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
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
"Logistic Map: Onset of Chaos"
Wolfram Demonstrations Project
Published: March 7 2011