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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.
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. [1] [2] From the 9th century onward, a range of sophisticated geometric patterns based on polygonal tessellation began to appear in Islamic art, eventually becoming dominant. [3]
Islamic art mostly avoids figurative images to avoid becoming objects of worship. [4] [5] This aniconism in Islamic culture caused artists to explore non-figural art, and created a general aesthetic shift toward mathematically based decoration. [6]
Authors such as Keith Critchlow [lower-alpha 1] 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. [7] [8] In Islamic culture, the patterns are believed to be the bridge to the spiritual realm, the instrument to purify the mind and the soul. [9] David Wade [lower-alpha 2] 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." [10] 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." [10] Against this, Doris Behrens-Abouseif [lower-alpha 3] 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". [11]
Many Islamic designs are built on squares and circles, typically repeated, overlapped and interlaced to form intricate and complex patterns. [1] 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. [1] [13] They are constructed on grids that require only ruler and compass to draw. [14] Artist and educator Roman Verostko argues that such constructions are in effect algorithms, making Islamic geometric patterns forerunners of modern algorithmic art. [15]
The circle symbolizes unity and diversity in nature, and many Islamic patterns are drawn starting with a circle. [16] 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. [16] [17] A similar design forms the logo of the Mohammed Ali Research Center. [18]
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." [2] 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." [2] 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. [2]
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. [19] [20] [21]
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. [22] [23] Moroccan geometric woodwork from the 14th to 19th centuries 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. [24]
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. [25]
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. [25]
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. [25]
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. [25] 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. [25]
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. [25]
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. [25] [lower-alpha 4]
Several artforms in different parts of the Islamic world make use of geometric patterns. These include ceramics, [27] girih strapwork, [28] jali pierced stone screens, [29] kilim rugs, [30] leather, [31] metalwork, [32] muqarnas vaulting, [33] shakaba stained glass, [34] woodwork, [28] and zellij tiling. [35]
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. [27] Thus an unglazed earthenware water flask [lower-alpha 5] 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. [36]
Girih are elaborate interlacing patterns formed of five standardized shapes. The style is used in Persian Islamic architecture and also in decorative woodwork. [28] 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. [28] [37] The visible pattern does not coincide with the underlying construction lines of the tiling. [28] 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. [38]
Jali are pierced stone screens with regularly repeating patterns. They are characteristic of Indo-Islamic architecture, for example in the Mughal dynasty buildings at Fatehpur Sikri and the Taj Mahal. The geometric designs combine polygons such as octagons and pentagons with other shapes such as 5- and 8-pointed stars. The patterns emphasized symmetries and suggested infinity by repetition. Jali functioned as windows or room dividers, providing privacy but allowing in air and light. [29] Jali forms a prominent element of the architecture of India. [39] The use of perforated walls has declined with modern building standards and the need for security. Modern, simplified jali walls, for example made with pre-moulded clay or cement blocks, have been popularised by the architect Laurie Baker. [40] Pierced windows in girih style are sometimes found elsewhere in the Islamic world, such as in windows of the Mosque of Ibn Tulun in Cairo. [41]
A kilim is an Islamic [30] flatwoven carpet (without a pile), whether for household use or a prayer mat. The pattern is made by winding the weft threads back over the warp threads when a colour boundary is reached. This technique leaves a gap or vertical slit, so kilims are sometimes called slit-woven textiles. Kilims are often decorated with geometric patterns with 2- or 4-fold mirror or rotational symmetries. Because weaving uses vertical and horizontal threads, curves are difficult to generate, and patterns are accordingly formed mainly with straight edges. [17] [42] Kilim patterns are often characteristic of specific regions. [43] Kilim motifs are often symbolic as well as decorative. For example, the wolf's mouth or wolf's foot motif (Turkish: Kurt Aǧzi, Kurt İzi) expresses the tribal weavers' desires for protection of their families' flocks from wolves. [44]
Islamic leather is often embossed with patterns similar to those already described. Leather book covers, starting with the Quran where figurative artwork was excluded, were decorated with a combination of kufic script, medallions and geometric patterns, typically bordered by geometric braiding. [31]
