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
Interlaced video (also known as interlaced scan) is a technique for doubling the perceived frame rate of a video display without consuming extra bandwidth. The interlaced signal contains two fields of a video frame captured consecutively. This ...
, as can
arabesque
The arabesque is a form of artistic decoration consisting of "surface decorations based on rhythmic linear patterns of scrolling and interlacing foliage, tendrils" or plain lines, often combined with other elements. Another definition is "Foli ...
s (with which they are often combined), to form intricate and complex patterns, including a wide variety of
tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
s. 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
Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings ...
. These include
kilim carpets,
Persia
Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...
n
girih and
Moroccan zellij tilework,
muqarnas decorative vaulting,
jali pierced stone screens,
ceramics,
leather
Leather is a strong, flexible and durable material obtained from the tanning, or chemical treatment, of animal skins and hides to prevent decay. The most common leathers come from cattle, sheep, goats, equine animals, buffalo, pigs and hog ...
,
stained glass
Stained glass is coloured glass as a material or works created from it. Throughout its thousand-year history, the term has been applied almost exclusively to the windows of churches and other significant religious buildings. Although tradition ...
, woodwork, and metalwork.
Interest in Islamic geometric patterns is increasing in the West, both among
craftsmen
Craftsman may refer to:
A profession
*Artisan, a skilled manual worker who makes items that may be functional or strictly decorative
*Master craftsman, an artisan who has achieved such a standard that he may establish his own workshop and take o ...
and
artists like
M. C. Escher
Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints.
Despite wide popular interest, Escher was for most of his life neglected in t ...
in the twentieth century, and among
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
s and
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate cau ...
s such as
Peter J. Lu and
Paul Steinhardt.
Background
Islamic decoration
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. The Islamic geometric patterns derived from simpler designs used in earlier cultures:
Greek,
Roman
Roman or Romans most often refers to:
* Rome, the capital city of Italy
* Ancient Rome, Roman civilization from 8th century BC to 5th century AD
*Roman people, the people of ancient Rome
*''Epistle to the Romans'', shortened to ''Romans'', a lett ...
, and
Sasanian
The Sasanian () or Sassanid Empire, officially known as the Empire of Iranians (, ) and also referred to by historians as the Neo-Persian Empire, was the last Iranian empire before the early Muslim conquests of the 7th-8th centuries AD. Named ...
. They are one of three forms of
Islamic decoration, the others being the
arabesque
The arabesque is a form of artistic decoration consisting of "surface decorations based on rhythmic linear patterns of scrolling and interlacing foliage, tendrils" or plain lines, often combined with other elements. Another definition is "Foli ...
based on curving and branching plant forms, and
Islamic calligraphy
Islamic calligraphy is the artistic practice of handwriting and calligraphy, in the languages which use Arabic alphabet or the alphabets derived from it. It includes Arabic, Persian, Ottoman, and Urdu calligraphy.Chapman, Caroline (2012). ...
; all three are frequently used together.
Purpose
Authors such as
Keith Critchlow
Keith Barry Critchlow (16 March 1933 – 8 April 2020) was a British artist, lecturer, author, Sacred Geometer, professor of architecture, and a co-founder of the Temenos Academy in the UK.
Biography
Critchlow was educated at the Summerhill ...
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".
File:Tiles inside the Jame Mosque of Yazd 01.JPG, Tiles inside the Jame Mosque of Yazd, Persia, with geometric and vegetal patterns
File:Bou inania DSCF2978.jpg, Bou Inania Madrasa, Fes, Morocco, originally c. 1350, with geometric patterns in zellij tilework
File:162-MoroccoOpenDoors.jpg, A variety of vernacular decorative Islamic styles in Morocco
Morocco (),, ) officially the Kingdom of Morocco, is the westernmost country in the Maghreb region of North Africa. It overlooks the Mediterranean Sea to the north and the Atlantic Ocean to the west, and has land borders with Algeria to A ...
: wooden panels, zellij tilework, stucco calligraphy, and floral door panels
File:Alhambra Detail 17.JPG, Arch in the Alhambra with Mocárabe stalactite work
File:Jar Met 56.185.15.jpg, Ayyubid
The Ayyubid dynasty ( ar, الأيوبيون '; ) was the founding dynasty of the medieval Sultanate of Egypt established by Saladin in 1171, following his abolition of the Fatimid Caliphate of Egypt. A Sunni Muslim of Kurdish origin, Saladin ...
