ॐ The Butterfly Effect

Edward Lorenz, an MIT meteorologist who tried to explain why it is so hard to make good weather forecasts and wound up unleashing a scientific revolution called chaos theory, He died April 16 of cancer at his home in Cambridge. He was 90.A  professor at MIT, Lorenz was the first to recognize what is now called chaotic behavior in the mathematical modeling of weather systems. In the early 1960s, Lorenz realized that small differences in a dynamic system such as the atmosphere--or a model of the atmosphere--could trigger vast and often unsuspected results.These observations ultimately led him to formulate what became known as the butterfly effect--a term that grew out of an academic paper he presented in 1972 entitled: "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas? The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does
Chaos theory is a field of study in applied mathematics, with applications in several disciplines including physics, economics, biology and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions; an effect which is popularly referred to as the butterfly effect. 
The butterfly effect is a metaphor that encapsulates the concept of sensitive dependence on initial conditions in chaos theory; namely a small change at one place in a complex system can have large effects elsewhere. Although this may appear to be an esoteric and unusual behavior, it is exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position. The butterfly effect is a common trope in fiction when presenting scenarios involving time travel and with "what if" cases where one storyline diverges at the moment of a seemingly minor event resulting in two significantly different outcomes.

Evan Treborn (Ashton Kutcher), who suffered severe traumas as a boy (Logan Lerman) and a teenager (John Patrick Amedori), blacks out frequently, often at moments of high stress. While entertaining a girl in his dorm room, he finds that when he reads from his adolescent journals, he travels back in time, and is able to basically "redo" parts of his past, thereby causing the blackouts he experienced as a child. There are consequences to his choices, however, that he then propagates back to the present: his alternate futures vary from frat boy to prisoner to amputee. His efforts are driven by the desire to undo the most unpleasant events of his childhood which coincide with his mysterious blackouts, including saving his childhood sweetheart Kayleigh (Amy Smart) from being molested by her father (Eric Stoltz) and harassed by her aggressive brother (William Lee Scott).
The actions he takes, and those he enables others to take during his blackouts, change the timeline in the new future wherein he awakes. As he continues to do this he realizes that even though his intentions are good his actions have unforeseen consequences. Moreover, the assimilation of dozens of years' worth of new memories from the alternate timelines causes him brain damage and severe nosebleeds. Ultimately he decides that his attempts to alter the past end up only harming those he cares about. But the focal point for all of these traumatic timelines appears to be Kayleigh. So Evan travels back in time once more to the first day he met her and by scaring her away finally succeeds in saving Kayleigh's life. He then destroys all of his journals so that he's not ever tempted again to make any more changes.
The film ends eight years in the future with Evan leaving an office building in Manhattan and passing Kayleigh on a crowded daytime sidewalk. They alternately pause and turn after spotting and passing each other. While Kayleigh seems to have only a vague intimation of having seen him somewhere before, Evan remembers her very well and allows the moment to pass without attempting to speak to her.

The director's cut of the film ends with Evan travelling back to the day of his birth, and as a fetus, strangles himself with his umbilical cord. A voice-over replays of the fortune teller saying that he doesn't have a soul and was never meant to have been born and his mother saying she had miscarriages before him. The resulting time-line shows his friends and family happier without him. Another voice-over replays his mother's confession (originally heard when visiting the fortune teller earlier, saying that he was the third of three brothers, the other two having died during birth), this time altered to her telling her fourth child, now a daughter, that she survived while her three children before her did not. This is because his father kept going back in time trying to save one of his sons to make sure a child was born, unknowingly making them like him, making Evan not the cause of the butterfly effect but the butterfly effect itself. It then shows Evan's mother with a new husband with a daughter and Kayleigh marrying someone she met in her new life.
Another alternate ending shows Evan and Kayleigh stopping on the sidewalk when they cross paths. They introduce themselves and Evan asks her out for coffee.
Another ending is similar to the one shown in the film, except this time Evan, after hesitating, turns back and starts following Kayleigh.This ending was utilized in the film's novelization, written by James Swallow and published by Black Flame.
The final alternate ending is again similar to the previous one, Evan and Kayleigh hesitantly stop on the street when they cross each other but do not meet each others gaze and continue on their original path.