Largest cluster: —
Hull length: —
Spanning: —
log(Hull)/log(Size): —
Site percolation: each site occupied with probability p. Critical threshold p_c ≈ 0.5927 (Kesten 1980 bond, site exact unknown).
Spanning cluster: a connected cluster touching both left and right edges.
Hull (external frontier): boundary between the spanning cluster and empty space. Fractal dimension d_f = 7/4 (Grossman-Aharony 1986).
Colors: cyan=spanning cluster, blue=other clusters, red=hull boundary sites, yellow=isolated sites.
Bottom chart: measures hull length vs cluster size across multiple realizations to estimate d_f.
Spanning cluster: a connected cluster touching both left and right edges.
Hull (external frontier): boundary between the spanning cluster and empty space. Fractal dimension d_f = 7/4 (Grossman-Aharony 1986).
Colors: cyan=spanning cluster, blue=other clusters, red=hull boundary sites, yellow=isolated sites.
Bottom chart: measures hull length vs cluster size across multiple realizations to estimate d_f.