Wave coarsening drives time crystallization in mechatronic metamaterials

When metals are magnetized¹, emulsions phase separate², or galaxies cluster³, domain walls and patterns form and irremediably coarsen over time. This coarsening is universally driven by diffusive relaxation towards equilibrium. Here we discover a vibrational counterpart-wave coarsening-in active elastic media^4-13: vibrations emerge and spontaneously grow in wavelength, period and amplitude, before a globally synchronized state called a time crystal^14-17 forms. We observe wave coarsening in one- and two-dimensional mechatronic metamaterials and capture its dynamical scaling. We further arrest the process by breaking momentum conservation and reveal a far-from-equilibrium nonlinear analogue to chiral topological edge modes^18-24. Our results open new questions about the transient physics of systems with non-potential interactions^15,25-28 and suggest an organizing principle for nonlinear waves in acoustics^29,30, optomechanics^31,32, living matter^6,33 and soft robotics⁹.