Two-dimensional fractional brownian motion

Educação Superior::Ciências Exatas e da Terra::MatemáticaEnsino Médio::MatemáticaTwo 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)|αdt^h. Ordinary Brownian motion has h=1/