Abelian Sandpile Model

Implementation of the Abelian sandpile model. The program calculates model's states and saves them as BMP images at a specified frequency.

Initial State

The initial state is defined by a TSV file that specifies the number of sand grains in each cell, excluding empty cells. Based on this data, the grid size is calculated - the minimal rectangle that encloses all the cells.

File Format

Each line in the TSV file contains information about one cell, with the format x, y, number of grains in (x, y), separated by tabs. The number of grains in one cell should fit uint64_t range and the coordinates should fit int16_t range.

Model Details

1. New sand grains are only added during initialization.
2. The next generation of cells' state only depends on the previous grid state.
3. If a sand grain attempts to topple outside the grid's boundaries, the grid's size will increase by 1 in that direction.
4. The image of the current state is generated according to the rules:
   • The image size equals the size of the grid.
   • Each pixel corresponds to a grid cell.
   • Pixel color depends on the number of sand grains in the cell:
     • 0 - white
     • 1 - green
     • 2 - yellow
     • 3 - pink
     • > 3 - black
   • Encoding of 1 pixel takes no more than 4 bits.

Command-line Arguments

The program is a console application supporting the following command-line arguments:

• -i, --input: A TSV file containing initial data.
• -o, --output: Path to the directory to save images to.
• -m, --max-iter: Maximum number of toppling iterations.
• -f, --freq: The frequency at which images should be saved (if 0, only the final state is saved).

Example Input

--input=/Users/SupercoolMe/Desktop/params.tsv --max-iter=92233720368547 -f 1000000000 -o /Users/SupercoolMe/Desktop/gallery/