The emergence of stationary spatially multiperiodic or even spatially chaotic patterns is analyzed for a simple model of convection, reaction, and conduction in a cross-flow reactor. Spatial patterns emerge much like dynamic temporal patterns in a mixed system of the same kinetics. Moving waves are formed in an unbounded system but they are transformed into stationary spatially inhomogeneous patterns in a bounded system. The sequence of period doubling bifurcations is determined numerically. The incorporation of a slow nondiffusing inhibitor leads to chaotic spatiotemporal patterns.