voss1g {Voss}

Fractal Brownian function on 1D grid with a generic Voss algorithm

Description

voss1g() function generates realizations of a fractal Brownian function on uniform 1D grid (FBF(x)) with a generic version of the Voss algorithm (random sequential additions).

Usage

voss1g(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 1D grid is based on an iterative partitioning of the initial segment into smaller subsegments by linear 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

Moskalev P.V. (2008) Visualization of wavelet spectra of fractal Brownian motion, Technical Physics, Vol.53, No.10, pp.1261-1266, doi:10.1134/S1063784208100022.

See Also

voss2g, voss1d

Examples

# Example 1: FBF(x) with a s[i]=dchisq(i,df=2)
set.seed(20120522)
plot(voss1g(), type="l", xlab="x", ylab="y",
     main="FBF(x) with a s[i]=dchisq(i,df=2)")
abline(h=0, lty=2)

# Example 2: FBF(x) with a s[i]=dlnorm(i,sdlog=1)
set.seed(20120522)
voss <- voss1g(p=cbind(n=0.5^-seq(0,7)+1,
                            s=dlnorm(seq(0,7), sdlog=1)))
plot(voss, type="l", xlab="x", ylab="y",
     main="FBF(x) with a s[i]=dlnorm(i,sdlog=1)")
abline(h=0, lty=2)

# Example 3: FBF(x,y) with a s[i]=df(i,df1=7,df2=7)
set.seed(20120522)
voss <- voss1g(p=cbind(n=0.5^-seq(0,7)+1,
                            s=df(seq(0,7), df1=7, df2=7)))
plot(voss, type="l", xlab="x", ylab="y",
     main="FBF(x) with a s[i]=df(i,df1=7,df2=7)")
abline(h=0, lty=2)