A three-dimensional model for the coupled evolution of ice-surface temperature and elevation in the Martian polar ice caps is presented. The model includes 1 enhanced heat absorption on steep, dust-exposed scarps, 2 accumulation and ablation, and 3 lateral conduction of heat within the ice cap. The model equations are similar to classic equations for excitable media, including nerve fibers and chemical oscillators. In two dimensions, a small zone of initial melting in the model develops into a train of poleward-migrating troughs with widths similar to those observed on Mars. Starting from random initial conditions, the three-dimensional model reproduces spiral waves very similar to those in the north polar ice cap, including secondary features such as gull-wing–shaped troughs, bifurcations, and terminations. These results suggest that eolian processes and ice flow may not control trough morphology.