Evolution of the location of the nodes closest to the surface of the n = 9, 10, 11 and 12 modes. In order to increase visual clarity, the nodes of the n = 9, 11 and 12 modes have been shifted by values of 0.034, −0.030 and −0.060 in core hydrogen fraction. This aligns the modes before and after the avoided crossing, as in Fig. 6. Immediately after the first cascade of avoided crossings, the n = 12 mode has settled in at the position of the n = 11 mode just before the cascade, the n = 11 mode at the position of the n = 10 mode and finally the n = 10 mode at the position of the n = 9 mode.