2D Random Walk & Diffusion
Multiple walkers diffusing from origin — track MSD and compare to theory ⟨r²⟩ = 4Dt
Steps: 0
MSD: 0.00
Theory: 0.00
Walkers: 50
Diffusion: A 2D random walk with step size σ yields mean squared displacement ⟨r²⟩ = 4Dt where D = σ²/2 is the diffusion coefficient.
Each walker takes a step in a random direction each timestep. The left panel shows walker positions (colored by age) and trails.
The right panel plots MSD vs. time (green) against the theoretical prediction 4Dt (dashed white). Deviations arise from finite-sample noise.
This is the continuum limit of Brownian motion — connecting microscopic randomness to macroscopic heat flow (Einstein 1905).