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In Version 9 FindProcessParameters[x, FractionalBrownianMotionProcess[h]] returns {h -> -0.0257885} without an error message. However, since h should be non-negative, this is an invalid result. In fact ProcessParameterQ[FractionalBrownianMotionProcess[-0.0257885]] gives the error message with and returns False: In Version 10, rather than ...


9

The image taken from MathWorld appears to be something like this: Image @ Rescale @ Table[Mod[x^2 + y^2, 100], {x, -50, 50}, {y, -50, 50}] In my opinion this is not a fractal, and it certainly isn't produced by iteration. You described it as "Moiré-like", which is a far better description. It is simply a uniformly sampled 2D parabola, modulo some ...


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Mathematica's estimation routines are able to recover the Hurst exponent from the sample: BlockRandom[SeedRandom["mathematica.SE/58539"]; tlow = 1; thigh = 1000; tinc = 1; hurst = 0.4; dataz = RandomFunction[FractionalBrownianMotionProcess[hurst], {tlow, thigh, tinc}, 1]]; FindProcessParameters[dataz, FractionalBrownianMotionProcess[h]] {h -> ...



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