Effects of randomization of characteristic times on spiral wave generation in a simple cellular automaton model of excitable media

Vincent Vangelista, Northeastern Illinois University
Karl Amjad-Ali, Northeastern Illinois University
Minhyeok Kwon, Northeastern Illinois University
Paulo H. Acioli, Northeastern Illinois University


Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions such as epilepsy and atrial fibrillation. We used a simple cellular automaton model to study propagation in excitable media, with a particular focus on understanding spiral wave behavior. The main ingredients of this cellular automaton model are an excitation condition and characteristic excitation and refractory periods. The literature shows that fixed excitation and refractory periods together with specific initial conditions generate stationary and stable spiral waves. In the present work, we allowed the activation and refractory periods to fluctuate uniformly over a range of values. Under these conditions, this very simplistic model can recreate the meandering and breakup of spiral waves that were observed in more elaborate models in the literature.