A basic python implementation of the classic Bak–Tang–Wiesenfeld model, including the avalanche distribution plots, written as an example for my phd thesis. The power-law distributions of avalanche durations and sizes result from the self-organized criticality (SOC) behavior.
To run the model, choose the simulation parameters and run the script src/run_single.py. Important parameters are the lattice size, the number of grains to be dropped and the type of model. At this moment only the classic sandpile model is implemented, but a few variations are already implemented, such as grains of sand dropping on random sites and/or toppling to random neighbors.
The main model methods can be found at src/sandpile.py.
Plot parameters can be modified in the src/plot_avalanches.py script as necessary.
To save simulation time, the avalanche durations and sizes are stored in a folder results after each simulation is complete (so you can run only the plot script independently).
The avalanche plots and power-law fits require the powerlaw package.
A single simulation of the classic sandpile model on a lattice of size (100, 100) and 100000 grains of sand yields the following avalanche distributions:
The lattice also looks reasonably pretty, even for such small parameters.
