MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

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

Consider a set of Wang Tile such that all the edges are either 1 or 0.... there are 16 elements in such a set.

Now, I wish to characterize all the periodic tilings of this set (better if they are characterized by the appearing frequency of each type of the tiles)... Is there some way that I could do any such kind of characterization?

Thank you.

share|cite|improve this question
I gather that you are mainly asking about which lists of 16 numbers adding to 1 could be the relative proportions . restricting to the 4 tiles having 1 on the top and bottom edges might be a good start. it is impossible to have the proportions be $1/3$ each for having sides (left right) $00$ $01$ $10$ so a certain obvious condition is not sufficient. – Aaron Meyerowitz May 3 '14 at 2:06

Your Answer


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

Browse other questions tagged or ask your own question.