text: The simulation on the right was completed using a Brownian dynamics simulation. Starting with a Langevin equation for the system,
  where  is the friction term,  is a fluctuating force on the particle, and  is the amplitude of the fluctuation. At equilibrium the frictional force is much greater than the inertial force, . Therefore, the Langevin equation becomes,
  For the Brownian dynamic simulation the fluctuation force  is assumed to be Gaussian with the amplitude being dependent of the temperature of the system .  Rewriting the Langevin equation,
  where  is the Einstein relation. The integration of this equation was done using the Euler–Maruyama method to numerically approximate the path of this Brownian particle.