Is this double pendulum simulator free?

Yes. It runs free in your web browser on WebGL 2, with no install, no account and no ads. On a slower device it releases fewer pendulums to keep the motion smooth.

Is the physics exact?

Yes. Each pendulum's equations of motion are solved step by step with the standard Runge-Kutta method, and the runs are deterministic: the same start always gives the same swing. Only the starting angles differ, by about a billionth of a radian.

Is this a strange attractor?

No. A double pendulum without friction doesn't settle onto an attractor; it keeps its energy and wanders. The strange attractor simulator on this site shows a different kind of chaos, where every path is drawn onto the same shape.

Where's the full version?

The Everdust app has many more live worlds of physics and space. It is free on the App Store for iPhone, iPad and Apple Vision Pro, on Google Play for Android and on the Meta Horizon Store for Meta Quest.

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Pendulums · I

Double pendulum simulator: the butterfly effect

1,500 double pendulums swing as one white pendulum for a few seconds, then fan out into a rainbow bloom.

Drag to turn it, pinch or scroll to zoom, double-tap to reset.

The idea: Chaos for real: the pendulums start a billionth of a radian apart, and the exact physics amplifies that invisible difference until they all go their own way. A new release every 20 seconds.
With music: Kicks flash the bobs, arms and trails; vocals lengthen the trails; treble makes the bobs sparkle. Tap Demo beat for our own beat, or Your music to let it hear the room.
How it runs: It’s the same live simulation as in the Everdust apps, running in your browser on WebGL 2. If your device struggles, it lowers the detail a step at a time to keep the motion smooth.

Why is a double pendulum chaotic?

A single pendulum is the picture of predictability: it swings back and forth at a steady rhythm, which is why it was used to keep time for centuries. Hang a second pendulum from the end of the first, and everything changes.

The two arms trade energy back and forth, and the motion never settles into a pattern. Worse, it depends on the starting position with extreme sensitivity. Start two double pendulums at angles that differ by a billionth of a radian, far less than any ruler could measure, and for a few seconds they swing together. Then the tiny difference grows, roughly doubling again and again, until the two have nothing in common.

That is chaos in the mathematical sense: completely fixed rules, no randomness at all, yet the future can't be predicted far ahead because the starting point can never be known exactly enough. It is the same reason weather forecasts run out after about two weeks.

Here 1,500 double pendulums are released a billionth of a radian apart. Each one follows the exact equations of motion, so you see them move as one white pendulum, then bloom into a rainbow fan. A new release starts every 20 seconds. Our blog post on double pendulums and chaos goes deeper.

Questions

Is this double pendulum simulator free?: Yes. It runs free in your web browser on WebGL 2, with no install, no account and no ads. On a slower device it releases fewer pendulums to keep the motion smooth.
Is the physics exact?: Yes. Each pendulum's equations of motion are solved step by step with the standard Runge-Kutta method, and the runs are deterministic: the same start always gives the same swing. Only the starting angles differ, by about a billionth of a radian.
Is this a strange attractor?: No. A double pendulum without friction doesn't settle onto an attractor; it keeps its energy and wanders. The strange attractor simulator on this site shows a different kind of chaos, where every path is drawn onto the same shape.
Where's the full version?: The Everdust app has many more live worlds of physics and space. It is free on the App Store for iPhone, iPad and Apple Vision Pro, on Google Play for Android and on the Meta Horizon Store for Meta Quest.

This is one world, in your browser

The full version is in the Everdust app.

The app has many more live worlds at full detail, games built on the same physics and narrated stories you step inside. It’s free to download, with no ads, on the App Store for iPhone, iPad, Apple Vision Pro and Apple TV, on Google Play for Android phones and tablets, on the Meta Horizon Store for Meta Quest and from everdust.ai for Mac.