Is he the greatest living painter in the United States?

So asked the headline of an August 1949 LIFE magazine article that helped cement Jackson Pollock’s reputation. It was a question Pollock spent much of the rest of his life struggling to answer — while desperately hoping to show the skeptics why LIFE might be right ask the question in the first place.

As the single most recognizable practitioner of abstract expressionism — the movement that put America and, specifically, post-WWII New York at the very center of painting’s avant-garde — Pollock was a genuine art star. But he soon abandoned the radical “drip” technique that had earned him both fame and, among some art critics, vilification, and spent the last few years of his life battling the twin demons of depression and alcoholism.

Here, LIFE presents outtakes from photographer Martha Holmes’ 1949 shoot with Pollock — images that offer a unique portrait of the artist’s home life on Eastern Long Island (with wife and fellow painter Lee Krasner) and the singular working method that made him an art-world icon.

With a down payment loaned to them by art dealer Peggy Guggenheim, Pollock and Krasner bought the land and moved into the house that would be Pollock’s residence for the last decade of his life. Pollock converted a barn just outside the house into a studio, where he was to create his most famous works. As his fame grew, the hamlet attracted other artists and writers, including Willem de Kooning, Kurt Vonnegut, Nora Ephron, Philip Roth and Joseph Heller.

Despite moving out of the city to live on a farm near the ocean, it’s hard to say that nature was an inspiration for Pollock’s paintings, which were so abstract that their only apparent source was the artist’s subconscious. Still, nature found its way into his paintings in the form of sand and other materials that the artist routinely applied to his canvas along with his paints.

Pollock’s work was often referred to as “action painting,” as the dance-like performance in which he engaged while making a painting was at least as important to him as the result on the canvas. Instead of using an easel, he’d stretch a canvas on the floor of his barn and scamper around all four sides of it as he painted. Rather than using brushes, he used sticks to flick and drip paint, or he poured it straight from the can, favoring wet household enamels over traditional oils.

Today, a painting from Pollock’s “drip period” can fetch north of $100 million at auction.

After he became famous and successful, Pollock would buy his own open-air carriage, a 1950 Oldsmobile 88 convertible. This was the vehicle he was driving on August 11, 1956, when, less than a mile from this house, he drove off the road and flipped the car, killing himself and a passenger, Edith Metzger, and injuring his mistress, Ruth Kligman.

Krasner, a talented abstract painter in her own right, had put her career on the back burner during their decade together in the Long Island house in order to support her husband’s career. After his death, she began painting in the barn that had been his studio. By the time she died in 1984, at age 76, she was finally recognized for her own work and not merely as “Mrs. Jackson Pollock.” Today, the farmhouse and barn studio comprise a museum devoted to the study of the married painters’ working lives.