Jorn was born in Vejrum in northwest Jutland, not here. Silkeborg entered his life twice. As a teenager he came to train as a teacher at Vinthers Seminarium in the town — he was around sixteen, and he had already been diagnosed with tuberculosis at fifteen. Then in 1951 he came back, impoverished and seriously ill with the disease again, at the point where a life can simply stop. It didn't. By 1953 he was working in ceramics again, and from the early 1950s until his death in 1973 he built the collection that became this museum.

That is the answer to the question every visitor eventually asks. Not Copenhagen, not Paris where he had made his name, not anywhere with a market. The town that had him when he was nothing got the pictures.

In the autumn of 1948, Jorn founded CoBrA with Christian Dotremont and Constant. The name is an acronym of their three cities — Copenhagen, Brussels, Amsterdam — and the work that came out of it was fast, figurative, high-colour and deliberately raw. The group lasted three years and dissolved in 1951, which is roughly the standard lifespan for a movement of that intensity.

Jorn's next affiliation was stranger. He was at the 1957 conference that founded the Situationist International and had known Guy Debord since 1954; the two collaborated on artist's books. He left in 1961 — amicably, not in one of the expulsions the Situationists became famous for. He still believed in the group's aims and went on funding it, but thought its new strategy would not work. He was probably its most generous patron long after he stopped being a member.

The collection is not a monograph. Museum Jorn holds over 30,000 works by more than 600 artists, and the point of the arrangement is to show what Jorn looked at, not only what he made. Hanging alongside his own paintings, ceramics, prints and drawings are Max Ernst, Francis Picabia, Fernand Léger, Man Ray and Le Corbusier — the older figures he took from or argued with. The CoBrA circle is here in depth: Pierre Alechinsky, Karel Appel, Constant, Reinhoud d'Haese, Theo Wolvecamp. So are the Danes around him, Carl-Henning Pedersen, Egill Jacobsen, Henry Heerup, Ejler Bille, Sonja Ferlov Mancoba, Wilhelm Freddie.

The 1950s bring in Jean Dubuffet, Wifredo Lam, Matta, Henri Michaux, Enrico Baj, Pinot Gallizio and Group SPUR; later Danish holdings run through Per Kirkeby and Poul Gernes to Georg Baselitz and Andreas Slominski. Two large ceramic walls, gifts from Dubuffet and Alechinsky, face visitors in the courtyard, where Erik Nyholm's blue ceramic stones are set into the ground.

The institution grew slowly and awkwardly around the gift. The Silkeborg og Omegn museum association made its first art purchases in 1940. In 1951 a single room in the town's local history museum was converted for modern art. An exhibition opened in a school building in 1961, the independent Silkeborg Museum of Art was founded in 1965, and by 1973 it had taken over the whole school, where it stayed until 1982.

The purpose-built museum opened on 3 March 1982 — Jorn's birthday, nine years after his death — on an 8,000-square-metre site by the Gudenå. Niels Frithiof Truelsen designed it, drawing on the reconstruction of Constantin Brâncuși's studio that stands in front of the Centre Pompidou in Paris. It was too small almost immediately. Truelsen's extension of 1998 pushed the exhibition area to 3,200 square metres and added a daylight-free basement gallery for works on paper. A major renovation in 2010 came with the change of name to Museum Jorn and a new Cobra Forum, where visitors can work through the museum's research material on Jorn in books and electronic media.

Jorn died in Aarhus on 1 May 1973, aged fifty-nine, and is buried not in Denmark at all but in the churchyard at Grötlingbo on the Swedish island of Gotland. He never saw the building his birthday opens. The collection he assembled has roughly doubled since he stopped adding to it, through the museum's own acquisitions and through donations from other artists and collectors who understood what he had started.

He is generally reckoned Denmark's most significant artist of the twentieth century, which is a heavy label for work that was made, deliberately, to look unfinished and a little wild. The museum's own answer to that tension is not to solve it. Walk the galleries and the argument he spent his life having — between the trained hand and the untrained impulse, between the individual painting and the collective movement — is still going on across the walls.