Asawa’s sculptures are intricate, organic-seeming things, made from crocheted copper, brass, galvanized steel and iron wire. They have an aura of casual prowess and the concision of crunched-down equations describing the curves of water droplets or summer weeds shooting skyward in spirals. You don’t expect sculpture to function as a visual correlative to swimming in air. Asawa found a way and, in so doing, found her voice.

The show has been installed across four galleries in the Pulitzer’s Tadao Ando-designed building. The main gallery, which creates a snaking path through a relaxed cluster of elongated hanging forms, is especially fine, and a reminder that Asawa loved the way her sculptures cast shadows and interacted with their siblings. One of seven children herself, she hated to see anything in isolation.

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Asawa was born to Japanese parents in a rural area outside Los Angeles in 1926. Her family grew vegetables, which they sold at market in L.A. On Saturdays, she and her siblings attended a Japanese school, learning the language and culture — including brush-and-ink calligraphy.

After the Japanese attack on Pearl Harbor, FBI agents arrested her father, Umakichi, and detained him in New Mexico for two years. Ruth wouldn’t see him again for more than six years. Two months later, the rest of the family was interned in the stables at a racetrack in Arcadia, Calif., along with 120,000 other people of Japanese descent, more than half of them (like Asawa) American citizens.

In the camp at Arcadia, Asawa met three men who had worked as animators for Walt Disney. They taught her to draw. After six months, the family — still missing Umakichi — was relocated to Arkansas, where Ruth finished high school. A $100 scholarship from a Quaker woman living in Pennsylvania got her to Milwaukee State Teachers College. She studied to be an art teacher while working as a domestic servant.

Asawa has one of those life stories that threatens to overwhelm the impact of the work. Until, that is, you see the work.

It has been easily visible in San Francisco — at the de Young and elsewhere — for years. In 1968, Asawa made her first representational sculpture, a fountain in Ghirardelli Square. The commission increased her local popularity (who doesn’t like mermaids?) — so much so that she became known as “the fountain lady.” But it may have set back her art world reputation.

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A broader, more discerning appreciation of Asawa’s work, and a recognition that she was underappreciated for most of her lifetime, has been building since 2011, when curator Helen Molesworth included her in “Dance/Draw,” a group show at Boston’s Institute of Contemporary Art. Two years later, she was given her first solo show in New York since 1958.

By then, Asawa was 87 and had been battling lupus for almost 30 years. She died three months later at her home in San Francisco.

In the five years since, resurgent interest in Black Mountain College, the small, experimental liberal arts college in North Carolina that had an outsize impact on midcentury art, dance, music and poetry, has continued to fuel the fascination with Asawa. Encouraged by someone she met in Mexico, she attended Black Mountain in the late 1940s in the company of Merce Cunningham, John Cage, Robert Rauschenberg and Buckminster Fuller.

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Her war experiences may partly explain this. She encountered appalling intolerance, both then and later, but she told an interviewer in 1994: “I hold no hostilities for what happened; I blame no one.” Rather than overturning Asawa’s inner creative convictions, Black Mountain’s Bauhaus-inspired ethos gave them a chance to put down roots.

Asawa had come there after a 1945 bus trip to Mexico with her sister Lois. Returning to Mexico two summers later, she saw craftsmen in Toluca making wire baskets for carrying eggs. She asked to be taught the technique and returned to Black Mountain with her life’s work implanted within her, like a secret algorithm awaiting the input of life’s data.

At first, she used the technique to make baskets, but she quickly adapted it to create closed-form hanging sculptures with undulating hourglass or teardrop shapes. Asked to account for these voluptuous, symmetrical forms, she connected them to the lines her shifting toes had made in the sand when, as a child, she rode on the back of horse-drawn farm equipment. But they were inspired, too, by forms in nature: “plants, the spiral shell of a snail, seeing light through insect wings, watching spiders repair their webs in the early morning, and seeing the sun through the droplets of water suspended from the tips of pine needles while watering my garden.”

Lest you think Asawa, while meditating on all these phenomena, was living the solitary life of a Zen adept in a mountaintop monastery, she wasn’t. She had met and married Albert Lanier, an architecture student, at Black Mountain. They had six children. Determined to keep the various aspects of her life integrated rather than compartmentalized, Asawa made her work in the midst of the family maelstrom.

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The sophistication of her sculptural forms, derived from her drawings, advanced quickly. She began nesting spherical forms inside hourglass shapes and created elaborate interplays of inside and outside that can bend your brain if you try to figure them out. Beginning with a smaller form like a sphere, she would stop short of closing it at its base and instead fold it upward so that the sphere’s exterior surface became the interior of the bigger, encompassing shape. She might repeat that inversion several times in the same sculpture. Often, her fluting or tapering forms travel through one another from inside to outside and back again.

The nesting and interwoven surfaces produce variations in density and thus in light and shade. Asawa paid careful attention to all this, as well as to the shadows her works cast. She used different-colored wire to produce different effects. She loved that air could move freely through her work.

From closed forms, she went on to experiment with forms that opened out, such as flowers with frilled edges or seaweed. She also tied bunches of wire with knots, dividing them out into thinner and thinner branches, so that the whole came to resemble giant dandelions or the tips of trees in winter. She submerged some of the tied wire works in sulfuric acid for weeks at a time, enjoying the crusty, greenish growths that formed on their surfaces.

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Asawa’s works on paper, concentrated in a lower gallery, are mostly in black and white or blue but sometimes in saturated colors, too. They’re unified not by style or technique but by a persistent curiosity about effects of transparency and movement and a feeling for the simple, childlike delights of forms multiplied, repeated, and extended.

The show, organized by the Pulitzer’s Tamara H. Schenkenberg, is billed as the first museum show of Asawa’s work outside the West Coast (although it should be noted that the dealer David Zwirner mounted a large Asawa exhibition in New York last year and published an impressive catalogue to go with it). It could hardly be lovelier. It is certainly worth traveling to see.