fractal.dim {RandomFields} | R Documentation |
The function estimates the fractal dimension of a process
fractal.dim(x, y = NULL, z = NULL, data, grid=TRUE, gridtriple = FALSE, bin= seq(min(ct$x[3, ]) / 2, min((ct$x[2,]-ct$x[1,]) / 4, vario.n * min(ct$x[3,]) + 1), min(ct$x[3,])), vario.n=5, sort=TRUE, fft.m = c(65, 86), ## in % of range of l.lambda fft.max.length=Inf, fft.max.regr=150000, fft.shift = 50, # in %; 50:WOSA; 100: no overlapping method=c("variogram", "fft"), mode=c("plot", "interactive"), pch=16, cex=0.2, cex.main=0.85, PrintLevel = RFparameters()$Print, height=3.5, ...)
x |
matrix of coordinates, or vector of x coordinates; if
|
y |
vector of y coordinates |
z |
vector of z coordinates |
data |
the values measured. |
grid |
determines whether the vectors |
gridtriple |
logical. Only relevant if |
bin |
sequence of bin boundaries for the empirical variogram |
vario.n |
first |
sort |
If |
fft.m |
numeric vector of two components; interval of frequencies for which the regression should be calculated; the interval is given in percent of the range of the frequencies in log scale. |
fft.max.length |
The first dimension of the data is cut into pieces
of length |
fft.max.regr |
If the |
fft.shift |
This parameter is given in percent [of
|
method |
list of implemented methods to calculate the fractal dimension; see Details |
mode |
character. A vector with components 'nographics', 'plot', or 'interactive':
Usually only one mode is given. Two modes may make sense in the combination c("plot", "interactive") in which case all the results are plotted first, and then the interactive mode is called. In the interactive mode, the regression domain is chosen by two mouse clicks with the left mouse; a right mouse click leaves the plot. |
pch |
vector or scalar; sign by which data are plotted. |
cex |
vector or scalar; size of |
cex.main |
The size of the title in the regression plots. |
PrintLevel |
integer. If |
height |
height of the grahics window |
... |
graphical parameters |
The function calculates the fractal dimension by various methods:
variogram method
Fourier transform
The function returns a list with elements
vario
,
fft
corresponding to
the 2 methods given in the Details.
Each of the elements is itself a list that contains the following elements.
x |
the x-coordinates used for the regression fit |
y |
the y-coordinates used for the regression fit |
regr |
the return list of the |
sm |
smoothed curve through the (x,y) points |
x.u |
|
y.u |
|
regr.u |
|
D |
the fractal dimension |
D.u |
|
Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/~schlather
variogram method
Constantine, A.G. and Hall, P. (1994) Characterizing surface smoothness via estimation of effective fractal dimension. J. R. Statist. Soc. Ser. B 56, 97-113.
fft
Chan, Hall and Poskitt (1995)