Regardless of material, scale and technique, the lines and geometric motifs used in Islamic art are practically always the same. Complex geometric forms are reached through applying the principle of multiplication and sub division to achieve a symmetrical repetition of an extraordinary variety of figures. Geometric motifs, are sometimes based on abstractions of the natural world, and may often have a symbolic meaning.
Decorations on textiles, fabrics and rugs are mostly composed of straight-line plain bands, zigzags and boxes. These representations often appear schematic and flat, as the use of figurative representation was highly schematic, geometric and abstracted, figures are rendered unrecognizable. The artistic schematization of fabric design carries on into the decoration of ceramics. The ceramics are often worked with very simple geometric shapes or schematized plant motifs, which are highly abstracted. In seeking to emphasize form, radial lines were used to decorate bowls, plates and other open vessels, as horizontal lines were used to decorate closed ones. 
Islamic artists adopted elements from the classical tradition, but then elaborated upon them in order to create a very different visual language based on logic, order, and unity. Geometric patterns, calligraphy and vegetal patterns are the three main ornamental elements in Islamic art. In terms of line, forms were often created using schemes based on repetitive and intertwining geometric patterns. Within the Islamic artistic tradition, the circle was regarded as the fundamental form from which squares, diamonds or rhombuses, hexagons, octagons, and complex stars were composed. The Islamic tradition, which was heavily rooted in astronomy and mathematics, was thus incorporated into the visual field as the compass and ruler became the main instruments of artistic design. 
Calligraphy was viewed as the geometry of line, which sought to combine geometric shapes, in a structural manner, in order to attain complex patterns. These patterns are made of a small number of repeated shapes. Simple geometric forms such as the circle, line and square are systematically juxtaposed, combined and duplicated. The systematical arrangement of the shapes is achieved through the use of a grid; two types of grids are used, one based on the equilateral triangle and the other based on the square. Thus rather than being freehand, expressive, or emotional the lines in Islamic art are often very mathematic and objective. The firmness of the line, as it is being used a contour line or outline endows most works of art with a sense of solidity and two dimensionality and establishes it as a pattern or abstract representation rather than an illusionistic image. The artist, having to follow an already existing scheme, is dawn away from a subjective or emotional treatment of the work towards a more rigid and structured one.
Carol Hourani
Sources:
Newman, Rochelle, and Martha Boles. The Golden Relationship: Art, Math, Nature. Book 1. Universal Patterns, 2nd rev. ed. Book 2. The Surface Plane. Bradford, Mass.: Pythagorean Press, 1992.
Baer, Eva. Islamic Ornament. Edinburgh: Edinburgh University Press, 1998.
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