How geometry becomes ornament

What is the pattern doing?

Ornament means decoration. On the prayer niche above, it divides a large surface, more than three metres high, into smaller areas. Pale lettering follows the blue outer frame. Curling stems fill the space above the pointed arch, while stars and polygons, or straight-sided shapes, fill the upper part of the recess.

A mihrab, or prayer niche, marks the direction of Mecca. This one comes from the Madrasa Imami, a religious school in Isfahan, and is dated 1354–55. Its makers set small pieces of glazed ceramic into mortar, so what looks like a drawn line is often the boundary between two pieces.

The geometric pattern sits alongside calligraphy, or decorative writing, and plant ornament. All three became prominent in Islamic religious architecture, where human and animal figures were generally avoided. Figures appear widely in manuscripts, ceramics and other secular arts; we will meet them later in the paintings. A mosque’s decoration is only one part of this broader artistic tradition. The Met on figures in Islamic art [2]

To see how a pattern works, begin with a single shape. A star keeps the same angles when you make it larger or smaller, but its spacing, colour and material change how it looks. The drawings below let you separate those choices before returning to the objects.

From drawing to pattern

Each exercise follows a star from its first construction lines to a finished pattern. The shape picked out from those lines is the motif; arranging it makes the pattern. These are modern teaching examples, not reconstructions of a particular workshop’s methods. When a star matches itself several times during a full turn, it has rotational symmetry. Fivefold means five matches.

How the shapes fit together

Once you repeat a star, its neighbours matter. Turn an eight-point star by 45° and it matches its starting outline. Put stars on a square grid, and the whole arrangement needs a 90° turn to match again. Try turning the drawings below, then turn them again to see when both match.

The gaps matter too. Our stars leave spaces between them; to cover a surface without gaps or overlaps, those spaces need shapes of their own. This kind of covering is called a tessellation. Circles and polygons such as squares can help you draw more complex patterns. The Met on geometric ornament [3]

Regular pentagons have equal sides and angles. Put three together with a corner of each meeting at the same spot. Their inside angles of 108° leave a gap too small for another pentagon. That is why regular pentagons alone cannot cover a flat surface. Designs with fivefold symmetry can combine different shapes, or grow around a shared centre, like the medallion above.

A wooden window shutter in Istanbul’s Süleymaniye Mosque shows how much further this can go. In her study, Serap Ekizler Sönmez examines different ten-point stars at the shutter’s centre and corners. Turning parts of the design, or reversing them as in a mirror, makes new compositions. How the shapes fit together determines how the pattern can extend. Read the illustrated study (PDF, pp. 533–538) [4]

From a drawing to wood and stone

Follow a line in the mihrab and you often follow a join between tiles. The doors below use fitted pieces of wood instead. Their joints have to hold the doors together while letting the material expand and contract. Stone presents different choices: fit separate coloured pieces, as in the marble panel, or carve openings through a solid screen.

Pattern inside a painting

Patterns also help painters describe a room. These two sixteenth-century manuscript paintings bring decorated walls and floors onto a page: a change in pattern shows where one surface ends and another begins. Select a detail to see the geometric shapes, fine meshes and curling stems at closer range.

Here, human figures share the page with geometry, writing and plant ornament.

What colour changes

Pale lettering stands out against the dark blue of the Isfahan mihrab. Turquoise, yellow and green divide the surrounding decoration into smaller forms. Following one colour helps you pick out a shape among the crowded lines. The mihrab’s colours and inscriptions [10]

You can test this without drawing new lines. In the two patterns below, swap the colours of the stars and the background. Which shapes do you notice first? Then remove the fills to see the same design as a network of outlines.

In the photograph of the sandstone screen, the openings look dark. In a window they would let light through, casting the pattern into the room.

Make your own pattern

The studio below lets you change the scale, colours and outlines of a design. Click or tap a piece to recolour it. Try making the spaces between the stars stand out.

Further reading

If you would like to draw patterns on paper, begin with Eric Broug’s practical guide. The other books take you further into the buildings, objects and history behind the designs.