For the curious kid.
A playground swing is easy to predict: push it, and it swings back and forth, back and forth. Boring, in the best way.
This machine is just two swings, one hanging off the end of the other. That tiny change breaks prediction completely. Drag the lower weight up high, let go, and watch: it doesn't repeat, it doesn't settle, it flips and lurches like it's making it up as it goes. Nothing is random in there (the machine follows exact rules with no dice anywhere) and still, no one on Earth can tell you what it will be doing one minute from now.
Want proof? Press Summon the twin. A ghost pendulum appears, started in almost exactly the same spot, off by less than the width of a hair. For a few seconds they dance together. Then they disagree. Then they've never heard of each other. That's what "chaos" means to a scientist: not messiness, sensitivity. The tiniest difference in how things start grows into a completely different future.
Deeper.
The double pendulum is one of the simplest mechanical systems that is genuinely chaotic. It is fully deterministic (its motion follows from the Euler-Lagrange equations of a two-degree-of-freedom system), yet nearby trajectories separate exponentially fast, at a rate measured by its largest Lyapunov exponent. Doubling your measurement precision doesn't double your forecast horizon; it buys you only one more sliver of it. That's the practical wall weather forecasters hit: not ignorance of the laws, but arithmetic of error growth.
Two honest details about what you're watching. First, at low energies (let both arms hang nearly straight down and nudge them) the system is not chaotic; it swings in orderly, almost-periodic patterns. Chaos lives at high energy, when the second arm can flip over the top. Order and chaos are both in here, in different rooms of the same house. Second, the simulation integrates the exact equations of motion with a fourth-order Runge-Kutta method and no friction, so energy is very nearly conserved. What looks like wildness is not error piling up; it is the honest solution doing what the mathematics demands.
The present determines the future, but the approximate present does not approximately determine the future. (After Edward Lorenz.)