Random 2D cellular structures are generated from distributions of spins given by a ferromagnetic Ising model with nearest-neighbour couplings on a square lattice. Topological correlations between pairs of neighbouring cells, are expressed as rational functions of even-number spin correlations, involving two, four and six spins, which are exactly known for the square Ising model, The latter correlations have been calculated numerically in the vicinity of the Curie point, They agree with computer simulation results.