If Lady Gaga has an abundance of anything, it's ideas. Following The Fame and Born This Way, she sought to craft a more free-form, message-light and upbeat collection with her third album, Artpop. But what the 2013 album eschewed in terms of anthemic ideologies, it certainly had in terms of Gaga's characteristic ambition. For some, Artpop may at first have seemed like a party album you needed a doctorate to understand. The confrontational Jeff Koons cover art, styling the singer-songwriter as a space-age Venus giving birth to one of Koons' Gazing Balls, was as bold a visual statement as she had ever made, placing her at a distance from the softer, more accessible tone of the world's then-fastest rising star, Taylor Swift. It was as if Gaga was deliberately stepping back from that rat race. This was a party you gained entry to only on her terms.

Musically, the sonic energy of Artpop's fizzy, synth-driven EDM bangers remained compelling. Lead single "Applause" scaled Gaga's former peaks, its hi-NRG Europop charm securing it Top 5 chart placings across the globe. A homage to her devoted fans' support, "Applause's" battalion of songwriters suggested a wide search for winning ingredients, though notably absent was RedOne, who had steered so many of the early successes that this song drew from. He could, however, be found on "Gypsy" – one of Artpop's best tracks, and an anthemic 80s throwback. For every accessible moment, however, Lady Gaga appeared determined to push back with something more demanding.

Artpop's title-track is an electro-waltz during which Gaga claims "My artpop could mean anything," finding little argument from fans puzzling over her latest move. "Swine" is an anarchic pop-rock statement that spoke the language of the dancefloor while drenching the listener in something far darker. Elsewhere, "Donatella" is canny satire bathed in producer Zedd's trademark effervescent synths. It's one of three tracks he contributes to. Likewise, the decision to overlook the disco-shuffle of "Fashion" for single release seems extraordinary in hindsight. With the help of David Guetta and will.i.am, the song apes the exuberance of other celebrated throw-your-inhibitions-in-the-air anthems. Perhaps it was too obvious at the time, but it's also so different to a track such as "Jewels N' Drugs" (featuring TI) that it's hard to imagine them coming from the same project.

Artpop remains Lady Gaga's most complex record, its characteristic explosion of creative energy seemingly searching for tighter focus. Gaga's hunt for an audience had been decisively secured; many of her messages had been heard...and so now what? The answer appeared – in time – to be to strip things back (her next record, Joanne, was very different) and explore new platforms (star turns on TV and in Hollywood brought renewed acclaim). But on Artpop, an atom bomb of energy produced bursts of blinding brilliance that sometimes carried with them a chaotic aftershock. Soak up the heat, but be prepared to bunker down, too.