Chaos Lab Home · Explorer · Chaos Art
Explorer · Grades 3–4

Chaos Art

We tied a paintbrush to the end of a swinging double pendulum. Press Paint and watch it draw a picture that has never existed before — and will never be made the exact same way again.

Paint

Colors

Brush

What just happened?

Your picture is one-of-a-kind

Every time you press New painting, the brush starts from a tiny bit different spot — and because the swing is chaotic, that tiny change sends the brush on a completely different journey.

Nobody, anywhere, will ever paint exactly the same picture. Not even you, twice!

The big idea

Same brush, endless pictures

There are no random numbers here. The brush follows the same swinging rules every time. The only thing that changes is where it starts — and that's enough to change everything.

That's the butterfly effect, turned into art. Save your favorite and print it out!

For teachers & grown-ups

The brush rides the tip of a double pendulum (the same chaotic system as the Explorer Double Pendulum tool), integrated with 4th-order Runge–Kutta — no randomness anywhere. "New painting" only nudges the starting angles slightly; sensitive dependence on initial conditions does the rest, so each run produces a visually distinct curve. It's a gentle, memorable entry to the idea that deterministic (rule-following) does not mean predictable. Nice extension questions: can you ever get two paintings to look the same? (Only by starting from the exact same numbers — which the "New painting" button never does.) Why does the picture stay inside a roughly circular region? (The pendulum's reach is fixed — a physical attractor boundary.)