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: