Description Usage Arguments Details Value References See Also Examples
The function estimates the fractal dimension of a process
1 2 3 4 5 6 7 8 9 10 11 12 13 14  RFfractaldim(x, y = NULL, z = NULL, data, grid,
bin=NULL,
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 = if (interactive ()) c("plot", "interactive") else "nographics",
pch=16, cex=0.2, cex.main=0.85,
printlevel = RFoptions()$basic$printlevel,
height=3.5,
...)

x 
\argX If

y,z 
\argYz 
data 
the values measured; it can also be an sp object 
grid 
\argGrid 
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 argument is given in percent [of

method 
list of implemented methods to calculate the fractal dimension; see Details 
mode 
character. A vector with components
Usually only one mode is given. Two modes may make sense
in the combination 
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 graphics window 
... 
graphical arguments 
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 xcoordinates used for the regression fit 
y 
the ycoordinates 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 

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, 97113.
fft
Chan, Hall and Poskitt (1995)
1 2 3 4 5 6  RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
x < seq(0, 10, 0.001)
z < RFsimulate(RMexp(), x)
RFfractaldim(data=z)

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