Einstein 1905: ⟨r²⟩ = 4Dt in 2D. Each particle takes random steps; the mean squared displacement grows linearly with time, letting us extract D = k_BT / (6πηa). This is how Perrin measured Avogadro's number.
Watch trajectories (left) and mean squared displacement vs. time (right). The slope of ⟨r²⟩ vs t gives 4D. Each colored particle is one Perrin-style colloid.