Propagating chemical waves are typically studied in homogeneous, excitable reaction mixtures. Chemical waves in an inhomogeneous excitable medium are examined in this paper. Cation exchange beads, loaded with ferroin, are bathed in Belousov-Zhabotinsky reaction mixtures containing no catalyst. Spiral waves are spontaneously initiated above a critical bromate concentration, which is dependent on the size of the ferroin-loaded beads. At high bromate concentrations, irregular patterns are formed due to an overcrowding of spirals. An upper limit in the number of individual waves is exhibited, which is independent of the bead size. Regular and irregular patterns are analyzed by calculating spatial correlation functions from digital images.