Chaos
by Manfred Füllsack
This model illustrates the creation of "deteministic chaos", or, in other words, the limits of predictability.
Pushing one of the buttons <lorenz>, <roessler>, <tinkerbell> or <logistic> followed by the <go>-button generates the respective chaotic map. On "lorenz", "roessler" and "tinkerbell", you can vary the maps by moving the sliders that are not set on zero. Note for example, how the roessler-curve chaotically leaves it's attraction orbit when the a-slider is moved just slightly to the right. The buttons <x/y>, <x/z> and <y/z> let you change perspectives.
Pushing the button <n-bodies> demonstrates the possibility of chaos when more than two dynamics interact - shown on the example of three bodies attracting each other.
The <n-bodies>-button positions two bodies on an orbit around the center of the display. The <go>-button makes them cycle. When switching on the <gravity>-switch the bodies start attracting each other with the factor that is set on the <attraction>-slider. Note that when leaving the attraction-factor as initially positioned (on 13) the bodies will produce a nice pattern that hardly anybody would call a chaos. For making this more distinct, you can speed up the movement with the <speed>-slider at the top of the display.
Now switch off <gravity> again and change the <bodies>-switch to "3". Pushing <setup> now will produce three bodies, <go> makes them cycle again. See what happens when you turn on the <gravity>-switch. Speed up and watch the plot recording the distance of the bodies.
Check out various attraction-factors, for example 50 and see how the three bodies after some time of chaos eventually find trajectories along which they seem to settle.
For more details on Chaos Theory and other examples see:
Robert Doerner's Chaos interaktiv
Peter Selinger's Double Pendulum
Jack Hardie's Swinger (not exactly chaos, but very beautyful)
Related and also quite nice: Fractals
Code by Manfred Füllsack (source code on demand), Sept. 2008 (enhanced April 2009)