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The Mathematica Programmer: Fractional Brownian Motion

Roman Maeder
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Journal / Anthology

The Mathematica Journal
Year: 1996
Volume: 6
Issue: 1
Page range: 38-48

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.

*Mathematics > Discrete Mathematics > Cellular Automata
*Mathematics > Probability and Statistics