the employment of symmetrical tessellation

The employment of symmetrical tessellation is an important feature of its abstract decoration. Tessellation is the covering or tiling of an entire plane with non-overlapping shapes. Regular tessellation makes use of one shape of tile; semi-regular uses more than one. In 'wallpaper' symmetry, the pattern is repeated in all directions, up and down and sideways. In 'frieze' symmetry the pattern runs in one direction only. In 'rosette' symmetry the design motif is reflected or rotated, but without further repetition. The mathematician George Pólya has proved that there are nine basic frieze patterns and seventeen basic types of wallpaper pattern. All seventeen are to be found in Islamic art. The most obvious application of tessellation in the Alhambra is in the tile work of the various dados, where repetitive pattern is used to rest the eye. There is a kind of playfulness in this kind of pattern generation - and particularly in the way that it is often impossible to determine what is foreground and what is background. This playfulness attracted the Dutch artist who is most famous for his paradoxes, M.C. Escher. He claimed to feel an affinity for the Moors even before visiting the Alhambra. He first went there in 1926 and then again in 1936. However, though he admired Moorish tessellation techniques, he thought it a pity that they did not employ figurative imagery in their patterning. This is, of course, what Escher is famous for - making patterns based on interlocking fishes and birds, or black demons and white angels. In the course of the last century or so the study of tessellation has become an important field of mathematics in its own right, something which gives force to the following observation by the painter Tom Phillips: 'Just as art is hidden everywhere in ornament, so science also finds many of its formulations already inherent in ornamental practice. The implications of map theory, game theory, topology, the fractals of chaos theory, game theory, topology, the fractals of chaos theory, have all lurked in ornament, awaiting their elevation to science.' The Alhambra is a stone book in more than one sense, for not only are its walls decorated with religious and poetical texts, but those texts are framed by geometrical designs that are, to all intents and purposes, demonstrations of mathematical theorems.

Robert Irwin

The Alhambra. 2004. p.118-121