Penrose tiling (PT) is well known for its non-periodic pattern. But I am just wondering if it is possible at all to create a Moiré pattern that possesses a periodic pattern by combing two or more than two Penrose tiling.

There is a youtube video shows Roger Penrose using two paper sheets with PT on a projector and he got a nice crossing lines. https://www.youtube.com/watch?v=th3YMEamzmw&t=2120s The limited size of the paper sheet he used does not allow one to know whather those patterns are repeated periodically or not.

  • $\begingroup$ I believe that the fact that the tile-frequencies are irrationally related means that there can be no overlapping of two Penrose tilings in order to achieve a periodic pattern. The resulting pattern will always be aperiodic. $\endgroup$ – Dan Rust Oct 15 '18 at 21:17

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