Popularity Polynomial

It's a fact of life that something which portrays itself as "cutting-edge" is eventually going to become mainstream, and from there passé. However, given enough time -- usually about 20 years -- what had been seen as behind the times, old hat, or just plain uncool suddenly begins to make a comeback. It's gone through the ups and downs of the Popularity Polynomial.

How often the item cycles back and forth between "cool" and "not cool" depends on many factors. If something reached a peak when you and your friends were kids, then when you become teens, it is a reminder of a childish time -- and as the fear of childishness and the desire to be very grown up kick in, you don't want to think about it. But when you become adults again, it is seen as harmless. And once your kids discover it, it may even become cool again (as long as they don't associate it with their uncool parents). Now apply that on a larger scale.

Given enough cycles, it becomes an equivalent of Cyclic Trope for shows.

The name comes from the fact that we like alliteration, and some of us are math geeks. Here's also a more detailed explanation about what a polynomial is and what it has to do with the ups and downs of popularity.

Explanation
A polynomial in x is a sum of non-negative powers of x which are each multiplied by a real number. You might know some simple polynomials: y=ax+b, the equation for a straight line where a is the slope and b is the y-intercept, is a polynomial (it can be written as: y=a(x^1)+b(x^0)). That's called a polynomial of degree 1, because the highest power of x that appears is 1. A polynomial of degree 2 (y=a(x^2)+bx+c) is called a parabola, and if you plot its graph it looks like a dish (which could be wide or narrow, or turned upside down, depending on what a, b, and c are).

Of course, there are polynomials of a higher degree than that, like y=4(x^5)+8(x^4)+15(x^3)+16(x^2)+23(X^1)+42, which is of degree 5. Higher degree polynomials can create all sorts of curves when you plot them. Apart from the line and the parabola, you can get a lot of shapes, such as a lot of hairpin curves or a roller-coaster shape that goes on for a while before diving up or diving down.

So basically, in a polynomial in x of a high-degree you can expect y to go up and down as x grows. The trope name is about looking at the popularity of something as a polynomial in time: as time progresses, it becomes less popular, then more popular, then less popular again, and so on and so forth. Generally speaking, the higher degree the polynomial, the more times you switch from "cool" to "stupid" and back. The points where the popularity rises, flatlines, and then begins to decline are known as the polynomial's Jumping the Shark moments, and when it does the opposite- reverses a decline and starts to climb- rigorous mathematical notation is that it is Growing the Beard. Some fringe lunacy groups insist on an alternative terminology having to do with derivative signs and whatnot, but they can be safely ignored.

So if you were wondering what a polynomial was, now you know.

See also Colbert Bump (a resurgence triggered by a specific factor), Dead Artists Are Better (when a person's death rehabilitates his or her reputation), Cyclic Trope (when this happens to tropes) and Discredited Meme. Compare with Two Decades Behind, Career Resurrection, Nostalgia Filter and Vindicated By History. Contrast with Deader Than Disco.

Film

 * The 1967 film To Sir With Love laid this trope bare for the audience in a scene where Mark Thackeray (Sidney Poitier) informs his disbelieving students about many things that are Older Than They Think: their clothing is from the 1920s, their hairstyles from the 16th century, and so on. A trip to a museum later in the film re-lampshades it when one of the students is shown with his head next to that of a Renaissance statue -- and they both have the same haircut.
 * For much of the late 20th century, film musicals were Deader Than Disco, having been killed by the 1969 flop of the film version of Hello, Dolly!. The genre got a breath of new life with 2001's Moulin Rouge, but the comeback truly kicked off the following year with the Oscar-winning film of Chicago, and has continued into the present with the likes of Dreamgirls, Hairspray and Mamma Mia. Disney even managed to make a highly successful franchise out of High School Musical, to the point where the third film was upgraded to a theatrical release. And now there's Glee...
 * Hardly any ancient history films between Cleopatra and Gladiator. Then...
 * In the first half of The Nineties, the horror genre (and the Slasher Movie genre in particular) was seen as stale, Cliche Storm and behind the times, filled with bad writing, cheap scares and not-so-subtle misogyny. New horror movies were flopping at the box office left and right (even in the normally-reliable month of October), and the slasher icons of The Eighties viewed as walking punchlines. Then came Scream, which deconstructed, parodied and lampshaded all the genre's conventions, put them all back together, and single-handedly restored the genre to commercial viability, which it retains to this day.
 * Zombie Apocalypse movies, and zombies in general, were practically forgotten throughout the '90s. It wasn't until the early 2000s that Twenty Eight Days Later, the Dawn of the Dead 2004 remake and Shaun of the Dead kickstarted the genre again.
 * Disney has gone through ups and downs. During The Golden Age of Animation, Disney's films were successes. However, after the death of Walt Disney, the confused company released a string of weak, underperforming films in The Seventies. By The Eighties, Disney was better known as a theme park operator than a film maker. However, in 1989, The Little Mermaid, an animated film deliberately reminiscent of the Golden Age films of the 1940s and 1950s, became an unexpected critical and commercial success and kicked off the Disney Renaissance that lasted throughout the entire Nineties. By the Turn of the Millennium though, audiences, tiring of the increasingly cliched formula prevalent in these films, drifted towards the then-new All CGI Cartoon popularized by Pixar and Dreamworks Animation. Disney responded by impulsively shutting down their traditional animation studio and releasing a string of their own CGI cartoons, none of which made much of an impact. It is yet to be seen if they will return to form in the future. The Princess and The Frog, Tangled, and Winnie the Pooh were fairly well-received, though overshadowed by Up and Toy Story 3.
 * Dykesploitation films - not that it hasn't always been an interest to some people.

