Imagine a very special “Unsolved Mysteries” segment directed by the guy who made “Fight Club” and “Se7en” and you have “Zodiac,” a new movie that presents the true story of a creepy serial killer who terrorized California in the late ’60s and early ’70s.

After each murder, the killer would leave the cops and the press cryptic defiant messages belittling their efforts to identify him. The Zodiac evaded the police without an arrest ever being made. But the investigators were not without a prime suspect.

The Zodiac case, which also inspired the plot of “Dirty Harry,” was never offically closed and the investigation is still open.

The film not only gruesomely dramatizes the murders, but centers on the investigative efforts of two San Francisco Chronicle newspapermen, crime reporter Paul Avery (Robert Downey Jr.), cartoonist Robert Graysmith (Jake Gyllenhaal); and one SFPD detective David Toschi (Mark Ruffalo).

Evidence points to one Arthur Leigh Allen who died in 1992, although fingerprints and handwriting experts convey otherwise.

In the film, when questioned by police about bloody knives he was carrying on the day of the murder, the lead suspect chillingly says he was “killing chickens” that day.

Downey, who always makes extremely interesting choices as an actor, is a lot of fun as the journalist Paul Avery. Downey’s portrayal reminds me of a cross between Dustin Hoffmann’s Carl Bernstein in “All the President’s Men” and Johnny Depp’s Hunter S. Thompson in “Fear and Loathing in Las Vegas.”

It’s funny seeing Downey as a nervous, boozing, chain-smoking reporter, firing a Magnum at the shooting range immediately after he’s been personally threatened by the Zodiac via a Halloween Card.

Gyllenhaal’s very good as Graysmith, the cartoonist who becomes obsessed with the Zodiac and eventually writes two bestselling novels about the facts of the case.

But even as Gyllenhaal stars, it’s Ruffalo who steals the show as Inspector Toschi, by delivering a convincingly heartfelt and idiosyncratic performance as the man who reportedly inspired Steve McQueen’s Lt. Frank Bullitt and Clint Eastwood’s Dirty Harry Callahan.

Who better to handle this kind of material than Fincher, a director who can paint a frame and performance as beautifully composed and thematically iconoclastic as master directors Alfred Hitchock and Stanley Kubrick. Much on screen in a Fincher picture is clinically calculated, visually arresting and effectively suspenseful.

I liked Fincher’s visual references to the ‘70s classic film “All the President’s Men” with Downey and Gyllenhaal’s work echoing the dynamic of the cinematic Woodward and Bernstein.

The production is filled with great period authenticity and at times I felt like I was watching a gritty ‘70s crime picture. Certain shots in Zodiac also pay homage to that decade’s ultimate psycho picture, Martin Scorsese’s “Taxi Driver.”

Fincher brings that same love of the history and craft of movies into the plot. The film alludes to evidence that the killer may have beensomewhat of a film buff, as references to a 1932 film “The Most Dangerous Game” apparently feature in the patterns of his killings and letters. In that film, an insane man hunts people for sport after they’re shipwrecked on an island.

“Zodiac” does an outstanding job of presenting the facts of the case and as such, the movie ends up being nearly three hours long. Despite its length, “Zodiac” never feels unweildy. Skillfull cinematic storytelling and top notch acting make for a satisfying, thrilling experience at the movies.

Nearly 30 years ago, the Zodiac wrote to the Chronicle. “I am waiting for a good movie about me.” Fincher’s new film isn’t a bad candidate.

(Three stars out of four.)