Curvature induced periodic attractor on growth interface

We experimentally address the long-time dynamics of an artificially curved growth interface in directional solidification. Repetitive cell nucleations are found to appear in a disordered way but to eventually organize themselves coherently, at long times. This behavior is recovered by simulation of a nonlinear advection-diffusion model for the phase dynamics. The existence of a periodic attractor is shown by deriving a Liapunov functional for the cellular pattern organization on time ranges that include the singular events of cell nucleation.