Live Action TV

 * Although easy to forget now that it's a massive media juggernaut seemingly beloved by all, Doctor Who was considered a joke in the years between 1989 (and, arguably, earlier) and 2005. When it was brought up outside of its fanbase during this period, it was something for people to sneer at and assert that, no, they never watched if they wanted to maintain a shred of credibility. Then Russell T Davies and Christopher Eccleston came along, and suddenly everything changed. The show became a huge success with 7-10 million viewers per episode now.
 * Years before its cancellation, it was actually a popular show, far more so than a cult following. The process of its diminish began gradually throughout the early-mid 1980s.
 * Game shows in general tend to go through cycles. They went through their first boom in The Fifties, and fell hard after it was revealed that several of them (most infamously Twenty One) were rigged in order to create tension for viewers. Except for the Panel Game variants like Ive Got a Secret and low-stakes parlor games like Password, American audiences wouldn't trust game shows again until The Seventies, when shows like Family Feud, The Price Is Right, and The $10,000 Pyramid (and its variants) became popular. This started to die down in the '80s and early '90s — many just couldn't compete against the success of the syndicated Wheel of Fortune and Jeopardy, and the market did get quite saturated around that point (no fewer than a dozen shows debuted in 1990 alone, including quite a few revivals, with none lasting more than a season). In the early 1990s, daytime game shows pretty much went by the wayside. Except for the juggernaut The Price Is Right, there wasn't a single daytime game show between the end of Caesars Challenge in 1993 and the Let's Make a Deal revival that bowed in 2008.

The genre returned in a big way in the late '90s/early 2000s with Who Wants to Be A Millionaire and The Weakest Link, as well as shows like Greed and the Revival of Hollywood Squares. This boom also caused a deluge of their assorted clones. In the early 2000s, Millionaire and Link pulled in tens of millions of viewers and were watercooler discussion fodder, and their hosts (Regis Philbin and Anne Robinson, respectively) were household names. Then their networks began marketing them to death (ABC aired Millionaire almost every night of the week), and reality shows like Survivor, American Idol and The Amazing Race started taking off and providing what were then innovative alternatives to the traditional quiz show model. Almost overnight, the shows were only surviving in syndication -- and even that wasn't enough to keep Link alive. To this day, their catch phrases ("Is that your final answer?" for Millionaire; "You are the weakest link. Goodbye!" for Link) are considered annoying as all hell.
 * Power Rangers is very close to its 20 year mark, and it's quickly becoming a good example of this. It was a huge phenomenon in the early 90s, but it began to slowly dwindle until about 2002, when it was bought by Disney, when It Got Worse. It had a short burst of success then, but Disney was apathetic to the show at even the best of times, and it essentially culminated in its cancellation in 2009 after Power Rangers RPM. However, soon after, the show was bought back by Saban, hopped over to Nickelodeon, and the franchise seems to be back on an upswing.

