A new fully adaptive multiresolution method is applied for the simulation of the complex dynamics of waves in excitable media in electrocardiology, where the membrane kinetics are given by the Aliev–Panfilov or Luo–Rudy II models. Numerical experiments show that the automatic adaptation strategy tracks the spatio-temporal pattern accurately at a substantially reduced computational cost if compared with fine-grid simulations. The nonlinear dynamics of complex multiscale patterns can thus be computed efficiently, also in the chaotic and turbulent regime which are currently beyond the frontiers of methods using regular discretizations.