Random Sequential Adsorption — Jamming & Rényi Parking

Objects are placed randomly, one at a time, and rejected if they overlap an existing object. The process jams when no more objects fit. For 1D intervals of length 1 on [0, L], the jamming coverage converges to the Rényi parking constant M ≈ 0.7476847... (not close-packing!). For 2D disks, jamming ≈ 54.7%.

Mode

Object size (radius): 15 px Step speed (per frame): 5 Max attempts/step: 20

Objects placed: 0

Coverage: 0.000

Rényi constant: 0.7477

Attempts failed: 0

Jammed: No

1D Rényi (1958): P(jamming) → M
M = ∫₀^∞ exp(-2∫₀^x (1-e^{-t})/t dt) dx
M ≈ 0.74757... (Rényi parking constant)

2D disks (RSA): θ_j ≈ 0.5472
NOT same as random close packing

Applications: protein adsorption,
car parking, virus attachment

Random Sequential Adsorption — Jamming Limit

Mode