Raqqa ware stoneware glazed jar with overlapping circles grid
An overlapping circles grid is a geometric pattern of tessellation, repeating, overlapping circles of an equal radius in two-dimensional space. Commonly, designs are based on circles centered on triangular lattice, triangles (with the simple, two ...
pattern. Syria, 12th/13th century
File:Green mosque archway.JPG, An archway in the Ottoman Green Mosque, Bursa
( grc-gre, Προῦσα, Proûsa, Latin: Prusa, ota, بورسه, Arabic:بورصة) is a city in northwestern Turkey and the administrative center of Bursa Province. The fourth-most populous city in Turkey and second-most populous in the ...
, Turkey (1424), with girih 10-point stars and pentagons
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
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two ...
, including pentagon
In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.
A pentagon may be sim ...
s 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 tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
s, which can extend indefinitely and thus suggest infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions am ...
. They are constructed on grids that require only ruler and compass
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...
to draw. Artist and educator Roman Verostko argues that such constructions are in effect algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
s, making Islamic geometric patterns forerunners of modern algorithmic art
Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called ''algorists''.
Overview
Algorithmic art, also known as computer-generated art, is a subset o ...
.
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
Yazd ( fa, یزد ), formerly also known as Yezd, is the capital of Yazd Province, Iran. The city is located southeast of Isfahan. At the 2016 census, the population was 1,138,533. Since 2017, the historical city of Yazd is recognized as a Wor ...
, 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
The Topkapı Scroll ( tr, Topkapı Parşömeni) is a Timurid dynasty pattern scroll in the collection of the Topkapı Palace museum.
The scroll is a valuable source of information, consisting of 114 patterns that may have been used both indirect ...
, 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.
The mathematical properties of the decorative tile and stucco
Stucco or render is a construction material made of aggregates, a binder, and water. Stucco is applied wet and hardens to a very dense solid. It is used as a decorative coating for walls and ceilings, exterior walls, and as a sculptural and a ...
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 group
A wallpaper is a mathematical object covering a whole Euclidean plane by repeating a motif indefinitely, in manner that certain isometries keep the drawing unchanged. To a given wallpaper there corresponds a group of such congruent transformati ...
s 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.
File:Topkapi Scroll P290.JPG, Two-dimensional designs for two quarter-dome muqarnas – as a seashell
A seashell or sea shell, also known simply as a shell, is a hard, protective outer layer usually created by an animal or organism that lives in the sea. The shell is part of the body of the animal. Empty seashells are often found washe ...
(top), as a fan (bottom). Topkapı Scroll
The Topkapı Scroll ( tr, Topkapı Parşömeni) is a Timurid dynasty pattern scroll in the collection of the Topkapı Palace museum.
The scroll is a valuable source of information, consisting of 114 patterns that may have been used both indirect ...
, 15th century
File:Darb-i Imam shrine spandrel.JPG, Girih tiling in the decagonal pattern on a spandrel from the Darb-e Imam
The shrine of Darb-e Imam ( fa, امامزاده درب امام), located in the Dardasht quarter of Isfahan, Iran, is a funerary complex, with a cemetery, shrine structures, and courtyards belonging to different construction periods and styles. ...
shrine
File:Spandrel-large scale pattern.svg, Construction of girih pattern in Darb-e Imam spandrel (yellow line). Construction decagons blue, bowties red. The strapwork cuts across the construction tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
.
File:OctagonalTesselations2.png, Analysis of octagonal patterns in Mughal architecture by Ernest Hanbury Hankin, 1925. 8-pointed stars emerge (lower right) where heavy black lines cross.
File:Decoration on the wall of the masoleoum of Itmad-ud-Daulah's tomb 1.jpg, Decoration in Tomb of I'timād-ud-Daulah, Agra
Agra (, ) is a city on the banks of the Yamuna river in the Indian state of Uttar Pradesh, about south-east of the national capital New Delhi and 330 km west of the state capital Lucknow. With a population of roughly 1.6 million, Agra ...
, showing correct treatment of sides and corners. A quarter of each 6-point star is shown in each corner; half stars along the sides.
File:Architectural Drawing for brick vaulting, Iran, 1800-70.JPG, Architectural drawing for brick vaulting, Iran, probably Tehran, 1800–70
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
Qazvin (; fa, قزوین, , also Romanized as ''Qazvīn'', ''Qazwin'', ''Kazvin'', ''Kasvin'', ''Caspin'', ''Casbin'', ''Casbeen'', or ''Ghazvin'') is the largest city and capital of the Province of Qazvin in Iran. Qazvin was a capital of the ...
