Magnetic domains in ultrathin films show a wide variety of patterns. Recent instrument developments, in particular in spin-polarized low-energy electron microscopy (SPLEEM), have allowed real-time observation of magnetic domain patterns in thin films. Recent SPLEEM experiments have shown that the magnetic anisotropy, and hence magnetic domain patterns, in a Co/Ni multilayer changes with the number of layers. We simulate the magnetic domain pattern formation on the surface of a Co/Ni multilayer. The numerical simulations well reproduce the magnetic domain patterns that were observed in the experiments. Copyright © 2014 John Wiley & Sons, Ltd.