5 ms·

It would be awesome to see this turned into a library for dynamically generating aperiodic Wang tiles[0] for one "idea". (ie: grass or cobblestone that doesn't

• andrewla 12y ago
  I imagine that there is additional research in the area, but what you would want is not so much a Wang tile as described in the article, because then all of the triangular tiles would have to be mirrored. With the existing set, to get anything looking realistic, you would have to define the "left-yellow", "right-yellow", "up-yellow", and "down-yellow" variants of the yellow triangle, with the left and right variants being tileable. I feel like it should be possible to define a variant of Wang tiles where only complementary colors can be matched. That said, although aperiodic Wang tiles force all possible tilings to be aperiodic, I'm not aware of anything that says that a regular set of tiles, for which periodic tiles are possible, require that all tilings be periodic. That is, it should be possible to create an aperiodic tiling of less difficult tiles. In fact, this is obvious by a projection of the Wang tiles onto less pathological tiles -- we can take the set of 13, call the first six "black" and the second seven "white", and obey the Wang tiling rules and produce an aperiodic tiling consisting of just black and white tiles.
• bglazer 12y ago
  http://research.microsoft.com/en-us/um/people/cohen/WangFinal.pdf http://research.microsoft.com/en-us/um/people/cohen/WangFina... Microsoft research published a paper on using aperiodic Wang tilings to generate textures.
• lmm 12y ago
  Wang tile patterns may be aperiodic but they still look "geometric".