Deterministic Chaos - Advanced |
Cat Mapping: A transformation equation is applied to an image of a cat. Although many of the frames appear to contain rather random images, some frames contain ghost-like images of the cat. After 300 iterations, the original image returns. This type of transformation is called "invertible." |
Here's a FAQ about non-linear systems that includes sections on chaos. This site has an algebraic introduction to the mathematics of chaos. It also has a nice applet for investigating bifurcations about halfway down the page. A handful of applets -- driven pendulum, chaos wedge, double pendulum, diode resonator and coupled resonator are examples of dynamic systems that become chaotic. The mathematics discussed with each example do require some knowledge of calculus. Physicists (and others) use the idea of the "Standard Map" to describe chaotic systems. An easy-to-understand introductory tutorial and applet can be found here. How science comprehends chaos - a lecture explaining chaos and other nonlinear complexities as well as how such phenomena fit into the scientific framework. |
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