We show several Wang tilesets which admit a "local" generation procedure. Informally, it means that the cells can be filled with a controlled amount of coordination between them. It is made precise in [1], in which we propose a formal definition capturing this idea (we call \(\mathcal{L}^0\) the class of tiling spaces that admit a local generation procedure).

[1] Tom Favereau, Mathieu Hoyrup. Local generation of tilings. Ergodic Theory and Dynamical Systems 45(11):3377-3418 (2025)
[2] Tom Favereau, Mathieu Hoyrup. Local generation of tilings: the bicolor Wang tilesets. Preprint (2025)

In [1] and [2], we investigate in particular the tilesets with two colors and an even number of each color in each tile. We show for instance that the following tileset is not in \(\mathcal{L}^0\):
Below, we show some of the tilesets that belong to \(\mathcal{L}^0\). The images are randomly generated using the procedures described in the articles.