Excitable media are spatially distributed systems with a stable state that responds to perturbations in a distinctive way. If the normal resting state of the medium is perturbed sufficiently strongly, the perturbation is amplified before the system returns to the resting state. Such excitable media are commonly found in nature, and self-organized wave patterns in these systems control the behavior of many physical and biological systems (Zykov, 1987; Mikhailov, 1994; Kapral and Showalter, 1995). Surface catalytic oxidation reactions often proceed through the propagation of excitable waves of oxidation that sweep across the surface of the catalyst. The oxidation of CO on Pt surfaces has been especially well studied in this context (Ertl, 2000). In biological systems waves of this type occur in the aggregation stage of the slime mould Dictyostelium discoideum, where the chemical signaling is through periodic waves of cAMP; also, the Ca+2 waves in systems such as Xenopus laevis oocytes and pancreatic β cells fall into this category (Goldbeter, 1996). Electrochemical waves in cardiac and nerve tissue also depend on the excitability of the medium, and the appearance and/or breakup of spiral wave patterns (Fig. 24.1) are believed to be responsible for various types of arrhythmia in the heart (Winfree, 1987; Fenton et al., 2002; Clayton and Holden, 2004). Excitable waves have been extensively studied (Belmonte et al., 1997) for the BZ reaction, one of the first systems in which such waves were observed (Zaikin and Zhabotinsky, 1970; Winfree, 1972). Chemical waves in excitable media often take the form of spirals, and Fig. 24.2 shows spiral waves in the Belousov–Zhabotinsky reaction under conditions where this chemical medium is excitable.