  We argue that self-excited instabilities are the cause of spiral patterns in
simulations of unperturbed stellar discs. In previous papers, we have found
that spiral patterns were caused by a few concurrent waves, which we claimed
were modes. The superposition of a few steadily rotating waves inevitably
causes the appearance of the disc to change continuously, and creates the kind
of shearing spiral patterns that have been widely reported. Although we have
found that individual modes last for relatively few rotations, spiral activity
persists because fresh instabilities appear, which we suspected were excited by
the changes to the disc caused by previous disturbances. Here we confirm our
suspicion by demonstrating that scattering at either of the Lindblad resonances
seeds a new groove-type instability. With this logical gap closed, our
understanding of the behaviour in the simulations is almost complete. We
believe that our robust mechanism is a major cause of spiral patterns in the
old stellar discs of galaxies, including the Milky Way where we have previously
reported evidence for resonance scattering in the recently released Gaia data.
