The Language of Symmetry in Islamic Art

Throughout the ages mystics and theologians have used geometry as a contemplative focus, as it enables the viewer a vision of the underyling order of both the cosmos and the natural world. The cyclical movement of heavenly bodies, which Plato described as the ‘music of the spheres’, finds its Earthly reflection in the natural symmetries found throughout nature and most strikingly within the world of flowers, the proportions of which are governed by simple geometric laws. The origin of the word ‘cosmos’ is adornment (from which we derive the modern word ‘cosmetics’) and the adornment of sacred buildings with both floral and geometric patterns makes the viewer sensitive to the subtle harmonies uniting the natural world around us with the cosmos.

In Islamic art the geometric figure of the circle represents the primordial symbol of unity and the ultimate source of all diversity in creation. The natural division of the circle into regular divisions is the ritual starting point for many traditional Islamic patterns, as demonstrated in the drawings below.

The pattern above (15th century) from Yazd in Iran is derived from six regular divisions of the circle. From this a regular grid of triangles is established, on top of which the design is elaborated. Note how the complex tracery of pattern interweaves with the basic design which appears in white outline in the photograph above.

A family of geometric tiles (above) derived from the octagram (khatam – 8 pointed star) form a ‘jigsaw’ puzzle, which through different combinations can generate a myriad of stunning designs. These are typical of the ceramic cut tile pieces used in mosaics though out Morocco (al-Maghrib), where they are known as ‘zillij’ and  Andalucia (al-Andalus), where they are known as ‘alicatado’, from the early medieval period onwards. These shapes are still cut by hand in modern day Morocco.

In the Alhambra (14th C), Spain, geometric pattern is perfectly integrated with biomorphic design (arabesque) and calligraphy.  These are the three distinct, but complementary, disciplines that comprise Islamic art. They form a three-fold hierarchy in which geometry is seen as foundational. This is often signified by its use on the floors or lower parts of walls, as shown in the image above.

The decorative elements deployed use a range of symmetries that have now been classified as belonging to distinct mathematical groups, but the subtlety and beauty of the designs is unparalleled in modern mathematical thinking.

Islamic designers used the full range of Archimedean tilings (comprised of simple polygons) first discovered by the Greeks, but added to and expanded upon these with extraordinary visual and spatial ingenuity. The pattern above (after Paul Marchant) is based on elements of medieval designs typically found in Cairo. Notice the pattern of underlying polygons: hexagons, triangles, squares, dodecagons. The underling tiling pattern is usually hidden beneath the final design, as if behind a veil, but the viewer is always given an intimation of the hidden order and this is part of what gives the designs their meditative power.

With a compass and ruler a master craftsman can demonstrate a method for setting out a pattern which employs 10-fold radial symmetry. Note the construction of the decagram (10-pointed star). This is the key generative motif for Persian ‘girih’ patterns.

The four examples above show how to derive a range of classic motifs from the decagram (there are several more). These form the basis of 12th century Iranian ‘girih’ patterns, which have been linked to Roger Penrose’s famous non-periodic tilings, i.e. patterns that can extend to infinity without regular repetition.

(From an article published by Richard Henry / artist and teacher in Islamic geometric pattern. He works in painting, print and tile-mosaic. He has developed a number of courses for the British Museum in London’s World Arts and Artefacts program and has taught internationally).

Introduction to Geometric Design in Islamic Art

The principles and teachings of Islam as a way of life, a religious code, and a legal system were promulgated by Muhammad (ca. 570–632 A.D.), an Arab merchant from Mecca. These teachings were revealed to him over a period of many years beginning in 610 and were subsequently codified in the text known as the Qur’an. The word of God, as set out in the Qur’an and handed down in the sayings of Muhammad (known as Hadith, or Traditions), forms the core of the religion.

The primary premise of the Islamic faith is monotheism, a renunciation of all deities except one, Allah, who alone is the creator, sustainer, and destroyer of life. Islam is Arabic for  ”submission,“ here to the single entity of Allah. The recognition of Muhammad as Allah’s last prophet, a prophet like Abraham, Moses, Jesus, and the others that preceded Muhammad, is also a key element of the belief.

Neither the Qur’an nor the Traditions contain specific mandates against figural representation in art. However, both sources take a firm stance against idolatry and the worship of images. These precepts were interpreted strictly by early Islamic religious leaders and exegetes as an injunction against the depiction of human or animal figures, although extant examples of architectural decoration, objects in all media, and illustrated manuscripts belie that stricture. Four types of ornamentation can be found in Islamic art: calligraphy, figural forms (human and animal), vegetal motifs, and geometric patterns. These patterns, either singly or combined, adorn all types of surfaces, forming intricate and complex arrangements.

While geometric ornamentation may have reached a pinnacle in the Islamic world, sources for the basic shapes and intricate patterns already existed in late antiquity in the Byzantine and Sasanian empires. Islamic artists appropriated key elements from the classical tradition, then elaborated upon them to invent a new form of decoration that stressed the importance of unity, logic, and order. Essential to this unique style were the contributions made by Islamic mathematicians, astronomers, and other scientists, whose ideas and technical advances are indirectly reflected in the artistic tradition.

