- Implement the Abelian Sandpile Model
- Confirm the following power-laws:
- the number of clusters D(s) of size s scaled with some exponent τ : D(s) ∼ s^(−τ)
- Represents the square lattice which sand will be dropped on
- Contains nxn "Site" cells
- Keeps track of the number of avalanches
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void toppleAtThreshold(Site s, int t)- Method to check sites current state, if it exceeds the threshold, then topple and recursively check it's neighbors. It's here where we keep track of the temporary count of avalanches -
void topple()- Method to distribute give the sites grains to it's neighbors equally. -
void resetAvalancheCount()- Method to reset the current count for avalanche. Should be called at every timestep.
- Represents a single site on the grid
- Has a point on the grid (x, y)
- Keeps track of state, via an integer
int getState(), int setState(int state)void increment()- Increments the current state
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The main method contains a Map (TreeMap) for keeping track of Avalanche sizes vs Frequencies
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For experiments specifically, the main method runs for some T number of iterations. At each iteration, we randomly select a site to increment. If it's greater than the threshold => we call
toppleAtThreshold(randomSite, 3). -
Once toppleAtThreshold is done, we update the map for the correct number of times the avalanche of a specific size has occurred.
- Unit tests have been written to verify the correctness of the implementation with 3 guaranteed results obtained from the model (2 are from research papers, 1 is simply made up)
- You may find the tests in the projects root directory in the
testsfolder:MockGrids.javafor predefined Grids with known resultsGridTest.javafor methods related to the Grid. Tests for toppling and verifies that avalanche is counted correctly.