A tiling is periodic if, when translated in at least two non-parallel directions the tiling 'merges' with itself. A collection of tiles is aperiodic if the collection tiles the plane, but never in a periodic fashion. [[Roger Penrose]] discovered several such tilings in the 1970's. | A tiling is periodic if, when translated in at least two non-parallel directions the tiling 'merges' with itself. A collection of tiles is aperiodic if the collection tiles the plane, but never in a periodic fashion. [[Roger Penrose]] discovered several such tilings in the 1970's. |