We show several tilings that 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 of a class \(\mathcal{L}^0\) of tilings capturing the idea of a local generation procedure. In [1] and [2], we investigate in particular the sets of Wang tiles with two colors and an even number of edges of each color. We show for instance that the following tileset is not in \(\mathcal{L}^0\):
[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)

Below, you can see some of the tilings that belong to \(\mathcal{L}^0\). The images are randomly generated using the procedures described in the articles.