Random fractal maps

I wanted to share the results of my quest to produce random fractal maps. I eventually went with the GRASS r.surf.fractal script but before that I recreated the 2D midpoint displacement algorithm from Saupe (1988). The results are below. I think its solid but there still appears to be some artifacts which I have yet to track down.

fractal

    #MidPointFM2D####
    #X: doubly indexed array of size (N+1)^2
    #maxlevel: maximal number of recursions
    #sigma: initial standard deviation
    #H: Hurst exponent (determines fractal dimension)
    #addition: logical, turns random additions on/off
    #seed seed value for random numbers gen.
    
    #load libraries
    library(Oarray)
    library(raster)
    
    reps=10
    
    #load functions
    #interpolates inner points
    f4<-function(delta,x0,x1,x2,x3){
    return((x0+x1+x2+x3)/4+rnorm(1,1,delta))
    }
    #interpolates edge points
    f3<-function(delta,x0,x1,x2){
    return((x0+x1+x2)/3+rnorm(1,1,delta))
    }
    
    #inputs 
    6->maxlevel
    1->sigma
    0.4->H
    addition="FALSE"
    #seed<-101
    
    #for(kk in 1:reps){ 
    N<-2^maxlevel
    X<-Oarray(NA,dim=c(N+1,N+1),offset=0)
    #set initial random corners
    delta<-sigma
    #print(delta)
    
    X[0,0]<-rnorm(1,1,delta)
    X[0,N]<-rnorm(1,1,delta)
    X[N,0]<-rnorm(1,1,delta)
    X[N,N]<-rnorm(1,1,delta)
    D<-N
    d<-N/2
    
    for(stage in 1:maxlevel){
    delta<-delta*(0.5^(0.5*H))#going from grid type I to grid type II
    for(x in seq(from=d,to=(N-d),by=D)){#generate mid points;interpolate and offset points
    for(y in seq(from=d,to=(N-d),by=D)){
    X[x,y]<-f4(delta,X[x+d,y+d],X[x+d,y-d],X[x-d,y+d],X[x-d,y-d])
    }
    }
    #going from grid type II to type I
    delta<-delta*(0.5^(0.5*H))
    #interpolate and offset boundary grid points
    for(x in seq(from=d,to=(N-d),by=D)){
    X[x,0]<-f3(delta,X[x+d,0],X[x-d,0],X[x,d])
    X[x,N]<-f3(delta,X[x+d,N],X[x-d,N],X[x,N-d])
    X[0,x]<-f3(delta,X[0,x+d],X[0,x-d],X[d,x])
    X[N,x]<-f3(delta,X[N,x+d],X[N,x-d],X[N-d,x])
    }
    
    #interpolate and offset interior grid points
    
    if(stage==2){
    for(x in seq(from=d,to=(N-d),by=D)){
    for(y in seq(from=D,to=(D),by=D)){
    X[x,y]<-f4(delta,X[y+d,x],X[x,y-d],X[x+d,y],X[y,x-d])#try moving x input to y input and vice versa on first and third x,y term
    }
    }
    
    
    for(y in seq(from=d,to=(N-d),by=D)){
    for(x in seq(from=D,to=(D),by=D)){  
    X[x,y]<-f4(delta,X[x,y+d],X[x,y-d],X[x+d,y],X[x-d,y])
    }
    }
    }
    
    if(D<(N-d)){
    for(x in seq(from=d,to=(N-d),by=D)){
    for(y in seq(from=D,to=(N-d),by=D)){
    X[x,y]<-f4(delta,X[y+d,x],X[x,y-d],X[x+d,y],X[y,x-d])#try moving x input to y input and vice versa on first and third x,y term
    }
    }
    
    for(x in seq(from=D,to=(N-d),by=D)){  
    for(y in seq(from=d,to=(N-d),by=D)){
    X[x,y]<-f4(delta,X[x,y+d],X[x,y-d],X[x+d,y],X[x-d,y])
    }
    }
    }
    D<-D/2
    d<-d/2
    #print((sum(is.na(X))/length(X))*100) 
    outarray<-array(X,dim=c(N+1,N+1))
    }
    plot(raster(outarray))

###Reference

Saupe, Dietmar. “Algorithms for random fractals.” The science of fractal images. Springer New York, 1988. 71-136.

First Post

This is my first post on the new site. Glad to be migrated from Google Pages!