Physics of Jamming
Jamming is a phase transition in athermal particulate systems. As you inflate hard disks (or compress a box), the packing fraction φ increases.
At the jamming point φ_J ≈ 0.64 (random close packing in 2D ≈ 0.84), the system transitions from fluid-like to rigid. Pressure diverges as P ∝ (φ − φ_J)^1.
At jamming, each disk has exactly Z = 2d = 4 contacts on average (isostaticity condition).
Colors show contact number: green = few contacts, orange = many (jammed).