Continuum Percolation — Random Disk Model

Place N disks randomly; find connected clusters. Giant cluster spans box near ρ_c ≈ 1.128

N disks: -- Largest cluster: --% Percolating: No ρ_c ≈ 1.128
About: In continuum percolation, disks of radius r are placed uniformly at random in the unit square. Two disks are connected if they overlap (center distance < 2r). The system percolates when a connected cluster spans from left to right edge. The critical density is ρ_c = Nπr² ≈ 1.128 — a universal threshold independent of disk size (for large N). Each color represents a distinct connected component.