The tighter you hold on, the more things fly apart.
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.
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.