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Logistic Map: Onset of Chaos

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The logistic map is . By manipulating , you can view the onset of chaos in simple quadratic maps. By manipulating the seed under chaotic regimes (such as ), you can explore sensitive dependence on initial conditions.

Contributed by: Phil Ramsden (March 2011)
Open content licensed under CC BY-NC-SA

Snapshots

Details

Snapshot 1: convergence on a fixed point

Snapshot 2: convergence on a 2-cycle

Snapshot 3: convergence on a 4-cycle

Snapshot 4: convergence on a 6-cycle

Snapshot 5: apparent chaos

Snapshot 6: effect of small change in initial conditions in an apparently chaotic regime

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