The Mathematica Programmer

Fractional Brownian Motion

Volume 6, Issue 1
Winter 1996

Fractional Brownian motion is a generalization of ordinary Brownian motion that has been used successfully to model a variety of natural phenomena, such as terrains, coast lines, and clouds. We shall briefly describe the theory behind fractional Brownian motion and then look at three methods to generate such data in Mathematica. These methods pose a number of interesting programming problems. We shall also develop methods to visualize fractional Brownian motion, in Mathematica and with external renderers.