# One-Dimensional Fractional Brownian Motion

One-Dimensional Fractional Brownian Motion

Two methods for generating a fractional Brownian motion to simulate a natural surface are demonstrated here. The Hurst exponent describes the raggedness, with higher exponents leading to smoother surfaces. 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, coastlines, and clouds. It has the scaling property . Ordinary Brownian motion has .

h

V(t)-V(t+dt)∝

h

dt

h=

1

2