A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
In architecture, tessellations have been used to create decorative motifs since ancient times. Mosaic tilings often had geometric patterns. Later civilisations also used larger tiles, either plain or individually decorated. Some of the most decorative were the Moorish wall tilings of Islamic architecture, using Girih tiles in buildings such as the Alhambra and La Mezquita.
Tessellations frequently appeared in the graphic art of M. C. Escher; he was inspired by the Moorish use of symmetry in places such as the Alhambra when he visited Spain in 1936. Escher made four "Circle Limit" drawings of tilings which use hyperbolic geometry. For his woodcut "Circle Limit IV" (1960), Escher prepared a pencil and ink study showing the required geometry. Escher explained that "No single component of all the series, which from infinitely far away rise like rockets perpendicularly from the limit and are at last lost in it, ever reaches the boundary line."
Tessellated designs often appear on textiles, whether woven, stitched in or printed. Tessellation patterns have been used to design interlocking motifs of patch shapes in quilts.
The honeycomb provides a well-known example of tessellation in nature with its hexagonal cells