Percolation Cluster Hulls & Scaling

Percolation Parameters

Occupation prob p: 0.593 Grid size L: 80

Largest cluster—

Cluster count—

Spanning?—

p_c estimate0.5927

d_f (fractal)—

Percolation: p_c(site,square) ≈ 0.5927. At p_c: spanning cluster has fractal dimension d_f = 91/48 ≈ 1.896 (Nienhuis). Hull (outer boundary) = SLE₆ (κ=6, Smirnov 2001). Critical exponents: β=5/36 (order), ν=4/3 (correlation length), γ=43/18 (susceptibility). Each color = distinct cluster.