of the open boundaries of the muscle tissue are excited.

7.  A small fraction $\delta$ of cells are dysfunctional and have a small probability $\epsilon$ of not getting excited.

![The formation of fibrillatory re-entrant circuits in the Christensen-Manani-Peters model for a refractory period of $\tau = 50$. Excited cells are shown in white, resting (excitable) cells are black and cells which are refractory (unexcitable) are shown in grey. **(a)** A planar wave initiated by the pacemaker cells at the left boundary of the cylindrical heart tissue propagates from left to right along muscle fibres. **(b)** A dysfunctional cell fails to fire blocking the propagation of the signal along that fibre. Excited cells in the adjacent muscle fibre can re-excite the blocked fibre at the next vertical coupling, see Fig. \[fig:rotorform\]. **(c)** If the pathlength of the re-excitation is sufficiently long, the re-entrant excitation can escape the unexcitable region. **(d)** This escaped excitation initiates a continuously activated circuit from which chaotic waves propagate – this circuit is the driver of AF. **(e)** Fibrillatory waves spread across the whole tissue and prevent the formation of new planar wavefronts at the pacemaker cells on the left boundary. **(f)** If a dysfunctional cell in 