James Cumming was a lifelong one-off: a completely independent spirit who stood outside the mainstream of post-war painting in Scotland, even though he was a Royal Scottish Academician and lecturer at Edinburgh College of Art. His advice was his motto: 'Always go your own way!'

Born in Dunfermline in 1922, the son of a swimming pool superintendent, he showed such exceptional gifts for drawing at Dunfermline High School that Edinburgh College of Art offered him a place at the age of 16.

His studies, however, were almost immediately interrupted by the Second World War, during which he signed up for the RAF, training as a pilot in Texas and serving in Burma (now Myanmar) and India. On his return, Cumming worked for his degree – sometimes in uniform, like other penurious ex-servicemen – and was awarded a Travelling Scholarship in 1950.

Where fellow graduates went to Rome or Paris, Cumming applied to dispense with long-distance travel and went instead to the Outer Hebridean island of Lewis, eking out a few months' prize money for two full years.

'I went to an island I'd never seen and a people I'd never known,' he later explained in an interview. 'It seemed to offer unending material and a challenge to translate into paint the character of the Lewis islanders living and working in a land of gneiss rock – flat, wind-exposed, desolate. Seaweed and white sands, pipelines, boats, lochs and inlets, peat bogs and peat cutters and rolled up trousers and white sand shoes, herdsmen and animals.

'I saw tinkers, flat-nosed, pie-hatted musicians in odd clothes playing tin whistles; burnt-out machinery beside a black house; crofters of the Grazings Committee making irrevocable decisions amid wintry laughter. I had visions of curtains drawn at 4.30 to let in the cold early morning sunlight, the gun and last night's bouquet of field flowers lying on a kitchen table.'

Cumming lived in the village of Callanish, on the west coast of Lewis, where under-population drew the islanders close around the traces of past cultures, not least the ring of ancient standing stones known locally as The Men.

His 1961 painting The Callanish Man shows a figure as old as time, at one with the stony landscape itself. Callanish is one of many names commemorated in the artist's Hebridean paintings – The Grazings Committee Breasclet; The Charred Trolley Mangersta, a monochrome still life of bone white and storm grey with a single orange flash as if the trolley were still alight; and Garynahine Women, which glows with traces of tartan.

In letters from the 1950s, Cumming talks about the way the cold and dark reached into his bones, the island atmosphere filling his imagination with premonitory visions. The past was present to everybody everywhere on Lewis, and so was the future to certain islanders with the gift of foretelling known there as second sight.

The painter himself knew many such people, from the minister who wished to be rid of its curse, to the carpenter who bleakly knew the dimensions of each coffin in advance of the death, and the woman with second sight who brought milk to Cumming's cottage in an urn.

There is a painting of that very woman, seated among the Hebridean crofts and fields, defensive as a hermit crab, her mysterious gift embodied in eyes as wintry as the crescent moon above.

The most famous of these gifted islanders was a seventeenth-century labourer known as the Brahan Seer, whose prophecies were passed down by oral tradition. A terrible harvest of heads would happen upon a battlefield: Culloden.

Black metal horses would rush through the glens: the coming Highland railways. The Seer foresaw nuclear submarines, North Sea oil, a future Scottish Parliament. And he is said to have envisaged them all through a blue stone with a central hole, held up to his eye – which doubles as the eye itself in Cumming's 1961 masterpiece The Brahan Seer.

The Seer's great body moves left across the landscape, yet the head turns, the blue eye looking to the right as if he saw something in the future. The blue light in the eye, the flash of white moustache and the silvery bonnet seem reflected in a shining metal collar. The prophet is as enigmatic as a heron, a vision in and of the misty Lewis hills. And a further mystery is his whereabouts: the painting has not been shown in public for 60 years.

On Lewis, Cumming hit on the technique he would refine throughout his career, building up his semi-figurative paintings in veils of translucent colour (initially in oil, later acrylic).

Croft Table with Field Flowers and Wine Jars

Founded upon complex rhythmical structures, these slow and painstaking glazes are punctuated with pivotal details – buttons, fingernails, pinpricks of reflected light. Draughtsmanship underpins everything.

The island, and its memory, would continue to nourish his art right through marriage and the arrival of two children to the very end of the 1960s, with shows of the celebrated Hebridean series in Edinburgh, London and New York. And then, right at this peak of this success, Cumming suddenly switched subject.

His neighbour in Edinburgh, a surgeon at the Royal Infirmary, had introduced him to the revelations of the new electron microscope. Always fascinated by origins and microcosms – Cumming's prolific sketchbooks are full of such connections, the movements of the solar system minutely repeated in a pine cone's spirals, and so on – he could see the world in a grain of sand.

Infinity in close-up, the golden mean that ran through universal laws, the atomic particle and the chromosome: his whole way of painting shifted to something that appeared entirely abstract.

In works such as Hollow Vein, Silver and Poised Encounter, organisms scintillate on the surface of the painting like cells on a slide or stars glimmering in the night sky.

Gathering and dividing, they breed new forms and these invented bio-morphs are each given an energetic character of their own. In 1970, he took genes as his subject and painted by far his largest and most jubilant work: the glowing Chromosomes II. Arrays of vital symbols dance on translucent glazes of lemon, chrome and cadmium yellow.

And each little figure has larger affinities – moons, animals, faces, the dancing K-shape of the chromosome in the middle, which is both hieroglyph and letter, right at the heart of it all. It is a work of exaltation, in praise of what science had lately revealed: that the universal calligraphy turned out to be present even in the code of human life itself.

In the later 1970s, Cumming began to paint aerial abstractions of the places he had seen from high above in his wartime Dakota: Indian highways, Burmese villages, Texan and Mexican cities. Dallas is a joyful circus of geometric arcs and crescents, scarlet and crimson, balanced with ochre. Laredo is a radiant grid of sun-bleached avenues and plazas, a perfect metaphor for the place, remembered through forms and colours.

These minimalist abstractions are upliftingly lyrical, the extension of a lifelong fascination with the immense variety of forms a simple line can take. This has its ultimate exploration in Sumerian Source, a vital work for the artist. This has its origins in the earliest form of writing, cuneiform script, beginning with the briefest of lines (a single dot) and taking off in all directions.

Cumming retired from Edinburgh College of Art in 1983 to a cottage in the Scottish Borders with his wife, the tapestry weaver Betty Cumming.

James Cumming painting the Linlithgow Mural

His late paintings, like his earliest, are devoted to local people, studio still lifes and landscapes, especially the beauty of the garden his wife created. He was working on what would be his final commission – the immense, award-winning, summational mural The Festival of Time, in the Lowport Centre in Linlithgow – when terminal cancer was diagnosed. Cumming died on 11th January 1991. He was 68.

Music and medical science, outer space, myths and old movies: the diversity of Cumming's interests was as wide as his appetite for life and vivid conversation. He taught many other artists, including John Bellany, Sandy Moffat and the Turner Prize winner Richard Wright.

Renowned for his strength of mind and sparkling humour, his questing intellect and constant encouragement of others, he was a singular force in Scottish art. His paintings are in public and private collections all over the world, from Los Angeles to his birthplace in Fife.

Laura Cumming, journalist and critic, is the artist's daughter

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