The future of influential D.C. post-hard-core band Fugazi is uncertain. They haven’t performed together since 2002 and have no specific plans to do so again. But the band’s past is now just a mouse click away.

On Thursday, the Dischord label launches the Fugazi Live Series, a Web site that will offer more than 800 of the band’s live recordings. It’s a daunting archive, but each show should sound unique — according to singer-guitarist and Dischord co-founder Ian MacKaye, the quartet was always about the moment. “We weren’t trying to put on an act. We played as we were,” he said. “If we were happy, we played happy. If we were frustrated, we played frustrated.”

Designed by Dischord’s Alec Bourgeois, the site covers all sides of this definitive punk outfit, perhaps D.C.’s most famous band and certainly an iconic model for independent music worldwide. The series can be searched by song, year, venue, city, state or country, and each concert has its own illustrated, detail-filled page.

Browsing is like playing a game of Fugazi Clue. Say you saw the band play with Laughing Hyenas at D.C. Space in 1988 — just plug in those terms and compare your memories with audio reality.

Surf the site randomly instead, and maybe you’ll stumble on the June 1990 Chicago set in which the band let stage-storming skinheads take their instruments and play “Suggestion.” Or the October 1990 gig in Rome where the crowd continued singing “Waiting Room” during a sudden power outage. (Each show can be downloaded for $5 — the price Fugazi charged for concerts — or any other amount between $1 and $100, as long as you add a note explaining that choice.)

If a show you seek turns out to be one of the few the band didn’t capture, perhaps another visitor will submit a recording, and others will add photos, fliers or comments.

“I like the idea that it’s going to get out of our control at a certain point and become something that’s more a product of the community itself,” said Fugazi singer-guitarist Guy Picciotto. “There will be a self-regulating aspect, with people being able to determine which shows are worth their time and which ones aren’t.”

Not every band would embrace that lack of control and let every moment be heard. In fact, Fugazi once considered just creating a single live album, but culling a definitive set from so many tapes proved more troublesome than releasing them all.

“Once you make the decision to put everything out, it makes everything a hundred times easier,” Picciotto said. “There are moments in there that will be mortally embarrassing, but that’s okay.”

Said MacKaye: “I’ve said some crazy stuff onstage, and I hear some of it and think, ugh. But cleaning that up takes all the joy out of it.”

Indeed, the between-song banter at Fugazi shows has become nearly as legendary as the music. In the 1990s, when body-banging mosh pits were practically mandatory, MacKaye and Picciotto regularly called out dangerous behavior.

“I don’t think people realize just how insane the situation was, the kind of pandemonium and injuries that occurred,” MacKaye said. “Of course I’m going to speak out against that. We weren’t going to provide a soundtrack to it.”

Much of the band’s chatter was also wryly funny, as evidenced by a fan-made collage called “Having Fun Onstage With Fugazi” that has recently made Internet rounds.

“There’s high entertainment value in these exchanges,” drummer Brendan Canty said. “That’s the very present, be-here-now aspect of these recordings.”

Sound engineer Joey Picuri, who recorded Fugazi’s first show in 1987 and most gigs thereafter, recalled a Rhode Island set in which MacKaye deftly defused tensions between enthused fans and local police.

“It’s not controlling the crowd — it’s having an intelligent conversation with them,” Picuri said. “It shows you that crowds don’t always have to succumb to the lowest common denominator.”

This ongoing conversation between Fugazi and its audience — as MacKaye put it, “We’re making a show with you, not for you” — makes the interactive aspect of the site apt. But the best reason to offer this many shows is that no two were alike. The quartet never followed a predetermined set list and often improvised during songs. Search the site for versions of one tune and the differences can be striking.

“They were constantly trying to keep it interesting,” Picuri said. “It’s like they’d want to see if they could lose their balance on the edge of a cliff and then pull themselves back in.”

Joe Gross, a veteran rock critic, saw the band play many times in Washington and elsewhere. “At times they reminded me more of song-based jazz than rock,” Gross said. “When they got a good head of steam going, you really thought, ‘Man, this is the best live rock band of their generation.’ ”

It might seem odd that a group so tuned to the moment would put so much effort into preserving its past. But Picciotto said that offering everything unedited does justice to all the moments.

“It helps delineate the line between creating a nostalgic document and a historic document,” he said. “That concept of the moment was how we approached shows, and I don’t think documentation can erase that fact.”

The members of Fugazi, which also includes bassist Joe Lally, still see themselves as in the moment, despite not currently performing or recording. MacKaye, who now plays in the Evens, said Fugazi’s “indefinite hiatus” status is no dodge.

“We are still an entity to ourselves,” he said. “We are still discussing things. I think what this [site] really reminds me to do is to write a song — to get back to work.”

Whether or not Fugazi ever plays again, the Live Series site could become a living entity of its own.

“Hopefully it will create some sort of overarching context that will make all the chaos make sense,” Canty said. “But I don’t know if it needs to make sense. Maybe it will ultimately show that the chaos is the story.”