Abelian Sandpile Model

How to run:

RUSTFLAGS="-C target-cpu=native" cargo build --bin abeliansandpile --release

Then

time ./target/release/abeliansandpile 200 40000 [mirror] [format]

Where:

• 200 is the grid size
• 40000 is the number of sand particles
• [mirror] (optional) is any value to enable mirroring along the diagonal
• [format] (optional) is the output format: "csv", "html", "png", or "all" (default is "all")

Examples:

# Output to all formats (CSV, HTML, PNG)
./target/release/abeliansandpile 200 40000

# Output only to HTML format
./target/release/abeliansandpile 200 40000 mirror html

# Output only to CSV format
./target/release/abeliansandpile 200 40000 none csv

(at the moment this takes about 15 minutes) (takes 1.7 seconds after optimizations)

Which produces the following:

Also this:

Optimizations

Found many useful tips in the Rust Performance Book.

Use the rustc-hash provided FxHashSet instead of the built-in HashSet. Gave almost double performance.

Comnpile with RUSTFLAGS="-C target-cpu=native".

Sources

Computations on sandpile models in SAGE https://doc.sagemath.org/html/en/thematic_tutorials/sandpile.html#introduction

https://mathoverflow.net/a/149934

Chip-Firing and Rotor-Routing on Directed Graphs

We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing open problems. https://arxiv.org/abs/0801.3306

gif https://docs.rs/gif/latest/gif/

Apollonian structure in the Abelian sandpile

The Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 neighbors. When begun from a large stack of chips, the terminal state of the sandpile has a curious fractal structure which has remained unexplained. Using a characterization of the quadratic growths attainable by integer-superharmonic functions, we prove that the sandpile PDE recently shown to characterize the scaling limit of the sandpile admits certain fractal solutions, giving a precise mathematical perspective on the fractal nature of the sandpile. https://arxiv.org/abs/1208.4839

Pattern formation in growing sandpiles https://arxiv.org/abs/0808.1732

Primer for the algebraic geometry of sandpiles https://arxiv.org/abs/1112.6163

Publications of Wesley Pegden https://www.math.cmu.edu/~wes/pub.html

Similar projects

Animation of steps one by one (also have an idea on how to parallellize) https://github.com/jamais-vu/sandpile

Python implementation https://github.com/kivyfreakt/sandpile

https://pi.math.cornell.edu/~levine/gallery/

https://people.reed.edu/~davidp/sand/program/program.html