What is the Lorenz attractor?
The path traced by three linked equations Edward Lorenz used to model convection. It loops forever in a butterfly shape without ever repeating.
// maths › Chaos & Dynamics
Lorenz Attractor
The Lorenz system traced in 3D - a never-repeating 'butterfly' that shows why tiny changes make weather hard to predict.
the butterfly effect in 3D
A mind behind this: Edward Lorenz 1917–2008
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Frequently asked questions
What is the butterfly effect?
Tiny differences in starting conditions grow into completely different outcomes - the reason long-range weather forecasts are uncertain.
Is chaos the same as randomness?
No. The system is fully deterministic - the same start gives the same path - but it is so sensitive that prediction quickly breaks down.
Where does this matter?
Weather and climate modelling, population biology, electronics and even heart-rhythm studies.
Why does it look like a butterfly?
The trajectory orbits two centres and swaps between them unpredictably, tracing two wing-like lobes.