Spiral instabilities in N-body simulations

N-body simulations of disc galaxies that display recurrent transient spiral patterns are comparatively easy to construct, but are harder to understand. In this paper, I summarise the evidence from such experiments that the spiral patterns result from a recurrent spiral instability cycle. Each wave starts as rapidly growing, small-amplitude instability caused by a deficiency of particles at a particular angular momentum. The resulting large-amplitude wave creates, through resonant scattering, the conditions needed to precipitate a new instability.