A Short Introduction to Butterfly Effect

Chaos theory is a famous field of study in mathematics. It deals with the ways in which dynamic systems, which are extremely sensitive to the initial conditions, behave. The responses that one receives are popularly known as Butterfly Effect. Technically butterfly effect can be defined as the sensitive dependency on the initial condition s where a minute change in any particular state might result in huge differences at a later stage of time. The definition is based upon the assumption that initial state belongs to that of a ‘deterministic nonlinear system’.

The term butterfly effect was first coined by the American mathematician, Edward Lorenz. He named the effect based upon an example of hurricane details like the exact formation time and path traversed, might be influenced by very minor changes like butterfly wings flapping quite a number of weeks earlier. This example was of course metaphorical in nature. Lorenz discovered this effect during the runs of weather model, where he found out that the initial data that was rounded of did not produce the same results as the unrounded initial data.

Butterfly effect can be observed in daily activities. For example, while throwing dice the random outcomes depend on the features that amplify the minor differences in the initial conditions, like precise direction, orientation and thrust of the throw that would make the dice to traverse in different paths. These paths would be created in such a way because of the minute changes in the initial conditions that in would be nearly impossible to replicate the exact paths again.


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