Fractal dimension of landscape generated with Fournier's midpoint algorithm (recursive subdivision) is 2.0 no matter what. Why?

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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?