  In physical networks, like the brain or metamaterials, we often observe local
bundles, corresponding to locally aligned link configurations. Here we
introduce a minimal model for bundle formation, modeling physical networks as
non-equilibrium packings of hard-core 3D elongated links. We show that growth
is logarithmic in time, in stark contrast with the algebraic behavior of lower
dimensional random packing models. Equally important, we find that this slow
kinetics is metastable, allowing us to analytically predict an algebraic growth
due to the spontaneous formation of bundles. Our results offer a mechanism for
bundle formation resulting purely from volume exclusion, and provide a
benchmark for bundling activation and growth during the assembly of physical
networks.
