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Exact fractals of nonlinear waves that rely on strong dispersion and nonlinearity and arise spontaneously out of magnetic media were observed for the first time. The experiments make use of a microwave to excite a spin wave in a quasi-one-dimensional magnonic crystal. When the power of the input microwave (P₈₍) is low, the output signal has a power-frequency spectrum that consists of a single peak. When P₈₍ is increased to a certain level, new side modes are generated through modulational instability, resulting in a comblike frequency spectrum. With a further increase in P₈₍, each peak in the frequency comb can evolve into its own finer comb through the modulational instability. As P₈₍ is increased further, one can observe yet another set of finer frequency combs. Such a frequency-domain fractal manifests itself as multiple layers of amplitude modulation in the time-domain signal.
Richardson et al. (2018) studied this question.