On paper, “Inside Out” sounded like another lunatic gamble: an adventure that takes place entirely within the head of an 11-year-old girl, featuring her Emotions as characters — although if anyone could pull off a logline like that, it would be the team that made us care about rats who cook, toys that bond, and robots who fall in love. Sure enough, in execution, Pixar’s 15th feature proves to be the greatest idea the toon studio has ever had: a stunningly original concept that will not only delight and entertain the company’s massive worldwide audience, but also promises to forever change the way people think about the way people think, delivering creative fireworks grounded by a wonderfully relatable family story.

Could “Inside Out” be Pixar’s best movie? Frankly, that question is almost beside the point. Objectively speaking, several of the studio’s previous films work better in terms of character appeal or narrative accomplishment (though when it comes to cartoons, playing favorites is inevitably a subjective game). In terms of its ambitious underlying concept, however, “Inside Out” blows the others away, going beyond the screen to become something audiences will carry around for the rest of their days — not as tie-in merchandise or spinoff theme parks (although there will inevitably be plenty of both), but as an elegant and iconic visual metaphor for understanding their own emotions, and empathizing with others’.

“Do you ever look at someone and wonder what is going on inside their head?” asks Joy, a radioactive-yellow gal (voiced by Amy Poehler, at her peppiest) who serves as both narrator and chipper team captain for a group of five Emotions assigned to Headquarters: the place in Riley’s brain where all her thoughts and feelings originate. As the upbeat young heroine’s dominant Emotion, Joy serves alongside blue Sadness (Phyllis Smith), violet Fear (Bill Hader), fiery red Anger (Lewis Black) and green Disgust (Mindy Kaling) to manage memories, generate ideas and otherwise help Riley deal with life’s challenges.

Just when her Emotions think they’ve got everything under control, Riley’s parents decide to move from Minnesota to San Francisco, sending her Emotions into turmoil — because it’s not enough for Pete Docter and co-director Ronnie Del Carmen to introduce such a compelling model for how the brain really works; they’re also expected to craft an interesting story around it. For the first 11 years of Riley’s life, her Emotions have stood crowded around an instruments panel of what looks like an air-traffic control tower inside her head. Amusingly swift glimpses into the minds of other characters suggest everyone is wired more or less the same way, while still allowing for wild variation in the efficiency of the five Emotions they’ve been dealt.

In Riley’s case, she’s young and her Emotions are still hammering out the dynamic between themselves. Like, what’s Sadness’ role exactly? “I’m not actually sure what she does. I’ve checked,” Joy says, hinting at one of the points on the film’s positive-minded agenda: helping young audiences to understand and appreciate what role Sadness plays in their own lives. (If only the film could also teach them that Boredom isn’t necessarily bad, either, but merely the sign of an inactive mind.)

Incoming memories are stored in bright glowing orbs, color-coded according to whatever Emotion was dominant at the time she experienced it, then stored in the appropriate place in the vast landscape of her mind. (Oddly, while Riley’s memories play like little movies, projected inside her head but seen from an objective outside view, her dreams are made at a movie studio with a subjective p.o.v. camera.) Riley’s brain might as well be another planet — unusually dangerous, all things considered, with different islands for each of her key qualities. It’s full of amusing nooks and crannies, like Imagination Land and the more sinister Subconscious, which this fantastic voyage takes time to visit along the way, giving composer Michael Giacchino the chance to augment his heartening score with separate mood-appropriate themes for each of these realms.

Too often, movies that introduce wildly fantastical parallel worlds never find time to explore them — the way Dorothy only visits one corner of Oz in the 1939 film, or how “Wreck-It Ralph” only taps into a few of its potential gaming universes. Docter and Del Carmen make it a point to poke around here, and though the film absolutely could have been denser, they’ve opted for just the right balance of context and story, lest spending too much time with the Emotions deprive auds of experiencing the actual emotions that come from connecting with Riley and her family.

