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Two-Dimensional Fractional Brownian Motion

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method
random additions
Fourier synthesis
points
20
Hurst exponent h
0.5
randomize
Two methods for generating a fractional Brownian motion to simulate a natural surface are demonstrated here. The Hurst exponent
h
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
V(t)-V(t+dt)∝
h
dt
. Ordinary Brownian motion has
h=
1
2
.
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