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An elaborate 17th Century Safavid carpet from Iran, a 15th Century Mameluke carpet from Egypt and a floral-design rug of the Ottoman Empire period are among the items on view through Feb. 24 in an exhibition at the Textile Museum in Washington.

The exhibition, ”Visions of Infinity: Design and Pattern in Oriental Carpets,” was arranged by the museum`s curator, Carol Bier.

She culled nine 15th through 19th Century Persian carpets from the museum`s 1,400-piece rug collection, and she says the show is an intellectual exploration of pattern.

Bier focused the central point of each carpet`s pattern precisely 61 inches from the floor. As a result, from carpet to carpet, the eye travels the room, tracing the infinite unfolding of patterns.

A guidebook accompanying the exhibition cautions that it is not easy to read a pattern and challenges viewers to identify each axis of symmetry and each repeated pattern.

The guide asks: Are the axes vertical? Horizontal? Is there a radial pattern?

The patterns also offer a means of understanding the spirituality of Islamic art, the curator says.

”In the Western mind, Islamic art is decorative and ornamental,” she said, pointing out repeated designs that could be found on each carpet, ”but if you try to approach it culturally, it is infused with spirituality that has its ramifications in the aesthetic, and a lot of that is pattern.”

Three carpets are tribal pieces created by weavers, and the patterns were passed down through the generations, from mothers to daughters; six are the work of designers in royal courts or cities` workshops.

But all, whether destined for the imperial court or the nomadic life, are based on repeating patterns of varying intricacy and configuration. Even in a relatively humble piece, Bier said, there is a conscious play between finite borders and the concept of infinity.

The Textile Museum`s collection of 12,000 textiles and 1,400 carpets is housed in two historic, turn-of-the-century buildings in northwest Washington, originally the home of George Hewitt Meyers, a textile collector who founded the private, not-for-profit institution in 1925.

One of the museum`s most popular offerings is a ”rug”` morning on Saturdays, when people can bring in Oriental rugs to be studied by volunteer specialists.

The museum also offers curatorial and conservation consultations for a $5 fee on the first Wednesday of every month, from September through May.

”It is more focused than rug mornings,” said George Rogers, a spokesman for the museum. ”We have people who want to know about the origin of a piece, or how to mount or clean it. They will bring in everything from pre-Columbian fragments and a piece of Chinese embroidery to a quilt their mother made.”