Metal artefacts share the same geometric designs that are used in other forms of Islamic art. However, in the view of Hamilton Gibb, the emphasis differs: geometric patterns tend to be used for borders, and if they are in the main decorative area they are most often used in combination with other motifs such as floral designs, arabesques, animal motifs, or calligraphic script. Geometric designs in Islamic metalwork can form a grid decorated with these other motifs, or they can form the background pattern. [32]
Even where metal objects such as bowls and dishes do not seem to have geometric decoration, still the designs, such as arabesques, are often set in octagonal compartments or arranged in concentric bands around the object. Both closed designs (which do not repeat) and open or repetitive patterns are used. Patterns such as interlaced six-pointed stars were especially popular from the 12th century. Eva Baer [lower-alpha 6] notes that while this design was essentially simple, it was elaborated by metalworkers into intricate patterns interlaced with arabesques, sometimes organised around further basic Islamic patterns, such as the hexagonal pattern of six overlapping circles. [46]
Muqarnas are elaborately carved ceilings to semi-domes, often used in mosques. They are typically made of stucco (and thus do not have a structural function), but can also be of wood, brick, and stone. They are characteristic of Islamic architecture of the Middle Ages from Spain and Morocco in the west to Persia in the east. Architecturally they form multiple tiers of squinches, diminishing in size as they rise. They are often elaborately decorated. [33]
Geometrically patterned stained glass is used in a variety of settings in Islamic architecture. It is found in the surviving summer residence of the Palace of Shaki Khans, Azerbaijan, constructed in 1797. Patterns in the "shabaka" windows include 6-, 8-, and 12-point stars. These wood-framed decorative windows are distinctive features of the palace's architecture. Shabaka are still constructed the traditional way in Sheki in the 21st century. [34] [47] Traditions of stained glass set in wooden frames (not lead as in Europe) survive in workshops in Iran as well as Azerbaijan. [48] Glazed windows set in stucco arranged in girih-like patterns are found both in Turkey and the Arab lands; a late example, without the traditional balance of design elements, was made in Tunisia for the International Colonial Exhibition in Amsterdam in 1883. [49] The old city of Sana'a in Yemen has stained glass windows in its tall buildings. [50]
Zellij (Arabic : الزَّلِيْج) is geometric tilework with glazed terracotta tiles set into plaster, forming colourful mosaic patterns including regular and semiregular tessellations. The tradition is characteristic of Morocco, but is also found in Moorish Spain. Zellij is used to decorate mosques, public buildings and wealthy private houses. [35]
It is sometimes supposed in Western society that mistakes in repetitive Islamic patterns such as those on carpets were intentionally introduced as a show of humility by artists who believed only Allah can produce perfection, but this theory is denied. [52] [53] [54]
Major Western collections hold many objects of widely varying materials with Islamic geometric patterns. The Victoria and Albert Museum in London holds at least 283 such objects, of materials including wallpaper, carved wood, inlaid wood, tin- or lead-glazed earthenware, brass, stucco, glass, woven silk, ivory, and pen or pencil drawings. [55] The Metropolitan Museum of Art in New York has among other relevant holdings 124 mediaeval (1000–1400 A.D.) objects bearing Islamic geometric patterns, [56] including a pair of Egyptian minbar (pulpit) doors almost 2 m. high in rosewood and mulberry inlaid with ivory and ebony; [57] and an entire mihrab (prayer niche) from Isfahan, decorated with polychrome mosaic, and weighing over 2,000 kg. [58]
Islamic decoration and craftsmanship had a significant influence on Western art when Venetian merchants brought goods of many types back to Italy from the 14th century onwards. [59]
The Dutch artist M. C. Escher was inspired by the Alhambra's intricate decorative designs to study the mathematics of tessellation, transforming his style and influencing the rest of his artistic career. [60] [61] In his own words it was "the richest source of inspiration I have ever tapped." [62]
Cultural organisations such as the Mathematical Sciences Research Institute and the Institute for Advanced Study run events on geometric patterns and related aspects of Islamic art. [63] In 2013 the Istanbul Center of Design and the Ensar Foundation ran what they claimed was the first ever symposium of Islamic Arts and Geometric Patterns, in Istanbul. The panel included the experts on Islamic geometric pattern Carol Bier, [lower-alpha 7] Jay Bonner, [lower-alpha 8] [66] Eric Broug, [lower-alpha 9] Hacali Necefoğlu [lower-alpha 10] and Reza Sarhangi. [lower-alpha 11] [70] In Britain, The Prince's School of Traditional Arts runs a range of courses in Islamic art including geometry, calligraphy, and arabesque (vegetal forms), tile-making, and plaster carving. [71]
Computer graphics and computer-aided manufacturing make it possible to design and produce Islamic geometric patterns effectively and economically. Craig S. Kaplan explains and illustrates in his Ph.D. thesis how Islamic star patterns can be generated algorithmically. [72]
