- Have a look at Alexis Brandeker's pages (specifically his MSc thesis), among many on the Internet with sources for generating multidimensional fBm (power law) distributions, including multifractals.

The link is http://www.astro.su.se/~alexis/. You may want to write him for the C code.

The 1D fBm (and fGn) time series are just generalisations of n-dimensional fractal distributions.

Annealing is fine as well.

Cheers

Syed

On Monday, June 13, 2005, at 12:17PM, Peter Bossew <Peter.Bossew@...> wrote:

>Hi list,

>

>I need to generate a field f(x,y) with given variogram. More precisely, I

>have N points (x,y) and I want to assign f(x,y) such that the variable f

>has a spatial autocorrelation structure according to a given variogram

>model.

>

>My impression is that the way to do it is simulated annealing, as

>described in chapter 11 of the GSLIB manual. Is that correct ? Any other

>methods ? Is there any easy-to-use & free software for this purpose ? Any

>recommended literature ?

>

>For time series (1-dim case with regular grid) there is the possibilty of

>random walk, or more generally Levy flights to produce autocorrelated

>series, or alternatively, define a Fourier spectrum with given slope of

>the continous log-log power spectrum and inverse transform. Is there an

>analoguos technique for the 2- (or n-) dim. case ?

>

>A possibly related question: How to produce a field with given (geometric

>or stochastic) multifractal structure ?

>

>

>Thanks for any hint

>Peter

>

>

>=================================================================

>Dr. Peter Bossew

>Department of Physics and Biophysics, University of Salzburg, Austria

>

>peter.bossew@...

>peter.bossew@...

>

>

>

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> > Hi list,

It is easy to simulate a Gaussian random field of given geometry with

>

> I need to generate a field f(x,y) with given variogram. More precisely, I

> have N points (x,y) and I want to assign f(x,y) such that the variable f

> has a spatial autocorrelation structure according to a given variogram

> model.

>

> My impression is that the way to do it is simulated annealing, as

> described in chapter 11 of the GSLIB manual. Is that correct ? Any other

> methods ? Is there any easy-to-use & free software for this purpose ? Any

> recommended literature ?

given spatial correlation function using the package RandomFields, in the

free GNU statistical system R. For example, i could make N.sim such random

fields with a Gaussian variogram and save them all as text files with

these lines of code:

--------------

mcolasim9<-function(N.sim){

#Grid definition

x<-seq(1,180,1)

y<-seq(1,540,1)

#Variogram model

param<-c(6.63,2.24,1.82,4.36)

#Major loop

for(i in 1:N.sim){

mcola<-GaussRF(x=x,y=y,param=param,grid=TRUE,model="gauss")

file1.out<-paste("mcolasim9",i,"txt",sep=".")

write(t(mcola),file1.out,ncol=ncol(t(mcola)))

}

}

---------------

RandomFields will use simulated annealing if convenient but will use

another method if this other method is best for the case at hand, and will

select the method automatically. You can also force RandomFields to use a

given method if you want.

In R 2.1.0, from

citation("RandomFields")

i get

Martin Schlather, (). RandomFields: Simulation and Analysis of

Random Fields. R package version 1.2.16.

http://www.unibw-hamburg.de/WWEB/math/schlath/schlather.html

Cheers,

Ruben