MARFA, Texas—Donald Judd’s sculptures are ticking. In the high desert 100 gleaming aluminum forms — each the exact same size — are aligned in rows with military precision inside two former artillery sheds, just as Judd had ordered. Pristine and silver, they reflect light pouring through giant window walls that Judd designed to replace aging garage doors. The installation, yielding views of the endless landscape, could make a believer of anyone who ever scoffed at Minimalist art.

But listen closely and you can hear the metal sculptures as they expand and contract. Some have inched out of alignment, heating up to 120 degrees — not quite hot enough to fry an egg — in buildings without climate control. Their custodians at the Chinati Foundation, which stewards the collection of works by Judd and a dozen major artists he invited to this remote town, must decide how best to mitigate the heat without compromising the holistic experience meticulously calibrated by Judd four decades ago. The foundation also has to replace the eroding barrel-vaulted metal additions Judd positioned atop the sheds to improve drainage. But he wasn’t an architect. The roofs still leak.

Tick tock. Drip drop.

Judd came to far West Texas in 1971 looking for space and conceived a singular vision integrating art, architecture and landscape. As bristly as the terrain, he wanted distance from the New York art world where he first made a name in the early 1960s as an art critic and then as a rigorously experimental sculptor exploring color and form and the space around his geometric works, fabricated from industrial materials. Too often he felt that museums mishandled the installation and transport of these pieces, sometimes returning them with shipping labels stuck carelessly to the surface of his plywood boxes, mistaking them for containers of art rather than the art itself.

“The installation of my work and of others’ is contemporary with its creation,” he declared in 1977. “The space surrounding my work is crucial to it.” He added, “Somewhere there has to be a place where the installation is well done and permanent.”

That would be Marfa, population 1,800 and a three-hour desert drive from the public airports in El Paso and Midland.

“He looked on a map for the least populated place still within America,” said his daughter, Rainer Judd, a filmmaker, artist, and president of the Judd Foundation. (She was named for the dancer Yvonne Rainer.)

As children, she and her brother, Flavin, accompanied their father when he started buying up vacant buildings in Marfa. He renovated two airplane hangars and adjacent former Army offices as their family residence and ideal setting for his own art, furniture designs and 13,000-volume library. (Judd bought 22 buildings in and around Marfa as living and working spaces, now open by appointment through the Judd Foundation.)

With funding from Dia Art Foundation in 1978, Judd acquired 34 more buildings on 340 acres: Fort D.A. Russell, a decommissioned Army base outside of town, and three structures downtown, for displaying his own work and those of his friends Dan Flavin, the famed light artist (his son’s namesake), and John Chamberlain, whose assemblages of crushed auto parts implicated a throwaway culture. In 1983, Judd opened his first architecturally modified warehouse dedicated to 23 monumental sculptures by Chamberlain and worked simultaneously to install his own 100 aluminum sculptures in the artillery sheds, along with 15 concrete sculptures on the fort grounds.

When Dia pulled back on its substantial financial commitment, Judd threatened to sue for breach of contract and lawyers negotiated a settlement in which he gained possession of all the art, buildings and land. He never spoke again with Dan Flavin, who refused to sever ties with Dia. In 1986, Judd established the Chinati Foundation as a curatorial forum for permanent installations and temporary projects, a kind of anti-museum where the artist was paramount.

Judd expressed his deep antipathy for museums and for the commodification of art — “conquered as soon as it’s made,” as he wrote in 1987. “The public has no idea of art other than that it is something portable that can be bought.” In counterpoint, he invited artists including Claes Oldenburg and Coosje van Bruggen, Richard Long, Roni Horn, David Rabinowitch, Ilya Kabakov and Ingolfur Arnarsson to place work at Chinati, where it would be preserved in perpetuity. Others, including Robert Irwin, Carl Andre, John Wesley, found a home there, too.

Michael Govan, director of the Los Angeles County Museum of Art, recalls visiting Marfa in the early 1990s as deputy director of the Guggenheim Museum, which had recently acquired the Panza Collection of Minimalist and Conceptual art, including works by Judd that the artist had renounced. Govan was tasked with the job of opening communication with the artist. “In a way, I was on his side, as a young person who felt that museums weren’t doing what they could do for artists,” Govan said, calling the experience life changing.

“Judd was a domineering person to some people,” he said, “but his principles make Marfa special — the reclaiming of America’s abandoned landscape of industrial buildings to create spaces honest and good for the art; the sense of space and light; the commitment to long-term installations to endure through cycles of taste where it’s out of favor.”

Judd died unexpectedly in 1994 at age 65, shortly after a diagnosis of lymphoma. He left behind family, loved ones and acolytes deeply committed to him and his vision, myriad unfinished projects, prolific writings on art and architecture, and one of the most important installations of American contemporary art. It has become a pilgrimage site for artists, architects, collectors, art professionals and cultural tourists from all over the world. Now the foundations charged with preserving his work are debating how best to move forward.

It’s a complicated legacy to interpret. Always looming is the question, “What would Donald Judd do?”—a bumper sticker once seen around town. “I was 23 and Flavin was 25 when our dad passed away,” said Rainer, who is 52. “I spent a good deal of time considering whether I should receive the challenge my Dad asked of me.”

His will dictated that his works be “preserved where they are installed” for study and appreciation. But Judd also left huge debts , which took years for his children to settle. A Christie’s sale of Judd’s artwork in 2006 raised $28 million for the endowment, which has a current value of $60 million.

