Rotors or vortex action potentials with a diameter of about 1 centimeter and a rotation period of about 0.1 second occur in normal myocardium just before transition to fibrillation, a disorderly pattern of action potential propagation. Numerical models and corresponding mathematical analysis have recently suggested candidate mechanisms, all two-dimensional, for this transition from periodic electrical activity to something resembling turbulence. However, comparably recent experiments unanimously show that rotors, and the spiral waves they radiate, remain stably periodic in two-dimensional myocardium. This seeming paradox suggests a transition mediated through disorderly dynamics of the electrical vortex in three dimensions, as a "vortex filament."