This work analyzes spatiotemporal patterns that exist in a one-dimensional isothermal fixed-bed reactor with bistable or oscillatory kinetics. The model accounts for an oscillator with a diffusing activator and immobile inhibitor. Patterns emerge due to self-induced gradients of the fluid phase and the patterns are different from those reported for uniform excitable or oscillatory media. Pattern selection is determined by the phase planes spanned by the reactor and the ratio of the two slowest time scales: front residence time and period of oscillations. The main sustained spatiotemporal patterns in the bed were classified as parallel bands, oscillatory fronts (or sticking fronts), and split bands. Parallel bands represent a periodic sequence of pulses and appear when the bed spans the oscillatory domain. Split-band patterns appear when new fronts are generated inside the reactor but they cannot propagate due to refractory trail of the previous pulse.