Sand

Sand pile simulation

---

About

Sand piles have been shown to exhibit power-law dynamics, with small avalanches being extremely common and large avalanches extremely rare.

Installation

Install using Poetry

poetry install

Usage

sand simulate --info --show-pile --show-plots --seed 42 --steps 1000 --size 20 --stability-threshold 4

Output

As output you should see a 2D representation of the sand pile:

 [[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  1  2  0  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  1  1  2  4  5  2  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  4  6  8  9  6  3  1  0  0  0  0  0  0]
  [ 0  0  0  0  0  3  4  7 10 12 12  9  6  3  0  0  0  0  0  0]
  [ 0  0  0  0  2  5  7 10 13 16 16 12 10  6  3  0  0  0  0  0]
  [ 0  0  0  0  3  6 10 13 16 20 19 17 13  9  6  3  0  0  0  0]
  [ 0  0  0  2  5  9 13 16 20 23 22 19 16 12  8  4  1  0  0  0]
  [ 0  0  1  0  3  7 11 15 19 22 24 20 16 12  8  4  1  0  0  0]
  [ 0  0  0  0  1  5  8 11 15 18 20 16 12  9  5  1  0  0  0  0]
  [ 0  0  0  1  3  2  5  8 11 14 16 12  9  5  2  1  0  0  0  0]
  [ 0  0  0  0  0  2  2  5  7 10 12  9  5  2  2  2  0  0  0  0]
  [ 0  0  0  0  0  0  0  3  4  6  8  5  2  2  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  1  1  0  3  4  1  0  1  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  0  1  1  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]
  [ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0]]

as well as a frequency histogram of cascade sizes:

1: 156
2: 100
3: 41
4: 26
5: 13
6: 4
7: 1
9: 1
10: 1

Note that at each cascade size the frequency approximately halves. By updating the parameters of the simulation, you can change this coefficient. This is scale-free!