Wang tiles, mentioned only at the end of the article, encode Turing-equivalent computation in their simple color-matching rule. It is unknown exactly how useful Wang tiles are to theory of computation, other than as a wonderful demonstration of how easily Turing-complete systems arise naturally.

I suspect that tiling may have applications in resource management, particularly when allocating resources like memory which have an underlying topological structure.

Edit: https://arxiv.org/pdf/1506.06492.pdf is worth considering, but I don't yet know what its relevance is.