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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.
Contributed by:
Phil Ramsden
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
RELATED LINKS
Chaos
(
Wolfram
MathWorld
)
Logistic Map
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Logistic Map: Onset of Chaos
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/LogisticMapOnsetOfChaos/
Contributed by:
Phil Ramsden
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Related Topics
Chaos Theory
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Related Curriculum Standards
US Common Core State Standards, Mathematics
HSF-BF.A.1
HSF-IF.A.1
HSF-IF.A.3
HSF-IF.B.4
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