Time Series and Cobwebs for Arbitrary Recursive Maps on the Unit Interval

Requires a Wolfram Notebook System

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

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The logistic map is probably the most famous and simplest example of a function from the unit interval onto itself that produces chaotic behavior. Images of its time series and cobweb diagrams are iconic to many introductory textbooks on nonlinear dynamics. This Demonstration lets you vary an interpolating function by dragging 2D control points to construct arbitrarily shaped maps from the unit interval to itself.


Some of these functions generate chaos and others do not. By interactively changing the curve, you can learn intuitively what shapes lead to the celebrated period doubling and chaotic behavior. The cobweb diagrams and time series adjust accordingly and instantly.

You can find many interesting scenarios that show the interplay between multiple repellers and attractors, including some intermittence and state-switching behavior. See snapshots and bookmarks for sample settings.

The time direction is upward in the time series plot.

Please avoid placing a control point immediately above another; in such a case there is no interpolating function, so the program slightly resets the points.

You can choose either of two modes to clip when the interpolation function plot goes outside the unit interval range. The first is basic clipping (button "C") and the second is modular clipping (button "M").


Contributed by: Vitaliy Kaurov (April 2013)



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.