Claire Boucher — the 24-year-old Montreal singer who performs as Grimes — had to smile last month when the video for her fluttery new single, “Genesis,” approached nearly 2 million views after a week on YouTube.

In the clip, Boucher roams the California desert in a black Escalade, brandishing medieval weapons with a costumed passel of pals who appear to be carpooling to Comic-Con 2072.

Think it’s weird? Maybe you’re weird.

“I think it’s weird that people think it’s weird,” Boucher says of the flummoxed responses to her work. “My dad is always like, ‘What genre is it?’ I’m like, ‘I don’t know, Dad. I think genres are kinda archaic.’ ”

Boucher’s music has emerged from the choppy digital ocean we’re all swimming in these days. As our access to music continues to grow online, young artists are embracing a sweeping array of influences, causing genre barriers to melt like so much polar ice. The results often upend our definitions of “weird,” not to mention “pop.”

So while Boucher tries to figure out where she stands in all this — hint: on top — she tours incessantly, working to earn fans in the three-dimensional world. (U Street Music Hall will host her first headlining Washington gig Sept. 29.)

Visions,” the third Grimes album in two years, was released in January, and its popularity has spiked with the release of each new music video — cinematic clips in which the singer has donned sci-fi shoulder pads and glammed-up hoodies. If she was dancing in a pair of khakis from Old Navy, would it still be Grimes?

“No,” Boucher says flatly over the phone from Edinburgh, Scotland, where she was recently on tour. “I know a lot of people consider being concerned about your image to be vapid, but in this day and age, context is everything. And the context that you give to people is going to be completely defined by the way you look and the visuals surrounding your project.”

But onstage, even her wildest threads fail to eclipse the music itself — hazy electronic mists that often float atop crisp drum-machinery. As a singer, she vaporizes her consonants, mewling her strange fairy-prattle in a style that makes her lyrics almost impossible to discern.

Her approach places her in a league of young, female solo artists recording dreamy pop under chic aliases (Bat for Lashes and Charli XCX are expected to release new recordings this fall), as well as a generation of artists who grew up as natives to the Internet (Laurel Halo performs at DC9 on Sept. 23).

After rushing home from elementary school to snatch up gobs of free music on Napster, Boucher is now flooding the bandwidth with tunes of her own. She says an early diet of the Spice Girls, Marilyn Manson, OutKast and Skinny Puppy drove her to build pop songs out of the harsher sonic textures she rarely heard on the radio.

“I always try to ride this line between pushing boundaries and remaining really addictive,” Boucher says. “A 10-minute noise song can be grating or alienating, but there are a lot of things in there that I really like. If I could make it [sound] more like TLC, that would be a really good, in-between place. I feel like I’m always trying to get to that in-between place.”

It’s a trait she shares with today’s most adventurous pop artists. Why bother climbing to the top of a genre mountain when you can run wild in the valleys? But Boucher thinks those valleys still have borders.

“That’s the one thing I’m afraid of being: too sentimental,” she says. “I love a lot of very sentimental music, but I shouldn’t necessarily be the person who makes it.”

She’s wary of the backlash — another element of the artist-audience relationship that’s been amplified in the digital age — because “that’s when you’re being the most honest,” she says.

So instead, Boucher operates in the space between provocation and pleasure, working to elicit a response that’s physiological and timeless.

“Success, for me, is a song that can deliver shivers,” she says.

Grimes performs at the U Street Music Hall on Sept. 29.