Autorhythmicity was initiated in modified virtual ventricular cells and tissues of the Luo-Rudy (LRd00) family (Faber, 2000) by (1) [Ca²⁺]_i oscillations due to [Na⁺]_i overload and (2) block of the time-independent potassium current I_K1. The voltage-clamped (dV/dt = 0, V = -80 mV) calcium subsystem at low levels of [Na⁺]_i has stable, steady-state [Ca²⁺]_i (Fig. 1). For [Na⁺]_i just above 14 mM, very low rate [Ca²⁺]_i oscillations emerge. As [Na⁺]_i is further increased to 16 mM, the period of the oscillations decreases to 0.65 s. In a modified LRd00 endocardial cell (100% inhibition of I_Na-K, two-fold increase of I_ns(Ca) conductance, CSQN_th = 7 mM, initial [Na⁺]_i = 20 mM and [K⁺]_i = 125 mM), these [Ca²⁺]_i oscillations drive sub-threshold voltage oscillations that lead to spontaneous action potentials. Down-regulation of g_K1, the maximum conductance of I_K1, can induce autorhythmicity in ventricular cells (Miake et al., 2002). Reducing fractional g_K1 to about 0.3 in LRd00 induced low-rate membrane potential oscillations. With complete block of I_K1 the cells oscillate with periods ranging from 308-369 ms (Fig. 1). Qualitatively similar results are found with the model of ten Tusscher et al. (2004) for human virtual ventricular cells, with oscillations emerging at fractional g_K1 = 0.078 and a period of 0.8 s with complete I_K1 block. The large decrease in the period of the [Ca²⁺]_i and voltage oscillations close to their emergence at a bifurcation suggests homoclinic rather than Hopf bifurcations. For all cell types, the minimal length of [Na⁺]_i overloaded tissue required for the initiation of propagating autorhythmic activity in 1-D homogeneous tissue strands was 1.6 mm. For reduced I_K1, the minimal length was 5.2 mm in 1-D homogeneous strands and the minimal radius was 3.8 mm in 2-D homogeneous tissues.