The paradigm of self-organized criticality was introduced about a decade ago by Bak, Tang, and Wiesenfeld, and has attracted considerable interest, mostly in the physics community. Presumably, it can be used to explain statistical features for a wide variety of open systems with many components, ranging from geology to biology and economics. The mathematical properties of related models are incompletely understood, however. The aim of the current research is to perform computer simulations for a so-called sandpile model, to extract statistical information from the simulations, and to compare these with analytical results. This will lead to better understanding of the process of self-organization and of the behavior of systems that work at the critical state.
Numerical simulation is the method of choice to understand the model.
Simulation may be in terms of configurations and topplings or local slopes and trapping sites. The latter was found to enhance the computing efficiency by two orders of magnitude. The second strategy was found to be more powerful. We collect the avalanche sizes at each time step, and plot it against the time steps in our first graph. This is confirmed using the log-log plot, which is our second plot.