10217
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
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
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Discrete Logistic Equation
Marek Bodnar
Chaos While Sledding on a Bumpy Slope
Robert M. Lurie
Symmetric Chaos in the Complex Plane
William Shaw
Sledding on a Bumpy Slope: Chaos and Strange Attractor
Robert M. Lurie
IFS: Rotation, Translation, and Scaling
Phil Ramsden
Chaos and Order in the Damped Forced Pendulum in a Plane
Francisco Javier Sanchez Chapado
Pen Falling Off a Finger
Michael Trott
Forced Pendulums with Damping
Rob Morris
Classic Logistic Map
Robert M Lurie
Orbit Diagram of the Logistic Map
Ed Pegg Jr
Related Topics
Chaos Theory
College Mathematics
Dynamical Systems Theory
Browse all topics
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
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+