Metric features of self-organized criticality states in sandpile models

A new characterization of self-organized criticality (SOC) states is developed by using metric features of the configuration's space. Quantities mainly referring to the partition formalism, as mutual factorization, Shannon entropy and Rohlin distances with their distributions and power spectra, are considered. Time series for these observables give account of geometrical and dynamical complexity through the interdependence of fractality and flicker noise. For Bak-Tang-Wiesenfeld and Manna automata, new indicators enforce previous results given by standard parameters and allow a deeper insight into the structure of SOC configurations and their time behaviour. Moreover, we obtain indications regarding a possible split in the universality class of the two automata.