We present a data reduction and visualization approach for the microdomain dynamics in block copolymers and similar structured fluids. Microdomains are reduced to thin smooth lines with colored branching points and visualized with a tool for protein visualization. As a result the temporal evolution of large volume data sets can be perceived within seconds. This approach is demonstrated with simulation results based on the dynamic density functional theory of the ordering of microdomains in a thin film of block copolymers. As an example we discuss the dynamics at the cylinder-to-gyroid grain boundary and compare it to the epitaxial cylinder-to-gyroid phase transition predicted by Matsen [Phys. Rev. Lett. 80, 4470 (1998)].