Dihedral Escherization

摘要

"Escherization" is a process that finds an Escher-like tiling of the plane from tiles that resemble a user-supplied goal shape. We show how the original Escherization algorithm can be adapted to the dihedral case, producing tilings with two distinct shapes. We use a form of the adapted algorithm to create drawings in the style of Es-cher's print Sky and Water. Finally, we develop an Escherization algorithm for the very different case of Pen-rose's aperiodic tilings.