A study of the properties of multifractal estimators applied to point distributions, with the aim of classifying galaxy structures

The application of the multifractal formalism to point sets is investigated, with the aim of characterizing galactic structure by the distribution of H II regions. In this work we test two of the commonly used estimators of the multifractal dimension, namely the correlation sum method and the minimal spanning tree (MST) method, on two multifractals: a multiplicative fractal (beta-model) and the Henon attractor. For the MST method we investigate the effect of varying the range of short or long edges that are rejected (a procedure required to reduce noise and improve the stability of results), and show that large variations in the dimensions can occur. The spurious predictions also appear to be convergent and hence are misleading. The correlation sum method performs much better, agreeing well with the analytic expression for the multifractal spectrum of the beta-model.