The tighter you hold on, the more things fly apart.
Chaos #1
I’m starting a new series based on chaotic dynamical systems.
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Islands of stability
This time I mapped the pendulum angle and time onto the surface of a cone to create a tunnel effect. For the parameter space I’m looking at, you can really see how the paths will converge for a while and then suddenly diverge wildly.
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Sensitive dependence on initial conditions
This next demo highlights the butterfly effect. These curves show the same pendulum as before, this version has the time axis wrapped around the center of the screen and the exponential of the angle as the radius. All the pendulums start at a very similar initial position and for some driving functions they diverge wildly and others they all stay pretty close.
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Now we’re getting somewhere
Ok, I’ve made a few tweaks. Removed a close path call that was adding an extra random line. I’ve played around with the 3d projection and I’ve tweaked the color scheme, line width and alpha settings.