Predictability and Scaling in a BTW Sandpile on a Self-similar Lattice

This paper explores the predictability of a Bak–Tang–Wiesenfeld isotropic sandpile on a self-similar lattice, introducing an algorithm which predicts the occurrence of target events when the stress in the system crosses a critical level. The model exhibits the self-organized critical dynamics characterized by the power-law segment of the size-frequency event distribution extended up to the sizes ∼ L β , β = log 3 5 , where L is the lattice length. We establish numerically that there are large events which are observed only in a super-critical state and, therefore, predicted efficiently. Their sizes fill in the interval with the left endpoint scaled as L α and located to the right from the power-law segment: α ≈ 2.24 > β . The right endpoint scaled as L 3 represents the largest event in the model. The mechanism of predictability observed with isotropic sandpiles is shown here for the first time.