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This page isn't intended to give an (even brief) overview of chaos and non-linear dynamics. For that, try a few of the following links:
I also have a DVD of an old (1989) NOVA series documentary "The Strange New Science of Chaos" that you are free to borrow if you wish. It's 60 minutes long. It gives a nice introduction to the ideas of chaos and non-linear dynamics and the topics of study encompassed in this branch of science. Or, better yet, go watch it in the library.
I also recommend reading the book "Chaos: making a new science" by James Gleick. This is easy reading and quite informative. This book was one of my earliest exposures to the subject. The library owns 8(!) copies.
The links and activities below are intended to give you a tiny glimpse of what's "cool" about non-linear systems and to give you a little taste of what it would be like to do a senior thesis or independent study experience in this field.
Using Matlab (no programming required), try the following exercises that I gave to a Freshman Seminar class. (Come talk to me if you have trouble with the Matlab scripts.)
Cornstarch movie: Watch the video about what happens when a little cornstarch is mixed with water and vibrated...It 's real surprising. (Turn up the volume, there is audio too...)
Avalance movie: This is a visualization of Per Bak's sandpile model. Black squares = no sand, dark = 1 grain, light = 2 grains, white = 3 grains. Red squares show the avalanche front. Different colored shadings indicate different avalanche events.
Bifurcation Difference movie: Shows the *difference* between the attractors (bifurcation diagram) of two logistic maps coupled together in a master-slave configuration, as a function of increasing coupling strength (denoted "alpha" in the plots).
Scatter plot animation: Shows the "scatter plot", animated as a function of the coupling parameter alpha, for the master-slave-couped logistic maps system.
Scatter plot animation: Same as above but for a symmetrically-coupled system. Animation 2: same except for a narrower range of the coupling parameter.
Diffraction: Diffraction simulation for a double slit experiment