Spatial patterns are investigated in a nonuniform Belousov-Zhabotinsky (BZ) reaction medium, a thin layer of ferroin-loaded cation-exchange resin bathed in a BZ reaction mixture containing no catalyst. Two different nonuniform systems are investigated : (i) a system composed of two resin layers with different refractory periods (longer one, T-r) separated by a sharp boundary, and (ii) a system in which one of the two layers in system i is replaced by a layer of a mixture of two different resin beads. Wave patterns in each type of nonuniform systems are critically influenced by wave periods. In a system i, when periods of waves originating from either side of the boundary are longer than T-r, the waves with a shorter period grow over those with a longer one and cover the whole space in the medium. When the period of waves in one of the two layers is shorter than T-r, a 2:1 entrainment is established for the waves propagating in the same direction on either side of the boundary. The waves propagating in opposite directions form independent patterns on either side of the boundary. In a system ii, two sets of waves are observed, one propagating along the upper part and another along the lower part of the layer. When waves are initiated with a period shorter than T-r, they propagate initially only in the upper part of the layer. After the waves cover the whole space of the mixture layer, new waves appear in the lower part of the layer. The upper and lower waves propagate independently of each other. When waves with a period longer than T-r propagate in the mixture layer, the upper and lower waves show complete spatiotemporal entrainment.