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Barnett Newman, Ad Reinhardt and Mark Rothko exercised a particular fascination for her at this time and her work of the late 1950s, with its bright bands of colour or floating rectangular forms, owes much to theirs. Within a year or two, however, she had begun to develop a visual language of her own, distinguished by its muted palette; its reliance on lines and grids, with a particular emphasis on the horizontal; its fascination with surface and mark-making and painting as process; its resolutely human scale.

Martin dated her own artistic maturity from around 1960, and she would eventually destroy much of the work that had predated her move to New York. She settled now on the method that would sustain her for the rest of her career: a square format; canvas primed with two layers of gesso; hand-drawn pencil lines; thin layers of paint, first in oils, then in acrylic which she preferred because it was much quicker to dry. It brought her great commercial and critical success. She even found herself (rather against her wishes) being acclaimed as a major influence by a younger generation of artists, the emerging Minimalists.

By the mid-1960s, however, she was beginning to find the pressures of the New York art world too much, and with her Coentis Slip studio facing demolition, she seems to have undergone some sort of personal crisis. In 1967 she gave away her possessions, including all her painting materials, and drove off in a pickup truck across Canada and the West, before settling finally back in New Mexico. There she built a remote house (as well as a studio and four other buildings) with her own hands, and lived a solitary, spartan life. She did no painting for seven years.

By the time she began to paint and exhibit again in 1974 she had become something of a legend, revered by yet another generation of artists and critics. Her work was more avidly collected (and more expensive) than ever before. Yet she continued to live a reclusive and determinedly simple life in New Mexico, moving in the early 1990s back to Taos.

She was satisfied now with her work, after 20 years. “I finally got to an absolute abstract painting.” To the end of her days her methods and concerns remained the same. She had no studio assistants (“I don’t know what they’d do”), and her only concession to age was to reduce the size of her canvases (after 32 years) from 6ft by 6ft to 5ft by 5ft so that she could still lift and carry them herself.

Well into her eighties she was working in the studio from 8.30 to 11.30 each morning. She would then have lunch in her favourite restaurant in Taos, and read at home in the afternoon — Agatha Christie was a favourite author — before going to bed by about 8 o’clock. She never owned a television, and by the time she died had read no newspaper for 50 years.

It was the life she wanted. “I have a very quiet mind,” she said a few years ago. “I worked hard for that. It took a lot of discipline.”

Agnes Martin, painter, was born on March 22, 1912. She died on December 16, 2004, aged 92.