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Fractals deal with special sets that exhibit complicated patterns in every scale. Fractal sets usually have a Hausdorff dimension different from its topological dimension. Examples include Julia sets, the Sierpinski triangle, the Cantor set. Fractals naturally appear in dynamical system, such as iterations in the complex plane, or as strange attractors to continuous dynamical systems, (see Lorentz attractor).
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Relationship between the Hurst exponent and the alpha parameter
I have a question about the relationship between the Hurst exponent $H$ and the $\alpha$ parameter in the autocorrelation function when long memory is present. As we know in this case the decay of the …