Two physicists, Peter J. Lu and Paul Steinhardt, attracted controversy in 2007 by claiming [73] that girih designs such as that used on the Darb-e Imam shrine [lower-alpha 12] in Isfahan were able to create quasi-periodic tilings resembling those discovered by Roger Penrose in 1973. They showed that rather than the traditional ruler and compass construction, it was possible to create girih designs using a set of five "girih tiles", all equilateral polygons, secondarily decorated with lines (for the strapwork). [74]
In 2016, Ahmad Rafsanjani described the use of Islamic geometric patterns from tomb towers in Iran to create auxetic materials from perforated rubber sheets. These are stable in either a contracted or an expanded state, and can switch between the two, which might be useful for surgical stents or for spacecraft components. When a conventional material is stretched along one axis, it contracts along other axes (at right angles to the stretch). But auxetic materials expand at right angles to the pull. The internal structure that enables this unusual behaviour is inspired by two of the 70 Islamic patterns that Rafsanjani noted on the tomb towers. [75]
Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief of a divine creator of the universal geometer. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monuments, altars, and tabernacles has sometimes been considered sacred. The concept applies also to sacred spaces such as temenoi, sacred groves, village greens, pagodas and holy wells, Mandala Gardens and the creation of religious and spiritual art.
Tiles are usually thin, square or rectangular coverings manufactured from hard-wearing material such as ceramic, stone, metal, baked clay, or even glass. They are generally fixed in place in an array to cover roofs, floors, walls, edges, or other objects such as tabletops. Alternatively, tile can sometimes refer to similar units made from lightweight materials such as perlite, wood, and mineral wool, typically used for wall and ceiling applications. In another sense, a tile is a construction tile or similar object, such as rectangular counters used in playing games. The word is derived from the French word tuile, which is, in turn, from the Latin word tegula, meaning a roof tile composed of fired clay.
Takht-e Soleymān or Adur Gushnasp, is an archaeological site in West Azerbaijan, Iran dating back to Sasanian Empire. It lies midway between Urmia and Hamadan, very near the present-day town of Takab, and 400 km (250 mi) west of Tehran.
The Ben Youssef Madrasa is an Islamic madrasa (college) in Marrakesh, Morocco. The madrasa is named after the adjacent Ben Youssef Mosque, and was commissioned in 1564–65 CE by the Saadian sultan Abdallah al-Ghalib. Functioning today as a historical site, the Ben Youssef Madrasa was the largest Islamic college in the Maghreb at its height, and is widely recognized as a pinnacle of Saadian and Moroccan architecture.
Mudéjar art, or Mudéjar style, was a type of ornamentation and decoration used in the Iberian Christian kingdoms, primarily between the 13th and 16th centuries. It was applied to Romanesque, Gothic and Renaissance architectural styles as constructive, ornamental and decorative motifs derived from those that had been brought to or developed in Al-Andalus. These motifs and techniques were also present in the art and crafts, especially Hispano-Moresque lustreware that was once widely exported across Europe from southern and eastern Spain at the time.
Moroccan architecture reflects Morocco's diverse geography and long history, marked by successive waves of settlers through both migration and military conquest. This architectural heritage includes ancient Roman sites, historic Islamic architecture, local vernacular architecture, 20th-century French colonial architecture, and modern architecture.
In the history of art and design, strapwork is the use of stylised representations in ornament of ribbon-like forms. These may loosely imitate leather straps, parchment or metal cut into elaborate shapes, with piercings, and often interwoven in a geometric pattern. In early examples there may or may not be three-dimensionality, either actual in curling relief ends of the elements, or just represented in two dimensions. As the style continued, these curling elements became more prominent, often turning into scrollwork, where the ends curl into spirals or scrolls. By the Baroque scrollwork was a common element in ornament, often partly submerged by other rich ornament.
A jali or jaali is the term for a perforated stone or latticed screen, usually with an ornamental pattern constructed through the use of calligraphy, geometry or natural patterns. This form of architectural decoration is common in Indo-Islamic architecture and more generally in Indian architecture. It is closely related to mashrabiya in Islamic architecture.
The Saadian Tombs are a historic royal necropolis in Marrakesh, Morocco, located on the south side of the Kasbah Mosque, inside the royal kasbah (citadel) district of the city. They date to the time of the Saadian dynasty and in particular to the reign of Ahmad al-Mansur (1578–1603), though members of Morocco's monarchy continued to be buried here for a time afterwards. The complex is regarded by many art historians as the high point of Moroccan architecture in the Saadian period due to its luxurious decoration and careful interior design. Today the site is a major tourist attraction in Marrakesh.