, 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
Al-Andalus translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label= Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, al-Ándalus () was the M ...
.[ 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
The Alaaddin Mosque (Turkish: Alaaddin Cami) is the principal monument on Alaaddin Hill (Alaadin Tepesi) in the centre of Konya, Turkey. Part of the hilltop citadel complex that contained the Seljuk Palace, it served as the main prayer hall f ...
at Konya
Konya () is a major city in central Turkey, on the southwestern edge of the Central Anatolian Plateau, and is the capital of Konya Province. During antiquity and into Seljuk times it was known as Iconium (), although the Seljuks also called it D ...
, Turkey in 1220, and in the Abbasid
The Abbasid Caliphate ( or ; ar, الْخِلَافَةُ الْعَبَّاسِيَّة, ') was the third caliphate to succeed the Islamic prophet Muhammad. It was founded by a dynasty descended from Muhammad's uncle, Abbas ibn Abdul-Mutta ...
palace in Baghdad
Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon ...
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
Fatehpur Sikri () is a town in the Agra District of Uttar Pradesh, India. Situated 35.7 kilometres from the district headquarters of Agra, Fatehpur Sikri itself was founded as the capital of Mughal Empire in 1571 by Emperor Akbar, serving this ...
in India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...
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
The Ayyubid dynasty ( ar, الأيوبيون '; ) was the founding dynasty of the medieval Sultanate of Egypt established by Saladin in 1171, following his abolition of the Fatimid Caliphate of Egypt. A Sunni Muslim of Kurdish origin, Saladin ...
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
)), is an adjective which means "white-colored mixed with black".
, motto =
, image_map =
, mapsize =
, map_caption =
, image_map1 =
...
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
Stucco or render is a construction material made of aggregates, a binder, and water. Stucco is applied wet and hardens to a very dense solid. It is used as a decorative coating for walls and ceilings, exterior walls, and as a sculptural and a ...
, and mosaic faience
Faience or faïence (; ) is the general English language term for fine tin-glazed pottery. The invention of a white pottery glaze suitable for painted decoration, by the addition of an oxide of tin to the slip of a lead glaze, was a major ...
tilework. In woodwork, especially in the Safavid
Safavid Iran or Safavid Persia (), also referred to as the Safavid Empire, '. was one of the greatest Iranian empires after the 7th-century Muslim conquest of Persia, which was ruled from 1501 to 1736 by the Safavid dynasty. It is often conside ...
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
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
Fatehpur Sikri () is a town in the Agra District of Uttar Pradesh, India. Situated 35.7 kilometres from the district headquarters of Agra, Fatehpur Sikri itself was founded as the capital of Mughal Empire in 1571 by Emperor Akbar, serving this ...
and the Taj Mahal
The Taj Mahal (; ) is an Islamic ivory-white marble mausoleum on the right bank of the river Yamuna in the Indian city of Agra. It was commissioned in 1631 by the Mughal emperor Shah Jahan () to house the tomb of his favourite wife, ...
. 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. Jali forms a prominent element of the architecture of India. 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. 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.
Kilim
A kilim is an Islamic flatwoven carpet (without a pile), whether for household use or a prayer mat. The pattern is made by winding the weft
Warp and weft are the two basic components used in weaving to turn thread or yarn into fabric. The lengthwise or longitudinal warp yarns are held stationary in tension on a frame or loom while the transverse weft (sometimes woof) is dra ...
threads back over the warp
Warp, warped or warping may refer to:
Arts and entertainment Books and comics
* WaRP Graphics, an alternative comics publisher
* ''Warp'' (First Comics), comic book series published by First Comics based on the play ''Warp!''
* Warp (comics), a ...
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.[ Kilim patterns are often characteristic of specific regions. 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
The wolf (''Canis lupus''; : wolves), also known as the gray wolf or grey wolf, is a large canine native to Eurasia and North America. More than thirty subspecies of ''Canis lupus'' have been recognized, and gray wolves, as popularly un ...
.
