Islamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures.

The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, or may retreat into the background around other motifs. The complexity and variety of patterns used evolved from simple stars and lozenges in the ninth century, through a variety of 6- to 13-point patterns by the 13th century, and finally to include also 14- and 16-point stars in the sixteenth century.

Geometric patterns occur in a variety of forms in Islamic art and architecture. These include kilim carpets, Persian girih and Moroccan zellij tilework, muqarnas decorative vaulting, jali pierced stone screens, ceramics, leather, stained glass, woodwork, and metalwork.

Interest in Islamic geometric patterns is increasing in the West, both among craftsmen and artists like M. C. Escher in the twentieth century, and among mathematicians and physicists such as Peter J. Lu and Paul Steinhardt.

Background

Islamic decoration Islamic geometric patterns are derived from simpler designs used in earlier cultures: Greek, Roman, and Sasanian. They are one of three forms of Islamic decoration, the others being the arabesque based on curving and branching plant forms, and Islamic calligraphy; all three are frequently used together. From the 9th century onward, a range of sophisticated geometric patterns based on polygonal tessellation began to appear in Islamic art, eventually becoming dominant.

Islamic art mostly avoids figurative images to avoid becoming objects of worship. This aniconism in Islamic culture caused artists to explore non-figural art, and created a general aesthetic shift toward mathematically based decoration.

Purpose

Authors such as Keith Critchlow argue that Islamic patterns are created to lead the viewer to an understanding of the underlying reality, rather than being mere decoration, as writers interested only in pattern sometimes imply. In Islamic culture, the patterns are believed to be the bridge to the spiritual realm, the instrument to purify the mind and the soul. David Wade states that "Much of the art of Islam, whether in architecture, ceramics, textiles or books, is the art of decoration – which is to say, of transformation." Wade argues that the aim is to transfigure, turning mosques "into lightness and pattern", while "the decorated pages of a Qur’an can become windows onto the infinite." Against this, Doris Behrens-Abouseif states in her book Beauty in Arabic Culture that a "major difference" between the philosophical thinking of Medieval Europe and the Islamic world is exactly that the concepts of the good and the beautiful are separated in Arabic culture. She argues that beauty, whether in poetry or in the visual arts, was enjoyed "for its own sake, without commitment to religious or moral criteria".

Pattern formation

Many Islamic designs are built on squares and circles, typically repeated, overlapped and interlaced to form intricate and complex patterns. A recurring motif is the 8-pointed star, often seen in Islamic tilework; it is made of two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is the polygon, including pentagons and octagons. All of these can be combined and reworked to form complicated patterns with a variety of symmetries including reflections and rotations. Such patterns can be seen as mathematical tessellations, which can extend indefinitely and thus suggest infinity. They are constructed on grids that require only ruler and compass to draw. Artist and educator Roman Verostko argues that such constructions are in effect algorithms, making Islamic geometric patterns forerunners of modern algorithmic art.

The circle symbolizes unity and diversity in nature, and many Islamic patterns are drawn starting with a circle. For example, the decoration of the 15th-century mosque in Yazd, Persia is based on a circle, divided into six by six circles drawn around it, all touching at its centre and each touching its two neighbours' centres to form a regular hexagon. On this basis is constructed a six-pointed star surrounded by six smaller irregular hexagons to form a tessellating star pattern. This forms the basic design which is outlined in white on the wall of the mosque. That design, however, is overlaid with an intersecting tracery in blue around tiles of other colours, forming an elaborate pattern that partially conceals the original and underlying design. A similar design forms the logo of the Mohammed Ali Research Center. The logo's construction is demonstrated in an animation on the MOHA website.

One of the early Western students of Islamic patterns, Ernest Hanbury Hankin, defined a "geometrical arabesque" as a pattern formed "with the help of construction lines consisting of polygons in contact." He observed that many different combinations of polygons can be used as long as the residual spaces between the polygons are reasonably symmetrical. For example, a grid of octagons in contact has squares (of the same side as the octagons) as the residual spaces. Every octagon is the basis for an 8-point star, as seen at Akbar's tomb, Sikandra (1605–1613). Hankin considered the "skill of the Arabian artists in discovering suitable combinations of polygons .. almost astounding." He further records that if a star occurs in a corner, exactly one quarter of it should be shown; if along an edge, exactly one half of it.

