Fig. 4: Tight-binding simulations of an edge wavepacket propagating in a fractal lattice.

a–e Evolution of topological edge states in the fractal SG(4) lattice. a Intensity distribution of the initial field constructed from a truncated topological edge state in the fractal lattice. b–e Intensity distribution at propagation distances Z = 0, 10, 20, 30, 40cm. f–j Evolution in the fractal lattice containing an on-site disorder of \(0.1c_0\), the position of which is marked by the blue dot. The wavepacket displays topologically protected edge transport around the corners and is unaffected by the disorder. The color bar indicates the field intensity. The parameters for the numerical simulation are the same as in Fig. 2