ABSTRACT
In this chapter we will discuss the theory of pattern formation in excitable media, specifically spirals and scrolls. Spirals are self-organized two-dimensional waves of excitation whose front can be described as an involute of a circle. In three dimensions, the corresponding waveform is called a scroll, which can be thought of as contiguous spirals stacked on top of each other. The two-dimensional cross-section of the scroll would thus be a spiral wave. In this chapter, we will describe the origin and dynamics of these patterns of excitation in homogeneous excitable media. Here the word homogeneous implies that the properties of the medium such as its excitability, diffusion coefficient, ionic currents, and conductances, etc., are uniform and do not vary across the medium.
