Sandbox method for factorial moments and anomalous fractal dimensions

For the purpose of the intermittency analysis of high-energy heavy-ion data, the definition of factorial moments is reformulated in terms of horizontal averages determined by the sandbox method. It is shown that the sandbox method gives the correct anomalous fractal dimensions for exactly solvable models of geometrical multifractals when the box-counting method usually used in heavy-ion physics fails. For the RQMD generated event sample with two-particle correlations, the anomalous fractal dimensions obtained by the both methods differ significantly.