Two representations in multifractal analysis

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Abstract
Two representations in multifractal analysis, the so-called q and tau representations, are discussed theoretically and computed practically. Complementary to the standard q-representation, the so-called tau -representation is especially suited to resolving the most rarified subsets of the distributed measure. Moreover, these two representations are especially adapted, respectively, to the well known fixed-size and fixed-mass box-counting algorithms. Both strategies are first applied to iteratively constructed mathematical measures. Once tested in this way, we use them to analyse the mass distribution and the growth probability distribution of an experimental electrodeposited pattern.