It takes two hours and forty-five minutes to get from Los Angeles to San Diego by train, and a little longer than that if there is a mechanical delay, which on this day there was. Claire Boucher, curled up in a window seat on the train’s non-ocean-view side, didn’t seem to mind, or even notice. It was July, 2014, and, because she hates flying and doesn’t relish driving, she was heading, slowly, to Comic-Con, which attracts huge numbers of geeks, many of whom bring along their alter egos. Boucher’s alter ego is Grimes, the name under which, since 2009, she has been producing and singing home-brewed electronic music that is irreducibly weird but insistently pop, a term that describes both its sound and, increasingly, its reception. She fills tents at festivals, and this summer she toured with Lana Del Rey; her music videos have amassed tens of millions of views on YouTube. That weekend, CraveOnline, a media company aimed at young men, had hired Boucher—or, rather, Grimes—to be the celebrity d.j. at a party aboard the U.S.S. Midway, a decommissioned aircraft carrier moored in San Diego Bay.

“Should my d.j. set be more chill?” Boucher wondered, not for the first time. (“Chill,” one of her favorite adjectives, can mean “mellow” or “good” or, most often, both.) “Or more dance?” She was thinking about songs, as she almost always is.

The intensity of Boucher’s musical obsessions can make her seem like a mad pop scientist. On her bustling Tumblr page, she keeps track of her research into a cultural universe that seems, like its physical counterpart, to be expanding at an increasing rate. Her followers might encounter a snippet from the Japanese soundtrack composer Yoko Kanno, or a fan-made video set to the music of the electronic producer Aphex Twin, or a recent Selena Gomez single—which, Boucher has discovered, sounds particularly arresting in a car equipped with subwoofers. In her own songs, Boucher takes delight in rewriting the old music-industry story of the female performer in the spotlight and the male mastermind behind the curtain. “It’s like I’m Phil Spector, and then there’s Grimes, which is the girl group,” she says. She got her start in Montreal, part of an underground experimental-music scene, but now she herself is the experiment, as she tries to figure out what “pop star” means in 2015, and whether she might become one.

For the moment, many of Boucher’s fans come from the world of indie rock, which has championed her as a new kind of pop auteur. One of her signature songs is “Oblivion,” an upbeat but ominous dance track; Boucher doesn’t sing it so much as haunt it. “Oblivion” never appeared on any Billboard chart, but last year Pitchfork, the definitive indie publication, called it the best song of the decade so far, which was a complicated sort of compliment. “Oblivion” was a great choice to top the Pitchfork list precisely because it was not an obvious choice.

These days, Boucher seems fascinated by the idea of making music that is as direct—as obvious—as the pop songs she loves. She acquired some important allies in 2013, when she signed with Roc Nation, the artist-management company founded by Jay Z, which counts Kanye West and Shakira among its clients. But Boucher still records for a small label, 4AD, which gives her freedom from just about any imperative except the financial one—she can’t afford not to think practically about her career. She had accepted the nautical d.j. gig to fund her next music video. But it also gave her an excuse to go to Comic-Con, where she hoped to bump into someone from “Game of Thrones,” the HBO series. “Every season, there’s a wedding, and they have a band play,” she said. “I really want to do it. ” She looked across the aisle at Lauren Valencia, a Roc Nation executive who was travelling with her.

“It has to happen,” Valencia said, playing along. “You might have to dye your hair, though—dark brown.”

“Darling Elizabeth! How I long to hold you betwixt my giant industrial clamps.” Facebook

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“I’ll do it,” Boucher said. Her hair was bleached Khaleesi white, with a swath of purplish brown near her shoulders, and she was wearing clothes that marked her as someone with no particular fear of standing out: a slouchy men’s pin-striped blazer with short sleeves; baggy tuxedo pants; Adidas sandals with socks; round-lensed reflective sunglasses; and, on her sternum, an uneven coating of rainbow glitter. Her style is an imaginative elaboration of goth, drawing influences from gutter punk, high fashion, and Japanese culture. (She carries a fuzzy gray purse in the likeness of Totoro, the friendly spirit from a Hayao Miyazaki film.) The electronic producer known as d’Eon, who became friends with Boucher in Montreal, says that she has always had a knack for self-presentation; in the old days, she kept a tattoo gun in her bag, so that she could embellish herself whenever the mood struck. “I’ve met people that have never met her, that have the same hand tattoos that she has, just because they think it’s cool,” he says. More recently, Boucher has become an occasional presence in the fashion world. Karl Lagerfeld proclaimed her “fresh,” and dressed her in Chanel for the 2013 Met Gala. She is gangly enough to fit into sample sizes, and she has found fashion magazines to be surprisingly congenial—all that matters is that she look cool.

Boucher has a hard time censoring herself in interviews, or on social media, which means that she provides a steady stream of content for music Web sites, whose readers love to express their sharply differing opinions of her. “I feel like if I read about myself from the media I would hate me,” she says. “I’d be, like, ‘Fuck that bitch!’ ” Online, she has shared not only her enthusiasms but also her frustration with the music industry, where “women feel pressured to act like strippers and its ok to make rape threats but its not ok to say your a feminist.” Her outspokenness has helped to make her something of a role model. Musicians are now expected to advertise their political beliefs, but Boucher is unusually thoughtful and passionate about social injustice and environmental degradation. (She travels with a canteen, and has essentially banned plastic water bottles from her tour bus.) One particularly trenchant Tumblr post, from 2013, earned a vigorous endorsement from Spin, under the headline “GRIMES’ ANTI-SEXISM MANIFESTO IS REQUIRED READING (EVEN IF YOU’RE NOT A FAN).” That last phrase hints at what is, for Boucher, a disquieting possibility: that her online presence might be even more popular, and more influential, than her music.

This predicament owes a lot to Boucher’s painstaking and intensely self-critical creative process. “Visions,” the album containing “Oblivion,” was released in January, 2012, and Grimes fans have been waiting ever since for the follow-up. The few tracks that Boucher has released, to keep them patient, seem to have had the opposite effect: “REALiTi,” a warm and hazy eighties-inspired song about disillusionment, appeared online earlier this year, to general acclaim, but Boucher now downplays it, saying, “It’s not that great.” She has mixed feelings about lyrics, although she recognizes that they are an important part of nearly every hit in history. Often, she conceals her voice behind reverb, a very un-pop thing to do: radio programmers usually reward the kind of clarity that can be found more reliably in Boucher’s social-media posts than in her songs. “REALiTi” comes from an album that Boucher recorded and then scrapped—it was too “disturbing,” she says, and she decided that she wouldn’t feel right disseminating such a hopeless message.