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PileOfSand

by Carlos Pedro Gonçalves (Submitted: 06/26/2003)

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WHAT IS IT?

This is a simulation of a model inspired in Per Bak's pile of sand

HOW IT WORKS

Each site in a plane world has a certain height (which was set to have a minimum of 0 and a maximum of 4).
Sand falls (one grain at a time), at each time step, into a random location in the world, once a given site attains a height of four all of its sand falls into the four north, south, east and west sites.

THINGS TO NOTICE

Notice how the system advances towards criticality, and how, after it attains criticality the mean height is approximately constant.

THINGS TO TRY

It would be interesting to try and change the world's shape, this changes the borders of the world, and changing the rules in accordance.

EXTENDING THE MODEL

The code is divided into three sections, in each of these sections there are changes that can be made. Here are some suggestions of extensions for each section:

Section 1 - The World:

Instead of a random initial configuration of heights it might be interesting to add the feature of allowing the user to personalize the landscape or to choose between random and different non-random initial configurations.

Section 2 - Main Procedure for the Pile of Sand

Possible extensions could be different rules.

Section 3 - Statistical Analysis

Try adding new statistical quantities.
The most important would be a plot of the power law behaviour discussed by Bak.

CREDITS AND REFERENCES

The main reference for this model was Per Bak's book:

Quand la Nature S'Organise, Translated by Marcel Filoche, Flammarion, Paris, 1999.

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