Interference of waves is important and used in many areas of science and technology but does not extend to static magnetic fields which lack the wave structure. On the other hand, magnetic fields can be spatially modulated using microstructured materials comprising magnetic and non-magnetic domains. Here, we show that when such spatial modulation is coupled to the dynamics of magnetic particles, it can give rise to interference-like patterns. These patterns are imprinted into thin polymer films by overlaying "stamps" presenting periodic arrays of magnetic and nonmagnetic regions. The structures that emerge from such a superposition are sensitive to any motions of the stamps, can depend on the history of these motions, can produce features significantly smaller than those in the stamps, and can be either planar or three-dimensional.