Multifractal properties of power-law time sequences: application to rice piles

Abstract

We study the properties of time sequences extracted from a self-organized critical system, within the framework of the mathematical multifractal analysis. To this end, we propose a fixed-mass algorithm, well suited to deal with highly inhomogeneous one-dimensional multifractal measures. We find that the fixed-mass (dual) spectrum of generalized dimensions depends on both the system size L and the length N of the sequence considered, being stable, however, when these two parameters are kept fixed. A finite-size scaling relation is proposed, allowing us to define a renormalized spectrum, independent of size effects. We interpret our results as evidence of extremely long-range correlations induced in the sequence by the criticality of the system.