The basic instruments for constructing geometric designs were a compass and ruler. The circle became the foundation for Islamic pattern, in part a consequence of refinements made to the compass by Arabic astronomers and cartographers. The circle is often an organizing element underlying vegetal designs; it plays an important role in calligraphy, which the Arabs defined as “the geometry of the line”; and it structures all the complex Islamic patterns using geometric shapes. These patterns have three basic characteristics:

1. They are made up of a small number of repeated geometric elements. The simple forms of the circle, square, and straight line are the basis of the patterns. These elements are combined, duplicated, interlaced, and arranged in intricate combinations. Most patterns are typically based on one of two types of grid -one composed of equilateral triangles, the other of squares. A third type of grid, composed of hexagons, is a variation on the triangular schema. The mathematical term for these grids is “regular tessellation” (deriving from Latin tesserae, i.e., pieces of mosaic), in which one regular polygon is repeated to tile the plane.

2. They are two-dimensional. Islamic designs often have a background and foreground pattern. The placement of pattern upon pattern serves to flatten the space, and there is no attempt to create depth. Vegetal patterns are may be set against a contrasting background in which the plantlike forms interlace, weaving over and under in a way that emphasizes the foreground decoration. In other instances, the background is replaced by a contrast between light and shade. Sometimes it is impossible to distinguish between foreground and background. Some geometric designs are created by fitting all the polygonal shapes together like the pieces of a puzzle, leaving no gaps and, therefore, requiring no spatial interplay between foreground and background.

The mathematical term for this type of construction is “tessellation.” The conception of space in Islamic art is completely different from Western models, which usually adopt a linear perspective and divide the picture space into foreground, middle ground, and background. Artists of the Islamic world were largely uninterested in linear perspective. Of the various styles of Islamic art, it was in Persian painting that a type of three-dimensional space was used in which figures could interact, but this space presented multiple viewpoints and simultaneously featured bird’s-eye and worm’s-eye views.

3. They are not designed to fit within a frame. Geometric ornamentation in Islamic art suggests a remarkable degree of freedom. The complex arrangements and combinations of elements are infinitely expandable; the frame surrounding a pattern appears to be arbitrary and the basic arrangement sometimes provides a unit from which the rest of the design can be both predicted and projected.

(Extract from ‘Islamic Art and Geometric Design / Activities for learning’. Published by The Metropolitan Museum of Art, New York 2004).

Towers of the Alhambra, a curiosity board game

Towers of the Alhambra, a new game of skill and strategy created by the author and inventor Paco López Martín, is a two-player game inspired in the Monument, played on an inlaid woodcraft board with 35 squares, made of Sycamore, Oak and Walnut tree woods and 10 pieces (towers) made of gold and copper.  Size of board: 38 x 27.5 cm.

The set also includes a study on the towers of the Alhambra, written by Paco López with the support of Alhambra and Generalife archaeology advisor Jesús Bermúdez. The study comes in Spanish, English and French, and contains history, anecdotes and legends concerning the towers. The set is completed with a DVD containing the game instructions, also in three languages.

Players move five Alhambra towers to try to conquer the opponent’s fortress. Of the ten towers used in the game, five are based on towers along the northern wall of the Alhambra and are finished in old gold, while the other five correspond to the southern wall and are finished in copper.

Towers of the Alhambra is not just any game. “It is also a collector’s item, and great care has gone into every detail”. Several professionals were involved in creating the pieces, including Granadan sculptor Juan Manuel Gabarrón, who designed the miniature towers, and marquetarian Tomás Lara Bimbela, expert craftsman in ‘taracea’, the Moorish inlaid wood design works. (See also our post: Taracea, an Arabic influence crafts from Granada).

This Nasrid strategy game, it’s a fun, instructive, educational tool, and can be acquired at the Alhambra Museum Gift and Book Shops and from www.alhambratienda.es

Table games as ‘alquerque’ and checkers, were popular in mediaeval courts, particularly chess, the game of strategy based on the battlefield that requires great skill and intelligence. The game was introduced into the Spanish Middle Age kingdoms by the Muslims, although the name comes from a Persian word ‘shatranj’ (that in Spanish was rendered as ajedrez).

This game is from the family of Halma (‘Jump’ in Greek), devised by George Howard Monk in 1883 (supposedly inspired on previous English game called Hoppity, 1854) and more popularly known in its version of Chinese Checkers  from publication with star-shaped board, published in Germany in 1893 with the title of Stern-Halma. In these games the pieces jump, onto each other above, to fill out the checkerboard squares opposite. Although this family of games can be linked in form of movement with the traditional game of Checkers or Draughts, the pieces are not removed.

We can understand the rules in this video:

http://www.youtube.com/watch?v=yJCONHMQcr0