Chaos theory (nonfiction): Difference between revisions
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In [[Mathematics (nonfiction)|mathematics]], '''chaos theory''' refers to the behavior of dynamical systems that are highly sensitive to initial conditions -- a response popularly referred to as the butterfly effect. | [[File:Lorenz_attractor.png|thumb|Visualization of a [[Lorenz system (nonfiction)|Lorenz system]], one of the classic images of chaos theory.]]In [[Mathematics (nonfiction)|mathematics]], '''chaos theory''' refers to the behavior of dynamical systems that are highly sensitive to initial conditions -- a response popularly referred to as the butterfly effect. | ||
Small differences in initial conditions (such as those due to rounding errors in [[Computation (nonfiction)|numerical computation]]) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. | Small differences in initial conditions (such as those due to rounding errors in [[Computation (nonfiction)|numerical computation]]) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. | ||
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== In the News == | == In the News == | ||
<gallery | <gallery> | ||
File:Edward Lorenz.jpg|link=Edward Lorenz (nonfiction)|[[Edward Lorenz (nonfiction)|Edward Lorenz]] hailed as pioneer of chaos theory. | |||
</gallery> | </gallery> | ||
== Fiction cross-reference == | == Fiction cross-reference == | ||
* [[Crimes against mathematical constants]] | |||
* [[Did you step on a butterfly in Texas during a tornado while watching Jurassic Park in Brazil under the influence of JJ-180?]] | |||
* [[Gnomon algorithm]] | |||
* [[Gnomon Chronicles]] | |||
* [[Benoit Mandelbrot]] | |||
* [[Mathematician]] | |||
* [[Mathematics]] | |||
== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* [[Arnold's cat map (nonfiction)]] | |||
* [[Fractal dimension (nonfiction)]] | |||
* [[Lacunarity (nonfiction)]] | |||
* [[Edward Lorenz (nonfiction)]] | |||
* [[Lorenz system (nonfiction)]] | |||
* [[Benoit Mandelbrot (nonfiction)]] | |||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
* [[Stability theory (nonfiction)]] | |||
External links: | External links: | ||
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[[Category:Nonfiction (nonfiction)]] | [[Category:Nonfiction (nonfiction)]] | ||
[[Category:Mathematics (nonfiction)]] | |||
Latest revision as of 12:28, 2 November 2020
In mathematics, chaos theory refers to the behavior of dynamical systems that are highly sensitive to initial conditions -- a response 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.
The theory was summarized by Edward Norton Lorenz as:
Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
In the News
Edward Lorenz hailed as pioneer of chaos theory.
Fiction cross-reference
- Crimes against mathematical constants
- Did you step on a butterfly in Texas during a tornado while watching Jurassic Park in Brazil under the influence of JJ-180?
- Gnomon algorithm
- Gnomon Chronicles
- Benoit Mandelbrot
- Mathematician
- Mathematics
Nonfiction cross-reference
- Arnold's cat map (nonfiction)
- Fractal dimension (nonfiction)
- Lacunarity (nonfiction)
- Edward Lorenz (nonfiction)
- Lorenz system (nonfiction)
- Benoit Mandelbrot (nonfiction)
- Mathematics (nonfiction)
- Stability theory (nonfiction)
External links:
- Chaos theory @ Wikipedia