In the first scene of director James Gray’s new film “Armageddon Time,” a young boy named Paul delights his classmates by sketching a caricature of their teacher. Later that day Paul tells his grandfather that he wants to be a famous artist, then scurries upstairs to pore over his copy of H.W. Janson’s “A History of Art.”Mr. Gray’s film is largely autobiographical: Like Paul, he dreamed of becoming an artist until filmmaking stole his heart. “Armageddon Time” is set in New York on the eve of the 1980 presidential election, and Mr. Gray, 53, envisaged the film as “a kind of ghost story” because many of the characters are based on family members—parents, grandparents and elderly relatives—who are no longer alive. The plot of the film centers on Paul’s friendship with a Black schoolmate, and Mr. Gray says he wanted “to examine the fault lines of class and race” from a child’s perspective.

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