General

 * The market for contemporary dance-pop music has seen great periods of popularity and decline, starting with the mid- to late 1980's led by Michael Jackson's Thriller and Madonna's early period, then falling to Grunge and hip-hop in The Nineties. It returned with the rise of the Spice Girls, Backstreet Boys, N*Sync, Hanson, Christina Aguilera and Britney Spears in 1998-1999, then gained a new audience when Disney Channel and Nickelodeon stars like The Jonas Brothers, Hilary Duff and Miley Cyrus branched out into teen pop careers in the mid-to late 2000's. Justin Bieber, Cody Simpson and Burnham seem to be flying the flag for the 2010's.
 * Actually dates before them, but arguably most popular when The Beatles broke - The Monkees were an effort to capitalize on the "new" boy band craze.
 * Vinyl records. They went out of style in The Eighties as the compact disc took over the market, and they saw themselves pushed back to the indie rock genre and niche applications (particularly DJ-ing). However, the last five years have seen them come back to the forefront, thanks to a combination of factors: the audio distortion caused by the Loudness War having a nasty effect on CD audio quality (an effect that was not heard on vinyl, since such loudness can't be achieved on that medium), a growing preference for the sound of vinyl records (possibly for the reason discussed), the obsolescence of CDs themselves due to the internet, and the surging popularity of indie rock and dance music, the two genres that made the most use of vinyl records since The Eighties.
 * Well, such loudness can be achieved on vinyl, but the bass and treble can be adjusted, which makes it possible to even out the recording somewhat, something that can't really be done with CDs. If a vinyl is mastered too distorted, it can cause the needle to jump out of the groove, so there is that.
 * Thrash Metal had a sort of comeback in the mid to late 2000s. The album covers began being designed again by Ed Repka and many hundreds of thrash bands appeared out of nowhere, like in the 80s. Unfortunately, this was somewhat of a marketing ploy, many of the bands sounded nothing like 80s thrash and were essentially death metal. Unsurprisingly, this did not last very long, but thrash as a genre is now more popular than its ever been.
 * Swing music started off as a fringe genre, but through the '30s and '40s grew to be wildly popular. Then, in the aftermath of World War II, it suddenly fell out of favor. Teens and dancers abandoned swing for rock-n-roll or crooners like Frank Sinatra, while dedicated jazz fans abandoned swing for the more complex bebop. Up-and-coming jazz musicians preferred playing bebop, because it gave them more soloing time, and jazz clubs preferred booking bebop combos because they were smaller and thus less expensive than swing bands.
 * Duke Ellington and his orchestra--who had originally been famous in the swing era--managed to make their comeback in 1956, when their performance at that year's Newport Jazz Festival drove the crowd to pandemonium. In the aftermath Duke was more renowned than he was back when swing was in, and this surge in popularity lasted until his death in 1974.
 * Swing in general did not make a comeback with Duke. It did, however, make a brief revival in the '90s, largely thanks to musicians like Big Bad Voodoo Daddy and Brian Setzer.
 * Hard to believe today, but rock music in general was as good as dead in the early '60s. Elvis Presley got drafted and then turned to acting, the Day the Music Died took the life of Buddy Holly, Little Richard became born-again and started recording exclusively gospel songs, Jerry Lee Lewis derailed his career by marrying his 14-year-old cousin, Chuck Berry did the same with his own run-ins with the law, and the remaining artists were mostly recording forgettable novelty songs. It was felt that, soon, Rock and Roll would be swept in the dustbin of history where the Moral Guardians felt it belonged. Then came The British Invasion, providing a new jolt of creativity and mainstream appeal to the genre, and since then it hasn't looked back.
 * Rap music tends to sporadically go in and out of style. It enjoyed its first peak of mainstream success during the late '80s and early '90s, with artists like MC Hammer, Run DMC and Vanilla Ice bringing it out of the South Bronx and onto MTV and mainstream pop radio. However, the rise of Gangsta Rap and Hardcore Hip Hop in the mid '90s, while now remembered as something of a golden age for rap music, earned the ire of the era's Moral Guardians due to its hard-edged lyrical content, causing rap to be driven off of mainstream radio playlists. The rise of Grunge and Alternative Rock around the same time didn't help matters either. Rap came back in the late '90s through the mid '00s when Jay-Z, Fifty Cent, Lil Jon and other artists made Glam Rap a fixture of nightclubs and parties all across America, while Eminem put a white face on gangsta rap to become one of the biggest (and most controversial) stars of the era. Currently, it seems to be entering another hiatus, particularly now that Synth Pop and other forms of Electronic Music are back in vogue and competing with rap for attention at the aforementioned clubs and parties.
 * Speaking of Synth Pop, it dominated pop music in the '80s, but was supplanted by R and B, idol singers and alternative rock during the '90s and '00s, and was viewed as overly-synthesized and artificial by listeners from those decades. Now, however, artists like Lady Gaga, Kesha, La Roux and Owl City have brought it back into the mainstream.

Specific
"As such Dark Side has outlasted almost all vagaries of fashion. Punk Rock pilloried it, but the CD age rescued it; the hardcore late 1980s spat upon it, but the chemical generation spaced out to it; Britpop made it obsolete, but Radiohead made it more relevant than ever. And not for one second did it ever stop selling."
 * When The Monkees debuted in the mid-'60s, they had a string of Top 40 hits and a television program. However, desperate to break out of the mold, they produced the movie Head, which was such a colossal Mind Screw that it killed whatever popularity they had left. But when MTV reran their TV show to celebrate their 20th anniversary, their career got a second wind, and a single off their greatest hits album (That Was Then, This Is Now) re-entered the Top 40 after a 20+ year absence (at the time, it was a record).
 * It's easy to forget now, but near the end of his life, Michael Jackson was known for only two things: his degenerating physical appearance, and allegations of pedophilia. However, his death has erased those bad memories, or at least pushed them far enough into the background where it's become somewhat disrespectful to bring them up. Radio stations are freely playing his hits again, whereas just the year before his death, the only song of his that would receive any airplay was "Thriller" around Halloween. By way of Dead Artists Are Better, Michael Jackson has been rescued from Deader Than Disco status.
 * Between 2004 and 2008, Britney Spears was viewed as the Distaff Counterpart of Michael Jackson. People felt that her career and reputation were beyond repair, and that she'd literally kill herself through her out-of-control lifestyle and craziness. Some people were already writing her obituary. The release of her albums Circus and Femme Fatale, however, have put her music back on top of the charts, restoring her to a level of popularity not seen since her Teen Idol days, while her being placed in the conservatorship of her father has taken her name out of the tabloids.
 * Arguably, Weezer's music video for "Buddy Holly" is the ultimate illustration of the 20-year cycle: a video made in The Nineties about a TV show from The Seventies that was itself nostalgic for The Fifties.
 * Pink Floyd, most specifically The Dark Side of the Moon, has been described in a book as this:


