Charles Avery, on show in Edinburgh

“Hats matter,” says Charles Avery as, walking into his studio in Hackney, east London, I collide with a huge plaster bonnet painted with stars, circles and pentagons in a kaleidoscope of light and dark colours. “Hats represent different philosophical schools — empiricists, rationalists, revelationists,” the Scottish artist explains. “The philosophers meet in bars — you know, the logical positivists have a to-do with the metaphysicians. They get salaries because they attract tourists: a bit like stand-up comics.”

Since 2004, Avery has worked exclusively on a beguiling, obsessively detailed project called “The Islanders”. His large, chaotic two-storey studio (recently acquired, with floors and stairs that are still makeshift — “I have minus no money,” he says) bursts with drawings, installations, texts describing the imaginary city of Onomatopoeia on an island that resembles yet differs from the Isle of Mull where Avery grew up in the 1970s. Every work is a “reportage from the island,” with its own intellectual backdrop.

A lean, unassuming, casual figure in jeans and sweatshirt, Avery speaks softly but quickly, with a faint Scottish lilt. “That hat,” he says of the flamboyant bonnet, which occupied him “on and off” for a year, “I hesitate to call it ‘utopian’ but I was thinking of a perfectly patterned city, at dusk and at day, seen on different sides of the hat. I wanted it to look like a firework display. I was listening to Bertrand Russell, whose analogy for relativity was being in a balloon in the night sky, seeing fireworks.”

This summer another “export” — from Onomatopoeia’s municipal garden Jadindagadendar — comes to Waverley Station for the Edinburgh Festival. Avery shows me drawings of the looping, sinuous branches of a five-metre bronze tree. This is Avery’s first public commission; delightfully, it is sited at Britain’s only railway station with a fictional name (a reference to the series of “Waverley” novels by Sir Walter Scott).

At Ingleby Gallery next door, The People and Things of Onomatopoeia will amplify Avery’s own fictional universe. Limpid, large-scale painting-drawings depict groups of islanders lounging around damp graffitied harbour walls. Youths with attitude sport philosophical T-shirts (“We don’t stay here because of gravity we stay because we like it”). A canoeist advertises the restaurant L’Escargot Quadrato. Rubbish, including a red hole-punch, lurks among seaweed in the transparent shallows.

I’m part of the art world but there are standardising forces in the art market inimical to creativity

These depictions are characterised by Avery’s willowy line, inventive conviction and ability to make detail arresting yet laconic. “That’s a product of drawing from imagination,” he says. “I really inhabit the figures. On the Tube I’m staring at people and they get up and walk away.” His drawings rise above anecdotal illustration; nevertheless, they might make you think you know this place. But geography only gets you so far in an environment constructed from philosophy, geometry, history and fantasy. “The Islanders” is smart conceptual art — games about the nature of representation and reality — dressed up as whimsical figuration and storytelling.

“Philosophically, I believe reality to be a quality of things, like greenness or weight. I don’t give it supremacy,” Avery says. His “Squared Snail” references “Mussolini — he had a square coliseum built outside Rome — and the idea that by force of will you could impose squareness on the ultimate icon of circularity”. The hole-punch is a narrative talisman: stamped “made in Onomatopoeia”, it is a gift from local girl Miss Miss to Avery’s protagonist, Hunter, a searcher after truth who initially tells her she is an apparition. “Everything is real,” she snaps back.

“Hunter is me a bit, the viewer a bit, the vital spark. I don’t want gratuitous invention, I need a way in, a gunpowder line: Hunter arriving on the island — either the author or the viewer — simultaneously inventing and discovering the world. I’m interested in mathematical philosophy, I love drawing, I love making . . . pure maths is at one end of the gamut — two plus two is four. At the other end you have the cat walking across the keyboard: that’s nonsense. Halfway between pure logic and the scrambling cat, you have a phrase: the square circle. It makes sense but it’s nonsense, in the exalted sense of the word.”

Squares are banished in Onomatopoeia. “Islanders don’t use the number four, they use a different counting system. They don’t like the quadrilinear. It’s too brutal, it creates awkward relationships, people sitting opposite or at right-angles.” Avery pulls battered chairs up to a three-sided curving table and offers coffee. “The natural way is at a 120-degree angle, like we’re sitting now.” And the Islanders don’t drink from glasses but from curvaceous pipe-like vessels which look like a cross between diving birds with long beaks and Brâncuși abstractions.

If “these little tweaks make it like another country”, as Avery says, “The Islanders” is really “a place to put ideas, a way of thinking rather than a defined project. It’s important to take the territory of art-making back into thinking. That’s what ‘The Islanders’ enables me to do: explore this wandering. Sometimes it comes to nothing. It’s not coherent to the outside world now but it will be when it reaches critical mass!”

One day Avery would “love to coalesce the output into a great book in several volumes, a structured, considered thing that could be used in schools as a conversation piece about identity, subjectivity, religion, philosophical issues”.

Literary antecedents, from Gulliver to Borges, are obvious; visual ones less so. “It was my mum,” he says. “She was a painter, my father was an architect. On a wall of our house she painted a very imaginative map of our part of Mull: sea monsters, headless horsemen galloping through the glen.” With Avery’s godfather, his mother also published a book “with beautiful drawings” called The Adventures of Only about a kid on Mull — “me!” — which was “a proto-Islanders”.

Avery “always had an urge to draw, and a taste for the epic project”. “I look at people who draw: Schiele, Daumier, Redon, Frank Lloyd Wright’s architectural drawings, New Yorker cartoons — not comics. I like expressiveness in drawings. And top quality American television like The Wire, which overcomes the linearity of film. I find very little in contemporary art to inspire me. I’m part of the art world . . . but there are certain standardising forces in the art market inimical to creativity. ‘The Islanders’ gave me a way out. The art world provides opportunities but excludes lots of reflective people, deterred by its esoteric nature, who might enjoy this project. I feel this is for them.”

Nevertheless, Avery acknowledges: “The art world is an exchange of ideas: you sell your wares to continue your work. That’s embedded in ‘The Islanders’: Hunter comes back with his wares to fund his next expedition.” And this summer Avery returns his fictional wares to Mull, where he spends a third of the year, accompanied by his wife and three daughters during school holidays. He has “wildly ambitious” plans to build an actual jetty, “a beautiful geometric form” that started as a design for “The Islanders”. “The fiction has been strongly influenced by Mull,” he says. “Now fiction is reinforming reality.”

‘Charles Avery: Tree no 5 (from the Jadindagadendar)’ is commissioned by Edinburgh Art Festival and Parasol unit foundation for contemporary art with Parasol Public/Parasolstice — Winter Light 2015, Edinburgh Art Festival, July 30-August 30, edinburghartfestival.com; ‘Charles Avery: The People and Things of Onomatopoeia’, Ingleby Gallery, Edinburgh, July 30-October 3, inglebygallery.com

Photograph: Howard Sooley