Brownian motion is the chaotic motion of small particles in a liquid or in a gas. Brownian motion is caused by the collisions of molecules. The amount of these collisions is directly related to temperature.
Albert Einstein is credited for creating the kinetic theory of Brownian motion. The main implication of this theory is the fact that the square of the displacement < r2 > of a Brownian particle from its initial state, averaged over many Brownian particles, changes in direct proportion with time (in accordance with the law of diffusion). The coefficient of proportionality, in turn, is proportional to the absolute temperature, T.
The computer model you now see in front of you shows the chaotic motion of a Brownian particle. The computer determines the coordinate of a given Brownian particle over equal intervals of time, and calculates the square of its displacement from the state of equilibrium, averaged over the previous calculations of its coordinates. After 100 of such steps, the computer automatically switches to another particle.