Life as Form: Biomimetic Transport Networks in Complementary Active Matter

Abstract In this work, I characterize the out-of-equilibrium behavior of active oscillator ensembles governed by chiral symmetry breaking. Operating under a complementary interaction scheme, these systems generate a structural competition between spatial motility and phase coordination, driving endogenous dynamical frustration. Through purely local rules, the collective self-organizes into multi-branch routing topologies characterized by optimal geometric junctions and autonomous self-repair capabilities. Statistical signatures reveal a non-equilibrium phase-space confinement rooted in weak ergodicity breaking, where scale-free fluctuations are sustained far from criticality. The system departs from traditional disordered frameworks, such as spin-glasses, by actively harnessing its glassy complexity: the active medium exploits internal frustrations to guide its own structural remodeling and maintain operational closure. These findings establish a decentralized organizational paradigm where a frustrated stability landscape is transformed into a functional, autopoietic computational substrate, providing a novel theoretical realization of biomimetic transport networks.