Dynamic self-assembled material systems constantly consume energy to maintain their spatiotemporal structures and functions. Programmable self-assembly translates information from individual parts to the collective whole. Combining dynamic and programmable self-assembly in a single platform opens up the possibilities to investigate both types of self-assembly simultaneously and to explore their synergy. This task is challenging because of the difficulty in finding suitable interactions that are both dissipative and programmable. We present a dynamic and programmable self-assembling material system consisting of spinning at the air-water interface circular magnetic micro-rafts of radius 50 μm and with cosinusoidal edge-height profiles. The cosinusoidal edge-height profiles not only create a net dissipative capillary repulsion that is sustained by continuous torque input but also enable directional assembly of micro-rafts. We uncover the layered arrangement of micro-rafts in the patterns formed by dynamic self-assembly and offer mechanistic insights through a physical model and geometric analysis. Furthermore, we demonstrate programmable self-assembly and show that a 4-fold rotational symmetry encoded in individual micro-rafts translates into 90° bending angles and square-based tiling in the assembled structures of micro-rafts. We anticipate that our dynamic and programmable material system will serve as a model system for studying nonequilibrium dynamics and statistical mechanics in the future