Two pendulums chained together. Tiny changes in starting position lead to wildly different paths — chaos.
Two double pendulums start with positions differing by less than a degree. After a few seconds, their motions are completely different. Why?
two double pendulums released a hair apart (0.02 rad). They track together for a moment, then diverge completely — tiny differences blow up. That's deterministic chaos; hit Reset to see it again.
Deterministic but unpredictable
Each pendulum's motion is fixed by Newton's laws — no randomness anywhere. But the slightest uncertainty in where it starts blows up so fast that, in practice, you can't say where it'll be a few seconds later. Chaos isn't disorder; it's order that's *exquisitely* sensitive.
Same idea behind the 'butterfly effect' in weather — the atmosphere is a giant chaotic system, which is why forecasts fade out after about a week.
Hallmarks of chaos
- Sensitive dependence on initial conditions.
- Fully deterministic equations — no luck involved.
- Bounded motion that never exactly repeats.
- Appears in weather, populations, fluids, even some electrical circuits.