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I am using Fournier's midpoint algorithm (recursive subdivision) to construct a landscape of 1025 x 1025 gridpoints, then I am using an advanced version of box counting to find fractal dimension, D. No matter what Hurst exponent I use in Fournier's algorithm, I get D = 2.0. Has anyone checked Fournier's algorithm for fractal dimension? Does it actually produce a fractal?

user993563
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  • What does a plot of $\log N(r)$ vs $\log r$ look like for your box counts? Have you checked if the 1D version has $D > 1$? – Claude May 06 '21 at 14:12
  • @Claude Looks like textbook. Linear with a slight drop at large r (a few points that I discarded when I did regression). Now I did variogram analysis, and I am getting the same results, D between 2.0 and 2.1 no matter what H I use in the Fournier algorithm. I have not checked the 1D version yet but I will. – user993563 May 06 '21 at 16:43

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