symmetry.

    Penrose's patent on the tiling expired at about the time Feldman was building his new house, so he decided to include it in the house.

  3. mjswart 78 months ago | reply

    Wow, I didn't know that there was a patent on that pattern. Could someone have claimed prior art to get around that?

  4. tiwonge 78 months ago | reply

    That's not quite the same thing. A significant feature about the Penrose tiling is that it's aperiodic.

    Dr. Feldman said that at the time that he was tiling this, some company in Britain designed Penrose-tiled toilet paper. At the request of Penrose, they didn't market it. Dr. Feldman says he'd have loved to have stocked this bathroom with that toilet paper.

  5. dmswart 78 months ago | reply

    The islamic patterns were aperiodic as well, they were discovered to be so recently.

    Other aperiodic tilings existed before Penrose tilings. What's new with Penrose tilings is that he reduced the number of tile shapes to two.

  6. Chillindointile... 75 months ago | reply

    this is very cool..i bet the setter had to keep looking at the print..

  7. dmswart 75 months ago | reply

    After 4 months on and off - I found the little error - of course with the help of the note.

  8. tiwonge 75 months ago | reply

    That's the error. He had a workman helping him install it, and that's where they started. (It has five-fold symmetry from that point.) The workman figured that's the way it was supposed to go, making nice, neat patterns like that. After the workman laid those tiles down erroneously, the professor told him how they should be laid.

  9. alnewtile 62 months ago | reply

    wow ive tiled some strange patterns in my time but this one is crazy complex !!!!

  10. Zigpha 57 months ago | reply


    Congratulations! Your photo has been nominated as an "Tiling ,Inscription & Pattern Art "
    You are invited to add your wonderful picture to Tiling ,Inscription & Pattern Art Group

  11. tiwonge 16 months ago | reply

    It wasn't mine, but he had to have the tiles custom-cut. Penrose doesn't license the pattern, so it's not available commercially.

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