It’s not hard to make a complicated movie. Authentic complexity, an organic intricacy of thought and expression – now that’s something unusual. Anyone can be willfully ambiguous; subtlety is a tough line of work. “Intellectual” cinema is rife with elusive themes and subjects, but only the most acute sensibilities know how to channel the invisible energies of life in their images and make movies that pulse and throb and buzz with phantom forces.

Meet Lucrecia Martel, writer-director of “The Holy Girl.” Complexity, subtlety, and intelligence only go so far in accounting for the enchantment of this, the richest film to have emerged to date from the new Argentinean cinema. “The Holy Girl” is original, something entirely new; it exposes a fresh membrane of human consciousness and trickles stimuli along the quivering surface. Once seen, it will never be forgotten – though understanding exactly what you’ve seen may prove a bit of a puzzle.

The easiest way to start thinking about “The Holy Girl” is to classify its genre: the coming-of-age film. Once you’ve done that, you can marvel at the boldness with which Ms. Martel has reinvented the form from the bottom up.

In the provincial backwater La Cienaga (“The Swamp”), teenage Amalia (Maria Alche) lives at the Hotel Termas, a muggy, moldy operation run by her mother Helena (Mercedes Moran). Amalia attends Catholic school with her best friend, Josefina (Julieta Zylberberg). The opening sequence, in which we are introduced to the girls, announces tremendous aesthetic innovation.

Faces loom in the frame, detached from spatial context, a mysterious montage of portraiture. The soundtrack collages song and catechism: We are at a choir practice, where the teacher attempts to answer the girls’ spiritual concerns. If I hear the voice of God in the night, how will I know it isn’t the devil? How will I recognize my calling?

The hotel is hosting a conference of ear, nose, and throat specialists (we might count Ms. Martel among them). One afternoon, Dr. Janco (Carlos Belloso) goes out for a walk and encounters Amalia. She has gathered with a crowd to marvel at a street musician, who conjurs ghostly sounds from his theremin. Janco moves up behind, very close, and presses against her. Amalia remains motionless, then moves her hand to touch him. Janco flees in panic. The holy girl has found her calling.

Motivated by awkward sexuality and an even more confused notion of salvation, Amalia develops an odd fixation on the doctor. Her mother, meanwhile, is hearing different voices. A bothersome ambient noise keeps her awake at night. God or the devil? She consults Janco; a relationship develops.

The points in this bizarre love triangle inexorably collapse in the trajectory of “The Holy Girl.” This coming-of-age film is also an ironic metaphysical tragicomedy. Ms. Martel is interested in things caught at the threshold of visibility: sexuality and spirit, pattern and coincidence, miracles and the mundane.

Like Claire Denis, who would seem to be an influence, Ms. Martel approaches her material from odd, unexpected, but carefully considered angles. Her images are curious, mischievous; for all the torpor of the setting, the movie keeps you on your toes. And here is the most exciting sound design since “Elephant,” a remarkable texture of amplified butane hiss, muffled bells, crystal cascades of water.

A sly, beguiling young actress, Ms. Alche hits the screen with a touch of the blunt Cro-Magnon effect Severine Caneele brought to “L’Humanite.” Slippery as her interior life is, she registers as a hard physical fact. Ms. Moran beautifully underplays her role as a midlife matriarch, keenly aware of her dwindling radiance. Mr. Belloso handles a very tricky part with great delicacy; Janco is as stuck in his own swamp of confusion as all the rest. His actions aren’t asked to be condemned but to be reflected on with the same wise bemusement that infuses every frame of “The Holy Girl.”

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“It’s hard to tell that the world we live in is either reality or a dream,” reads a title at the end of “3-Iron,” the new movie by Kim Ki-Duk. Audiences may likewise find it hard to determine that this festival favorite is not, in fact, a thoughtful work of allegorical minimalism but a mannered and risibly obtuse swindle.

Your 10 bucks ensures a hefty dose of the Alienated Asian Arthouse: idiosyncratic scenario, minimal dialogue, studied compositions, chic languor, ineffable malaise, detachment. Piloting his high-end BMW motorcycle through a South Korean suburb, Tae-Suk (Jae Hee) rides from house to house attaching restaurant menus to doorknobs. Sometime later, if the flier hasn’t been removed, he knocks on the door.

If no one answers (and no one ever answers), he breaks in and plays the answering-machine message (every house has an answering machine) to find some clue as to how long the resident will be gone (they are all on vacation and leave specific time frames for their return). Under the influence of a vapid metaphorical impulse, Tae-Suk makes himself at home but does no damage. He takes baths, does his laundry, fixes a snack from the fridge, and photographs himself leaning into the large-scale family portraits hanging on the wall (every home has one).

One night, having broken into an upscale suburban mansion, Tae-Suk finds himself face to face with the occupant, a battered woman named Sun-Hwa (Lee Seung-Yeon).They size each other up with mute mutual understanding, and a dubious bond is formed. Sun-Hwa’s abusive husband returns home for further aggravation, and Tae-Suk responds by slamming a couple of golf balls into his gut with the eponymous sporting implement.

Tae-Suk absconds with Sun-Hwa, who becomes his partner in criminal pretentiousness. Their existential house-sitting is complicated by the discovery of a dead body, Tae-Suk is jailed, and Sun-Hwa is returned to her monstrous husband. An improbable jailbreak leads to an insipid reunion predicated on an egregiously whimsical conceit.

It’s not hard to tell that “3-Iron” borrows heavily from Tsai Ming-Liang’s “Vive L’Amour,” a masterpiece of allegorical real estate ennui. Indeed, everything in “3-Iron” feels second-hand, facile, disingenuous. Mr. Kim does achieve one moment of integrity: By offering up that ridiculous quote at the end, he seems to encourage his audience to shrug off his wishy-washy would-be art film.