Evidence item

Here we show that odd-shaped cavities formed in hyperbolic media suppress chaotic wave dynamics and instead give rise to hyperbolic wave attractors: robust, chiral, broadband and scale-invariant states that organize wave motion analogously to limit cycles in nonlinear dynamical systems. Their defining properties differ from both conventional resonant cavities and chaotic modes. We experimentally demonstrate this phenomenon using elastodynamic waves in a hyperbolic metamaterial and reveal attractor phase transitions, symmetry-driven features and robustness against defects.