 * The Spice Girls ' popularity and fame could easily be described as a challenging hike through a treacherous mountain range. They first came into the scene in late 1996 and eventually ended up spreading their recognition into various parts of the globe through 1997, then in 1998, their popularity and fame eventually began to decline, especially with Geri "Ginger Spice" Halliwell ditching them when they were about halfway through their world tour, so the remaining four had to continue on and eventually release a third album without her, then they disbanded altogether and went their "separate" ways like Halliwell did. The group then surprisingly reunited in 2007 for a special tour, though it wasn't that widely known, considering that it ended in early 2008. However, there still may be hope for the group to reunite once again for the 2012 Summer Olympics in London.
 * Elton John began as a critically acclaimed singer-songwriter celebrated for classic albums like Elton John, Tumbleweed Connection, Madman Across The Water and Honky Chateau. His public popularity grew in 1973 with the albums Don't Shoot Me I'm Only The Piano Player and the double album Goodbye Yellow Brick Road. which spawned some of the biggest hits of The Seventies. His popularity increased through the first half of the decade, and his outrageous image, employing crazy costumes and glasses made him a phenomenon and Teen Idol, even though the reviews were less enthusiastic. An infamous Rolling Stone magazine interview in 1976, where he declared himself bisexual (later he'd claimed homosexuality), costed him much of his Middle American fanbase, and his own wish to stop touring, saw his fame taper off. Although he had a successful free concert in Central Park in 1980, sales and airplay were nowhere near as they were in the 1970's. He returned in the mid-1980s with albums like Too Low For Zero and Breaking Hearts, and enjoyed more success in The Nineties after going sober (especially after co-writing songs for The Lion King), and he still has occasional comebacks to this day.
 * While few have ever denied the social and cultural impact of Al Jolson's work, from about the 1970s onwards it was generally considered not cool to give him anything more than the most cursory acknowledgement, partly due to the nature of his act, but mostly because of his Blackface makeup. It wasn't until the 2000s -- and ironically mostly through the efforts of modern-day black performers -- that Jolson started to become a widespread cultural icon again, with the turning point widely being seen as when the city of New York agreed to name a section of Broadway after Jolson.

Professional Wrestling

 * Hulk Hogan. At the height of his popularity in 1985, he hosted Saturday Night Live and was on the cover of Sports Illustrated. When 1994 rolls around, he's seen as a self-parody whose shelf life was such that he needed to ditch the hero routine altogether just to remain relevant. However, in 2002, his return to WrestleMania -- still in his villain persona -- resulted in the fans cheering him over the Rock. To this day, he and the Rock are among the closest things the WWE has produced to A-list deities.

Sports

 * This happens to pro athletes all the time, even more so today in the age of multi-million dollar contracts, free agency, and intense media scrunity. You'd never know it today, but Ted Williams was booed everywhere in the American League, including Boston, for at least half of his career -- but time (and military service) has left him in a more favorable light. Alex Rodriguez seems to be on a downturn right now, but was one of the most popular players in the past and probably will be again before it's all said and done. Jennifer Capriati went from "tennis phenom" to "troubled teenager" to "elder stateswoman of tennis". Mike Tyson alone has jumped back and forth at least twice each.
 * During The Fifties, the only place where Baseball wasn't in a sorry state was New York City. The minor leagues were collapsing due to the availability of major league games on television, old stadiums were growing increasingly decrepit, the dominance of New York teams (particularly the Yankees) was causing fans outside New York to tune out, some teams were still refusing to integrate long after Jackie Robinson had broken down the color barrier, and the sport had no real presence (other than the aforementioned minor leagues) in the fast-growing "Sun Belt" of the South and the West Coast. All of this gave football, both professional and college-level, enough room to build itself up as a serious rival to baseball's status as "America's pastime."

Then in 1957, the Brooklyn Dodgers and New York Giants moved to, respectively, Los Angeles and San Francisco, starting a trend for other teams looking to build new stadiums, which resulted in the sport's expansion beyond the East Coast and the Midwest. This was followed by the collapse of the long-running Yankees dynasty in The Sixties, meaning that fans of other franchises now had a chance to see their teams win the World Series. Suddenly, baseball was relevant again, and in a position to put up a real fight against football for the rest of the century.

