After a polymerizable hydrogelator self-assembles in water to form molecular nanofibers, post-self-assembly cross-linking allows the catalyst of the Belousov-Zhabotinsky (BZ) reaction to be attached to the nanofibers, resulting in a hydrogel that exhibits concentration oscillations, spiral waves, and concentric waves. In addition to the first report of the observation of BZ spiral waves in a hydrogel that covalently integrates the catalyst, we suggest a new approach to developing active soft materials as chemical oscillators and for exploring the correlation between molecular structure and far-from-equilibrium dynamics.