In this research, we propose a method for designing a tillable figure, that is, it fills a two-dimensional space by translation, rotation, and reflection with no gaps or overlaps. A tiling of the plane is a collection of one or several types of shapes, or tiles, that cover the plane without any gaps and overlaps. It is difficult to manually construct complex tiling patterns due to tight restrictions of tilings, i.e., preciously adjusting edges of adjacent tiles while taking account of concave-convex shapes should be needed.

In previous work, a method for isohedral tiling design was proposed, which analytically produces a tillable shape similar to a given shape. Whereas this method can obtain an optimal figure, its output changes depending on the small change of the input shape. Thus, it requires trial and error for slightly changes of the input shape.

The proposed method selects input point set and tiling pattern using genetic algorithm, allowing us to design better tillable shape with less trial and error effort than the previous method.

Asuka Hisatomi, Hitomi Koba, Makoto Kamizono, Kazunori Mizuno, Satoshi Ono: “Escher-like Tiling Design Using Hierarchical Optimization”, Genetic and Evolutionary Computation Conference (GECCO) , companion, pp.89-90 (2017).