Under repeated random desorption and readsorption the patterns of atoms which may arise on a square lattice depend on the size of the atoms in relation to the cell size, but irrespective of size all possible patterns become equally likely. The dynamic equilibrium of large atoms thus defined (Fermi–Dirac equilibrium) is in this paper characterized by a probabilistic process, which generates all possible patterns with equal probabilities for any specified K × ∞ lattice and adsorption density ρ . The general formulas developed are used to find and evaluate exact mathematical relations between occupation ratio and adsorption density on the 3 × ∞ lattice. An approximate polynomial expression for the ∞ × ∞ lattice taken from the literature is evaluated for comparison with the exact solutions for K = 2 and 3.