Monir Shahroudy Farmanfarmaian's work is grounded in the geometric designs of Islamic tradition, yet reconfigures that ancient aesthetic through the prism of western modern art. Her cut-glass mirror mosaics draw on architectural features of mosques across the Muslim world, fashioning an ornately crafted series of decorative works that can fit together in multiple configurations as ornaments to adorn a room.

She draws on the Safavid and Qajar period of Persian art, incorporating details from the exquisite stained-glass windows of her hometown of Qazvin, Iran, in designs culled from her extensive travels, both around the country and beyond.

"I've done a lot of travelling, particularly in the Islamic world," she says. "Many of the designs are taken from ancient architecture in Cairo, Damascus, Tehran - minarets, domes of mosques, palaces, shrines. And I did a lot of travelling inside Iran, studying the architecture at Isfahan, Shiraz and Tabriz. The Shah Cheraq shrine in Tabriz and the palace of Golestan were major influences."

Farmanfarmaian, who turned 87 this year, brings a modernist's sense of the avant-garde to bear on the religious tradition, so that her works are imbued with the kind of analytical geometry you see in a Mondrian, for instance, while taking on something of the minimalism of American artists such as Robert Morris.

Her latest series advances on her previous Bisection of a Circle series of 2008 which was shown at last year's Sao Paulo Biennale, moving from the pure simplicity of the circle to more complex explorations in polygrammatic form.

Fragmented panels of mirror are mounted on surface reliefs so that, like huge pieces of jewellery, they become sculptural in form while owing much to the Art Deco movement of the 1920s. Their complex arrays of symmetries are dazzling, both in the intricacy of their detail and in the shimmering play of reflections they throw off, so that the multifaceted array of the surface dances with tricks of light.The interplay of vertical and horizontal planes can give rise to bizarre optical distortions, so that perspectives seem to flip, much in the way of Op art and the illusionist movement. As the title of the series suggests, individual pieces combine to form highly schematised alternative arrangements. As in fractal mathematics, the beauty lies in the minutiae of the detail.

"So far as I am aware, no other artist has made works in five or six pieces that can be arranged in different ways as a collection," she says. "For two or three of them, I came up with the designs myself, then went to work on the framing. But most are taken from the geometric designs of old Islamic architecture.

"I take one classic piece of architecture and then design around it with strips or squares, half-circles, hexagons or octagons. The first ones were quite simple, and then I began making them more complex.

"Then I went in the other direction, simplifying them down as far as I could go."

It's a craft she's honed for more than 40 years, ever since a chance encounter in the late 1960s with the man she dubs the "mirror master", the glass craftsman Hajji Ostad Mohammad Navid. Their meeting came during a period that she spent touring the country, rediscovering Islamic craftsmanship and Persian architecture after her years abroad.

Farmanfarmaian had travelled to New York from Tehran at the end of the Second World War, enrolling at Parsons School of Design and spending more than a decade in the United States, during which she became close to many of the emerging contemporary artists of the 1950s. Her circle included the artists Jackson Pollock, Willem de Kooning, Frank Stella and Andy Warhol, with whom she worked in the shoe department of the store Bonwit Teller.

"Andy would do the drawings, and I'd do the layouts," she recalls of those days before either had made their name. "He was incredibly shy, but we used to swoon over the shoes being sold."Following her return to Iran, she toured the country extensively, gaining inspiration from the age-old artisan's craft of glass-cutting, traditionally passed down from father to son.