Logistic Map: Onset of Chaos

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.

SNAPSHOTS

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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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Related Curriculum Standards

US Common Core State Standards, Mathematics