So today in class when we were talking about chaos, I attempted to describe this gif:
It's pretty cool and illustrates lag pretty well. The top rod goes back and forth (duh) but the bottom rod lags behind and over compensates for the changes, leading to the cool pattern. According to wikipedia this is "one of the simplest dynamical systems that has chaotic solutions." The article has lots of math, but some other very cool visuals, some of which I do not understand.
Also this shell apparently looks like a representation of chaos called rule 30, which was developed by the guy behind Wolfram Alpha. If you're looking for a fin Wikipedia hole to fall down, chaos theory is a good place to start.