Sandpile

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Python implementation of the Sandpile Model

• Required packages
• Usage
  • Program example
• Examples
  • 2^18 grains
  • 2^20 grains

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The Abelian sandpile model, also known as the Bak–Tang–Wiesenfeld model, was the first discovered example of a dynamical system displaying self-organized criticality.

To know more read https://en.wikipedia.org/wiki/Abelian_sandpile_model

Required packages

This module requires matplotlib, numpy and PIL to be installed.

pip3 install matplotlib numpy Pillow

Usage

To run the model, choose the simulation parameters and run the script sandpile/example.py. Important parameters are the grid size and the number of grains to be dropped.

The main model methods can be found at sandpile/sandpile.py.

Construct a sandpile:

from sandpile import Sandpile
pile = Sandpile(options)

options may contain:

• rows - height of sandpile
• cols - width of sandpile
• max_sand - max count of sandpile grains

It gives you a zero sandpile

Also you can create sandpile from array, if you give array to constructor

from sandpile import Sandpile
pile = Sandpile([[0,1,0],[1,0,1],[0,1,0]])

Add sand to sandpile:

pile.set_sand(x, y, number)

where x and y - coordinates of sandpile grid, number - count of sand grains

Run the model:

pile.run()

Visualisations:

If you would like to plot sandpile and show it, you can use

pile.show(options)

options may contain:

• save - true = if you want save picture, false = if don't want
• filename - name of the file, where would be picture of sandpile

If you just want to save the picture , then use

pile.save(filename)

where filename - name of the file, where would be picture of sandpile

Program example

You can find this example in /sandpile/example.py

from sandpile import Sandpile

pile = Sandpile(rows = 201, cols = 201)
pile.set_sand(100, 100, 2**16)

pile.run()

pile.show(save = True, filename = "2^16 grains(1).png")
pile.save(filename = "2^16 grains(2).png")

Examples

2^18 grains

Fractal in a 401x401 lattice created from an initial 2^18 (262144) grains in the center

2^20 grains

Fractal in a 801x801 lattice created from an initial 2^20 (1048576) grains in the center