Bifurcation Diagram of the Hénon Map

The Hénon map is the two-dimensional map described by the equations
The plot shows the last 36 coordinates after iterations of the Hénon map using the initial point .
To obtain an interesting region of periodic and chaotic behavior, we use values between 0.91 and 1.41 with . Changing these values will give very similar results.
You can click anywhere in the diagram to see a magnified inset in the lower-left corner.



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


Using the lowest values for and will let you quickly find an appropriate region to inspect. Larger values will show a cleaner, more detailed plot.
The idea for the Locator-magnifier was taken from Ed Pegg Jr.
    • 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 © 2018 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+