Microstructure plays an essential role in determining the properties of crystalline materials. A widely used method to influence microstructure is the addition of nucleating agents. Observations on films formed from clay-polymer blends indicate that particulate additives, in addition to serving as nucleating agents, may also perturb crystal growth, leading to the formation of irregular dendritic morphologies. Here we describe the formation of these 'dizzy dendrites' using a phase-field theory, in which randomly distributed foreign particle inclusions perturb the crystallization by deflecting the tips of the growing dendrite arms. This mechanism of crystallization, which is verified experimentally, leads to a polycrystalline structure dependent on particle configuration and orientation. Using computer simulations we demonstrate that additives of controlled crystal orientation should allow for a substantial manipulation of the crystallization morphology.