We have studied the magnetic interaction of circular magnetic islands with a dipole character on a square lattice. The square pattern consists of lithographically prepared polycrystalline PdFe islands, 150 nm in diameter and a periodicity of 300 nm. Below the Curie temperature at 260 K, the islands are in a single domain state with isotropic in-plane magnetization. Below 160 K, there is an onset of interisland interaction that leads to a change of the shape of the hysteresis, an increase of coercivity, and a development of in-plane anisotropy. Photoemission electron microscopy with circularly polarized incident x rays tuned to the L3 edge of Fe confirms the increasing correlation of the magnetic islands and the formation of elongated chains, as predicted by Vedmedenko et al. [Phys. Rev. Lett. 95, 207202 (2005)] for contributions from pole interactions of higher order than the dipolar one. Neighboring chains are found to be irregularly oriented either parallel or antiparallel.