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Tutorial: Penrose Tiling

16

Robin Wilson explores the automation of creating Penrose Tile patterns with Blender, and provides a ready to use Python script to achieve the effect.

Robin writes:

Penrose tiling is known both for the beautiful patterns it can generate and the peculiar mathematical properties it possesses. It's unusual for two reasons:

1) It's pentagonally symmetric (while most tiling patterns are not)
2) It's non-periodic, that is, it doesn't regularly repeat itself over space.

Because Penrose tiling is non-periodic, it is not possible to construct the patterns in Blender using the array modifier. Instead, I used Blender's scripting tools, and made this video.

If you want to learn how to generate your own Penrose tiling patterns in Blender, you can check out this tutorial.

Happy Tiling!

16 Comments

  1. Very cool! On a side note, after viewing this and looking @ text, the text appears to be moving! With the right color combo I'm sure the effect would be even greater.

      • I think Robin is trying to hypnotize BN! I've seen similar graphic illusions recently that makes it looks like walls have worms/crawling. Pretty freaky side effects.

    • Lawrence D’Oliveiro on

      I think it’s called “adaptation”. Your visual processing system has low-level sensors for all sorts of things, such as areas of colour, edges and motion. But if they’re continuously stimulated, they get fatigued and stop responding. So when the stimulus stops, you get the illusion of the opposite stimulus.

      So: stare for a long while at an object of one colour (e.g. green), and when you glance away at a white area, you see the opposite colour (e.g. magenta).

      Drive along a long straight road with scenery moving towards your eyes for a long while, then when you stop, stationary things look like they’re moving away from you.

  2. Cool work Robin. I would just like to add that 2) follows from 1). A pentagonally symmetric pattern cannot be periodic, but only quasi periodic. Right?

    • That's pretty much what I've read, yes :-)
      Or course, you can build pentagonally symmetric objects in the array modifier, but you can't get them to extend indefinitely.

      • There are some students in my solid state physics course who want to do a presentation about quasi crystals. I will point them to you add on.

    • Really? I had no idea about that - thanks for the heads up.
      Can you actually claim copyright on a mathematical pattern? I thought copyright ony covered the expression of ideas, not the ideas themselves.

        • Hi, I've asked around a bit about what happened.

          Apparently, Penrose did have a a patent on the pattern (so it wasn't a copyright
          issue). Before publishing anything about his pattern in a science
          journal (which would free it up for public use), Penrose had patented
          the tiling pattern.

          From what I've read, the patent has expired, so there shouldn't be an issue.

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