Random Walk & Brownian Motion

Explore stochastic processes: from discrete random walks to continuous Brownian motion, Levy flights, and self-avoiding walks.

Controls

Number of Steps 500

Simultaneous Walks 3

Step Size 1.0

Animation Speed 50

Mean Displacement

RMS Displacement

Max Displacement

Theoretical RMS (sqrt(n))

Diffusion Coeff D

Walks Completed

Connection to the Heat Equation: ∂u/∂t = D ∇²u — The probability density of a random walker satisfies the diffusion (heat) equation as step size → 0.