Exclusive interview: The mistress of reinvention Björk remixes herself yet again (for her new album called... Bastards)

She's a world-renowned musician –but in Reykjavik, she'll never be a star. As she reinvents her last album, Björk tells Emily Mackay why she'll always be a work in progress

Iceland is a landscape in a constant state of reinvention, bubbling and heaving with glaciers, geysers and volcanoes. In 1963, an eruption began that lasted four years and gave birth to the new volcanic island of Surtsey. Little wonder that Björk, born in 1965, proud Icelander, child musical prodigy, teen punk, former member of Reykjavik's post-punk pranksters The Sugarcubes, 1990s dance diva and now high-art-concept multi-disciplinarian, finds imagining and reimagining her work in endless ways second nature.

We meet on a cold, bright morning in a Reykjavik cafe. It's around the corner from where I'm staying, the Hotel Borg, a grand old 1930s affair for which Björk's grandfather did the wiring, and just a couple of minutes' walk from her modest, black wooden waterfront house, where last year we discussed, for four hours, the themes behind Biophilia, the epic conceptual album which her new album, the sweetly titled Bastards remixes.

She cuts an arresting a figure among the latte-sippers as she arrives, enveloped in a massive white padded jacket beneath which she sports a white lace dress and long, royal-blue-tipped tresses. Her hometown, though, where she now lives for half the year (the other six months are spent in her artist boyfriend Matthew Barney's favoured New York) is a keep-your-feet-on-the-ground sort of place. Before long a teenage boy approaches, giggling, to ask for her autograph in Icelandic, only to be met with a brisk “Nei!”. He's taking the mickey, she informs us – Reykjavik is too small for celebrity. “Everybody knows each other, so it's kind of silly.” As if to prove her point, the son of her former Sugarcubes bandmate Einar Orn later walks in and gives her a friendly wave.

Click here or on "View Images" for the changing face of Bjork in pictures

As with many things, Björk was an early adopter as a remixer. Her hugely successful 1993 album Debut was swiftly followed by the nattily titled EP The Best Mixes From the Album Debut For All the People Who Don't Buy White Labels, a collection of overhauls by the likes of Underworld, The Black Dog and Sabres of Paradise that betrayed the curating hand of someone interested in more than just keeping one finger on the dancefloor. Telegram, her 1995 full-length remix album, ranged across the Brodsky Quartet, Dilinja and Eumir Deodato, a fascinating, challenging listen that demonstrated the breadth of Björk's taste.

“To me it goes all the way back to being in The Sugarcubes and [her early gothic punk band] Kukl before,” she explains, nervily sipping coffee (loading up on caffeine so she's wired enough to talk about herself is her standard interview tactic). “For about 10 years I was in the indie circuit, and I think a lot of people that were doing that were doing it half-heartedly, and didn't really belong there. Then when acid house came, half of the indie rock people were like, whoosh! Jumped over to the other boat. Going to all those first raves, it was really obvious that there wasn't really one correct way of doing a song.”

So began Björk's 1990s turn as dancefloor diva, with the beat-driven likes of “Big Time Sensuality” and “Violently Happy”. These days, she's a 46-year-old mother of two (to 26-year-old son Sindri and 10-year-old daughter Isadora) with more than 25 million albums sold worldwide, and is happier playing tracks from her iPod at a small Reykjavik bar than at Ministry of Sound. Bastards doesn't just offer dancification, finding many ways to remodel the cosmic grandeur of last year's Biophilia album. It opens with the rambunctious Arabian rave-up that is Syrian party-master Omar Souleyman's reworking of “Crystalline”, then winds its way through the sparkling emotionality of Glaswegian beatmaster-to-the-stars Hudson Mohawke's take on “Virus”, and the brutal starkness of ferocious future-rap firebrands Death Grips on “Sacrifice” and “Thunderbolt”.

