midpoint {FieldSim} | R Documentation |
The function midpoint
yields discretization of sample path of a fractional Brownian field
by the midpoint displacement method.
midpoint(H,nblevel=8)
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. |
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).
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 |
Alexandre Brouste (http://ljk.imag.fr/membres/Alexandre.Brouste) and Sophie Lambert-Lacroix (http://ljk.imag.fr/membres/Sophie.Lambert).
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.
# 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")