The idea of  butterfly effect is that small things can have non-linear impacts on a complex system.

The butterfly effect is the theory that unimportant details can have unexpected effects on complicated systems. Typhoons are thought to be created by a butterfly beating its wings.

Of course, a typhoon cannot be started by a single event, like a butterfly flapping its wings. However, little occurrences sometimes act as catalysts to change the initial conditions.

Additionally, some systems, according to John Gribbin in his cult classic book Deep Simplicity, "are very sensitive to their starting conditions, so that a tiny difference in the initial "push" you give them causes a big difference in where they end up. And because there is feedback, what a system does affects its own behaviour.

Nagasaki was bombed. The armaments facility was the initial target of the US plan to bomb Kuroko, Japan. Cloudy weather prevented military personnel from seeing the factory as they flew overhead on the day the US planned to attack. Before the pilots gave up, the plane flew over the city three times. Locals in bunkers braced themselves for catastrophe as they heard the hum of the plane about to drop the nuclear bomb. Kuroko, however, was never bombed. Due to better visibility, military personnel chose Nagasaki as the target. That instantaneous choice had enormous consequences. If that day had not been foggy, history would have taken a very different turn that we can't even begin to imagine.

For want of a nail the shoe was lost,
For want of a shoe the horse was lost,
For want of a horse the rider was lost,
For want of a rider the battle was lost,
For want of a battle the kingdom was lost,
And all for the want of a horseshoe nail.

Although the butterfly effect has been discussed for a while, Edward Lorenz (1917–2008), who first identified it as a unique effect, is credited with its discovery. Lorenz, a mathematician and meteorologist, successfully integrated the two fields to develop chaos theory. In the 1950s, Lorenz looked for a way to forecast the weather since he believed that linear models were insufficient.

Lorenz found that the uncertainty in human measurements of physical occurrences could not be explained by a deterministic view of the cosmos. He noted that the interdependent cause-and-effect interactions found in nature are too complicated to understand. He started running parallel meteorological simulations using sets of slightly varying beginning conditions to estimate the most likely outcomes for such complicated systems as weather patterns. Today, we still do our regular weather forecasts using this technique.