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“The Imaginarium of Doctor Parnassus” is as unusual and idiosyncratic as its title. You’d expect no less from Terry Gilliam, and admirers of this singular filmmaker will be pleased to know that “Imaginarium” is one of his most original and accessible works.

Though “Imaginarium’s” head-spinning plot resists easy summation, the film, co-written by Charles McKeown, has a back story no one is likely to forget. When actor Heath Ledger died, this was the project he left half-finished. And it would have stayed that way if Johnny Depp, Jude Law and Colin Farrell had not pitched in to finish it seamlessly.

Ledger was attracted to the role of Tony — a hustler of uncertain morality — by an unplanned glimpse of the storyboards Gilliam and his team dreamed up. From the film’s opening images of a ramshackle horse-drawn show wagon as old as time moving slowly through modern London, the script lives up to the dialogue line that serves as its motto: “This world we live in is full of enchantment for those with the eyes to see it.”

That wagon is the domain of Dr. Parnassus (a letter-perfect Christopher Plummer), an ancient, far-seeing shaman who runs this traveling show with the help of young assistant Anton (Andrew Garfield), a sarcastic dwarf named Percy (Verne Troyer) and the doctor’s beautiful daughter, Valentina (Lily Cole).

The heart of the doctor’s show is a magic mirror that allows those who go through it to experience another dimension of their own minds. Once inside, people choose good or evil. As the doctor angrily puts it when asked what he’s playing at, “We don’t play; what we do is deadly serious,” which means nothing less than the eternal battle with the devil for the spirit of man.

This being a Gilliam film, the devil is no theological concept; he is the very real Mr. Nick, played with fiendish panache by Tom Waits. Mr. Nick loves a bet more than anything, and the past thousand years or so have been a series of wagers with the ever-gullible Doctor P. The result of one particularly painful loss has meant that the doctor has to give up his beloved Valentina on her 16th birthday, which is only a few days away. At the last minute, the action-seeking Mr. Nick proposes yet another bet — first person to win five souls gets to keep Valentina. The appearance of Ledger’s Tony and his gift of gab give Parnassus new hope, but Mr. Nick has no end of tricks up his sleeve.

When Ledger died, Gilliam’s first thought was to abandon the film, but he was prevailed on by his team to continue. As it turned out, what was left to shoot was a series of sequences of Tony behind the mirror, so once Gilliam tinkered with the script to make it clear that people physically change when they go through the glass, everything fell beautifully into place.

The real star of any Terry Gilliam film, of course, is the director and his unparalleled imagination. Nothing is neat and tidy in “The Imaginarium of Dr. Parnassus,” and the film itself advises, “Don’t worry if you don’t understand it all immediately.” But if you are looking for pure mad fantasy, for someone to take you through the doors of perception themselves, this is the place to go.