Symmetric Chaos in the Complex Plane

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.

This Demonstration shows symmetry-restoring bifurcations of a nonlinear complex map: , with , and and varying. The iteration starts at ; 10,000 points are visited and the first 10 iterations are discarded.

Contributed by: William Shaw (August 2007)
Open content licensed under CC BY-NC-SA



This Demonstration is an animation of the symmetric icons first seen in the beautiful book Symmetry in Chaos: A Search for Pattern in Mathematics, Art and Nature by M. Field and M. Golubitsky and developed in Complex Analysis with Mathematica, Chapter 7, "Symmetric chaos in the complex plane". Further information about the latter book is at its web page. This particular animation is tailored to showing the creation of symmetry through birfucation. You can also read about this in The Mathematica Journal (see the related links).

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.