Here is the algorithm abstract from the blog: Choose a cell at random, considering only the cells with the fewest possible values. Choose a random value to lock in for that cell, considering only the possible values for that cell. Propagate the effects of locking in the cell, removing the locked-in value from the possibilities of cells sharing the cell’s row, column, and 3x3 square. If during propagation, you removed the final possibility of a cell, give up and start again. (Note: "frequency hints" is also important) The one problem is that, unless the tile set is well chosen, the algorithm is probably too random to call "quantum", i.e. it probably won't lead to solutions of Schrödinger's equation. (The other problem is that step 4 is non-optimal. As mentioned in the post, a backtracking algorithm would be better).

Yes I'm quite interested in the WFC algorithm as well. It offers an interesting way to generate locally compatible structures. Should be fun to apply it to graphs and hyper-graphs. Also, the original WFC uses deterministic metric to collapse tiles, what will happen if stochastic process is used instead? I intend to explore WFC more when I get time.

Hi Giulio, I'm glad you like them (the game and the post)! I discovered the game 1 years ago when it was still in beta. Since then it has been giving me a lot of enjoying time. :)

Also, Silvia, nice work finding the WaveFunctionCollapse github, and the subsequent blog post. This is very well related to some of the other algorithms for growing Penrose tilings and to the Multicomputational Paradigm. Is anything like this available in Wolfram Function Repository? One interesting property of the Penrose tilings (if I remember correctly) is: For any patch of a tiling also a toplogical disk, orientation and placement of all interior tiles is determined by the ring of tiles around the edge of the disk. The whole solution on the region is just a function of the matching rules, shape and chosen boundary condition. In the case of non-tightly constrained tilesets, I would expect many different equivalent solutions with sufficiently large boundary. Sure the pictures turn out looking pretty, but it could also be an interesting combinatorial question how many patterns of square size $n \times n$ can be formed from some chosen initial data? The other way to go is try to make the algorithm more complicated, whether by machine learning / genetic algorithms, or by comparing with data. Maybe quantum chaos?

Designing Townscaper town on computable base-grid