Moorish architecture is a style within Islamic architecture which developed in the western Islamic world, including al-Andalus and what is now Morocco, Algeria, and Tunisia. Scholarly references on Islamic architecture often refer to this architectural tradition in terms such as architecture of the Islamic West or architecture of the Western Islamic lands. The use of the term "Moorish" comes from the historical Western European designation of the Muslim inhabitants of these regions as "Moors". Some references on Islamic art and architecture consider this term to be outdated or contested.
Stucco decoration in Islamic architecture refers to carved or molded stucco and plaster. The terms "stucco" and "plaster" are used almost interchangeably in this context to denote most types of stucco or plaster decoration with slightly varying compositions. This decoration was mainly used to cover walls and surfaces and the main motifs were those predominant in Islamic art: geometric, arabesque, and calligraphic, as well as three-dimensional muqarnas. Plaster of gypsum composition was extremely important in Islamic architectural decoration as the relatively dry climate throughout much of the Islamic world made it easy to use this cheap and versatile material in a variety of spaces.
Zellij is a style of mosaic tilework made from individually hand-chiseled tile pieces. The pieces were typically of different colours and fitted together to form various patterns on the basis of tessellations, most notably elaborate Islamic geometric motifs such as radiating star patterns. This form of Islamic art is one of the main characteristics of architecture in the western Islamic world. It is found in the architecture of Morocco, the architecture of Algeria, early Islamic sites in Tunisia, and in the historic monuments of al-Andalus. From the 14th century onwards, zellij became a standard decorative element along lower walls, in fountains and pools, on minarets, and for the paving of floors.
Girihtiles are a set of five tiles that were used in the creation of Islamic geometric patterns using strapwork (girih) for decoration of buildings in Islamic architecture. They have been used since about the year 1200 and their arrangements found significant improvement starting with the Darb-i Imam shrine in Isfahan in Iran built in 1453.
Girih are decorative Islamic geometric patterns used in architecture and handicraft objects, consisting of angled lines that form an interlaced strapwork pattern.
The Bou Inania Madrasa or Bu 'Inaniya Madrasa is a madrasa in Fes, Morocco, built in 1350–55 CE by Abu Inan Faris. It is the only madrasa in Morocco which also functioned as a congregational mosque. It is widely acknowledged as a high point of Marinid architecture and of historic Moroccan architecture generally.
Islamic ornament is the use of decorative forms and patterns in Islamic art and Islamic architecture. Its elements can be broadly divided into the arabesque, using curving plant-based elements, geometric patterns with straight lines or regular curves, and calligraphy, consisting of religious texts with stylized appearance, used both decoratively and to convey meaning. All three often involve elaborate interlacing in various mediums.
The Al-Attarine Madrasa or Medersa al-Attarine is a madrasa in Fes, Morocco, near the Al-Qarawiyyin Mosque. It was built by the Marinid sultan Uthman II Abu Said in 1323-5. The madrasa takes its name from the Souk al-Attarine, the spice and perfume market. It is considered one of the highest achievements of Marinid architecture due to its rich and harmonious decoration and its efficient use of limited space.
The Shah Nematollah Vali Shrine is a historical complex, located in Mahan, Iran, which contains the mausoleum of Shah Nematollah Vali, the renowned Iranian mystic and poet. Shah Nematollah Vali died in 1431 aged over 100. In 1436 a shrine was erected in his honor and became a pilgrimage site; with the attention of successive rulers contributing various additions over the centuries.
The Topkapı Scroll is a Timurid dynasty patterned scroll in the collection of the Topkapı Palace museum.
The al-Hamra Mosque or Red Mosque is a Marinid-era mosque in Fes, Morocco. It is a local Friday mosque located on the Grande Rue of Fes el-Jdid, the palace-city founded by the Marinid rulers.
Much of the art of Islam, whether in architecture, ceramics, textiles or books, is the art of decoration – which is to say, of transformation. The aim, however, is never merely to ornament, but rather to transfigure. ... The vast edifices of mosques are transformed into lightness and pattern; the decorated pages of a Qur'an can become windows onto the infinite. Perhaps most importantly, the Word, expressed in endless calligraphic variations, always conveys the impression that it is more enduring than the objects on which it is inscribed.
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