Brownian web Brownian web In probability theory, the Brownian web is an uncountable collection of one-dimensional coalescing Brownian motions, starting from every point in space and time. It arises as the diffusive space-time scaling limit of a collection of coalescing random walks, with one walk starting from each point of the integer lattice Z at each time. What is now known as the Brownian web was first conceived by Arratia in his Ph.D. thesis and a subsequent incomplete and unpublished manuscript. Arratia studied the voter model, an interacting particle system that models the evolution of a population's political opinions. The individuals of
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