**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*