The dynamics of spiral waves in excitable media has led to interesting developments in bifurcation theory for systems with Euclidean symmetry. I will review the relevant computational studies and show why Euclidean symmetry is important for spiral waves. I will demonstrate a fast simulation code (EZ-Scroll) for real-time interactive simulations of waves in three dimensions. Finally, I will describe two intriguing open mathematical questions motivated by the dynamics of spiral and scroll waves.

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