Self-assembly is a process in which interacting bodies are autonomously driven into ordered structures. Static structures such as crystals often form through simple energy minimization, whereas dynamic ones require continuous energy input to grow and sustain. Dynamic systems are ubiquitous in nature and biology but have proven challenging to understand and engineer. Here, we bridge the gap from static to dynamic self-assembly by introducing a model system based on ferrofluid droplets on superhydrophobic surfaces. The droplets self-assemble under a static external magnetic field into simple patterns that can be switched to complicated dynamic dissipative structures by applying a time-varying magnetic field. The transition between the static and dynamic patterns involves kinetic trapping and shows complexity that can be directly visualized.