Computational approach deciding whether a set of Wang Tile could tile the space up to some size

Question

As an applied person, I'm facing one practical problem deciding whether a set of Wang tile could tile the plane periodically or aperiodically. Although both problems seem undecidable, but I'm on a more practical aspect. Say, if the program accidentally ("or systematically") find some "periodic structure", then it stops and tells me there exists periodic pattern. If during running, it enumerates all the use of tile and finds that it simply cannot tile the plane, then it tell me this set of tiles cannot tile the plane. Even if the program didn't stop, then after running some steps, it returns me a few most ordered patterns that that could "possibly tile the plane".

For practical purpose, I simply assume if the tessellation are up to some size (maybe 1000*1000) then I say "it could tile the plane practically".

So my most interested question is: is there any established programs or algorithms that "try" to help me analyze a set of tile even if it might not halt ("but I could define some imposed halting condition").

For context why I am interested in this problem, here's the links:

coloring in lattice

Reference for Wang Tile

Periodic Tiling of Wang tile

Cross-posted to:

https://cs.stackexchange.com/questions/21502/computational-approach-deciding-whether-a-set-of-wang-tile-could-tile-the-space

Answer 1

There are a few theory papers tackling issue involved in Wang Tile:

Tiling groups for Wang tiles by Cristopher Moore, Ivan Rapaport, Eric Remila

Also recent development considering finite cases of Wang tile is considered here.

https://arxiv.org/abs/1305.2796

https://arxiv.org/abs/1212.3380

There are not yet exact answers to this problem as far as I know, but hope this helps....