On cloud nine: Turner Prize-winner Keith Tyson reveals the surprising ideas behind his mind-bending work

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You could say that, at first sight, the work of the artist Keith Tyson is simply inexplicable. But that's not strictly true: some of his paintings even come with explanations attached – although to understand them, it might help to have a grasp of algebra. Why does a sombre canvas resembling a Dutch still-life – with fruit, stuffed animals and a skull – also contain a brightly coloured toy cash register? The answer lies in a mathematical formula inscribed under the picture: pluses, minuses and a sigma symbol, along with the words "Retailer" and "Memento Mori". In another recent Tyson, tea has been splattered over a facsimile page from an 1841 book on popular folly and manias. Precisely how much tea (10 pints) and how it has been applied (in a spiral pattern) are determined by the equation below the picture.

Enigmatic as his creations are, Tyson himself is happy to explain his work in terms that make it seem transparent. "I've always been interested in how things come into being and the way we understand them," he says, gesturing around his studio at his series of "Operator Paintings". "All these paintings have an 'operator' – a mathematical or textual expression at the bottom – and a pictorial 'solution' at the top." In mathematical terms, Tyson says, his formulae are all strictly legit: "I'm mathematically literate. But the point of it, I think Warhol said, is to get things wrong."

The 40-year-old artist achieved widespread fame in 2002 when he won the Turner Prize. It was that year's Turner show that notoriously prompted the then-Culture minister Kim Howells to complain about modern British art being "cold, mechanical, conceptual bullshit". Tyson's work is certainly conceptual, and may well be (wilfully) mechanical, but it's anything but cold. As well as being extremely playful, it's often fabulous to look at.

At his new exhibition at London's Parasol Unit, along with his "Operator Paintings" and his "Cloud Choreography" series – an encyclopaedic collection of cloud formations, natural, atomic and other (seen behind the artist on the previous page) – Tyson will present his lushly beautiful "Nature Paintings". These are not, in fact, traditional paintings of nature, but are made by pouring paints and chemicals on to aluminium: the colours and textures formed by the resulting reactions could be described as nature doing paintings of itself.

Tyson's work is fuelled by outré philosophical humour and a commitment to absurdity that can veer into the existential. He made his name with a diverse series – paintings, sculptures, performances – supposedly created at the behest of the Artmachine, a system he devised for generating artworks. It provided the instructions, Tyson simply executed the works – works at once irreducibly eccentric and seemingly free of any personal signature. Although people assumed it was a metaphor, Tyson insists the Artmachine actually existed, though it was more "a conceptual machine" than a machine as such: a panoply of computingsystems, books and flow charts that took four years to prepare.

"It wasn't a structure that you came to and said, 'Good morning HAL, what shall I make today?' But I obeyed its rule, and I made things that I really despised – work that was just abhorrent to me in taste and style, even in conceptual content. I had this huge urge to change them, but the rule was that I didn't."

The abstruse logic behind Tyson's practice has caused him to be dubbed the "wacky boffin" of British art; his work often invokes disciplines such as astronomy and quantum physics. He has described his most spectacular work – "Large Field Array", a vast, system-like collection of 300 sculptures – as "the artistic equivalent of a particle accelerator". But, Tyson says, "I'm definitely not a scientist. I see myself more as a kind of poet, but I don't use words, necessarily."

Born in Ulverston, Cumbria, Tyson says he was an unusual child. "My whole approach to life and everything comes from a series of existential traumas I experienced when I was about six. I had a strong comprehension of my own being, and the shock at that – the full Sartre. I tried to talk to people about it – I generally got beaten or told I was a weirdo." Tyson isn't speaking figuratively about the trauma. "I've had several nervous breakdowns and been in a mental home," he says. "But at the same time, I'm displaced enough to see the comedy of that situation. I can't take that too seriously, I could never be like Edvard Munch."

Leaving school at 15, Tyson worked as a shipyard apprentice – an experience not entirely to his taste, as he was involved in building nuclear submarines. "When you see a Trident-missile tube, it strikes fear into you, because they're not making that thing not to work." Learning engineering in the process, he went on to study art in Carlisle, then Brighton, where he discovered French theory: "Great for thinking, very debilitating for practice."

For a long time, Tyson was in thrall to a gambling addiction: "I spent years losing; I had the Dostoevsky disease, where I couldn't stop." Gambling itself remains a theme in his work: the new exhibition's "Fractal Dice", for example, are sculptures of dice that have morphed into different shapes, following systematic rules that Tyson explains to me, but that I can't altogether comprehend. "I wanted to make something extremely tautological and complete – the idea that you roll an artwork into a room and it expands."

He now lives in Brighton with his family – his wife, the artist Xenia Tyson-Dieroff, and three sons – and has his studio in nearby Shoreham in a prosaic business park. The space – sited among paper mills and plumbers' suppliers – feels less an artist's studio than a neat industrial enterprise, with the down-to-earth Tyson as inventor-proprietor. The day I visit, eight assistants are at work on assorted large canvases. "The space isn't to make big things," Tyson tells me, "it's so I can have a lot of stuff on the wall and brewing in my mind. The work improves the longer the stuff's up."

One of the literary texts that most influenced Tyson was Jorge Luis Borges' short story "The Library of Babel", which imagines a world in which every possible book is to be found on a shelf somewhere. Tyson's own oeuvre tends towards a Gallery of Babel, exhausting all possible devices and forms, with a view to producing every artwork that could conceivably exist. Inevitably, many of his resulting creations seem freakish or facetious – albeit philosophically so.

"The humour," he says, "is about where the cosmic suddenly collapses into the human. We look at a picture of the Milky Way. People say, it's 100,000 stars – but it also contains this week's News of the World, it also contains an Ice Blaster lollipop – there's an absurdity about that. The universe, with all its majesty and extraordinary force," Tyson muses with a chuckle, "was there just to create the pickled-onion Monster Munch."

The recent Hayward Gallery group show Walking in My Mind featured three walls covered in Tyson's "Studio Wall Drawings". Apart from one huge complex piece, these personal, informal works are largely single sheets containing ad hoc notes and insights. One image is especially representative: shimmering flashes of electricity, as if from a Van der Graaf generator, or among the brain's synapses. The caption read: "The anatomy of a thought... in a mind full of starlings."

Tyson's own mental starlings swoop in unpredictable but obscurely logical formations. Critics sometimes balk at the unstoppable profligacy of his ideas, the often overpowering sense of cerebral cacophony. Having ideas in the first place may be the toughest challenge faced by most artists, but for Tyson, apparently, it has never been a problem. "The only reason you would never come up with more ideas," he says, "is because you're attached to the first one you had. If you think you own your ideas, game over – you're not open to the world." And the world, not the artist, Tyson insists, is where ideas come from. "I've never seen myself as the author of a single idea I've had."

Keith Tyson's Cloud Choreography and Other Emergent Systems is at Parasol Unit, London N1 (www.parasol-unit.org) from Wednesday to 11 November