ON THE MULTIFRACTAL ANALYSIS OF GALAXY CATALOGS WITH BOX-COUNTING METHODS

The influence of sampling and discreteness effects on multifractal (MF R) analysis performed with box-counting methods is discussed. Emphasis is put on the uniform mass (counting) measure, which is used in most analysis in astronomy. Finite sampling is shown to lead to a spurious point {alpha = 0, f(alpha) = 0} in the MFR spectrum. Such effect can g ive to a real fractal the appearance of a fractal with two scaling reg imes. To avoid such effect, one might be tempted to perform analysis a t scales larger than the mean interparticle distance. This is shown to give meaningless results and leads to the loss of the connection betw een Renyi dimensions and MFR spectrum. All these effects are illustrat ed on simple examples.