DUNDEE, Scotland — British kings and queens have worn it. Rebels, punk rockers and couture designers embraced or transformed it. And international drag stars like RuPaul and Cheddar Gorgeous strut their stuff in it.

It is tartan, the quintessential Scottish crisscross pattern famous for its use in kilts. And while Heritage Crafts, a British charity that works to safeguard traditional crafts, considers kiltmaking to be endangered, tartan itself is finding new audiences as contemporary fashion houses and avant-garde weavers do their best to explode that grid.

And “Tartan” also is the name of a wide-ranging exhibition set to open on Saturday at the V&A Dundee (a design museum connected with the Victoria and Albert Museum in London) on the banks of the River Tay.

[Kiltmakers and mills offer design-your-own services for tartans, including listing on a national registry.]

Experts say tartan is not just a textile but a pattern defined by some generally accepted rules: It should have at least two colors and a halftone that is created when they intersect; a grid motif that repeats; and a sense of proportion in which smaller and bigger spaces are balanced and harmonious.

“We’re really fascinated in how the grid can be disrupted and deconstructed by designers and artists, and used as a set of rules, really, to adapt, to reinvent,” one of the show’s curators, Mhairi Maxwell, 36, said recently, sitting in the museum’s cafe as she ran through a slide show of plans for the exhibition.

Another of its curators, Kirsty Hassard, 34, said the show was organized around five themes: the grid, innovation, identity, power and the transcendental aspects of tartan.

“We wanted to sort of blow apart tartan and put it back together,” she said. “So when you walk into the show, the first section you’re met with is ‘Tartan and the Grid.’ That’s really about how tartan is constructed and then how tartan has been used by designers, architects and artists alike as inspiration. How it’s the basis for loads of things in the world around us that you might not even know.”

(The main one, she said later, was that a tartan ribbon was the subject of the first color photograph, taken in 1861.) The exhibition’s section on identity examines how people have used tartan to express themselves through the centuries: by Scottish clans; as a symbol of rebellion in the Jacobite Risings and the subsequent British ban on Highland clothing in 1746; by the 1970s punk subculture; and by fashion designers like Vivienne Westwood and Alexander McQueen.

It also has been used by politicians, the military and royalty as a form of soft power. An example cited by the curators was a red and black tartan suit made for King George V in 1897 and later worn in the United States by his son Edward VIII. “It’s known as the suit of the two kings,” Ms. Maxwell said, “because, as far as we know, it’s the only suit that still survives that was worn by two kings.”

Serving as a sort of catalog for the exhibition is the book “Tartan” (2022 edition, Bloomsbury) by Jonathan Faiers, 63, professor of fashion thinking at the University of Southampton in southern England.

The author, who also served as a consultant curator for the Dundee show, said by email that he hoped visitors would understand “that tartan is so much more than just a ‘Scottish’ textile. I want visitors to be surprised!”

Royalty to Punks

Tartan’s origins remain elusive — even of the word itself. “It is possibly derived from the Gaelic tarsainn meaning across, the French tiretaine or tertaine, or the Spanish tiritana, all referring to woolen checked woven textiles,” Professor Faiers wrote.

Yet tartan remains popular, he noted, “because of its unique history, which means it is worn by radical and conservatives alike, from royalty to punks, provides an instant ‘tribal’ affinity with other tartan wearers, can be worn by all sexes and genders, and is visually stunning.”

One designer who unravels and reconstructs such cultural histories and identities is Olubiyi Thomas, 36.

Born in Nigeria and raised in Glasgow, he produced a work for “Tartan” called “Intersectional Family,” using ecru-colored mannequins of a mother, father and child wearing kilts, traditional West African headgear and copper masks. Behind them will be a textile he calls “Blood Line,” made of antique cotton and linen with a large hand-embroidered check pattern.

The mannequins are dressed in green and white, a color scheme he based in part on the Nigerian flag and in part on the colors of the Celtic soccer club in Glasgow. “When I was growing up, trying to figure out which team we supported,” Mr. Thomas said, “we went for Celtic because the color scheme was a direct link to the Nigerian flag.”

Questions about his own identity always arise, he said, and a tartan’s weave shows that identity, like tartan, is not as simple as being two things squashed side by side, and is more of a mesh that creates something new.

So he aimed to play off the tradition of tartan but also to “flip it, deconstruct it and then rebuild it and sort of present it in my own way,” he said. “Those lines, those squares, they’re all symbolic and significant of family, or eras or times or clans.”

The copper masks signify how slavery dehumanized people, reducing them to their economic value. “In Scotland, when people had slaves,” he said, “they would dress them head-to-toe in their family tartan so the people knew that the slaves belonged to them.”

Mr. Thomas used fabric woven in England by the textile designer Kirsty McDougall and in Scotland by the Vevar studio in Glasgow.

“We produced about six meters of handmade tartan” in cotton and wool for the Thomas project, in “a really beautiful range of pine and dark browns and greens” that gave the impression of an early, muted tartan, Ms. McDougall, 44, said during a recent interview at her studio in Hastings, a town on England’s southeastern coast.

