Percolation Cluster Hulls — Fractal Boundaries
Site percolation on square lattice: d
f
=91/48≈1.896 at p
c
≈0.5927 — hull fractal dimension d
H
=7/4
Parameters
Occupation prob p:
0.59
Grid size:
80
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Show/Hide Hulls
Show Perimeter Scaling
Clusters: —
Largest: —
Percolates: —
Hull perim: —
Critical percolation (Kesten 1980):
p
c
(bond,sq)=1/2 exactly; p
c
(site,sq)≈0.59275 numerically. At p
c
, largest cluster has fractal dimension d
f
=91/48. Cluster hull (external boundary) has d
H
=7/4. Boundary = SLE
6
(Smirnov 2001, Fields Medal 2010).