Does spatial scaling imply temporal scaling in sandpile type cellular automata?

Abstract

We study the relationship between the spatial and temporal scaling in sandpile type cellular automata and show that in the thermodynamic limit, for a regular lattice with identical toppling rules except possibly at the system boundary together with a uniform but random probability distribution of particle addition, scaling in the size of the avalanche is a natural consequence. However, we find that this sort of temporal scaling behavior is in general very sensitive to the underlying probability distribution of the particle addition into the system. Hence the underlying probability distribution of particle addition can act as an external fine tuning parameter for the system to have scaling behavior.