Brownian Motion and Random Walks

Theory

A large particle, randomly bombarded by invisible molecules, performs a random walk. Einstein (1905) showed that the mean squared displacement grows linearly with time: $⟨x^2⟩=2Dt$ — confirmed by Perrin, proving that atoms are real.

What to observe

• The orange path is irregular and never repeats.

Try this

• Raise the temperature: the grain jiggles more.

Also available in: Movimento browniano e passeio aleatório (Português) · Movimiento browniano y caminata aleatoria (Español)