This is an introductory talk about some amazing patterns and their mathematical analysis. A dangerous arrhythmia known as tachycardia is thought to be caused by pathological rotating waves of electrical activity in the heart. In two dimensions, these appear as spiral waves; in three, as scroll waves. Similar waves occur in the BZ chemical reaction and in models of coupled oscillators. I'll show videos of these phenomena and will analyze them using elementary ideas from topology and nonlinear dynamics.