Of course, New York sportswriters are still likely to remember The Fifties as baseball's "golden age", simply because it was the era in which the Yankees got the World Series rings they were entitled to, dammit! And if the Yankees didn't win, then the Dodgers or the Giants probably did.
 * On a much smaller scale, sports like figure skating, women's gymnastics and, depending on where you live, soccer. Every four years, during the Olympic Games and The World Cup, those sports take center stage and grab the headlines, and then afterwards, the athletes largely disappear into obscurity until the next big sporting event rolls around.
 * George Steinbrenner is generally remembered as controversial but successful as owner of the New York Yankees from 1973 until his death in 2010, but there was a time when he was considered much more controversial than successful. Within a few years of becoming owner, he established a reputation as an often tyrannical and capricious but effective owner, using his vast reserves of money and the newly instituted system of free agency to put together a dysfunctional but winning team, winning the World Series in 1977 and 1978. They continued to be mostly a winning team for the next decade, but repeatedly fell short of playoff success, and then finished with a losing season each year from 1989 to 1992. That, coupled with his being removed permanently from the Yankees' baseball operations in 1990 for hiring a gambler to dig up dirt on star player Dave Winfield, make his reputation that of a corrupt egomaniac who had ruined a once proud franchise. However, he was reinstated in 1993, and brought the Yankees back to their winning ways, partly because he took a less hands-on approach to the team, including stopping his infamous tendency to constantly replace managers. the Yankees won five more World Series before his death, insuring that his legacy would be overall positive.
 * Brett Favre will likely become an example of this in 2015 when he enters the Pro Football Hall of Fame. He was revered by fans as the guy who saved the Green Bay Packers franchise and brought them their first Super Bowl victory in 30 years when he retired for the first time following the 2007 season. He then un-retire before the 2008 season and was traded to the New York Jets. The move divided the Cheeseheads (Packers fans) to where the CBS affiliates in Green Bay and Milwaukee requested as many Jets games as possible to facilitate the large number of fans who still supported Favre. Following the season, Favre retired for a second time, then un-retired again only to sign with the Packers' hated rivals, the Minnesota Vikings which drew ire even from fans who'd continued to support him as a Jet. After a relatively successful year with the Vikings in which they beat the Packers twice, Favre retired again only to once-again come out of retirement. Fortunately for the Packers, It Got Better this time around. Not only did the Packers, led by former Favre understudy Aaron Rodgers easily avenge both of the previous years' losses to the Vikings en route to victory in Super Bowl XLV, but Favre had the worst season of his career that also saw him miss his first game since becoming the Packers starting QB in 1992 due to a late-season injury. To make matters worse, he was also involved in a scandal when it came to light that he attempted to have an extra-marital affair with a Jets cheerleader during his season in New York. He reitred for good following the 2010 season, and steps are already being taken on both sides to repair Favre's relationship with the Packers organization and fans.

