Fractional Brownian field simulation by the midpoint displacement method

Description

The function midpoint yields simulation of sample path of a fractional Brownian field by the midpoint displacement method.

Usage

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Arguments

process

an object of class process (namely an FBm).

Details

The subspace [0,1] x [0,1] is discretized in a regular space discretization of size (2^{\code{nblevel}}+1)^2. At each point of the grid, the fractional Brownian field is simulated using the midpoint displacement method described for example in Fournier et al. (1982).

Value

an object of class process with the simulated sample path in the corresponding slot values.

Author(s)

Alexandre Brouste (http://perso.univ-lemans.fr/~abrouste/) and Sophie Lambert-Lacroix (http://membres-timc.imag.fr/Sophie.Lambert/).

References

A. Fournier, D. Fussel and L. Carpenter (1982) Computer rendering of stochastic model, Communication of the AMC, 25, 371-384.

H.O. Peitgen and D. Saupe (1998) The science of fractal images, Springer-Verlag.

R.F. Voss (1985) Random fractal forgeries. NATO ASI Series, F17, 805-835.

See Also

fieldsim.

Examples

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# load FieldSim library
library(FieldSim)

plane.fBm<-setProcess("fBm-plane",0.9)
midpoint(plane.fBm)
plot(plane.fBm)