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The following web-page gives a very good account of the "butterfly effect" and its origin.
The term is used in in chaos theory to describe how small changes to a seemingly unrelated thing or condition (also known as an initial condition) can affect large, complex systems. The term comes from the suggestion that the flapping of a butterfly's wings in South America could affect the weather in Texas, meaning that the tiniest influence on one part of a system can have a huge effect on another part. Taken more broadly, the butterfly effect is a way of describing how, unless all factors can be accounted for, large systems like the weather remain impossible to predict with total accuracy because there are too many unknown variables to track.
In simple terms, it means that no matter how small an uncertainty of a varibale in a mathematical calculation is, such uncertainty would increase by itself during the mathematical process and leads to a final result much deviated from reality.