Brownian motion itself can be described approximately by a Langevin equation, an equation which involves a random force field representing the effect of the thermal fluctuations of the solvent on the Brownian particle. On long timescales, the mathematical Brownian motion is well described by a Langevin equation. On small timescales, inertial effects are prevalent in the Langevin equation. However the mathematical "Brownian motion" is exempt of such inertial effects. Note that inertial effects have to be considered in the Langevin equation, otherwise the equation becomes singular. so that simply removing the inertia term from this equation would not yield an exact description,
Brownian surface Brownian surface A Brownian surface is a fractal surface generated via a fractal elevation function. For instance, in the three-dimensional case, where two variables "X" and "Y" are given as coordinates, the elevation function between any two points ("x", "y") and ("x", "y") can be set to have a mean or expected value that increases as the vector distance between ("x", "y") and ("x", "y"). There are, however, many ways of defining the elevation function. For instance, the fractional Brownian motion variable may be used, or various rotation functions may be used to achieve more natural looking surfaces. As with