**Chaos theory** is a field of study in mathematics, with applications in several disciplines including physics, engineering, 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. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply *chaos*.

Chaotic behavior can be observed in many natural systems, such as weather. Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and PoincarĂ© maps.

Read more about Chaos Theory: Chaotic Dynamics, History, Distinguishing Random From Chaotic Data, Applications, Cultural References

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### Famous quotes containing the words theory and/or chaos:

“We commonly say that the rich man can speak the truth, can afford honesty, can afford independence of opinion and action;—and that is the *theory* of nobility. But it is the rich man in a true sense, that is to say, not the man of large income and large expenditure, but solely the man whose outlay is less than his income and is steadily kept so.”

—Ralph Waldo Emerson (1803–1882)

“To the indefinite, uncertain mind of the American radical the most contradictory ideas and methods are possible. The result is a sad *chaos* in the radical movement, a sort of intellectual hash, which has neither taste nor character.”

—Emma Goldman (1869–1940)