Wolfram Demonstrations Project

12,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Logistic Map: Onset of Chaos

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send