We investigate the impact of domain shape on wave propagation in excitable media. Channeled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration that repeats periodically in time. The phenomenon is numerically studied in a model for a photosensitive Belousov-Zabotinsky reaction. Spatial return maps for the height and position of the successive fronts are analytically obtained, and reveal the similarity between this spatial quasiperiodicity and the temporal quasiperiodicity appearing in forced oscillators.