**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:

“There never comes a point where a *theory* can be said to be true. The most that one can claim for any *theory* is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed.”

—A.J. (Alfred Jules)

“Figure him there, with his scrofulous diseases, with his great greedy heart, and unspeakable *chaos* of thoughts; stalking mournful as a stranger in this Earth; eagerly devouring what spiritual thing he could come at: school-languages and other merely grammatical stuff, if there were nothing better! The largest soul that was in all England.”

—Thomas Carlyle (1795–1881)