Fractal spectra in generalized Fibonacci one-dimensional magnonic quasicrystals

► Quasiperiodic magnonic crystals are arranged in accordance with the generalized Fibonacci sequence. ► Heisenberg model in exchange regime is applied. ► We use a theoretical model based on a transfer-matrix method together random-phase approximation. ► Fractal spectra are characterized. ► We analyze the distribution of allowed bulk bands in function of the generalized Fibonacci number.