Continuum Percolation — Boolean Model

Random discs of radius r · Giant cluster colored · Click canvas to regenerate

Boolean model: Poisson process of disc centers with intensity λ, each disc radius r. Percolation threshold: λ_c · πr² ≈ 0.6731 (critical covered area fraction η_c ≈ 1 − e^(−0.6731) ≈ 0.6763). Below threshold: finite clusters. Above: giant spanning cluster appears. Critical exponents same as 2D lattice percolation.