Time-Crystal Microdevice inspired by Fukuta–Cerin Triangle–Hexagon Symmetry

Time crystals are a class of non-equilibrium phases of motion characterized by spontaneous temporal symmetry breaking. We describe a time-crystal-inspired microdevice (TCIM) structured around a hexagonal shell encapsulating a central triangular motif. The geometry is derived from the Fukuta–Cerin theorem, where the centroid of each triangle aligns with that of the surrounding hexagon. In a TCIM flock, this leads to the emergence of controlled, oscillatory behaviour and symmetry-breaking phenomena driven by the internal geometry of the system. Indeed, the triangles introduce geometric frustration that allows the agents to maintain oscillations without relying on continuous external influence. The disruption of perfect synchronization enhances the flock’s ability to exhibit periodic, self-sustained oscillatory behaviour in response to minimal energy input or periodic perturbations, showcasing the system’s capacity for self-organization and dynamic patterns. Numerical simulations demonstrate that, under periodic driving, local alignment rules and structural frustration, the TCIM flock exhibits self-sustained subharmonic oscillations. These oscillations are characterized by a frequency shift to half the driving frequency, a key indicator of the emergence of time-crystal-like behaviour. This points towards the system’s ability to break discrete time-translation symmetry, another hallmark of time-crystal dynamics. TCIMs could enable the development of intelligent microdevices with internally regulated timing mechanisms like self-regulating sensors and synthetic bio-compatible materials that operate with minimal external control. TCIM-inspired devices, utilizing internal temporal rhythms, could also be applied in drug delivery systems, enabling the autonomous release of therapeutic agents in a timed, controlled manner without relying on continuous external inputs.