where 𝜎 Δ𝑥 𝐵 2 , 𝜎 Δ𝑦 𝐵 , and 𝜎 Δ𝑧 𝐵 2 are the variance of displacements in x, y, and z axis due to Brownian motion, respectively, and 𝑘 𝐵 is the Boltzmann's constant. From Equations ( ) and ( ), the random displacement due to Brownian motion is calculated by generating displacements that follow a probability distribution with a mean of zero and a variance of