Calculating the fractal dimension of borders

[ThomasWinning]

Hi Kyrcha,

I am attempting to conduct research where I calculate fractal dimensions of borders. I came across your previous work on calculating the fractal dimension of the Greek coastline on your blog (https://kyrcha.info/2013/04/19/calculating-the-fractal-dimension-of-the-greek-coastline-1-25) which I found extremely fascinating. I would like to know how I can adapt your code as a part of my investigation as I am simply a beginner/novice in R. I have used my own .jpeg image to form the basis of my trials:

However, when inputting the following code:

library(jpeg) rm(list=ls()) img <- readJPEG(normalizePath('Coastline.jpeg')) # filter out mainland img[img > 0.5] = 1 # divisors of 1600 # 1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800,1600 boxSizes = c(50, 40, 32, 25, 20, 16, 10, 8, 5, 4) h = img[,,1] data = data.frame() for(k in 1:length(boxSizes)) { b = boxSizes[k] x = dim(img[,,1])[1] ratio = x/b # https://stat.ethz.ch/pipermail/r-help/2012-February/303163.html k = kronecker(matrix(1:(ratio^2), ratio, byrow = TRUE), matrix(1,b,b)) g = lapply(split(h,k), matrix, nr = b) counter = 0; for(i in 1:length(g)) { counter = counter + any(g[[i]] < 0.999) } data = rbind(data,c(log(counter),log(1/b))) } names(data) = c("Y", "X") model = lm(Y~., data=data) cat(coef(model), "\n")

The output is 9.704228 1.220103

I would like to know what I have done wrong or how I can adapt the code in order to not only be outputted with the fractal dimension but also, a plot of both the logarithmic graph (much like the one in your blog) as well as a mapped plot of the .jpeg image with the boxes on it (if possible).

Many thanks,
Thomas