Many of the mediums from which art is made have been around for a long time. People have been painting on walls, for example, for about 40,000 years. Similarly, figures have been fashioned out of stone and metal for millennia, and still are. But if there is one ancient medium you might think was now definitely over and out, it would be tapestry.

But no! In this era of artificial intelligence and omniscient Google, the ancient practice of painstakingly twining coloured wool into pictures is undergoing an unexpected revival. The latest contemporary artist to give tapestry a go is Chris Ofili. His exhibition Weaving Magic at the National Gallery gives some clues as to why he — and other figures such as Grayson Perry, Marc Quinn and Craigie Horsfield — find it appealing.

Nearly 20 years ago there was a brouhaha when one of Ofili’s works was denounced by the then mayor of New York. The offence was that the painting in question contained elephant dung — balls of it — plastered on to a picture of the Madonna and supporting it like rather rough-hewn balusters.

Actually, as soon became clear, Ofili’s more recent art isn’t shocking or scandalous at all. Its transgressions are quite the reverse: mainly being altogether more charming than is normally the avant-garde way. Sometimes it verges on decorative, long a dirty word in the art world (though quite a positive one outside it). At the National Gallery, the tapestry is complemented by a monochrome frieze of figures the artist has painted on the walls of the gallery, making the whole room an integrated interior — wall-hanging plus mural — which Pope Leo X would have immediately understood.

His new tapestry, a triptych entitled ‘The Caged Bird’s Song’, is a sensuously gorgeous thing, full of curvilinear, twisting forms and sumptuous colour harmonies blended softly together: gold and turquoise in the right wing of the piece, purple and bluish green on the left. It’s easy to see the attraction of this new medium for Ofili. It provides extraordinary richness of texture.

Ofili has always been a figurative painter, but not a naturalistic one. His pictures don’t attempt to represent the world around us by creating an illusion of depth. Instead he has always aimed for an encrusted surface — adding glitter and glossy resin — more like an icon or mosaic than a conventional painting. Ofili has Byzantine tendencies and an affinity with art nouveau.

He was born and brought up in Manchester, to parents from Nigeria, and some of the effects in the work that made him famous had an African look, particularly the way he would pepper some works with map pins to create a bobbly pattern. The elephant dung was intended partly as a souvenir of Africa, but also — I suspect — as an extra bit of sculptural relief.

Tapestry offers another type of surface enrichment, soft and lustrous — and here it’s been put to an unusual, perhaps unprecedented, purpose. ‘The Caged Bird’s Song’ is a watercolour-and-charcoal design translated with amazing skill — by the Dovecot Tapestry Studio — into warp and weft. Ofili himself marvels on the accompanying film at how the weavers have been able to replicate pools of watery pigment, softly oozing into paper, in a mesh of woollen thread. Such effects create a good deal of the beauty of the result.

The title refers to Maya Angelou’s memoir I Know Why the Caged Bird Sings. One of the figures in the tapestry carries a bird in a cage, but much of the symbolism is hard to decode. The same could be said, however, of Gauguin’s ‘Where Do We Come From? What Are We? Where Are We Going?’, which poses perplexing questions, but actually depicts figures in a verdant landscape, with a distant sea behind.

That description would fit Ofili’s tapestry too. Indeed, like Gauguin, he is a western painter living and working on a tropical island (he moved to Trinidad a decade ago). Another name that comes to mind when one looks at ‘The Caged Bird’s Song’ is Matisse, especially his ‘Luxe, Calme et Volupté’. That’s just what Ofili’s figures — half-naked, shaded by greenery, playing musical instruments — seem to be enjoying. On the other hand, it isn’t entirely calm, a storm is brewing out to sea.

The late works in his Tate exhibition of 2010 suggested, worryingly to his admirers, that he might have lost his way. His earlier work had more edge — there was a hint of graffiti, a punk energy, those elephant droppings. Over time, it’s grown languorous.

Even so, this tapestry holds the eye. Maybe it’s the weirdness of morphing watercolour into textile that makes it compelling. If Ofili ever lost his mojo, he seems to have found it again — which is good news for those of us who like art that is lovely to look at.