ENTERING ALEX KATZ’S home and studio, on the block in New York’s SoHo neighborhood where he has lived and worked since 1968, is like stepping directly into his mind, from which his enveloping aesthetic world originates. When I arrive at his light-washed loft space late on a summer morning, Katz, who turned 95 this past July, is in the spare nook of the kitchen, where he has just put the finishing brushstrokes on a study of lavender peonies — one of the first iterative steps toward creating his monumental works, which are hung on walls and leaning against various surfaces in the living space and adjacent studio. The profusion of these paintings, the simple furnishings, the metal cart filled with brushes and paint that has been rolled into the kitchen: All of it evokes a place where work and life are indistinguishable. Through the doorway of a room off the kitchen, I glimpse his reclusive wife, Ada, 94, a spectral, gray-haired figure. Since 1957, when they met, he has depicted her nearly a thousand times in various media.