While not quite as "oh, that's neat" - a set of Wang dominoes might be interesting to people who know what it is (incidentally, Wang is the logician that had a conjecture that proved false and lead to the aperiodic set that Penrose came up with).

One aspect of the "this is undecidable" was that it to prove it is equivalent to solving the Halting Problem.

> In 1966, Wang's student Robert Berger solved the domino problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem (the problem of testing whether a Turing machine eventually halts) then implies the undecidability of Wang's tiling problem

https://en.wikipedia.org/wiki/Wang_tile

In one of the books I've found - Andrew Glassner's Notebook: Recreational Computer Graphics - they have a set of tiles that implement some program. https://books.google.com/books?id=_4ZMC_QBAC4C&lpg=PP1&dq=An... (some other Turing machine Wang tile sets - https://grahamshawcross.com/2012/10/12/wang-tiles-and-turing... )

All that said - if you're willing to go with printed square tiles that implement an aperiodic tiling with edge rules, that might be an option.

And all that said... http://www.tessellations.org/real-materials-tessellations-16... is the story of making a Penrose kitchen floor.

> A potter friend, Jim Morrison of Cold Mountain Pottery (dot com), made several molds from my cardboard patterns for the two tile shapes. Over a period of several months I made about 1,300 tiles one at a time with the molds.

Another option to consider... instead of tile, wood. It might be a bit easier to cut to the right specification, and then use the clear epoxy penny floor approach to protect it.