Sandpile · self-organized criticality simulation

Every critical point so far (Ising, percolation) had to be FOUND by tuning a knob to one magic value. Can a system drive ITSELF to criticality with no tuned parameter at all?

▶ Run the simulationSee the measured result

Units: grains per site, heights 0..3 (17/8 exact; 25/8 in the 1..4 convention)

How the lab tests it

Run the Bak–Tang–Wiesenfeld sandpile: drop grains on random cells of an L×L grid; a cell that reaches 4 topples one grain to each neighbour, possibly cascading into an avalanche; grains that fall off the open boundary are lost. Drive grain by grain from empty, track the stationary mean density ⟨ρ⟩, and histogram the avalanche sizes s (total topplings) in log-bins.

What it checks

the pile self-organizing — with NO tuned knob — to a stationary critical slope (⟨ρ⟩ → 17/8 = 2.125, the exact Priezzhev value), and scale-free avalanches P(s) ∝ s^(−τ) over decades (the SOC signature; the fitted τ is an effective slope — the 2-D BTW distribution is famously multifractal, not one clean exponent). Grains are conserved exactly.