The paper discusses the observation of Hofstadter's butterfly in moiré superlattices formed by bilayer graphene coupled to hexagonal boron nitride (hBN). This phenomenon, first theoretically discovered by Douglas Hofstadter in 1976, describes a self-similar recursive energy spectrum in 2D electron systems subjected to both a magnetic field and a periodic electrostatic potential. The authors demonstrate that the moiré superlattice in bilayer graphene and hBN provides an ideal-sized periodic modulation, enabling experimental access to the fractal spectrum. They confirm that the quantum Hall effect features associated with the fractal gaps are described by two integer topological quantum numbers, $s$ and $t$, and report evidence of their recursive structure. The study also highlights the emergence of anomalous quantum Hall states, characterized by Hall conductance plateaus at non-integer Landau level filling fractions, and the observation of recursive mini-QHE series within the main fan diagram. The experimental findings provide a deeper understanding of the fractal energy landscape and the interplay between the magnetic and periodic fields in two-dimensional electron systems.The paper discusses the observation of Hofstadter's butterfly in moiré superlattices formed by bilayer graphene coupled to hexagonal boron nitride (hBN). This phenomenon, first theoretically discovered by Douglas Hofstadter in 1976, describes a self-similar recursive energy spectrum in 2D electron systems subjected to both a magnetic field and a periodic electrostatic potential. The authors demonstrate that the moiré superlattice in bilayer graphene and hBN provides an ideal-sized periodic modulation, enabling experimental access to the fractal spectrum. They confirm that the quantum Hall effect features associated with the fractal gaps are described by two integer topological quantum numbers, $s$ and $t$, and report evidence of their recursive structure. The study also highlights the emergence of anomalous quantum Hall states, characterized by Hall conductance plateaus at non-integer Landau level filling fractions, and the observation of recursive mini-QHE series within the main fan diagram. The experimental findings provide a deeper understanding of the fractal energy landscape and the interplay between the magnetic and periodic fields in two-dimensional electron systems.