I spent a little time looking around the Wikipedia and Wolfram articles on Penrose Tiling, the Domino Problem, Wang Tiles, etc., but I'm having a little trouble getting into them. A lot of these resources are fairly non-linear in that they often have circular dependencies of concepts that you need to know.

For example, I can tell that aperiodicity is important somehow, but I don't know why and I'm not quite sure about the actual definition.

I keep seeing tiling linked in unexpectedly (e.g. L-systems, the Entscheidungsproblem) or in non-mathematical places (games, geometric art... even Neal Stephenson's Anathem) that it seems important and I'd really like to know more.

So, with that said: does anyone have any resources they'd recommend? I'm looking for something fairly complete or at least introductory, not just an article about a certain facet. Books are fine, visual or interactive resources are great. Would love descriptions of practical implications and relationships with other fields.

  • 1
    $\begingroup$ Quasicrystals are a physical instance of aperiodic tiling. Here is a video of the discoverer describing this finding. $\endgroup$ – anon Sep 22 '10 at 17:10

Chaim Goodman-Strauss has quite a few papers on his web page about this topic, including this specific one:


Goodman-Strass's publications page:



Try Miles of Tiles by Charles Radin.


I would definitely recommend M. Senechal's Quasicrystals and Geometry.

A bit more advanced but also much more complete is Aperiodic Order by Baake and Grimm.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.