Back in 1969, a self-confessed "teenage weirdo" from Portland, Oregon, fell under the spell of a newly-released double album called Trout Mask Replica by Captain Beefheart and His Magic Band. Over 40 years later, it remains Matt Groening's favourite record and one that he considers "the greatest album ever made".

That Trout Mask Replica was a formative influence on the imagination of the creator of The Simpsons is testament to the way in which Captain Beefheart's music has permeated popular culture in the most surprising ways. Though he retired from music in 1982 to concentrate on his other great obsession, painting, and his recorded legacy occupies the same place as it has always done – cherished by a devoted few and ignored by the many – he remains one of the most effortlessly eccentric musicians to emerge from rock culture.

Beefheart, who died on Friday aged 69 from complications arising from multiple sclerosis, was a sonic and linguistic visionary, an outsider artist whose fertile, often extreme, imagination could not be contained by the relatively narrow parameters of rock music. In Trout Mask Replica he created perhaps the most brilliantly difficult rock album ever made. As far back as 1964, though, he had fused Mississippi Delta blues with hard rock, creating an abrasive noise that would set the tone for much of what was to follow, both in terms of his creative iconoclasm and his lack of commercial success.

You can hear traces of that primitivist thrust in some of the most powerful rock music produced since: in the rock deconstruction tactics of post-punk groups such as PiL and Devo; in the swamp blues borrowed by Nick Cave and PJ Harvey: in the primal growl and stomp of Tom Waits and the gritty punk blues of White Stripes. "Once you've heard Beefheart, it's hard to wash him out of your clothes," Waits once said, "It stains, like coffee or blood."

He was born Don van Vliet in Glendale California in 1941, the son of Dutch immigrants who, it seemed, spoilt their headstrong son in the belief that he was a child art prodigy. As young as five, he was painting and sculpting birds, fish and trees, becoming so obsessive in his devotion to his art that, for a time, his parents fed him though the door of the bedroom-cum-studio he refused to leave. At high school in Lancaster, southern California, he met Frank Zappa, who shared his love for r'n'b and avant-garde jazz, and who would become both Beefheart's greatest champion and his most intense source of irritation.

One of van Vliet's first jobs on leaving school was managing a shoe store. "As a kind of art statement, I quit right in the middle of the Christmas rush, leaving the whole thing in chaos," he said later, unconsciously or otherwise providing a metaphor for his subsequent musical career. A short stint as a vacuum cleaner salesman followed in which he toted his wares around the desert communities of southern California. Once, legend has it, he knocked on the door of a mobile home and none other than Aldous Huxley answered. Beefheart pointed at a vacuum cleaner and shouted, "I assure you sir, this thing sucks." He made his sale.

Anecdotes about Beefheart's extreme behaviour are countless and, for the most part, seem to have been propagated by the man himself: he was a relentless self-mythologist. He was also a hard taskmaster given to bullying and harrying his musical charges. The stories that surround the recording of Trout Mask Replica are legion. He said that he sat down at the piano, having never played one before, and wrote all 28 songs in just over eight hours. He then kept the Magic Band imprisoned in his house until they learnt every note, browbeating them into submission with verbal threats, physical assaults, sleep and food deprivation and by applying brainwashing techniques. The latter story would seem to contain more than a degree of truth and drummer John French would later describe the atmosphere in the house as "cult-like".

For all that, the late John Peel, another tireless Beefheart champion, said of the record: "If there has been anything in the history of popular music which could be described as a work of art in the way that people who are involved in other areas of art would understand, then Trout Mask Replica is probably that work."

Beefheart made several other great, and certainly less difficult, albums, but it remains the yardstick by which his peculiar genius is measured. The curious might be best advised to start with the preceding album Safe As Milk before moving on to 1970's Lick My Decals Off, Baby or his brilliant, if underrated late album, 1980's Doc at the Radar Station. As the titles suggest, Beefheart was also a master of linguistic invention, an artist who refused to think, write or sing in a linear way, preferring instead to a kind of absurdist, punning, illogical wordplay that the James Joyce of Finnegan's Wake would surely have found entertaining. (The poet Ian McMillan chose Beefheart's pastiche of the easy listening tune Moonlight On Vermont on Desert Island Discs a few weeks back.)

Captain Beefheart was also a visionary in one other, often overlooked, way: he hymned the natural world in his own inimitably odd way on songs such as My Human Gets Me Blues and Wild Life. He was an ecological warrior long before it was fashionable. His death, after a long period of self-enforced seclusion, comes at a time when it is difficult to imagine anyone as eccentric – and as eccentrically gifted – finding a place in contemporary pop culture. In the era of The X Factor the old-fashioned showbusiness values that the 1960s rock revolution was meant to have swept away have returned with a vengeance. There is no place now in pop for the madcap and the beautifully demented, but there is always Trout Mask Replica. Approach with caution.