DIRECTORY / SANDBOXES / SANDPILE.ABELIAN

ABELIAN SANDPILE MODEL

Bak-Tang-Wiesenfeld self-organized criticality exhibiting power-law fractal avalanche distributions.

ABELIAN SANDPILE HUD

RUNNING

// GRAIN INJECTION MODE

// COLOR PALETTE

SUB-STEPS / FRAME 25x

TOTAL TOPPLES: 0

[Click on canvas to drop sand grains at cursor]

📚

Self-organized criticality, 1/f power-law avalanches, and Apollonian fractal gaskets.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Introduced by physicists Per Bak, Chao Tang, and Kurt Wiesenfeld in 1987 as the foundational model of Self-Organized Criticality (SOC).

// GOVERNING EQUATIONS

z(x, y) \ge 4 \implies z(x,y) \leftarrow z(x,y) - 4, \quad z(\text{neighbors}) \leftarrow z(\text{neighbors}) + 1

// BROWSER IMPLEMENTATION

Iteratively relaxes grid cells with 4 or more grains by distributing to 4 orthogonal neighbors until the lattice reaches a sub-critical equilibrium.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX

1Apollonian Circle Emergence

🎯 Action:Click 'Center Drop' (+60k grains) and set speed to 35x.

✨ Observe:Observe the spontaneous formation of self-similar fractal circular patterns and Sierpinski triangles.

// CURATED PAPERS, RFCS & RESOURCES

The landmark paper introducing self-organized criticality in statistical physics.