voss1d {Voss}

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

Description

voss1d() function generates realizations of a fractal Brownian function on uniform 1D grid (FBF(x)) with a classic version of the Voss algorithm (random sequential additions).

Usage

voss1d(g=7, H=0.5, r=0.5, center=TRUE)

Arguments

g

a number of iteration.

H

a Hurst parameter: (0<H)&(H<1).

r

a partition coefficient for iteration segments.

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 i.

In the classical version of the Voss algorithm a standard deviation is exponentially distributed by iteration: s[i] <- s0*r^(i*H), where the initial value s0 <- H*log(1/r).

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

voss2d, voss1g

Examples

set.seed(20120522)
plot(voss1d(), type="l", xlab="x", ylab="y",
     main="FBF(x) with a parameter H=0.5")
abline(h=0, lty=2)