Katz fractal dimension

Katz fractal dimension \(D = \\log_{10}(n - 1) / (\\log_{10}(n - 1) + \\log_{10}(d / L))\) of a 1-D signal. \(L\) is total path length and \(d\) is the diameter (max distance from the first sample).

Usage

kfd(x)

Arguments

x

Numeric vector.

Value

List with value (D), name, and extra (L, d, n).

Details

Reference: Katz, M.J. (1988) "Fractals and the analysis of waveforms", Comput. Biol. Med. 18(3):145–156.

Examples

# \donttest{
set.seed(1)
x <- cumsum(rnorm(1000))
res <- kfd(x)
res$value
#> [1] 2.142683
# }