Video Games

 * Duke Nukem Forever has gone through this cycle twice already. It was highly anticipated in the late 90s, became nothing more than a punchline to any joke about vaporware or Schedule Slip during the 2000s, and then became legitimately anticipated again when it was finally released in 2011. Unfortunately, this trope, combined with Two Decades Behind, is also a major reason why it received such a lukewarm reaction. Critics pointed out that, after 15 years in development, its style of gameplay and presentation didn't hold up well against the landscape of modern shooters.
 * Nintendo. In the '80s and early '90s, it was the embodiment of modern entertainment. In the late '90s and early 2000s, it became "the kiddy company" and slipped into last place. So what does Nintendo do? Rather than fight the "kiddy" associations, it embraces them (to the aggrieved cries of the hardcore gaming market), marketing the Wii to families, senior citizens, and other groups not traditionally viewed as "core" gamers. Thanks to this strategy, it is once again the dominant force in gaming. Casual gaming is largely responsible for Nintendo's resurgence.
 * Pokémon. Back in the late '90s, it was the king of kid fads. But it quickly faded among people who only played it to be "cool", and in a few short years, the only people who would still publicly admit to liking it were small children (though the games were still system sellers). Now, as the Turn of the Millennium comes to a close, it is making a comeback. Kids can safely admit to liking it in public again, longtime fans are no longer bashed for it, and those kids who were only fans back in the day are now grown-ups old enough to wax nostalgic about it. In fact, a Japanese clothing company released a line of Poké-merchandise specifically targeted at adult Poké-fans, with an "artsier" bent to it. However, the above is mostly restricted to the games: while there is not as much hate for the Pokémon anime as around the Johto arc, it still hasn't recovered quite as much as the games did.
 * Indie gaming and the Wii have brought back quite a few genres of gaming that were once assumed to have died during the switch to 3D.
 * 2D side-scrollers, such as Castlevania, Contra, Super Mario Bros and Double Dragon, once made up the bedrock of the industry. Later, they were viewed as quaint relics of the pre-Play Station era, and were relegated to handhelds and cheap Flash games... until New Super Mario Bros and New Super Mario Bros Wii tore up the charts, and titles like Braid and Eversion became critical darlings.
 * Retro gaming, in particular the 16 bit period. Emulators have led people to discover a lot of old classics that can be played for free, take up hardly any space and do not take any time to install. Companies have followed suit by reissuing older games.
 * PS 1 gaming is also making a comeback via the Playstation Network and emulation on PSP.
 * Except in Europe, where the Playstation Store still has to catch up with its Japanese and Northern American counterparts: for example, while the original Spyro the Dragon trilogy was released in the U.S. as a whole within a single month (as in, one title per week), it still has to make it to Europe. However, the "head, meet wall" part is averted as of late 2011, given SCEE somehow managed to release previously Japan-only titles as their answer to Nintendo's Hanabi Festival.
 * Mortal Kombat in The Nineties: a ridiculously popular fighting game, with blood and gore as a selling point. Mortal Kombat during the Turn of the Millennium: an overcomplicated, ridiculously unbalanced fighting game series that was past its prime (the Lighter and Softer crossover with DC not helping anything). Mortal Kombat starting with the 2011 reboot: a ridiculously popular fighting game, with blood and gore as a selling point.
 * The Sonic the Hedgehog series has gone on a wild roller coaster of this. When it came out, it immediately became on of the definitive games of the 16-bit era and put the Sega Genesis into a fierce competition with Nintendo. During the time of the Sega Saturn, the series was on main series hiatus, only existing through spinoffs. Come the Dreamcast, the leap to 3D with Sonic Adventure and Sonic Adventure 2 was wildly popular and highly acclaimed, but subsequent games would take their notable flaws in the camera and controls and cause the series to have a bad reputation of being in 3D. This was exacerbated by the over-the-top Darker and Edgier Shadow the Hedgehog and the infamous Obvious Beta Sonic the Hedgehog 2006, causing the series to fall into Snark Bait. After Sonic Unleashed introduced a new well-received style of play, with Sonic Colors and Sonic Generations refining it and removing any poorly received alternate gameplay styles, it's safe to say that the series has been brought back to its former glory as an A-list series for Sega.

Western Animation

 * Western Animation as a whole went through this from the late 1960s to the late 1980s. While animation was already becoming less and less popular through the 1950s and much of the 1960s (thanks in part to television and the rise of limited animation), the death of Walt Disney sent it completely into a dark age. While there was a lot of experimental and adult-oriented animation released during the 1970s, it was still seen as a gimmick used to entertain children, a sentiment that continued through the 1980s. Then Who Framed Roger Rabbit was released...
 * My Little Pony, after its enormous popularity during the 80s and early 90s, faded into obscurity by the latter half of the 90s. In 2010, along came My Little Pony Friendship Is Magic, which not only proved to be popular among viewers of an unexpectedly wide age range but also exploded onto the Internet, collecting more images, comments, and views on Know Your Meme than anything else.

