Fractional Brownian Motion

Fractional Browniam motion, fBm, is a generalization of Brownian motion in which the increments no longer are independent.
First, we present the basic idea of fBm, and a visual comparison with Brownian motion.
Fractional Brownian motion occurs in many types, related to one another through an index H.
Here is a method for simulating fBm.
The index H can be interpreted as a measure of the roughness.
Here are some examples of fBm in the plane.
Fractional Brownian motion includes correlations between events, but retains the short tails of the normal distribution.

Return to Random Fractals.