This study reports the experimental observation of Hofstadter's butterfly spectrum in moiré superlattices formed in bilayer graphene (BLG) on hexagonal boron nitride (hBN). The moiré superlattice provides a nearly ideal periodic modulation, enabling access to the fractal quantum Hall effect. The fractal energy spectrum is characterized by self-similar recursive structures, with quantum Hall effect features described by two integer topological quantum numbers, s and t. The Hofstadter spectrum is observed through the recursive structure of the quantum Hall conductance, which exhibits non-monotonic behavior and plateaus at non-integer Landau level filling fractions. The Hofstadter butterfly spectrum arises from the interplay between the periodic potential of the moiré superlattice and the magnetic field. The fractal energy spectrum is described by a Diophantine equation relating the normalized carrier density and magnetic flux. The spectrum exhibits a rich structure with fractal gaps that appear as minima in longitudinal resistance and quantized plateaus in transverse Hall resistance. The fractal gaps are characterized by their position in the Wannier diagram, which maps the normalized carrier density against the magnetic flux. The study demonstrates that the moiré superlattice in BLG/hBN provides a unique platform for observing the Hofstadter butterfly spectrum. The fractal gaps are observed in the quantum Hall regime, with the Hall conductance quantized to integer multiples of e²/h. The recursive structure of the Hofstadter spectrum is confirmed through the observation of fractal gaps at different magnetic fields, with the fractal gaps appearing as minima in longitudinal resistance and quantized plateaus in transverse Hall resistance. The fractal gaps are also observed to exhibit a linear trend in the Wannier diagram, consistent with the Diophantine equation. The study also highlights the importance of the moiré superlattice in enabling the observation of the Hofstadter butterfly spectrum. The moiré superlattice provides a nearly ideal periodic modulation, allowing for the precise control of the magnetic field and carrier density. The fractal gaps are observed to exhibit a rich structure, with the fractal gaps appearing at different magnetic fields and with different values of the quantum numbers s and t. The study provides experimental confirmation of the Hofstadter butterfly spectrum, demonstrating the unique properties of the fractal energy landscape in a system with tunable internal degrees of freedom.This study reports the experimental observation of Hofstadter's butterfly spectrum in moiré superlattices formed in bilayer graphene (BLG) on hexagonal boron nitride (hBN). The moiré superlattice provides a nearly ideal periodic modulation, enabling access to the fractal quantum Hall effect. The fractal energy spectrum is characterized by self-similar recursive structures, with quantum Hall effect features described by two integer topological quantum numbers, s and t. The Hofstadter spectrum is observed through the recursive structure of the quantum Hall conductance, which exhibits non-monotonic behavior and plateaus at non-integer Landau level filling fractions. The Hofstadter butterfly spectrum arises from the interplay between the periodic potential of the moiré superlattice and the magnetic field. The fractal energy spectrum is described by a Diophantine equation relating the normalized carrier density and magnetic flux. The spectrum exhibits a rich structure with fractal gaps that appear as minima in longitudinal resistance and quantized plateaus in transverse Hall resistance. The fractal gaps are characterized by their position in the Wannier diagram, which maps the normalized carrier density against the magnetic flux. The study demonstrates that the moiré superlattice in BLG/hBN provides a unique platform for observing the Hofstadter butterfly spectrum. The fractal gaps are observed in the quantum Hall regime, with the Hall conductance quantized to integer multiples of e²/h. The recursive structure of the Hofstadter spectrum is confirmed through the observation of fractal gaps at different magnetic fields, with the fractal gaps appearing as minima in longitudinal resistance and quantized plateaus in transverse Hall resistance. The fractal gaps are also observed to exhibit a linear trend in the Wannier diagram, consistent with the Diophantine equation. The study also highlights the importance of the moiré superlattice in enabling the observation of the Hofstadter butterfly spectrum. The moiré superlattice provides a nearly ideal periodic modulation, allowing for the precise control of the magnetic field and carrier density. The fractal gaps are observed to exhibit a rich structure, with the fractal gaps appearing at different magnetic fields and with different values of the quantum numbers s and t. The study provides experimental confirmation of the Hofstadter butterfly spectrum, demonstrating the unique properties of the fractal energy landscape in a system with tunable internal degrees of freedom.