Symmetry-Breaking in Oriental Carpets

The Case for Beauty

Carol Bier
Curator, Eastern Hemisphere Collections
The Textile Museum
2320 S Street, NW
Washington, DC 20008

© The Textile Museum, Washington, DC 2001

Mathematicians treat symmetry as an ideal. But it is in symmetry-breaking that beauty emerges from truth.

Symmetry-breaking requires an expectation of symmetry. Often, symmetry-breaking is confused with asymmetry. But, rather, asymmetry is simply the absence of symmetry. For symmetry-breaking to exist, a pattern must first be stablished. Symmetry then is expected, but somehow that expectation is not met.

There are many ways to effect symmetry-breaking in Oriental carpets. The study of Oriental carpets may lead one to suppose that in art, as in nature, it is in the approximation of symmetry, rather than in its precision, that beauty is to be found and appreciated.

What is an Oriental Carpet? No one ever set out to weave an Oriental carpet.

A woman, or a girl, or less often a young boy, simply set out to weave a carpet. The concept of Oriental carpet transcends original cultural origins; it is a Western construct. Typically, an Oriental carpet is oblong in format, with a central field surrounded by borders. Many different patterns are present.

All hand-made Oriental carpets are filled with symmetry-breaking.


All patterns, whether in nature or in art, exhibit a systematic organization. Symmetry offers several possibilities for the organization of a pattern, each of which results in sets of corresponding points. In rug weaving, the symmetrical repetition of a design to form a pattern is effected by counting and repeating sequences of knots.

Possibilities for the composition of a design are limitless, and rely upon choice. But possibilities for the repetition of a design are limited by the laws of pattern formation, subject to the constraints of symmetry.

Symmetry-Breaking in Oriental Carpets

There are many ways a weaver may choose to break the symmetry of a pattern. I have characterized twelve methods, which group into four categories of transformation:

Transformations of Color

Transformations of Shape

Transformations of Space

Transformations of Pattern

These often appear in combination with one another. Typically, in Oriental carpets, there are numerous examples of symmetry-breaking in any given carpet.

Transformations of Color

Color change (binary)
Camel trapping for wedding (detail)
Central Asia, Ersari, 18th century
The Textile Museum 1968.27.1, Gift of Joseph V. McMullan

Color change (algorithmic)
Carpet (detail)
Central Asia, Turkmenistan, 19th century
The Textile Museum R37.6.1
Acquired by George Hewitt Myers in 1914

Color change (random)
Carpet (detail)
India, 18th or 19th century
The Textile Museum R63.00.16
Acquired by George Hewitt Myers in 1920

Transformations of Shape

Change of shape (content)
Carpet (detail)
India, Lahore, Mughal style, 17th century
The Textile Museum 1994.12.1, Gift of James D. Burns

Change of shape (orientation)
Carpet (detail)
Central Asia, Bukhara, 19th century
The Textile Museum 1963.52.6
Gift of Mr. and Mrs. Frank M. Michaelian

Change of shape (addition)
Carpet (detail)
Turkey, Kurdish, 18th century
The Textile Museum 1993.35.1, Gift of Wells Campbell Klein

Transformations of Space

Change of space (placement)
Carpet (detail)
Caucasus, Karabagh, 18th century
The Textile Museum 1996.9.1
Ruth Lincoln Fisher Memorial Fund

Change of space (interlace)
Carpet (detail)
Spain, 16th century
The Textile Museum R44.2.1
Acquired by George Hewitt Myers in 1920

Change of space (illusion)
Carpet (detail)
Turkey, Konya, 19th century
The Textile Museum R34.2.14
Acquired by George Hewitt Myers in 1928

Transformations of Pattern

Border patterns (abutment)
Bag face (detail)
Iran, Bakhtiyari or Lori, 19th century
L1996.48.1, Private Collection

Field patterns (arbitrary cut-off)
Carpet (detail)
Central Asia, Turkmenistan (Tekke), late 19th century
The Textile Museum 1986.29.1, Bequest of Alvin W. Pearson

Multiple patterns (juxtaposition)
Carpet (detail of fragment)
Egypt, Cairo, Mamluk, 16th century
The Textile Museum R16.3.1
Acquired by George Hewitt Myers in 1925

Carol Bier is Research Associate at The Textile Museum in Washington, DC, where she had served as Curator for Eastern Hemisphere Collections for seventeen years from 1984 to 2001. She is author of The Persian Velvets at Rosenborg (Copenhagen, 1995), editor and contributing author of Woven from the Soul, Spun from the Heart: Textile Arts of Safavid and Qajar Iran (16th-19th Centuries) (Washington, 1987), and editor of The Textile Museum Journal. Her on-line exhibition, "Symmetry & Pattern: The Art of Oriental Carpets," at <>, has won numerous awards. It is a collaborative project of The Math Forum at Swarthmore College and The Textile Museum.