There’s a moment midway through FloriDada, the first song on Animal Collective’s new album Painting With, when a few seconds of the classic 1960s surf-rock hit Wipe Out flit in and out of aural view, like a tiny plane blipping on a radar display of a hurricane. It’s immediately recognisable – indeed, it would be hard to find a few seconds of any song so familiar – and thrilling for all its fever and speed.

That it soon proves so thoroughly subsumed, however – a distant memory in just a few more seconds, in fact – is a testament to the rush and density of a sound that has to be heard to be believed.

Animal Collective started out making creeping and crinkling gestures in the New York underground around 2000 before, slowly and methodically, becoming one of the most influential and sonically adventurous bands of recent times. Their influence can be deceiving, but it’s everywhere: in indie rock, strobing electronic dance music, day-glo fashion spreads, hyper-patterned textile design and worldly forays for arts of all kinds across the globe.

The list goes on, but what matters most is the music, which on Painting With ranks as some of the most lush and inviting of Animal Collective’s eclectic career. FloriDada opens in a bright, buoyant mode that governs much of the rest of the album, to the favour of antic anthems and strange sorts of sing-alongs that zig and zag while courting abstraction and catchiness with equal zeal.

For those who have not been acquainted, the American state of Florida – part of the inspiration for the album’s opening song – is one of the weirder places on Earth, with a mix of cultures and socioeconomic classes that could not be more vast. It’s the home of squeaky-clean Walt Disney World and quiet villages of old retirees seduced by warm weather and ocean breezes.

But then it’s also home to what seems like its own special kind of psychosis, with a teeming drug trade and behaviour so odd that a widely-followed Twitter feed, credited to @_FloridaMan, has been dedicated to news reports of many a typical “Florida Man” doing unseemly and perverse deeds. For example: “Florida man charged with assault with a deadly weapon after throwing alligator through Wendy’s drive-thru window,” Wendy’s being a fast-food restaurant. Mix that with Dada, the famous early 20th-century art movement devoted to all the beauty and bewilderment to be found in utter nonsense, and you are in the unique realm that Animal Collective haunts with songs like FloriDada.

Describing the sound of that realm is difficult. In many ways, Animal Collective remains a rock band, even though everything sonically speaking is electronic or, aside from some drum sounds, processed into a sort of all-over smeary abstraction more like painting than music. Beyond that, it is easiest just to say all the sounds are splattered, in every song.

The splatter aesthetic is highly organised though, and guided by adventurous ears tuned to music from different worlds. Hocus Pocus, the second track on Painting With, sounds like a slowed-down version of “Shangaan electro” music from South Africa, where artists – including those on a vital 2010 compilation titled Shangaan Electro: New Wave Dance Music From South Africa and released by the superb UK label Honest Jon’s – turn impossibly fast dance tracks into hypnotic, swirling wonders.

There are also certain inclinations toward elements at play in the newer sound of gqom, another South African movement that is darker and sparser, more suited for moody techno brooding. Highpoints of that can be heard on the new compilation Gqom Oh! The Sound of Durban Vol.1, which skitters and skulks through enticingly menacing atmospheres that turn out all kinds of wild imaginings and interestingly pitched drama. See, especially: Zulu War by Formation Boyz, a tense, entrancing fit of repetitive rhythms and foreboding sounds that casts a deep spell.

Animal Collective don’t make dance music exactly, but strains of it figure into a mix that draws energy from myriad sources, some fast and others slow. All the forces flowing through their songs, which often run like a river towards a waterfall, can put an impressionable listener in mind of the drones that course beneath Indian music or circular patterns from other traditions.

The gentle, lilting song Vertical features a series of circuitous voicings that spin in repeated patterns like the piano figures in Cuban salsa, and – owing to its title for sure but also melody lines that run long and take their time to resolve – Bagels in Kiev evokes a subtle sense of Eastern European Jewish music.

No such similarities are explicit or even likely intended, but it’s a credit to Animal Collective that excitable associations have come to surround them. It matches some of the mania in a sound marked by ping-ponging hyperactivity and vocals that evoke the kind of barbaric yawp summoned by the poet Walt Whitman. From his storied Song of Myself: “I too am not a bit tamed, I too am untranslatable / I sound my barbaric yawp over the roofs of the world.”

One can imagine a similar spirit coming over the group’s two main voices – Avey Tare and Panda Bear – when they shout and stammer over each other or, just as often, coalesce and hit upon heavenly harmonies. Over close to two decades now, the two have developed an inner language all of their own, with individual styles and a common idiosyncratic syntax. Panda Bear tends to be bright and sing-songy, while Avey Tare is more manic and jagged – together, they make fine foils for each other’s artful tendencies.

Everything in their music, in fact, is a foil of some kind and, more than anything, a source for surprise. Listening to Animal Collective at length can be a crazy-making exercise, for all the kinetic energy that burbles and abounds. But it can also profoundly recalibrate a listener’s sense of expectance and capacity for surprise in a way that is mesmerising in the end. In music so dynamic, there’s no telling what is going to happen from bar to bar, much less song to song. So the only thing to do is to lie back, burrow down and listen, intently.

Andy Battaglia is a writer in New York whose work appears in The Wall Street Journal, Frieze, The Paris Review and more.