voss2g {Voss}

Fractal Brownian function on 2D grid with a generic Voss algorithm

Description

voss2g() function generates realizations of a fractal Brownian function on uniform 2D grid (FBF(x,y)) with a generic version of the Voss algorithm (random sequential additions).

Usage

voss2g(p=cbind(n=0.5^-seq(0,7)+1,
               s=dchisq(seq(0,7), df=2)),
       center=TRUE)

Arguments

p

a matrix of parameters:
nrow(p) a number of iterations;
p[,"n"] a number of partition points in the iteration process;
p[,"s"] a standard deviation of normal pseudorandom additions;

center

logical; if center=TRUE then the y-coordinates of prefractal points will be centered.

Details

The Voss algorithm on 2D grid is based on an iterative partitioning of the initial domain into smaller subdomains by bilinear interpolation of additional points.

At each iteration, all values of the fractal Brownian function get normal pseudorandom additions with zero mean and standard deviation, which depends on the iteration index s[i].

By default, the iterative distribution of standard deviation in the generic version of the Voss algorithm is equal to the probability density of the chi-square distribution with 2 degrees of freedom: s[i] <- dchisq(i, df=2).

Value

A list of Cartesian coordinates of prefractal points.

Author(s)

Pavel V. Moskalev

References

Shitov V.V. and Moskalev P.V. (2005) Modification of the Voss algorithm for simulation of the internal structure of a porous medium, Technical Physics, Vol.50, No.2, pp.141-145, doi:10.1134/1.1866426.

See Also

voss1g, voss2d

Examples

# Example 1: FBF(x,y) with a s[i]=dchisq(i,df=2)
set.seed(20120522)
voss <- voss2g()
image(voss, xlab="x", ylab="y",
      main="FBF(x,y) with a s[i]=dchisq(i,df=2)")
contour(voss, levels=0, add=TRUE)

# Example 2: FBF(x,y) with a s[i]=dlnorm(i,sdlog=1)
set.seed(20120522)
voss <- voss2g(p=cbind(n=0.5^-seq(0,7)+1,
                       s=dlnorm(seq(0,7), sdlog=1)))
image(voss, xlab="x", ylab="y",
      main="FBF(x,y) with a s[i]=dlnorm(i,sdlog=1)")
contour(voss, levels=0, add=TRUE)

# Example 3: FBF(x,y) with a s[i]=df(i,df1=7,df2=7)
set.seed(20120522)
voss <- voss2g(p=cbind(n=0.5^-seq(0,7)+1,
                       s=df(seq(0,7), df1=7, df2=7)))
image(voss, xlab="x", ylab="y",
      main="FBF(x,y) with a s[i]=df(i,df1=5,df2=5)")
contour(voss, levels=0, add=TRUE)