The Perturbed Rat

Recently, Blanchard, Devaney, Garijo, and Russell have studied rational maps of the form , where and are complex-valued parameters. This Demonstration considers the special case when and . When both the real and imaginary parts of are equal to zero, we obtain a Julia set called "the rat". When is nonzero, there is a pole of order three at the origin that changes the structure of the Julia set and perturbs the rat.


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


When is sufficiently small, the Julia set has a structure analogous to a Cantor set of simple, closed curves for the map , for . This family of maps ("the rat maps") generalizes a result of Kurt McMullen.
To make higher-quality pictures, download the source notebook, increase the number of iterates, and decrease the step size used to create the mesh of points in the complex plane.
P. Blanchard, R. L. Devaney, A. Garijo, and E. Russell, "A Generalized Version of the McMullen Domain," International Journal of Bifurcation and Chaos, 18(8), 2008 pp. 2309–2318.
    • 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+