Picasso once said, very foolishly, that he would be remembered as “a Spanish poet who dabbled in painting”. He was kidding himself. The terrible poems and plays he began spewing out in the 1930s were the least convincing signs of genius he ever displayed. Geniuses, alas, have a tendency to fool themselves about the extent and range of their talent.

Which brings us to Bob Dylan, who was unveiled last week as an artist. A selection of his paintings has gone on show in Mayfair, and huge claims are being made for them. Not least by Andrew Motion, who has been wheeled out to write an effusive foreword to the catalogue. “The way in which the works feel at ease through their lack of ease” is what distinguishes Dylan’s painting, rambles the poet laureate, whose catalogue writing turns out to be as brittle and vacant as his poems.

Those of us who are Dylan fans - which must mean pretty much everybody with ears - have known for some time that the great man dabbled with paints. A couple of his album covers were decorated with his art. And various passages in Chronicles, his dazzlingly good memoir, make clear that doing art has been important to Dylan since he was a kid. I remember a passage in which he describes drawing on the kitchen table at home for hour after hour.

However, being a keen amateur is a different proposition from demanding that you be taken seriously as a visual artist with an ambitious unveiling in London. In fact, The Drawn Blank Series, as the show is Dylanesquely entitled, is not an overview of Dylan’s artistic career, as I was expecting, but a group of works produced specially for this show in curious circumstances. Back in 1994, Dylan published Drawn Blank, a book of drawings chronicling his life on the road in the late 1980s: the hotels he stayed in; the girls who were with him; the views from his window. Asked recently if he would exhibit these drawings, Dylan found they had disappeared. So he decided to have another go. A set of scans had been made of the original Drawn Blank drawings, and, in a fever of creativity, he threw himself at them and reworked them. And that is what we have here. A slow trickle of images about life on the road has become a mad outpouring done at home.

These are tortuous origins. The new paintings cannot be about life on the road. So what are they about? About imagining yourself to be an artist, would be my answer. Dylan obviously had enormous fun churning out these variations on his originals, and one of the best things about the show is its evident sense of enthusiasm. Glum Bob has become a kid in a classroom splashing the paint around.

Most of the scans have been redone more than once, with abrupt changes in colour and detail from version to version. Woman in the Red Lion Pub (in Portsmouth, apparently) wears a purple dress in one picture, but she is green and blue in another. Two Sisters features a couple of sexy girls stretched out on a hotel bed in outfits that materialise and dematerialise. A hairy chap with a beard sits in the corner of a room. By the next image, he has grown bald.

Working in series is a method with a venerable artistic pedigree. Monet did it, and, more recently, Warhol. Different colours create different moods. Different details give a picture a different thrust. This show’s most iconic image, a long view down a railway track, looks threatening and spooky when the sky is orange, but hot and summery when it is blue.

All this is reasonably interesting. Dylan’s art shares with his lyrics a sense of heightened awareness. He is the man in the corner looking hard where others don’t look at all. But that was already in evidence in the first incarnation of these images: the Drawn Blank book. Their transition into high art does little more for them. With its unrealistic felt-tip colours and a fierce sense of being dashed off, the new art tries to be fauve in too clichéd a way. Dylan can’t do faces or find proper character in others. The results are not disastrous, but they are vain. If you saw this work in the Royal Academy summer show, you wouldn’t give it a second look.

Bob Dylan at the Halcyon Gallery until July 13

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