Along with spools of colorful threads and remnants of cashmere fabric, there were several modern and traditional looms in the work space that had been threaded with current projects and samples for clients. One sample that she called “quite experimental,” a “kind of trompe-l’oeil tartan” in black, orange and off-white wool, was in progress on a digital jacquard loom, its threading plan programmed onto a laptop.

“It’s hand-weaving, but it’s digitally programmed,” she explained. “So it feels like me, like half analog and half digital. I think anyone in their 40s feels a bit like that.”

Weaving, Weaving, Weaving

Born on the Isle of Lewis in the Outer Hebrides, Ms. McDougall studied her craft at the Duncan of Jordanstone College of Art and Design in Dundee and the Royal College of Art in London. She counts high-fashion labels such as Balenciaga, Burberry, Erdem, Louis Vuitton, Marc Jacobs and Schiaparelli among her customers: “For the past three or four months, we’ve just been weaving, weaving, weaving Fashion Week things.”

“I love tartan. And I think that’s possibly to do with being a Scot living out of Scotland is one thing,” she said. “I think in the beginning, tartan was about regionality and the dye stuffs and the materials that you had. It was about making a cloth that properly spoke of the landscape that you lived in.”

Now, though, she loves subversion.

“I think I’ve probably made a career of trying to explode the grid,” she said. “Weaving a check or a tartan, you’re working to very strict guidelines. There’s so much precision involved. And as a person who’s not very precise, when I first started doing it, it was the thing that contained all that chaos for me, which was really good. But once I’ve kind of got into the discipline of it, I then wanted to break out of it.”

When it comes to a textile stereotype like a tartan, she said, “it’s about trying to push the parameters on the geometry of the loom. I’m always looking for ways, technically, to kind of get ’round this grid shape. It’s a challenge. And it’s a fun thing to do.”

Repeatedly moving the shuttle back and forth to capture threads could get boring. Not for her.

“I’m not a natural weaver in that I’m an impatient person. And there’s no instant gratification with weaving,” she said. “But I think there’s infinite possibility as a design and art and craft form. Each warp or group of threads that you put on is a new experience.”

In addition, she said, “You’re always thinking about where the thread travels through the cloth and how that creates a functionality. A drape, an aesthetic. And, you know, there’s always a form of sensuality with it as well. You’re thinking about the idea of touch.”

Living with Tartan

Tartan as a pattern has touched more than just fabric. The Dundee exhibition also shows how tartan is used across the world and on “a multitude of surfaces, whether that’s textiles, plastic, glass, metal,” said Ms. Hassard of V&A Dundee. “Almost anything you can think of, tartan has been transferred onto it.”

That is evident in items that form part of what the museum calls the People’s Tartan, comprising “donated pieces that are the sorts of objects that generally don’t end up in museums, everyday things people have in their homes or keep in their attics but with personal meanings,” Ms. Hassard said. Among the hundreds of items: tartan toilet paper, a tartan guitar and a tartan-upholstered Hillman Imp, a car first produced in the 1960s.

The tech world has also embraced tartan, Ms. Maxwell said, as she displayed a sample of the Xbox tartan commissioned by Microsoft to mark the 20th anniversary of the game console’s 2002 debut in Scotland. A fabric in predominantly black and (ironically) apple green covers the game’s wireless controller in a fine-wool pattern designed by Gordon Nicolson Kiltmakers in Edinburgh and woven at Lochcarron, a mill in Selkirk, Scotland.

“The inspiration behind this is pixels, and the neon colors speak to that world,” Ms. Maxwell said. “It’s so intricate, and it’s really pushing what a tartan can be.”

Tartan, contemporary or classic, also has its celebrity fans.

“I love it,” the Scottish actor Alan Cumming, 58, said in a voice message. He recently wore an array of tartan looks as host of the U.S. version of “The Traitors,” a reality TV show set in a Highland castle.

Tartan has “always been modern,” he said, “because I think of modern being about things that are au courant and very vital in our culture and our society.”

“It has been banned for being too dangerous. It’s been rebranded and reinvented and rediscovered by many, many different generations. And I just think it has this power. This weird collection of colors and lines and geometric patterns has sort of been used by so many different socioeconomic groups over the years to represent themselves. It’s both traditional and punk at the same time.”

When he wears it, he said, he feels more Scottish.

“I feel anyone can wear a tartan and they are making a statement of some kind. But when you’re Scottish and you wear it, you’re embracing a tradition and your whole sort of national identity. And it has an added layer of subversion, I think. And I do feel that tartan is very subversive, and I’ve worn it on several occasions for those very reasons.”

As for the future of tartan, Ms. Maxwell said that while “tartan is often defined by the outsider view — and that’s something we have fun with in the exhibition — it’s also what keeps it alive.”

“It’s so much a part of our kind of kitsch, parochial kind of pastiche, and of course we lean into that and we love to poke fun at ourselves,” she said. “But when you start to unpick tartan, and see how exciting designers — like Louise Gray, Olubiyi Thomas, Nicholas Daley, Owen Snaith and all these designers we’re featuring in the show — make it really relevant today, it’s really cool and it’s super fashionable and its relevancy just won’t go away.”