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Double Pendulum Chaos

Time 0.0 s
Start 0°
Energy - drift 0%
Split apart at not yet gap 0 mm

How to play

  1. Drag a bob to where you want it to start. Let go.
  2. Watch: at first all the pendulums move as one.
  3. Wait for the moment they split apart.
Do thisPhoneKeyboard
Set the startDrag a bob← → top rod, ↑ ↓ bottom rod (on the stage)
Play / PausePause buttonP
Start againResetR
Random startNew startN

What's happening?

  • Every pendulum starts just 0.001° further round than the last. That's far too small to see.
  • The computer uses the exact same rules for all of them. No randomness at all.
  • But a double pendulum is chaotic: tiny differences grow, doubling again and again.
  • Watch the gap readout. It grows from a hair's width to a whole swing.
  • The energy stays the same the whole time. That shows the maths is honest, not making things up.
  • This is why weather can't be forecast weeks ahead: we can never measure the start perfectly.

Try this: start both rods hanging only a little way out (drag a bob just off the bottom). Do they ever split? Now try a big swing.