Other

 * Adam West. In the late 1960s, he was a prime-time TV star and the actor charged with bringing Batman back to life. Head to the '80s and the return of the Dark Knight, and West is a persona non grata, firmly stuck as a reminder of the Dork Age Batman. But today? He's a staple voice actor in comedies such as Family Guy precisely because of his history as Batman, and trademark overdramatic voice.
 * In fact, the whole thing had a Lampshade Hanging in Batman the Animated Series. There was an episode wherein Bruce Wayne met the actor who'd played his childhood idol. The actor's life mirrored West's post-Batman life, and West did the voice acting.
 * The Seventies. Throughout the '80s and '90s, this decade was seen as America's Dork Age. Nowadays, it's seen as a more innocent time. (Think about that for a second.) Elements from the '70s which have made comebacks since then include:
 * Bell-bottom jeans.
 * The afro.
 * The medium-length bowl cut with the fringe.
 * Rollerskating thanks to Rollerblade pushing inline skates.
 * Stoners on TV.
 * Disco. A great deal of popular music for the past two decades has been essentially Disco that Dared Not Speak Its Name. However, the word still has a ways to go.
 * Thanks to bands like Daft Punk and LCD Soundsystem, it's on it's way back.
 * Blaxploitation also makes a comeback every few years, although this is mainly so that people can have a giggle at the loud fashions and overuse of Jive Turkey, rather than recall the genre's roots as a supplement of the Civil Rights Movement.
 * The Eighties have been getting this too, with the returning popularity of everything from Transformers to leg warmers. Yes, leg warmers.
 * Leg warmers + skirts = awesome.
 * The inverted version (leggings under skirts) seems to have made a comeback in the mid 2000s after being absent since the 80s as well in a more justified manner. When it made a comeback, it was obviously a pentalty for violating Dress Codes that are typically based on common decency standards that supposedly prevent men from stumbling and then eventually became a fad for quite some time.
 * There's a lot of synthpop inspired bands around these days, when it used to be the prime example for people to explain why the 80s sucked so much.
 * Some stuff from The Nineties is starting to come back, such as plaid flannel shirts and hi-top fades.
 * The Yo-Yo. Not so much Popularity Polynomial as Popularity Sinusoid. It really does come around that regularly.
 * Which is fitting, when you think about it.
 * At one point, this was because the Coca Cola Company gave yo-yos a marketing push about every three years or so.
 * Ventriloquism was once considered the deadest of all show business horses. Then all of a sudden Jeff Dunham came along, and earned his own TV special after several sold-out performances. Terry Fator also has his own Las Vegas show.
 * Skateboarding has fluctuated in and out of popularity so much that nobody seems to care whether or not it's "in," least of all the skaters themselves.
 * The game developers do; see also, Tony Hawk Pro Skater Ride.
 * Skateboarding was big in the mid-Seventies and late Seventies, largely on the back of the popularity of surfing at that time. It died away in the early Eighties, until, of all things, Back to The Future mainstreamed it again.
 * Modern social dance has undergone a huge revival, starting in the '90s. Latin clubs sprung up across the US, ballroom dancing got a big boost with Dancing With the Stars, and swing dancing was resurrected by college students across the US and Europe.
 * Combine that with The Seventies above, and you get the return of roller disco.
 * American cars from The Fifties are beloved today, with their huge tailfins and large amounts of chrome. However, when they went out of style in The Sixties, they went out hard. Back then, few people who could afford it would be caught dead driving around in a '57 Bel Air. It didn't help that a lot of that stylish chrome decoration had a tendency to fall off after a few years due to rust. It was only with the rise of Fifties nostalgia in general in The Seventies and especially The Eighties that cars from that decade started to be more appreciated.
 * The lifecycle of a car design has stretched considerably. Today, a new car can be exhibited at major shows almost a year before it hits the market; then comes a 5-7 year production cycle and upwards of a 20-year period before examples of a discontinued model that was popular when new are rare enough not to be an everyday sight. Expect at least another ten years after that for them to start showing up at classic-car events.
 * The recent trend towards environmentalism and energy efficiency in the cultural consciousness has done this for a lot of seemingly "outdated" technologies and vehicles:
 * The post-war American car market has constantly cycled between demand for larger, roomier, more powerful automobiles and smaller, more efficient ones. In The Fifties and The Sixties, the trend was toward "bigger is better" with land-yachts and muscle cars to show off the newfound wealth of America's middle class. Then, the Arab oil embargo caused demand to shift towards compact and midsize cars and, later, minivans for most of The Seventies and The Eighties. As a new generation came of age with little memory of the energy crises, large vehicles came back into style, this time in the form of large SUVs, in The Nineties and the Turn of the Millennium. Now, thanks to the spikes in gas prices of 2005 (post-Hurricane Katrina) and 2008, compounded with the economic recession, SUVs are out, and crossovers, hybrids and compacts are in, as well as...
 * Minivans. As mentioned, they were huge in The Eighties as a fuel-efficient alternative to land-yacht station wagons (the fuel crises of The Seventies still fresh in everyone's mind), but faded away in the late '90s, thanks to SUVs, the perception that the average minivan owner was a boring "soccer mom" suburbanite, and the fact that the styling was getting blander -- compare, say, the Chevy Lumina and the Toyota Previa (which look like cars straight out of The Jetsons) to the Ford Freestar. While they haven't shaken their uncool reputation, minivans have seen a small resurgence after the decline of the SUV market, due to their similar capacity and greater fuel efficiency.
 * Small "econo-box" autos and hatchbacks. During the height of the last "Bigger is Better" craze during The Nineties and the Turn of the Millennium, it seemed as though the only choices for new car owners were four-door sedans and body-on-frame SUVs. Lately, though, vehicles like the new Mini Cooper and various hybrids are selling so fast that it took years before the automakers could meet demand, and older models such as the Geo Metro and Volkswagen Beetle can sell for up to triple their Blue Book value on the used car market on the basis of fuel economy alone. The American automakers have even started importing some of their compact European models to meet this new demand, ending decades of No Export for You -- to such success that it has been cited as one of the reasons for the revitalization of Detroit's "Big Three" after decades of seemingly interminable decline.
 * Up until The Seventies, bicycles were seen primarily as transportation, and were built with full fenders and used either single speed or 3-speed internal gear hubs. Once the health craze launched a cycling boom, many people started switching to racing bikes, which strove to add more gears and lighter materials. Older cruisers, "English" 3-speeds, and even the steel 10-speeds made at the start of the biking boom came to be seen as extremely dorky. Recently, however, a shift back to the use of bikes for transportation has led to the return of internal gear hubs, single speeds, and even fixed-gear bikes, with specialty makers building custom steel frames instead of aluminum or carbon fiber. The racing bikes, by contrast, are now the ones that are seen as dorky, while the once-cool lycra riding uniforms associated with them are now viewed as symbols of the nadir of '80s fashion.
 * Streetcars. After World War II, a combination of cheap gas and the growing popularity of buses (and, arguably, some underhanded tactics by the auto industry) led to many streetcar lines falling out of use and eventually being dismantled. The few surviving ones, such as those in San Francisco and New Orleans, persisted more for their historical and tourism value than anything else. When cities did invest in mass transit, it would often be in the form of buses and subways that wouldn't threaten the flow of automobile traffic on the streets. In the Turn of the Millennium, however, the green movement and fears over rising gas prices led several cities to build or expand "light rail" systems, which are essentially streetcars with decades worth of new technology.
 * City centers. After World War II, when the G.I. Bill, cheap gas, cheap land, the new Interstate Highway System, and the postwar baby boom created an enormous demand for housing that couldn't be met by the cities alone. As a result, this lead to a massive boom in Suburbia and cities began to expand outward rather than upward leading to a phenomenon known as "white flight" in which middle-class white families moved out to the suburbs, taking their tax dollars with them and leaving the cities behind to decay. In recent times however since as early as The Nineties, city centers have seen a resurgence in popularity especially among younger folk due to factors such as better public transit and walkability, proximity to work and cultural attractions, and frustration with suburban life and automobile gridlock.
 * Facial hair in the West has gone in and out of style in a cyclical fashion for centuries among the elite following the same basic pattern as anything else: the ruling class has facial hair, everyone else has facial hair, the ruling class doesn't want to look like the lower class, the ruling class no longer has facial hair, and so on. The last time it was "in" in the West (i.e. would you expect your average CEO/congressman/stockbroker to have facial hair) was during the first several decades of the 20th century -- the last US president, for example, to have facial hair was William Howard Taft, who was President from 1909-1913.

