Finding Strange Attractors of Iterated Maps

This Demonstration searches for strange attractors of a nonlinear two-dimensional polynomial map. Both the and the polynomial maps of degree are defined by coefficients , one for each term , , .
To find an attractor, we compare two orbits of the map with the same coefficients but starting from nearby initial points. If the orbits become unbounded or move apart, another set of random coefficients is selected. If successive iterations move the orbits increasingly closer together, an attractor is detected and plotted and the search is stopped.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The strange attractors from the map used in this Demonstration and many others are described extensively in [1].
[1] J. C. Sprott, Strange Attractors: Creating Patterns in Chaos, New York: M&T Books, 1993.
    • 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 »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
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+