There’s a great episode of “The Simpsons” in which Roger Myers Jr., a cartoon producer who runs the hit show “Itchy & Scratchy,” attempts to introduce a new character into the series to rejuvenate declining ratings. Poochie, the sunglasses-wearing, surfboard-carrying dog the studio comes up with, is “a dog with attitude,” explains one of the network executives pushing the idea. “He’s edgy, he’s in your face. You’ve heard the expression ‘let’s get busy’? Well, this is a dog who gets biz-zay. Consistently and thoroughly.”

Poochie is a parody of a lot of different cartoon animals that have a group-friendly “attitude,” from Sonic the Hedgehog to Tony the Tiger. But perhaps the prime examples of the archetype are the Teenage Mutant Ninja Turtles — anthropomorphic reptiles with superpowers who live in the sewers beneath New York City, where they practice martial arts, chow down on pizza and spout hip 1980s catchphrases like “bodacious” and “cowabunga.”

Originally created in 1983 by the comic book artists Kevin Eastman and Peter Laird, the Teenage Mutant Ninja Turtles were imagined as a kind of postmodern, semi-ironic sendup of the popular superhero comics of the era, particularly Marvel’s Daredevil and X-Men. With their punky, slang-heavy bite and flip, easygoing demeanor, they were the embodiment of a certain brand of savvy Gen X cool that peaked with the arrival of the ’90s: sarcastic and streetwise, borrowing elements from prevailing trends like surf culture and hip-hop.

Ninja Turtles felt extremely of the moment, capturing the zeitgeist in a way that felt irresistible to kids. What’s remarkable is that the moment has yet to come to an end. Since its inception, the franchise has repeatedly reinvented itself with new iterations: live-action features, after-school cartoons, video games, graphic novels. It’s now back on Netflix with a new feature-length animated film, “Rise of the Teenage Mutant Ninja Turtles: The Movie.” The continual rejuvenation of a franchise that could have easily become just a pop-cultural relic begs an important question.

How have the Ninja Turtles remained popular for so long?

When I was a kid in the early ’90s, my most highly prized possession was the Teenage Mutant Ninja Turtles Pizza Thrower, a battery-operated, football-size toy truck that made an unbelievable amount of noise and emitted a faint scent of burning rubber, and whose “motorized disc-fire action” I used mainly to terrorize my much-aggrieved little sister.

The Pizza Thrower was the crown jewel of an extensive collection of Turtles-related merchandise that covered my suburban bedroom, which included not only action figures and accessories but coloring books, costumes, lunchboxes and PEZ dispensers. When I was 5, I had Turtles bedsheets; when I turned 6, I had a Turtles-themed birthday party. I was, in short, Turtles-obsessed.

I was hardly the only one. From the moment Eastman and Laird’s original Ninja Turtles comic book was adapted for broadcast syndication into an animated series of the same name in 1987, the four superpowered, wisecracking reptilian heroes at its center — Raphael, Donatello, Michelangelo and Leonardo, named after Renaissance artists in a manner typical of the franchise’s winking humor — became veritable matinee idols, cartoon superstars adored by children throughout North America and beyond.

Like “G.I. Joe” and “Transformers” before it, “Teenage Mutant Ninja Turtles” was created mainly to promote the various tie-in toys produced by Playmates, a company who also made action figures based on “Star Trek.” Even by those standards, the Turtles merchandise was enormously successful: Within the first four years of what came to be called Turtlemania, more than $1 billion of Turtles toys were sold worldwide, making them the third-best-selling toy franchise ever at that time.

The success continued through the ’90s: The animated “Turtles” series, in which the characters trained under their sensei, a rat called Splinter, while doing battle with their nemesis, the evil Shredder, ran for 10 seasons. A trilogy of live-action films aimed at a slightly older audience — “Teenage Mutant Ninja Turtles” (1990), “The Secret of the Ooze” (1991) and “Teenage Mutant Ninja Turtles III” (1993) — became surprise box office sensations, earning nearly $350 million and breaking box office records for independent productions. An early “Turtles” video game, Teenage Mutant Ninja Turtles: Turtles in Time, on Super Nintendo, became a best seller and has been ranked as one of the best games of its generation.

The Turtles’ versatility across a range of media properties helped amplify their popularity. Further adaptations — including several efforts to entirely overhaul or reboot the franchise — kept the Turtles fresh through the 2000s, albeit to varying degrees of effectiveness. A 2003 animated series on Fox and a 2012 digitally animated series on Nickelodeon both ran for multiple seasons and had their own enthusiastic fans. A 2007 animated movie, called simply “TMNT,” and a pair of big-budget blockbusters co-produced by Michael Bay, “Teenage Mutant Ninja Turtles” (2014) and “Teenage Mutant Ninja Turtles: Out of the Shadows” (2016), all found some commercial success, but were poorly received by both critics and longtime franchise fans.

There’s no doubt that these more recent “Turtles” iterations — including the latest for television, the animated reboot “Rise of the Teenage Mutant Ninja Turtles” (2018), which retooled elements of the basic premise and implemented some fairly drastic character redesigns — have introduced younger viewers to the franchise, many of whom have no doubt sought out new “Turtles” merch.

But an essential factor in the ongoing popularity of the Ninja Turtles are those very fans who adored “Ninja Turtles” as kids — children of the ’80s and ’90s who never outgrew them. Their nostalgia has effectively fueled the continuing relevance of a franchise that might have otherwise faded into quirky obsolescence, becoming another He-Man or Garbage Pail Kids.

I know a guy in his early 40s who recently got a giant Ninja Turtle tattooed across his right forearm. I know a CrossFit coach in his late 30s who names his workouts after Turtles settings and bad guys: the Sewers, Shredder, Bebop and Rocksteady. A new video game, Teenage Mutant Ninja Turtles: Shredder’s Revenge, is built from the ground up as a faithful replica of the Turtles games of the early 1990s. And the new Netflix film, while certainly goofy, is surprisingly dark and violent for a film aimed nominally at kids — until it occurs to you that maybe it’s not aimed at kids at all.

As a child, I found the seemingly grown-up style of the action and humor in “Ninja Turtles” essential to the appeal. It was a family-friendly cartoon, of course, but there was something about the attitude — hip, defiant, a tiny bit subversive — that made kids feel like they were tapped into something more aspirational than the other cartoons on TV at the time. I think it’s that sense of spiky coolness, what the Turtles would have called bodaciousness, that has kept so many fans coming back.