We represent animated elements in a three-dimensional spacetime domain, and view the animated packing problem as a three-dimensional packing in that domain. Every element is represented as a discretized spacetime mesh. In a physical simulation, meshes grow and repel each other, consuming the negative space in the container. The final animation frames are cross sections of the three-dimensional packing at a sequence of time values. The simulation trades off between the evenness of the negative space in the container, the temporal coherence of the animation, and the deformations of the elements. Elements can be guided around the container and the entire animation can be closed into a loop.