The Alhambra is a former palace and citadel of the Moorish kings of Granada, and perhaps the greatest monument to Islamic mathematical art on Earth. Because the Qur'an considers the depiction of living beings in religious settings blasphemous, Islamic artists created intricate patterns to symbolize the wonders of creation: the repetitive nature of these complex geometric designs suggested the limitless power of God. The sprawling citadel, looming high above the Andalusian plain, boasts a remarkable array of mosaics with tiles arranged in intricate patterns.

 

The Alhambra tilings are periodic; in other words, they consist of some basic unit that is repeated in all directions to fill up the available space. All 17 different groups of isometries – the possible ways of repeatedly tiling the plane – are used at the palace.

 

The designs left a deep impression on Maurits Escher, who came here in 1936. Subsequently, Escher's art took on a much more mathematical nature and over the next six years he produced 43 colored drawings of periodic tilings with a wide variety of symmetry types.