Simulations of isolated galaxy disks that are stable against bar formation readily manifest multiple, transient spiral patterns. It therefore seems likely that some spirals in real galaxies are similarly self-excited, although others are clearly driven by tidal interactions or by bars. The rapidly changing appearance of simulated spirals does not, however imply that the patterns last only a fraction of an orbit. Power spectrum analysis reveals a few underlying, longer-lived spiral waves that turn at different rates, which when super-posed give the appearance of swing-amplified transients. These longer-lived waves are genuine unstable spiral modes; each grows vigorously, saturates and decays over a total of several orbit periods. As each mode decays, the wave action created as it grew drains away to the Lindblad resonances, where it scatters stars. The resulting changes to the disk create the conditions for a new instability, giving rise to a recurring cycle of unstable modes.