The Fractal Note Gallery at the Visual Math Institute

This project extends the work reported in the book Chaos in Discrete Dynamical Systems (aka JPX) by Ralph Abraham, Laura Gardini, and Christian Mira, 1997. The studies reported in this book concern two families of simple mappings of the euclidean plane into itself. Both are defined by quadratic polynomials in two variables. Hence the acronym JPX, for Just Plane Chaos.

Our extension here is based on the extensive computations of Julian C. Sprott reported in his book Strange Attractors (aka SA) of 1993. These attractors:

• extend quadratic attractors from the simple cases of JPX into the most general cases,
• extend from quadratic polynomials to polynomials of degrees 3, 4, and 5, and
• extend from two dimensions (2D) to three (3D) and beyond.

Our primary focus in this project is on the bifurcations of these attractors as one of the polynomial coefficients is varied. These bifurcation sequences are presented as short movies, usually at a rate of ten frames per second. The occurence of windows of periodic (nonchaotic) behavior is of special interest from the point of view of bifurcation theory. Some of our movies have a sound track, each frame accompanied by one tenth of a second of granular audio data (100 samples) encoded at 1000 samples per second.

The primary engine of research in this project is NetLogo, with some help from MATLAB.

We are also interested in the application of our images, animations, and sounds in the sphere of digital art.

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