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I have a general question about multifractal analysis:

Suppose that I have two figures, that are multifractals. The question is, how I can compare how similar they are to each other? Can I do it by taking into consideration, that according to the Rényi Dimension, when $q=0$, this corresponds to the box square dimension? Or should I take $q=1$, that is the information dimension or $q=2$, that is the correlation dimension?


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Why only take one dimension when you can compare all dimensions? After all, it's multifractals we are talking about, so only specifying one dimension doesn't fully characterize them. – Raskolnikov Nov 18 '11 at 12:19
thanks @Raskolnikov, so do you mean that I should also compare the other dimensions q=1, q=2 etc., or I can take an sum over the values of all the different dimensions and average them? – Lila Nov 18 '11 at 12:21
You have in principle a full spectrum of dimensions, not just for integer values. So you should compare the two spectra in a way. But I'm not sure what the best measure of comparison would be. – Raskolnikov Nov 18 '11 at 12:51

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