Chapter 8
Fractional Brownian Motion

Overview

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.

Programs

fBm.m

Notebooks

fBm.nb

Color Plates

Plate 3-a

Plate 3-b

Resources on the Internet

Alta Vista search

Use Alta Vista to search for Web pages about fractional Brownian motion.