MAT517J2 Fractals, Chaos & Complex Systems

This is an optional module for students on the final year of the B.Sc. (Hons) Mathematics with Computing.

Fractals, chaos and complex systems are relatively ‘new kids on the block’ of science. If you want very rough definitions; a fractal is an object which no matter how closely you ‘zoom in’ on it looks the same or similar, and chaos & complexity are about simple things which look like they should be predictable be aren’t (chaos) or look like they couldn’t possibly give rise to anything interesting but do (complex systems).

One of the beauties of these topics is that they are highly visual. For example, the picture at the top of this web page is of the Mandelbrot set, whose infinite structure results from the iteration of the simple map (where z & c are complex numbers).

There are many useful applets and pieces of freeware available over the net, a few of which are-

· Applets to go with one of the recommended texts, The Computational Beauty of Nature by GW Flake (MIT Press 2000).

· Visions of Chaos is an excellent package. The free trial version has an unlimited life which still gives much of the functionality of the full version. One of the many things you can do with this package is generate chaotic music.

· An interactive Koch curve generator.

· An interactive logistic map generator.

Information last updated September 2007