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# What is Chaos Theory?

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###### 2011-02-21 16:52:52

Chaos theory is a field of applied mathematics with applications in many related fields, including meteorology, economics, and even philosophy. The basic premise is that small differences in the initial conditions of a system yield widely-varying outcomes, precluding attempts at longterm prediction. It is often instantiated using the "butterfly effect" to show how capricious chaotic systems can be, the critical things being (i) their complexity, and (ii) just how delicately balanced they can be.

The term "butterfly effect" is also reflective of the Lorenz Attractor plot, which is the fractal structure that corresponds to the long-term behavior of a Lorenz Oscillator, a 3-D dynamical system, whose motion is chaotic. The plot looks like the wings of a butterfly.

Some of the common misunderstandings of this theory:

1. Chaos is not simply how complicated a system is, or how many different variables there are to take into account.
2. Chaos does not mean a system is not deterministic. By this I mean there may be a well defined set of rules the system follows, and in principle you can predict, as accurately as you want, what is going to happen - assuming you have the instruments to measure the current state of the system accurately enough, and the computing power to do sufficiently accurate calculations.

A chaotic system is one that is so sensitive to initial conditions that it's impractical to predict its behavior far in advance, because of limited accuracy of measurement and computing power.

A good example is the logistic map. You start with a constant r. (This isn't chaotic for all values of r, but for most values between about 3.5 and 4 it is chaotic.) You pick a number x_0, between 0 and 1. Then you define the sequence x_0, x_1, x_2, ... as follows:

x_1 = r * x_0 * (1-x_0)

x_2 = r * x_1 * (1-x_1)

x_3 = r * x_2 * (1-x_2)

etc. This isn't a complicated system - the rule for calculating the next term in the sequence is easy to understand, and there is only one variable (x). It's also deterministic: If you know exactly what the value of x_0 is, you can calculate x_1000 exactly. (More accurately: if you know x_0 to enough decimal places and have a big enough computer, you can calculate x_1000 to, say, 10 decimal places.) But in practice any attempt to calculate x_1000 is doomed to failure.

Ed Lorenz' seminal paper in 1963, Deterministic Nonperiodic Flow, can be found at the related link below.

## Related Questions

No; chaos theory is more useful to explain why hurricanes CANNOT be predicted.

If you follow the link below it will lead you to references and articles on chaos theory.

The general Chaos Theory is plausible given its unpredictability in complex systems.

Well, there isn't really a symbol for the Chaos Theory, more a symbol representing Chaos in generall. It called a Chaosstar or Chaossphere

Chaos Theory - 2009 was released on: USA: 27 October 2009

Paramedics - 1998 Chaos Theory was released on: USA: 15 January 1999

Chaos Theory - 2012 was released on: USA: 7 November 2012 (AFI Fest)

Chaos Theory and the Theory of the Six Degrees have little to no overlap; they're not really related. There are some mathematical probabilities associated with the Six Degrees, and Chaos Theory is rooted in mathematics. But the former can be looked at as a "probability thing" and the latter an "anti-probability" or "probability resistant" thing.

The cast of Chaos Theory - 2009 includes: Russell Jeffrey as Andrew Ronald Smyck as Friend

According to the chaos theory, a butterfly.

Hollywood Unscripted A Chaos Theory - 2005 was released on: USA: 20 January 2005 (Hollywood, California)

Splinter Cell Chaos Theory - 2005 VG is rated/received certificates of: Australia:MA USA:M

system management chaos theory freedom-based management theory contingency theory

They do if you do them in front of a moderator.

Meteorologist Edward Lorenz pretty much invented chaos theory with his theory of the Butterfly Effect. The formal founder, however, was probably Benoit Mandelbrot who, several years later, began to really work with it.

The cast of The Chaos Theory - 2006 includes: Daz Jones as himself Ali Marshall as himself Si Tapley as himself

Chaos Theory - 2009 I Can Has Candy 1-11 was released on: USA: 1 December 2009

Chaos Theory - 2009 Exposed 1-22 was released on: USA: 16 February 2010

ER - 1994 Chaos Theory 9-1 was released on: USA: 26 September 2002

Chaos Theory - 2009 Shrinkage 1-7 was released on: USA: 12 November 2009

Chaos Theory - 2009 Cupcake 1-1 was released on: USA: 27 October 2009

The Cleaner - 2008 Chaos Theory 1-4 is rated/received certificates of: USA:TV-14

No, chaos is the preexistant state to the existence of the gods. Chaos. Take a look at chaos theory, the earth was without form and was void, and ...it gets a bit murkey here.... When you get to Logos, order to the chaos has emerged. Or at least was discovered.

Chaos Theory - 2009 Promoting the Coach 1-5 was released on: USA: 5 November 2009

Chaos Theory - 2009 Spare a Dime 1-17 was released on: USA: 12 January 2010

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