"I like stories that make you feel that all of a sudden you wake up and everything you thought was wrong." Viggo Mortensen is talking about his new film Jauja as he prepares himself a cup of mate tea. The surreal Argentinian Western about a Danish captain whose teenage daughter goes missing in 19th Century Patagonia certainly does that. It's nothing if not enigmatic, a minimalist period drama that is often mystifying with a mind-fuck ending.

It's the latest in a long line of challenging roles for the 56-year-old Danish-American actor, who seems to have turned his back on blockbusters since his career-making turn as Aragorn in The Lord of The Rings trilogy. Instead, he prefers to play loner types, usually inscrutable or morally ambiguous, who don’t like to talk much. But the man I meet in a sunny London hotel room is thoughtful and articulate as he chats about how the low-budget shoot brought back childhood memories of growing up in Argentina.

What drew you to the character of Captain Gunnar Dinesen?

Viggo Mortensen: I like the idea of showing what happens, which is often the case in Lisandro (Alonso)'s films, when someone is out of their element. The man I play brings his European world view and cultural bias to the country and to the people he encounters. He's very stubborn and insists on trying to find rational explanations even when things unravel and become strange.

He’s quite a strict dad…

Viggo Mortensen: Like most fathers he's just about the last man to realise his little girl has become a woman and he starts freaking out. He’s a man of his time and doesn't quite know how to deal with his daughter and the attention she's getting from men. In any situation when a child grows up, leaves the nest or they disappear, as happens in this story, all of a sudden you regret not having spent more time with them. Even if you're the best parent in the world, you always have regrets.

You’re known for your extensive research into roles. How did you prepare for this one?

Viggo Mortensen: I looked around until I found the uniform in Denmark and that sabre. Other than that I knew the landscape but my job was to pretend that I didn't. Now I was looking at it more in the way that my father might have. I had a newfound appreciation for him in the sense that what I felt was amusing as a child – his accent and his inability to understand why things worked differently there – now I understood it wasn't that easy being him.

One of the most distinctive things about the film is that it’s framed in vintage 4:3 aspect ratio. Was there a reason for that?

Viggo Mortensen: That was an accident. When Lisando got the footage back, the matte they had put on it in the lab wasn't quite right. It was chopping too much of the image off. So he said, “Just send it to me raw.” When they sent it to him with that look, he said, “That's the movie.” Even though he's very particular about his vision, he's open to accident, to contributions from others and what the day brings. That's the hallmark of a good artist.

What the hell is the ending all about?

Viggo Mortensen: I hesitate to talk about it. People should draw their own conclusions.

Jauja is out in cinemas Friday 10 April