Time is one fragile concept. The butterfly effect talks about how a butterfly flapping its wings a certain way can lead to a tornado. Of course, as one can guess, this attracts a lot of writers. The idea that a seemingly irrelevant action resulted in something phenomenal or catastrophic is a writer's heaven. Technically, almost every major event in fiction is a result of many, MANY different flaps, but what makes a story interesting is what writers choose to tell about it.
Since it would be impossible to cover every single use of this, I will cover Scrubs, Life is Strange and How I Met Your Mother. You can avoid reading any one of them to avoid spoilers. Also, since I have already covered Community's Remedial Chaos Theory, I will not be doing it here again. Also, I will not be talking about it in technical ways, but how it is used for storytelling and enforcing the themes.
Life is Strange
Life is Strange presented a relatively traditional concept in a beautiful way. Of course, anyone who has played the game knows this to be the main catch of the series. In the middle of the story, Chloe, in an attempt to dodge any self-acceptance she has to do which would lead to further pain, blames her father for dying in a car crash and starting a domino effect which led to her life getting systematically worse. Max, unable to see her suffer in this manner, manages to go back in time and save William from that accident. However good her intentions were, Max created one of the most controversial dilemma in gaming.
Attempting to stop this branch of timeline that would lead to Chloe feeling completely isolated from everyone, Max created a worse situation for Chloe. Now that her dad was alive, it led to a series of events where a reckless driver caused her spinal chord to snap and become paralysed below her neck. While the whole, "Good intentions lead to bad outcome" concept is not unfamiliar, Life is Strange gave Max the ability to actively go back in time and do something noble, which leads to an even stronger event I would talk about in a moment.
This alternate reality is truly depressing. In this timeline, nobody knows that Max created a ripple that changed everyone's lives. There is a looming sense guilt over Max and the player. The game is hinting us towards the inevitability of going back to the original timeline, and it is important for a narrative that the decision is Max's and not the universe's. For that, we use juxtaposition.
When observing the Price household in this alternate timeline, things get bleaker by the beat. Now, Chloe Price needs morphine to numb her pain instead of her creative methods. The independent Chloe Price needs someone's assistance to go to the bathroom or get out of bed. Finally, Chloe Price, the person who was willing to go to the ends of the earth to find and escape with Rachel Amber in search of a better life is now ready to die after having one memorable day with Max. Is it worse for Chloe to be depressed to the point of suicidal behaviour, or to have such an antagonistic view on everyone and everything that she is willing to sabotage her own life over and over?
By the time Max makes that decision, we are reminded what has to be done to go back to the original branch: You have to watch William, whom Max loved like her own family, walk to his death, promising his daughter that no one will ever leave her.
The butterfly effect is best used when it reinforces the themes of the story, and Life is Strange, despite not being the prime example of The Butterfly Effect, is the prime example for using this trope to provoke thoughts, discussions and most notably, evoking strong emotions of empathy.
Scrubs was a more creative show than its competitors and always tried to tell a new story out of old tropes. In one of its finest episodes, Scrubs told the story about how a butterfly's wing-flapping changed almost everything.
The episode starts with an actual butterfly in the hospital deciding whose chest to land on. This led to a chain of events where almost everything that could have gone wrong did go wrong. Everything started based on the awkwardness of dialogue based on the chest in question. The events first time around are not that interesting, but they set up a far more interesting timeline.
After JD faces remorse over his patient's death, feeling that he could have saved him if the events transpired differently, we go back in time as the butterfly makes a different decision. Just by this one change, it ripples throughout the hospital as everything that could have gone right did go right. This also helped characterise the main cast. The difference between Turk calling Carla out on her consistent apathy and consistent care is one nice event, that JD can never catch a pen but will always make an excuse, and that Dr Cox is on the margin of letting JD take the helm during diagnosis and ensuring that he never makes any decisions. The entire point of The Butterfly Effect in this episode is to highlight how different the circumstances can be if a very small detail is changed from the past.
However, in both timelines, JD's patient still dies. This actually highlights the factor that elevates Scrubs from other sitcoms: Scrubs can be a dark show, and it can often end on such note. After this timeline is shown to us, JD still thinks about how things could have gone differently. It is hard to accept that even if everything goes right in medicine, someone can still die. What JD wanted at the end of the first timeline is for everything to go right, but seeing that he can still not save him, JD imagines a better timeline where he still might have been able to save his patient. For JD, watching his patients die is not something he can let go.
I cannot believe how creative this show is. This was always passed around as the replacement for Friends, yet it felt so different from it. The entire show leads down to the idea of how small and insignificant events led to that fateful night in Farhampton Station. I always found it unsettling how the entire plot with the mother should NOT have worked yet it did, and there is a good reason for it to be discussed another time.
Right now, let's talk about future Ted telling the story. Unlike most stories, both Ted and the audience have a hindsight. We KNOW that Robin is not the one, and we know that Ted HAS to meet the love of his life. That means every time we have a close encounter, it kills us that they don't meet. The show seems full of mis-misdirections, where something relevant to the big "meet" turns out to be irrelevant, only to turn out relevant again in season 9.
The show tackled the butterfly effect near the end of season 4. It starts with a random encounter with someone after he is holding onto the legendary yellow umbrella, and Ted backs up each time he could have ended not being in the right place at the right time for that encounter. There is a rule in storytelling too where every event can seem like a contrivance if you already know how the story ends, so we have to be careful when spotting a true contrivance. Well, Ted doubles down on every event on his life just being one miraculous incident after another which got him with the best person in the world. In the end, the person turned out to be Stella, his ex-fiancé, which was another mis-misdirection.
Much like Scrubs, HIMYM ends on a dark note quite often. That is why usually, what holds comfort for us is that everything, from Ted having to sit alone in his bar and imagine what his life was like when his friends sat with him to Ted losing Robin over and over, it all leads up to the best moment in Ted's life. If his life was different, if he did not get a tramp stamp, if he did not break up with Robin, he would not find her. In this butterfly's story, we get the resolution at the very start and we can let Ted suffer over and over.
While stories like Until Dawn used this effect in a more technical and efficient manner, these were the examples where they used it to tell an amazing story. Instead of setting their themes and stories around this effect, they used the butterfly effect to the service of the product that was already created.