The simulation of cardiac electrophysiological waves are known to require extremely fine meshes, limiting the applicability of current numerical models to simplified geometries and ionic models. Mesh adaptation methods are extremely helpful to improve the accuracy of finite element simulations and can reduce the number of degrees of freedom required for a given accuracy. However, they also have a cost and it is not clear if they are competitive with respect to very fine uniform meshes especially for complex cardiac dynamics. The purpose of this work is to explore the efficiency of a three-dimensional anisotropic adaptive finite element method for simulating the spatio-temporal chaos in cardiac tissue. The computational efficiency of the proposed method is assessed using reference solutions obtained on a uniform refined mesh with more than 44 millions degrees of freedom. In addition to the monodomain, the bidomain model will be also employed and examples of ventricular fibrillation in cardiac tissue will be illustrated. Qualitative results will be presented showing that the proposed methodology reduces significantly the number of elements leading to huge saving in memory as well as in computational time.