Selected stages in the evolution of the numerical solution described in Sect. 4.2. Panel (a): Initial condition (solid black curve), resulting from the addition of the exact first symmetric self-similar harmonic (dashed red) and a finite antisymmetric perturbation of zero net flux (dashed green). In panels (d)–(f), the exact self-similar dipole harmonic evolving towards the final shape of the numerical solution is superimposed in cyan. Note the different ranges of the ordinate axes in the different panels. An associated animation is provided that shows intermediate stages including the solution (upper panel) and the corresponding diffusive flux (lower panel); the associated movie is available online.