Both foundations are carrying out long-range plans for preserving deteriorating buildings and posthumous completion of projects, with an estimated price tag of $40 million for Chinati and $30 million for the Judd Foundation. In April, Chinati completed its first phase, a $2.7 million restoration of the 23,000-square-foot Chamberlain Building — replacing the roof, upgrading the Judd-designed pivot windows and doors, restoring Judd’s garden planted with a grid of rosette-shaped sotols and his distinctive adobe wall enclosing a courtyard. The space is A.D.A.-accessible and open without appointment for the first time.

“The completion of the Chamberlain building is a demonstration that the foundation is capable of renovating one of Judd’s buildings in an exemplary fashion,” said Nicholas Serota, a longtime Chinati trustee and a former director of the Tate in London.

Yet on the heels of this success, Chinati’s board chose not to renew the contract of its director, Jenny Moore, after nine years. Moore, who helped raise $5 million to complete Robert Irwin’s largest permanent artwork in 2016, spearheaded the foundation’s master plan and oversaw the Chamberlain restoration, stepped down this summer.

The decision to look for new leadership “played along a difficult conversation that really centered around keeping the mission vital,” said Annabelle Selldorf, a prominent architect and Chinati trustee.

Moore came to be perceived as a divisive figure. Critics voiced concerns that attendance numbers, metrics and branding were being prioritized over the care of the art. The board had backed Moore a year earlier by refusing to renew the contract of Chinati’s longtime associate director, Rob Weiner, but that action caused a huge public outcry. Weiner, who came to Marfa to work as Judd’s assistant, stayed on after his death to help Judd’s romantic partner, Marianne Stockebrand, Chinati’s first director, steer the institution from financial brink. He worked closely with many artists, including Flavin (whom Stockebrand convinced to finishhis fluorescent light installations). Weiner’s dismissal roused a slew of artists affiliated with Chinati, who signed a group letter in The Big Bend Sentinel accusing its leadership of losing touch with Judd’s founding mission.

One critic was Christopher Wool, a Marfa resident and the only artist to have served on Chinati’s board, for seven years. Wool was one of several trustees to quit during this tumultuous period. “The board turned its back on deep institutional knowledge and instead insisted that Chinati be governed under a corporate model simply because that was their experience,” Wool said in an email. “The fact that it differed from formal museums was not a weakness but its most important strength.”

Jeff Jamieson, who assisted Judd and Irwin on installations, also voiced concerns to the board. “All the moves Don made were to set up that experience of coming to see his art in the best possible light,” he said, noting that changes in the shape of a path or the line of a roof could chip away and “degrade that experience.”

“Chinati is not a sexy museum with new things and galas,” he added. “You would do really quality work for the place if you just kept the roofs in good shape and took care of the work.”

Moore, who interned at Chinati early in her career, was the first director who did not know Judd personally. “There’s always a difficult transition period from the founder,” she said. “But I followed what I understood to be very clear priorities in this era” — namely, to create a plan to repair the buildings and to professionalize the organization and staff.

In its early days, visitors would roll up to the gate at Chinati and someone would hand them a key. In Moore’s time, attendance grew from 11,300 in 2013 to almost 50,000 before the pandemic. “We can’t do that anymore,” said Moore, who sees the need to create more restrooms, greater accessibility and affordable housing on the Chinati grounds for staff priced out of gentrified Marfa. But all these things require physical changes.

“It’s a public institution,” she insisted. “You can’t just be wackadoodle because it’s a place established by an artist. It’s not fixed in amber.”

Finding the balance between mausoleum and living institution is the challenge at hand. “How do we make sure that the ethos and unique presence of Chinati is upheld,” Selldorf said, “while knowing that a sense of welcome, inclusion, equity that every museum in the world has to deal with, apply to us as well?”

When the artist Theaster Gates began transforming buildings on Chicago’s South Side into cultural spaces with his Rebuild Foundation, he informally called his project “Black Marfa” — influenced by Judd’s “inexhaustible ambition for what art could be,” Gates said. But the issues faced by the Chinati and Judd foundations have him thinking about just how much he wants people to be ruled by his ideas in perpetuity.

At the Judd Foundation library in Marfa, Gates noticed that the sun had bleached a line across a book that no one had ever moved.

“Is it the artist’s intent that the book will never move?” he asked. Or is it better if the book is well used, “you rebind it and you allow the book to be a living thing?” He added, “This is a conversation of preservation writ large.”

In the meantime, Judd’s sculptures are sizzling in the artillery sheds — the next major restoration project in Chinati’s master plan. An open question is whether to apply film to Judd’s windows or replace them with glazed double glass to help cool the buildings, which could tint the view looking out. (And forget about adding air-conditioning — too intrusive.)

And then there’s the dilemma of fixing leaky roofs. Judd’s sketches of his barrel-vaulted additions noted that the ends should be made of glazed glass (the better to frame the view). Yet he completed the buildings with the ends closed and made of metal. Should Chinati replicate what’s been there since 1984, or achieve Judd’s expressed intention? What would Judd do?

Jamieson said: “If Don got something finished and said, ‘This is good,’ my idea is, Let’s keep it that way if we can.”

Serota, the Chinati trustee, who thinks the closed ends may have been Judd’s temporary solution, urged caution before moving ahead. “We feel very strongly that it’s important not to invent pastiche Judd,” he said. “If we build at all, it should be very clear what is new and what was Judd’s.”

Selldorf said of the rounds of board deliberations: “It is a bit subjective. The last word hasn’t been spoken.”