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 rare outtakes from photographer Martha Holmes’ 1949 shoot with Pollock — images that offer a unique portrait of the artist’s home life in the Hamptons (with wife and fellow painter Lee Krasner) and the singular working method that made him an art-world icon.