Leather
Islamic leather is often embossed with patterns similar to those already described. Leather book covers, starting with the Quran
The Quran (, ; Standard Arabic: , Quranic Arabic: , , 'the recitation'), also romanized Qur'an or Koran, is the central religious text of Islam, believed by Muslims to be a revelation from God. It is organized in 114 chapters (pl.: , ...
where figurative artwork was excluded, were decorated with a combination of kufic script, medallions and geometric patterns, typically bordered by geometric braid
A braid (also referred to as a plait) is a complex structure or pattern formed by interlacing two or more strands of flexible material such as textile yarns, wire, or hair.
The simplest and most common version is a flat, solid, three-strande ...
ing.
Metalwork
Metal artefacts share the same geometric designs that are used in other forms of Islamic art. However, in the view of Hamilton Gibb
Sir Hamilton Alexander Rosskeen Gibb (2 January 1895 – 22 October 1971), known as H. A. R. Gibb, was a Scottish historian and Orientalist.
Early life and education
Gibb was born on Wednesday, 2 January 1895, in Alexandria, Egypt, ...
, 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.
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 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.
Muqarnas
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.
Stained glass
Geometrically patterned stained glass
Stained glass is coloured glass as a material or works created from it. Throughout its thousand-year history, the term has been applied almost exclusively to the windows of churches and other significant religious buildings. Although tradition ...
is used in a variety of settings in Islamic architecture. It is found in the surviving summer residence of the Palace of Shaki Khans
The Palace of Shaki Khans ( az, Şəki xanlarının sarayı) in Shaki, Azerbaijan was a summer residence for the Shaki Khans. It was built in 1797 by Muhammed Hasan Khan. The palace was intended to house the Khans who were in charge of controlli ...
, Azerbaijan
Azerbaijan (, ; az, Azərbaycan ), officially the Republic of Azerbaijan, , also sometimes officially called the Azerbaijan Republic is a transcontinental country located at the boundary of Eastern Europe and Western Asia. It is a part of th ...
, 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. Traditions of stained glass set in wooden frames (not lead as in Europe) survive in workshops in Iran as well as Azerbaijan. 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. The old city of Sana'a
Sanaa ( ar, صَنْعَاء, ' , Yemeni Arabic: ; Old South Arabian: 𐩮𐩬𐩲𐩥 ''Ṣnʿw''), also spelled Sana'a or Sana, is the capital and largest city in Yemen and the centre of Sanaa Governorate. The city is not part of the Gover ...
in Yemen has stained glass windows in its tall buildings.
''Zellij''
'' Zellij'' () is geometric tilework with glazed terracotta tiles set into plaster, forming colourful mosaic patterns including regular and semiregular tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
s. The tradition is characteristic of Morocco
Morocco (),, ) officially the Kingdom of Morocco, is the westernmost country in the Maghreb region of North Africa. It overlooks the Mediterranean Sea to the north and the Atlantic Ocean to the west, and has land borders with Algeria to A ...
, but is also found in Moorish Spain. ''Zellij'' is used to decorate mosques, public buildings and wealthy private houses.
Illustrations
File:Persia p1070299.jpg, alt=Decoratively patterned ceramic bowl from Persia, Safavid
Safavid Iran or Safavid Persia (), also referred to as the Safavid Empire, '. was one of the greatest Iranian empires after the 7th-century Muslim conquest of Persia, which was ruled from 1501 to 1736 by the Safavid dynasty. It is often conside ...
bowl with radial and circular motifs, Persia, 17th century
File:Lustre tiles Iran Sufi divine breath shapes.JPG, Lustre tiles from Iran, probably Kashan, 1262, in the shapes of the Sufi
Sufism ( ar, ''aṣ-ṣūfiyya''), also known as Tasawwuf ( ''at-taṣawwuf''), is a mystic body of religious practice, found mainly within Sunni Islam but also within Shia Islam, which is characterized by a focus on Islamic spirituality, r ...
symbols for the divine breath
File:Samarkand Shah-i Zinda Tuman Aqa complex cropped2.jpg, alt=Complicated strapwork tiling, Glazed tilework Girih at Shah-i-Zinda in Samarkand
fa, سمرقند
, native_name_lang =
, settlement_type = City
, image_skyline =
, image_caption = Clockwise from the top:Registan square, Shah-i-Zinda necropolis, Bibi-Khanym Mosque, view inside Shah-i-Zinda, ...
, Uzbekistan
Uzbekistan (, ; uz, Ozbekiston, italic=yes / , ; russian: Узбекистан), officially the Republic of Uzbekistan ( uz, Ozbekiston Respublikasi, italic=yes / ; russian: Республика Узбекистан), is a doubly landlocked co ...