While it would seem that facial hair is about due for a comeback any decade now, there is good reason to believe that mainstream facial hair is out for good given the societal and cultural changes that have occurred in the past hundred years. Interpersonal and people skills are now more important than sheer strength and virility (of which facial hair is seen as being indicative of) in leaders, and studies show that on average men with facial hair are seen as less trustworthy, especially to women, whose cooperation and input actually matter now that we are finally evolving away from a patriarchal society to one in which the genders are equal. In short: appearing trustworthy to both men and women is now much more valuable than intimidating other men, so beards aren't expected to make a comeback anymore.
 * Posession of a moustache will lead to jokes about you being a creepy possible pedophile (if you're older than 30) or an insufferable hipster (if you're younger than 30).
 * Revolvers Are Just Better experienced this in The Nineties, at least in the American civilian market. The Eighties saw the rise of so-called "Wonder Nines," high-capacity 9mm handguns that held 15 rounds or more, vastly outstripping the six-round capacity of most revolvers. Police forces switched over immediately, and civilians took to the new guns almost as quickly. In 1994, however, the Assault Weapons Ban was passed, heavily restricting, among other things, the sale of high-capacity magazines that held more than ten rounds. This stripped the Wonder Nines of their chief advantage, allowing revolvers to retake market share. Even after the ban expired in 2004, this trope remained in effect in those states that still had their own laws on the books -- revolvers are noticeably more popular in, say, New York than they are in Florida.
 * Note that this doesn't apply to police departments -- their weapons choices weren't affected by the ban, and the greater magazine capacity is incredibly useful for their work.
 * At the dawn of The Nineties, most observers in the computer world had given up UNIX for dead, due to the fragmentation among vendors and the GNU Project's slowness in developing a free replacement. Then a Finnish grad student by the name of Linus Torvalds released the Linux kernel to the Internet. It was rapidly adopted by GNU and various Linux distributions (though Richard Stallman prefers you call it "GNU/Linux", thank you very much), have provided a viable alternative to Windows and Mac operating systems. Open source systems based on BSD also popped up in the early '90s (Mac OS X is based in part on FreeBSD.) They're most successful as servers and in high-powered applications such as animation rendering and supercomputers.
 * The programming language Lisp had been considered dead ever since the AI Winter caused all the funds for artificial intelligence research, which was the field most Lisp programmers worked in, to dry up. The language has seen a revivial of interest, however, in The Turn of the Millennium and The New Tens largely thanks to Paul Graham.
 * Baby names. There are some names that never go out of style, but others run in hundred-year cycles - in The Thirties "Shirley" was a little girl and "Zack" was a grizzled old prospector. Today Shirley's collecting Social Security and Zack's a young man in his teens or twenties. Such "time capsule names" tend to be popular for about 20 years and then become indelibly linked to the generation born when they were popular, until they're rediscovered a few decades after that generation dies off and then they become indelibly linked to the new one.
 * This is something for fiction writers to watch out for - one of the easiest ways to provoke a Did Not Do the Research reaction is to have an entire cast of 20- and 30-somethings with names that are popular baby names now but weren't in the '70s and '80s; or to have a period-set story where characters' names are typical of the generations that are that age today rather than the cohort the characters are supposed to belong to. An outlier or two is fine, but too many can be overwhelming.