Star patterns

Good to know

• Geometric pattern is the main decoration of Islamic architecture because the tradition avoids images of living things; the same few shapes, repeated and interlaced, cover walls, domes, doors and the pages of Qur'ans from Spain to India.
• Master craftsmen drew the patterns with a straightedge and compass from a grid of circles; a pattern can take a long time to design, but once the first star is drawn the rest follows by repeating it.
• The Alhambra palace in Granada, built mostly in the 13th and 14th centuries, is often said to hold examples of all seventeen ways to tile a plane with a repeating pattern; mathematicians still argue about whether every one is really there.
• The shapes are often said to suggest an order that goes on beyond the wall that holds it: a star pattern has no centre and no edge, and a viewer can take any point as the middle.
• The method used here, "polygons in contact", was set out by the English archaeologist Ernest Hankin in 1925 after he studied the patterns of Agra and Delhi; the Islamic craftsmen themselves worked with compass and straightedge, and a 30-metre scroll of pattern designs from the Topkapi Palace shows how they were handed down.
• The painter M. C. Escher visited the Alhambra in Granada in 1922 and again in 1936, copied its tiles for days, and said it was the richest source of inspiration he had ever tapped; his own tessellations of birds and lizards grew from them.
• In 2007 the physicists Peter Lu and Paul Steinhardt showed that some medieval patterns, such as those of the Darb-i Imam shrine in Isfahan (1453), are built from five kinds of tile that fit together in a nearly Penrose-like quasicrystalline way, five centuries before the mathematics of quasicrystals was discovered.