File:Side of a Minbar.jpg, alt=Finely carved Islamic wooden pulpit, Side of a wooden Minbar
A minbar (; sometimes romanized as ''mimber'') is a pulpit in a mosque where the imam (leader of prayers) stands to deliver sermons (, '' khutbah''). It is also used in other similar contexts, such as in a Hussainiya where the speaker sits a ...
(pulpit) with 12-point stars. 14th century. Turkish and Islamic Arts Museum
File:Salim Chishti Tomb-2.jpg, alt=Indian pierced stone screens, Jali pierced stone screens at the tomb of Salim Chishti
Salim Chishti (1478–1572) () was a Sufi saint of the Chishti Order during the Mughal Empire in India.
Biography
The Mughal Emperor Akbar came to Chishti's home in Sikri to ask him to pray for a male heir to the throne. Chishti blessed ...
, Fatehpur Sikri
Fatehpur Sikri () is a town in the Agra District of Uttar Pradesh, India. Situated 35.7 kilometres from the district headquarters of Agra, Fatehpur Sikri itself was founded as the capital of Mughal Empire in 1571 by Emperor Akbar, serving this ...
, India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...
File:Vintage Turkish Kilim Geometric Patterned Rug.jpg, alt=Simple geometric patterns on a flatweave rug, Woven wool Kilim from Turkey
File:'Ali ibn Abi Talib - Prayer Book - Walters W579 - Closed Top View A.jpg, alt=Finely worked leather bookbinding, Leather prayer book cover, Persia, 16th century
File:Kairo Rifai Moschee BW 5.jpg, alt=Iron gate from Egypt, forming a pattern of stars and kites, Iron gate with 10-point stars and kites at Al-Rifa'i Mosque, Cairo (1869–1912)
File:Flickr - Gaspa - Cairo, madrasa di Hasan (12).jpg, alt=Bronze doors from Egypt, decorated with strapwork, Detail of bronze
Bronze is an alloy consisting primarily of copper, commonly with about 12–12.5% tin and often with the addition of other metals (including aluminium, manganese, nickel, or zinc) and sometimes non-metals, such as phosphorus, or metalloids suc ...
door, Mosque-Madrassa of Sultan Hassan, Cairo
Cairo ( ; ar, القاهرة, al-Qāhirah, ) is the capital of Egypt and its largest city, home to 10 million people. It is also part of the largest urban agglomeration in Africa, the Arab world and the Middle East: The Greater Cairo metr ...
, decorated with strapwork
File:Isfahan Royal Mosque entrance.JPG, alt=Elaborate stepped vaulting in Iran, Muqarnas in Shah Mosque, Isfahan, Iran
Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...
File:Shaki khan palace 1.jpg, alt=Colourful stained glass patterns from Azerbaijan, Geometric shabaka stained glass in the 1797 Palace of Shaki Khans
The Palace of Shaki Khans ( az, Şəki xanlarının sarayı) in Shaki, Azerbaijan was a summer residence for the Shaki Khans. It was built in 1797 by Muhammed Hasan Khan. The palace was intended to house the Khans who were in charge of controlli ...
, Azerbaijan
Azerbaijan (, ; az, Azərbaycan ), officially the Republic of Azerbaijan, , also sometimes officially called the Azerbaijan Republic is a transcontinental country located at the boundary of Eastern Europe and Western Asia. It is a part of th ...
File:Traditional Window, Sana'a (11024852966).jpg, Traditional Window, Sana'a
Sanaa ( ar, صَنْعَاء, ' , Yemeni Arabic: ; Old South Arabian: 𐩮𐩬𐩲𐩥 ''Ṣnʿw''), also spelled Sana'a or Sana, is the capital and largest city in Yemen and the centre of Sanaa Governorate. The city is not part of the Gover ...
, Yemen
Yemen (; ar, ٱلْيَمَن, al-Yaman), officially the Republic of Yemen,, ) is a country in Western Asia. It is situated on the southern end of the Arabian Peninsula, and borders Saudi Arabia to the north and Oman to the northeast and ...
File:Mekhnes Place El-Hedine Mosaique.jpg, alt=Decorative brightly coloured tiling in Morocco, Glazed tile Zellij at Place el-Hedim in Meknes
Meknes ( ar, مكناس, maknās, ; ber, ⴰⵎⴽⵏⴰⵙ, amknas; french: Meknès) is one of the four Imperial cities of Morocco, located in northern central Morocco and the sixth largest city by population in the kingdom. Founded in the 11th c ...
