Ingmar Bergman’s 1966 film “Persona” may be a touchstone of mid-1960s cinema culture, but it was inspired by the simplest notion. The Swedish director, who died this July at 89, was laid up in a hospital with exhaustion and vertigo, thinking up a new movie he wasn’t sure he would have the strength to shoot.

Bergman had become fascinated with a Norwegian actress named Liv Ullmann, who was a close friend of Bibi Andersson. The latter had been a regular in Bergman’s films since 1955’s “Smiles of a Summer Night,” as well as his onetime lover. Tonight, Ms. Andersson will appear at the BAMcinématek to introduce a screening of “Persona” as part of the theater’s two-day, three-film program, Tribute to Ingmar Bergman.

“He wanted to do a film with the two of us, because he felt that we were alike,” Ms. Andersson said. “And then he came up with the idea of two women, isolated on an island. One of them talks and the other one listens, and that was the start of it.”

Ms. Andersson, now 72, had the speaking part in “Persona,” which shares a double bill with 1968’s “Shame” tonight. The mini-retrospective will conclude Wednesday with 1982’s “Fanny and Alexander,” to be introduced by its star, Pernilla August.

“‘Persona,’ it was how many years ago? Forty? Fifty? I am not so sure my memories are totally honest,” Ms. Andersson said, reached at her home near Nice, France.

The film was notorious as a classic psych-out. Ms. Andersson’s Nurse Alma bonds so thoroughly with Ms. Ullmann’s strangely mute stage actress Elisabeth Vogler that the two women begin to slip into each other’s identities — and not without a subtle sexual tension. In a sequence that was shocking at the time, Bergman combined a half of each woman’s face into a composite. As he related in a 1969 interview, the actresses failed to recognize themselves, each suggesting that the image was a really unflattering photograph of the other one.

“It’s a film that has been talked about a lot,” Ms. Andersson said. “I didn’t know that would be the case — it was just another of his films. I liked it because it was very Jungian. We didn’t know that much about Jung but we read the books we could come by. Bergman claimed it had nothing to do with Jung, that he hadn’t read him, but I doubt that was totally true.”

The opening sequence, which begins with the frames of a film spooling through a projector, is a montage of seemingly disconnected images (corpses in a hospital, a nail being hammered into a palm, actors in skeleton outfits romping in a silent movie) set to an abstract modernist score of woozy timpani drums, terse vibraphone, and anxious strings. It was basically Bergman — who may or may not have been represented by the bedridden boy trapped in a white room as the images pulse — dumping items out his satchel of used symbolism. Poetic then, it has proven inspirational to the point of cliché. Think of the forbidden VHS tape in “The Ring,” for instance. Or the spider, crawling across a milk-white screen, that appears for a few seconds in Todd Haynes’s multi-persona Bob Dylan fantasy “I’m Not There.” (The reference is to Mr. Dylan’s book, “Tarantula,” but the visual quote is straight from Bergman).

As the rest of “Persona” unfolds, it is remarkable how much its psychic seepage influenced David Lynch. Laura Dern’s performance as the splintering actress in “Inland Empire” is a forceful homage to what Ms. Andersson and Ms. Ullmann achieved.

“He wanted me to talk backwards, and I couldn’t talk backwards,” Ms. Andersson said, reflecting on the scene in which Alma has a breakdown and loses touch with language. She begins babbling a string of words that sound like nonsense. “I said, ‘My brain doesn’t function that way. I find that very complicated.'”

“He had a peculiar and interesting way how he got his ideas,” Ms. Andersson continued. “They were always very realistic, based on something he had met in life, or people, and then something he had read, and he made a mixture of it. Since I was going to play this talking lady. I said, ‘Why do I always have to be so un-erotic and simple, and everybody else is interesting?’ He said, ‘Yeah, you could have switched roles, but you know it’s not such a good idea because [Ms. Ullmann] speaks Norwegian. Ah, so what can we do? Make her a silent role until she learns to speak Swedish.'”

Ms. Ullman and Bergman became lovers during the making of “Persona,” which was shot in the summer of 1965 on the island of Faro, which also provided the landscape for subsequent films, including “Shame.”

“He just liked her,” Ms. Andersson said. “He had to write a role for her, and another role for me. She was mysterious to him because they didn’t know each other. And Liv I knew very well. We were illustrating his own relation to that.”

Ms. Andersson recalled meeting Bergman when she was about 16, and he cast her in a detergent commercial. “I thought everything he did was magic,” she said. “So when I had a chance to meet him I was very thrilled. Even if it was only a commercial he wanted me to play in I thought that was terrific. He told me that in my theater schooling I had to pay for myself and that I shouldn’t rely on my father. So I went home and told my father that he couldn’t pay for me, and he laughed. ‘Who will pay for you then? Is Bergman going to do that?’ It ended up that my father paid for me and Bergman put me to work.”

Today and tomorrow at the Brooklyn Academy of Music (30 Lafayette Ave., between Ashland Place and St. Felix Street, Brooklyn, 718-636-4100).