N discs = — |
Area fraction η = — |
η_c ≈ 0.676 |
Giant cluster = — |
Spanning: —
The Boolean model: place disc centers as a Poisson process with intensity ρ, each disc has radius r.
Two discs overlap if their centers are within 2r. The covered area fraction is η = 1 − e^{−ρπr²}.
At η_c ≈ 0.676 (equivalently ρπr² ≈ 1.128), a system-spanning cluster appears.
Colors indicate connected components; the giant cluster (if spanning) is highlighted in gold.