Double Pendulums - Chaotic, and Visualized

Pendulums - a weight suspended from a pivot point - are easy.  You learn about them pretty early on in physics, and move on to other stuff pretty rapidly
But a double pendulum - a pendulum with another pendulum attached to its end - well boy howdy, is it ever  something else!
via Revolution Analytics, we have this awesome animated gif of a double pendulum in action - chaos personified.

For more detail, go check out Wikipedia, which will tell you such fun stuff as

[a double pendulum] is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions.^[1] The motion of a double pendulum is governed by a set of coupled ordinary differential equations. For certain energies its motion is chaotic.

and so on. Fun stuff!

(the below is what you get when you stick LEDs on one of them...)