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##DATE: 06/07/10
##AUTHOR: Dan McGlinn
##CONTACT: dmcglinn@email.unc.edu
##PURPOSE: to provide algorithims that: 
##1) give an example of how to use the function 'midpoint' from the 
##package 'FieldSim'
##Literature Cited:
##Brouste, A.,  S. Lambert-Lacroix, and J. Istas. 2007.  On Gaussian random fields simulation. Journal of Statistical Software 1:23.
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library(FieldSim) 
##Currently FieldSim must be version 2.1 because the function 'midpoint' is not available in version 3.1 of FieldSim.
##However, Alexandre Brouste told me that he plans to include 'midpoint' on forthcoming releases of this package 
library(dichromat) ##for pretty colors

cls<-colorRampPalette(colorschemes$BluetoOrange.12,space="Lab")(100)

D <- c(2.01,2.5,2.95) ##fractal dimension
H <- 3-D ##Hurst parameter
res1 <- midpoint(H=H[1],nblevel=8)##nblevel sets the size of the grid
res2 <- midpoint(H=H[2],nblevel=8)
res3 <- midpoint(H=H[3],nblevel=8)

par(mfrow=c(1,3))
image(res1$Z,col=cls,axes=F)
image(res2$Z,col=cls,axes=F)
image(res3$Z,col=cls,axes=F)

3-quadvar(res1$Z)
3-quadvar(res2$Z)
3-quadvar(res3$Z)
##these are very close to the D-values we input