An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types is aperiodic if copies of these tiles can form only non-periodic tilings.
A portion of tiling by the Robinson tiles
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.
Zellige terracotta tiles in Marrakech, forming edge‑to‑edge, regular and other tessellations
A wall sculpture in Leeuwarden celebrating the artistic tessellations of M. C. Escher
A temple mosaic from the ancient Sumerian city of Uruk IV (3400–3100 BC), showing a tessellation pattern in coloured tiles
Roman geometric mosaic