midpoint {FieldSim}R Documentation

Fractional Brownian field simulation by the midpoint displacement method

Description

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

Usage

midpoint(H,nblevel=8)

Arguments

H a real in ]0,1[. H is the Hurst parameter of the fractional Brownian field to simulate.
nblevel a positive integer. nblevel is the level associated with the regular space discretization of the following form: [[0:2^{nblevel}]/2^{nblevel}]^2.

Details

The subspace [0,1] x [0,1] is discretized in a regular space discretization of size (2^{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

A list with the following components:

Zrow the vector of length 2^{nblevel}+1 containing the discretization of the x axis.
Zcol the vector of length 2^{nblevel}+1 containing the discretization of the y axis.
Z the matrix of size (2^{nblevel}+1)x(2^{nblevel}+1) in such a way Z[i,j] containing the value of the process at point (Zrow[i],Zcol[j])
time the CPU time

Author(s)

Alexandre Brouste (http://ljk.imag.fr/membres/Alexandre.Brouste) and Sophie Lambert-Lacroix (http://ljk.imag.fr/membres/Sophie.Lambert).

References

A. Fournier, D. Fussel and L. Carpenter (1982). Computer rendering of stochastic models. 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

quadvar,fieldsim

Examples

# load FieldSim library
library(FieldSim)

# Simulation
# H=0.3
res <- midpoint(H=0.3,nblevel=8)
# Plot
x <- res$Zrow
y <- res$Zcol
z <- res$Z
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")

[Package FieldSim version 1.2 Index]