The Topkapı Scroll, made in Timurid dynasty Iran in the late-15th century or beginning of the 16th century, contains 114 patterns including coloured designs for girih tilings and muqarnas quarter or semidomes. (subscription required)

The mathematical properties of the decorative tile and stucco patterns of the Alhambra palace in Granada, Spain have been extensively studied. Some authors have claimed on dubious grounds to have found most or all of the 17 wallpaper groups there. Moroccan geometric woodwork from the makes use of only 5 wallpaper groups, mainly p4mm and c2mm, with p6mm and p2mm occasionally and p4gm rarely; it is claimed that the "Hasba" (measure) method of construction, which starts with n-fold rosettes, can however generate all 17 groups.

Evolution

Early stage

The earliest geometrical forms in Islamic art were occasional isolated geometric shapes such as 8-pointed stars and lozenges containing squares. These date from 836 in the Great Mosque of Kairouan, Tunisia, and since then have spread all across the Islamic world.

Middle stage

The next development, marking the middle stage of Islamic geometric pattern usage, was of 6- and 8-point stars, which appear in 879 at the Ibn Tulun Mosque, Cairo, and then became widespread.

A wider variety of patterns were used from the 11th century. Abstract 6- and 8-point shapes appear in the Tower of Kharaqan at Qazvin, Persia in 1067, and the Al-Juyushi Mosque, Egypt in 1085, again becoming widespread from there, though 6-point patterns are rare in Turkey.

In 1086, 7- and 10-point girih patterns (with heptagons, 5- and 6-pointed stars, triangles and irregular hexagons) appear in the Jameh Mosque of Isfahan. 10-point girih became widespread in the Islamic world, except in the Spanish Al-Andalus. Soon afterwards, sweeping 9-, 11-, and 13-point girih patterns were used in the Barsian Mosque, also in Persia, in 1098; these, like 7-point geometrical patterns, are rarely used outside Persia and central Asia.

Finally, marking the end of the middle stage, 8- and 12-point girih rosette patterns appear in the Alâeddin Mosque at Konya, Turkey in 1220, and in the Abbasid palace in Baghdad in 1230, going on to become widespread across the Islamic world.

Late stage

The beginning of the late stage is marked by the use of simple 16-point patterns at the Hasan Sadaqah mausoleum in Cairo in 1321, and in the Alhambra in Spain in 1338–1390. These patterns are rarely found outside these two regions. More elaborate combined 16-point geometrical patterns are found in the Sultan Hassan complex in Cairo in 1363, but rarely elsewhere. Finally, 14-point patterns appear in the Jama Masjid at Fatehpur Sikri in India in 1571–1596, but in few other places.

Artforms Several artforms in different parts of the Islamic world make use of geometric patterns. These include ceramics, girih strapwork, jali pierced stone screens, kilim rugs, leather, metalwork, muqarnas vaulting, shakaba stained glass, woodwork, and zellij tiling.

Ceramics

Ceramics lend themselves to circular motifs, whether radial or tangential. Bowls or plates can be decorated inside or out with radial stripes; these may be partly figurative, representing stylised leaves or flower petals, while circular bands can run around a bowl or jug. Patterns of these types were employed on Islamic ceramics from the Ayyubid period, 13th century. Radially symmetric flowers with, say, 6 petals lend themselves to increasingly stylised geometric designs which can combine geometric simplicity with recognisably naturalistic motifs, brightly coloured glazes, and a radial composition that ideally suits circular crockery. Potters often chose patterns suited to the shape of the vessel they were making. Thus an unglazed earthenware water flask from Aleppo in the shape of a vertical circle (with handles and neck above) is decorated with a ring of moulded braiding around an Arabic inscription with a small 8-petalled flower at the centre.

Girih tilings and woodwork

Girih are elaborate interlacing patterns formed of five standardized shapes. The style is used in Persian Islamic architecture and also in decorative woodwork. Girih designs are traditionally made in different media including cut brickwork, stucco, and mosaic faience tilework. In woodwork, especially in the Safavid period, it could be applied either as lattice frames, left plain or inset with panels such as of coloured glass; or as mosaic panels used to decorate walls and ceilings, whether sacred or secular. In architecture, girih forms decorative interlaced strapwork surfaces from the 15th century to the 20th century. Most designs are based on a partially hidden geometric grid which provides a regular array of points; this is made into a pattern using 2-, 3-, 4-, and 6-fold rotational symmetries which can fill the plane. The visible pattern superimposed on the grid is also geometric, with 6-, 8-, 10- and 12-pointed stars and a variety of convex polygons, joined by straps which typically seem to weave over and under each other. The visible pattern does not coincide with the underlying construction lines of the tiling. The visible patterns and the underlying tiling represent a bridge linking the invisible to the visible, analogous to the "epistemological quest" in Islamic culture, the search for the nature of knowledge.

Jali