We seek to understand the origin of radial migration in spiral galaxies by analysing in detail the structure and evolution of an idealized, isolated galactic disc. To understand the redistribution of stars, we characterize the time evolution of properties of spirals that spontaneously form in the disc. Our models unambiguously show that in such discs, single spirals are unlikely, but that a number of transient patterns may coexist in the disc. However, we also show that while spirals are transient in amplitude, at any given time the disc favours patterns of certain pattern speeds. Using several runs with different numerical parameters we show that the properties of spirals that occur spontaneously in the disc do not sensitively depend on resolution. The existence of multiple transient patterns has large implications for the orbits of stars in the disc, and we therefore examine the resonant scattering mechanisms that profoundly alter angular momenta of individual stars. We confirm that the corotation scattering mechanism described by Sellwood & Binney is responsible for the largest angular momentum changes in our simulations.