MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can anyone suggest a survey (or surveys) that provides an update to Tilings and Patterns by Grunbaum and Shepard? If there's a more recent book, that would be fantastic, but I don't see one.

I am most interested in the combinatorics of Wang Tilings and other square tilings, with the motivation of applying those techniques to derive upper/lower bounds to constructions in self-assembly.

Thank you.

share|cite|improve this question
I know this doesn't answer your question, but The Symmetries of Things by Conway, Burgiel, and Goodman-Strass (2008), has quite a bit of detailed information on tilings:… – Joseph O'Rourke Apr 1 '11 at 1:11
@Joseph O'Rourke: Thanks very much. :-) – Aaron Sterling Apr 4 '11 at 13:36
up vote 6 down vote accepted

How is your German? MR2219468 (2006m:05054) Ardila, Federico; Stanley, Richard P. Pflasterungen. (German) [Tilings] Math. Semesterber. 53 (2006), no. 1, 17–43.

MR2133310 (2006e:52036) Zong, Chuanming What is known about unit cubes. Bull. Amer. Math. Soc. (N.S.) 42 (2005), no. 2, 181–211 (electronic).

MR2087242 (2005e:42071) Kolountzakis, Mihail N. The study of translational tiling with Fourier analysis. Fourier analysis and convexity, 131–187, Appl. Numer. Harmon. Anal., Birkhäuser Boston, Boston, MA, 2004.

MR2005953 (2004k:28011) Jackson, Steve; Mauldin, R. Daniel Survey of the Steinhaus tiling problem. Bull. Symbolic Logic 9 (2003), no. 3, 335–361.

MR1990769 (2004k:52027) Pak, Igor Tile invariants: new horizons. Tilings of the plane. Theoret. Comput. Sci. 303 (2003), no. 2-3, 303–331.

MR1242999 (94g:52026) Schulte, Egon Tilings. Handbook of convex geometry, Vol. A, B, 899–932, North-Holland, Amsterdam, 1993.

share|cite|improve this answer
I think the Ardila-Stanley article is actually a German translation of a survey paper they wrote in English (see – Henry Cohn Apr 1 '11 at 13:54
Thanks for the references. I've skimmed the non-German ones, and they look very interesting (though perhaps not immediately helpful on my current project). @Henry Cohn: Thanks for the link, I'll check it out. – Aaron Sterling Apr 4 '11 at 13:37

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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