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What's the CHAOS THEORY, the one which explains the BUTTERFLY EFFECT?


Definition

Chaos Theory is a branch of mathematics focusing on the behavior of dynamical systems (function that describes the time dependence of a point in a geometrical space) that are highly sensitive to initial conditions.




A more technical definition

'Chaos' is an interdisciplinary theory stating that within the apparent randomness of chaotic complex systems (A complex system is a system composed of many components which may interact with each other) there are underlying patterns, constant feedback loops, repetition, self-similarity, fractals (fractal is a detailed, recursive, and infinitely self-similar mathematical set whose Hausdorff Dimension strictly exceeds its topological dimension and which is encountered ubiquitously in nature), self-organization, and reliance on programming at the initial point known as sensitive dependence on initial conditions.


In the practical world The Butterfly Effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

Don't believe it to be practically possible?

Here's a list of 8 Examples of Butterfly Effect That Changed the World Forever: http://bit.do/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 of their behavior 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. This behavior is known as deterministic chaos, or simply chaos.

The theory was summarized by EDWARD LORENZ as:-

CHAOS: When the present determines the future, but the approximate present does not approximately determine the future.


Chaotic behavior exists in many natural systems, such as weather and climate. It also occurs spontaneously in some systems with artificial components, such as road traffic. This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications in several disciplines, including meteorology, anthropology, sociology, environmental science, computer science, engineering, ecology, philosophy etc.



-by Lipakshi rathor.

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