I am working on projects in solving ground state of generalized ising models. One recent work involves tiling with basic tiles that filled the whole lattice. For example, we could obtain results:

every row corresponds to one constructible structure with basic tiles being "Generating configurations of the structure".

The resulting structures could be shown as followed:

9 and 12 are more complicated (can be periodic or aperiodic) shown as followed:

I realize (with the help of community), this is actually related to Wang Tiles. So the first few steps I wish to approach this problem are looking into all established theorems on Wang Tiles. Could someone suggest some relevant reference?

(PS:From Engineering respective, I think we (in engineer department) commonly would agree that as long as we could keep tiling the plane to a sufficiently large extent( e.g use 100*100 tiles without conflict), then we blindly think these few basics tiles could tile the plane. So the undecidability is not too crucial...)