If you ever wondered what a Luc Besson version of “2001” might be like, here’s your chance to find out. “Lucy” jettisons the outer-space trappings of Stanley Kubrick’s masterpiece, but it borrows so many other elements from it that “homage” might at first seem an appropriate term. Of course, being a Besson product, it makes plenty of room for fights, bloodletting, car chases and cheesy special effects too. So “trashing” would appear to be a better characterization.

For one thing, the movie starts with a sequence that mimics Kubrick’s “Dawn of Man” prologue, but makes it crudely explicit by adding the observation that life was given to man billions of years ago and asking, “What have we made of it?” The sequence doesn’t culminate until the closing special-effects montage that copies the mind-bending finale of “2001,” but in it instead of a black monolith, the spark that inaugurates the process of human development is—Scarlett Johansson.

Or at least the eponymous character she plays in the movie, who, as explained in ponderously oracular tones by scientific theorist Professor Norman (Morgan Freeman, practically repeating his performance in “Transcendence”), becomes the first person capable of utilizing the full capacity of the human brain, while ordinary folk use only 10% of it. Her development—which will eventually give her telekinetic powers as well as the ability to transcend time and space—is the result of an accident, when her dissolute boyfriend forces her to deliver a case to brutal Taipei crime lord Jang (Choi Min-sik). It turns out to contain a newly-developed synthetic version of the substance that drives human fetal development, and Jang compels Lucy to become one of the mules that will carry the first supplies of it to the capitals of Europe. (The entire sequence of the poor girl being captured by the hoods is intercut with shots of gazelles being chased down by cheetahs, as if the dramatics alone weren’t to tell us she’s in a hopeless situation. The same technique of inserting snippets of such footage also occurs elsewhere—as in Norman’s discussions of the evolutionary process—and is presumably intended to jazz up the picture visually, although it actually treats viewers as though they were mentally dense or afflicted with ADD.)

During captivity before her planned departure, however, some of the drug seeps into Lucy’s system and endows her with the first expansion of her cerebral powers (intertitles will henceforth tell us the percentages she’s capable of). These apparently turn her into “Le femme Nikita” on steroids: she wipes out her captors, takes over a hospital emergency room where she orders a surgeon to remove the remaining drugs from her body, breaks into Jang’s penthouse to secure information on the whereabouts of the other mules, and then proceeds to Europe, enlisting the aid of Dr. Norman and a French cop (Amr Waked) along the way. It might seem curious that she doesn’t kill Jang, as she does so many of his minions. But on second thought it’s not odd at all, since the villain will be required for an ultimate showdown in Paris, without which Besson would lack a final act.

In any event, by the time Lucy gets to Paris she’s gained the ability to change her appearance in a single CGI swoop, the way Raven does in the “X-Men” movies; take control of phones, televisions and computers; sweep gunmen into the air and cars out of her way; and travel through time, achieving universal knowledge. She also appears to be losing touch with her emotional side, becoming a sort of female Spock, and threatening to literally dissolve into an incorporeal energy mass; but much of this remains unexplained and unexplored by auteur Besson. It all ends in a big mash-up with Jang and his army of black-suited thugs and Lucy becoming one with Norman’s computers via some very plastic-looking tentacles that apparently deliver to the professor a flash-drive suffused with uber-knowledge. Tall of that is accompanied by an explosion of supposedly mind-bending effects, including a return to the “Dawn of Man” opening. But from the standpoint of serious ideas, the effects-laden, action-packed picture ends up a gigantic muddle of sound and fury signifying little.

Apart from the opening reel, where she must go all out as a frantic damsel in distress, Johansson is in “Under the Skin” mode, impassive and businesslike. Choi makes up for her passionless persona by raging, snarling and screaming with absolutely no restraint, while Waked makes little impression as the cop thrust into becoming Lucy’s hapless aide. Nobody else in the cast has much to do, which is a good thing, as those who do have scenes tend to play them comically broad, like Pilou Asbaek as Lucy’s nefarious boyfriend, Analeigh Tipton as her ditzy best friend, and especially Julian Rhind-Tutt—if that’s his real name—as Jang’s histrionic lieutenant. The tech credits are generally medium-grade, with most of the effects second-rate at best and production design (by Hugues Tissandier) and cinematography (by Thierry Arbogast) that emphasize garishness in the mode of “The Fifth Element.” Eric Serra’s score is equally blatant.

There’s something outlandish about Besson trying to infuse ideas into his usual jumble of over-the-top action and comic-book violence. Unsurprisingly, the combination comes across as loony and laughable. Some, however, might mistakenly believe that some depth lurks beneath its shallow surface. To which you might repeat A.O. Scott’s deliciously witty put-down of Mike Cahill’s “I Origins”: “It may blow your mind, but only if you’re not in the habit of using it.”