HONR 300/CMSC 491Chaos (Flake, Ch. 8)

Prof. Marie desJardins, March 2, 2011

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Key IdeasKey Ideas Visualizing chaos

Time series graph State space graph

Types of regimes: Fixed points Limit cycles Quasiperiodic Chaos

Properties of chaos Determinism Sensitivity Ergodicity

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As Randall Munroe As Randall Munroe Sees ItSees It

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Fixed Point BehaviorFixed Point Behavior

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LimitLimit Cycle Cycle

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ComplexComplex Limit Cycle Limit Cycle

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ChaosChaos

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Bifurcations of the Bifurcations of the Logistic MapLogistic Map

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Properties of ChaosProperties of Chaos Determinism

Sensitivity to initial conditions

Ergodicity

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If you don’t believe in “the butterfly effect” or the conclusion of The Sound of Thunder, consider these thoughts: The Game of Life is much simpler than the world. Yet changing

the state of just one cell in the initial configuration can lead to a completely different state of the world in a very small number of iterations.

Millions of years is a really long time for the “compound interest” to take effect.

And remember the old saying: For want of a nail the shoe was lost.

For want of a shoe the horse was lost.For want of a horse the rider was lost.For want of a rider the battle was lost.For want of a battle the kingdom was lost.And all for the want of a horseshoe nail.

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Hang onto your hats...Hang onto your hats... Next week we’re going to see the fractal dimension rear

its Hydra-like head again!

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