In computer graphics, Wang tiles are used as a tool to generate non periodic textures and patterns. We develop a framework and a method for the tiling problem which is suitable for applications. In particular, we apply our methodology to a special kind of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2015 to model wall patterns. We generalise their result by provi...

Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography. In this direction, many people have tried to construct aperiodic tilings that are built from a single prototile with nearest neighbour matching rules, which is then called a monotile. One strand of the search for a planar monotile has focussed on hexagonal ...