Björk's willingness to give her Biophilia baby over to such rough nannies makes sense – it was always an open-ended, democratic project. Inspired by her fight with the Icelandic government to maintain the purity of the country's nature, its melding of musicology and science through interactive iPad apps and fantastical custom-made instruments (including a Tesla coil and enormous pendulum harps), grew from a longstanding dream of Björk's. She wanted to establish a “music house” that would drag the teaching of chords, scales and arpeggios out of the sort of abstract, academic education she received at Reykjavik's Barnamusikskoli and into a colourful, playful future where learner and listener were involved and empowered. Biophilia musicology and science workshops have been held in Manchester, New York and Buenos Aires, while in her hometown, the apps have been adopted as part of the school curriculum (she's also working on getting US educational authorities to recognise her courses).

“I don't want to promise anything,” she explains, “but I would like to find a future international home for Biophilia – even though it's actually in an app. My dream originally was that it would be a museum or something, in Iceland, in nature, where kids could come and do courses.”

Björk's approach, while conceptual, is also pragmatic. She recently threw her weight behind the imprisoned Russian punks Pussy Riot, selling T-shirts on her website to raise funds for their legal fight. She's enthusiastic about the online response to their plight, and phlegmatic about its failure to sway the Russian authorities towards a pardon.

“I guess that's the age we live in with globalisation and the internet. Some things that are actually quite precious get ironed out but the other things that are corrupt pop to the surface and just look ridiculous. Or out of date, like some fossil... I guess they [the Russian authorities] made the sentence milder. I'm always just hopeful... I guess they were too proud to let the world control them this time around, but next time around, they understand that it's a different world out there. And Pussy Riot gave them a platform to speak out, all these people.”

Back in the world of nature, she's also been working on a Channel 4 documentary that's partly a “making of”, partly a mutual love-in between her and her childhood hero and Biophilia narrator David Attenborough. Filming an interview with him in the basement of the Natural History Museum, where, to her distress, she was not allowed any coffee, Björk found herself overawed by Attenborough's professional poise.

“He would close off and take in whatever I was saying, and then just come out with the most beautifully formed sentences you ever heard,” she marvels. “He just composes them in his head... I once read an interview with Jay-Z and he was saying how he wrote his first rap on the subway and he built it up to 20 minutes because that was how long the journey home was. He couldn't have written it down, it's just linked in his mind.” We'll look forward to the Björk/Attenborough hip-hop album.

And, as Björk keeps pushing forward, others are following in her path – Lady Gaga has taken up the app-album idea, conceived by Björk as a way of picking a path through the potentials and pitfalls that the internet presents to the traditional write-record-release model. Björk is keen that she and others adopt the idea to fit the idiosyncracies of their music. “You know, like fashion and perfume, and I don't know... the Little Monsters! I don't wanna judge it, but she's obviously interested in other things.” She laughs. “I don't think she's a frustrated music teacher!” For her part, she is taking inspiration from her new favourite band Death Grips. “They really remind me of Public Enemy,” she says, “What attracts me to them is their musical energy and also that it's sort of cacophonic. It's almost like not a genre.”

She is now considering adopting the fan-funding model to raise money to reprogram Biophilia for Android. “It was always our target that it wouldn't be a coffee-table thing for rich kids. We are going to go to Paris in February and the West Coast of the States in the spring. And then we could go to South Central. And teach them about scales and chords. I'm kidding... No, I'm not, actually!”

She's definitely serious. As to what comes next, after Biophilia's glorious tying together of threads that had run through her whole career, it feels like the only thing is to wipe the slate completely clean.

She looks thoughtful. “I don't know... I feel like I could go both ways really. It took a long time to set Biophilia up. Now we actually have this all set up, I happen to know some of the best app programmers in the world, and I have the instruments I can just plug straight into the iPad and play whatever I have. So it seems kind of natural to work on an album where I don't have three years of prepping. But at the same time, it is a kind of extreme project. With every move you make, you had to add everything up...

“Everything has to be like,” she arranges the condiments on the table-top, “lined up like this, and then you can do this thing, you know.” She shifts a mustard pot. “And part of me is like, 'fuck you!'” She sticks her fingers up at the table. “'I'm gonna go and do an a capella album...'” It will probably be a bit of both if I know myself right.“

Well, why limit yourself to one idea? As Björk's work continues to insist, the world is nothing but possibility.

'Bastards' is released on 19 November on One Little Indian