, Morocco
Morocco (),, ) officially the Kingdom of Morocco, is the westernmost country in the Maghreb region of North Africa. It overlooks the Mediterranean Sea to the north and the Atlantic Ocean to the west, and has land borders with Algeria to A ...
Outside Islamic art
In Western culture
It is sometimes supposed in Western society that mistakes in repetitive Islamic patterns such as those on carpet
A carpet is a textile floor covering typically consisting of an upper layer of pile attached to a backing. The pile was traditionally made from wool, but since the 20th century synthetic fibers such as polypropylene, nylon, or polyester ...
s were intentionally introduced as a show of humility by artists who believed only Allah can produce perfection, but this theory is denied.
Major Western collections hold many objects of widely varying materials with Islamic geometric patterns. The Victoria and Albert Museum
The Victoria and Albert Museum (often abbreviated as the V&A) in London is the world's largest museum of applied arts, decorative arts and design, housing a permanent collection of over 2.27 million objects. It was founded in 1852 and nam ...
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. The Metropolitan Museum of Art
The Metropolitan Museum of Art of New York City, colloquially "the Met", is the largest art museum in the Americas. Its permanent collection contains over two million works, divided among 17 curatorial departments. The main building at 1000 ...
in New York has among other relevant holdings 124 mediaeval (1000–1400 A.D.) objects bearing Islamic geometric patterns, including a pair of Egyptian minbar
A minbar (; sometimes romanized as ''mimber'') is a pulpit in a mosque where the imam (leader of prayers) stands to deliver sermons (, '' khutbah''). It is also used in other similar contexts, such as in a Hussainiya where the speaker sits a ...
(pulpit) doors almost 2 m. high in rosewood and mulberry inlaid with ivory and ebony; and an entire mihrab
Mihrab ( ar, محراب, ', pl. ') is a niche in the wall of a mosque that indicates the ''qibla'', the direction of the Kaaba in Mecca towards which Muslims should face when praying. The wall in which a ''mihrab'' appears is thus the "qibla ...
(prayer niche) from Isfahan, decorated with polychrome mosaic, and weighing over 2,000 kg.
Islamic decoration and craftsmanship had a significant influence on Western art when Venetian
Venetian often means from or related to:
* Venice, a city in Italy
* Veneto, a region of Italy
* Republic of Venice (697–1797), a historical nation in that area
Venetian and the like may also refer to:
* Venetian language, a Romance language s ...
merchants brought goods of many types back to Italy from the 14th century onwards.
The Dutch artist M. C. Escher
Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints.
Despite wide popular interest, Escher was for most of his life neglected in t ...
was inspired by the Alhambra's intricate decorative designs to study the mathematics of tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of ...
, transforming his style and influencing the rest of his artistic career. In his own words it was "the richest source of inspiration I have ever tapped."[ which cites ]
Influence on the sciences
Cultural organisations such as the Mathematical Sciences Research Institute
The Simons Laufer Mathematical Sciences Institute (SLMath), formerly the Mathematical Sciences Research Institute (MSRI), is an independent nonprofit mathematical research institution on the University of California campus in Berkeley, Calif ...
and the Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...
run events on geometric patterns and related aspects of Islamic art. 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, Jay Bonner, Eric Broug, Hacali Necefoğlu and Reza Sarhangi. In Britain, The Prince's School of Traditional Arts
The Prince's Foundation School of Traditional Arts is a school in London which teaches students at the postgraduate degree level, and short open courses and in the community.
The school was founded in 2005 by King Charles III (then Prince of Wale ...
runs a range of courses in Islamic art including geometry, calligraphy, and arabesque (vegetal forms), tile-making, and plaster carving.
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 algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
ically.
Two physicists, Peter J. Lu and Paul Steinhardt, attracted controversy in 2007 by claiming that girih designs such as that used on the Darb-e Imam
The shrine of Darb-e Imam ( fa, امامزاده درب امام), located in the Dardasht quarter of Isfahan, Iran, is a funerary complex, with a cemetery, shrine structures, and courtyards belonging to different construction periods and styles. ...
shrine 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).
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.
Notes
References
External links
Museum with no Frontiers: Geometric Decoration
Victoria and Albert Museum: Teachers' resource: Maths and Islamic art & design
{{DEFAULTSORT:Islamic Geometric Patterns
Islamic architectural elements
Islamic art
Mathematics in the medieval Islamic world