For that reason, although “Inside Out” takes place almost entirely in Riley’s head, every so often, the film surfaces to check in on how she’s doing in real life, as if taking a deep breath of relatability before plunging back into her more abstract interior world, since it otherwise might been all too easy for the film to get “lost in thought.” We see Riley as an infant, at several stages in her childhood and again at 11 (Kaitlyn Dias), trying to cope with the disappointment of San Francisco, where the family’s house is a dump, new friends are hard to find and playing hockey isn’t the same as it was in Minnesota.

Though her parents (Diane Lane and Kyle MacLachlan) express concern, it’s up to Riley — and by extension, the five Emotions struggling to operate her mental command center — to keep her happy amid all these changes. But something’s off: Blame it on the cross-country move or the approach of puberty, but the Emotions don’t seem to work as they always have before. Most alarming, Sadness is tired of being excluded, but every time she touches something, it turns blue … and so does Riley.

Joy — who superficially resembles Disney’s favorite fairy, Tinkerbell, minus the wings — means well, but she’s a bit of a control freak, and in trying to protect Riley’s “core memories,” she accidentally ejects herself and Sadness from Headquarters. It’s a long way back, as the brain terrain crumbles around them, and in the interim, Riley’s mental state begins to unravel with Fear, Anger and Disgust left in control, unwisely deciding that the best idea is for Riley to run away. Given the sheer complexity of concept, it was wise for Docter and his team to keep the story simple, although one can’t help but wonder how an edgier emotional challenge — such as divorce, death or an unthinkably risky “trans-parent” situation — might have given Riley’s character so much more to deal with.

While Riley and her world look consistent with Pixar’s other human creations, dating all the way back to “Toy Story,” everything to do with her Emotions demanded a unique visual solution. Docter and Del Carmen seem to have reached into Disney’s past for inspiration, seizing on the 1950s-era style seen in shorts like “Toot, Whistle, Plunk and Boom” (plump, bespectacled Sadness looks just like that Oscar winner’s Professor Owl host), as well as then-rival UPA’s more abstract cartoon aesthetic (Fear resembles Gerald McBoing-Boing’s dad, while a crazy shortcut to Imagination Land embraces such deconstructionism outright).

In addition to linking the project to a period when advances in color film processes and stereoscopic 3D sparked wild visual experimentation in cinema, “Inside Out’s” retro look fits well with Pixar’s cutting-edge technology, blending vintage style choices with lighting and texture options previously unavailable to animators. Even something as seemingly basic as the Emotions’ skin texture — more of a pulsing mass of glowing electron-like particles, really — reflects unexpected solutions to infinite questions Docter’s gonzo idea must have raised. In other cases, it’s the streamlining of ideas that serves the material so well: from the vivid colors to the way the story always comes back to parent-child relations, playing equally well to both demographics.

As choices go, the voice casting couldn’t be better for all five of the Emotions. Smith’s Eeyore-like Sadness serves as the perfect foil to Poehler’s ebullient Joy, while Anger’s surprisingly cute appearance and diminutive stature make Black’s scenery-chewing performance that much funnier. Hader plays Fear as a nervous jitterbug, while Kaling’s disaffected Valley-girl delivery keeps Disgust (who has the least to do) feeling like an integral part of the team.

While the initial idea was directly suggested by Disney’s 1943 “Reason and Emotion” short — a wartime one-reeler that characterized the eponymous disciplines forever dueling for control — the Pixar team has rethought the model, giving it the most intuitive and indelible form, with the result that viewers can’t help but imagine a similar dynamic operating in their own heads. To borrow a notion from Malcolm Gladwell, the pic’s “stickiness factor” is through the roof, making it one of those rare movies that transcends the medium, the way Melies visualized a moon landing or Romero invented zombies.

Concepts like this come around maybe once a decade, but linger for centuries, and even if others (like early-’90s TV show “Herman’s Head”) got there first, you’ve gotta hand it to Pixar for making it endure. At the risk of hyperbole, people will still be thinking in terms of these anthropomorphized Emotions long after movies as we know them are gone, in the distant future, when screens are obsolete and immersive stories are beamed directly into your frontal lobe. There’s a reason they call Pixar’s inner team the “Brain Trust”: They can be counted on not only to imagine, but to execute such original ideas as these.