The Hofstadter model describes how electrons behave on a 2D lattice under a magnetic field, producing a fractal energy spectrum (the Hofstadter butterfly) with gaps labeled by Chern numbers. This model connects lattice physics with topological effects like the quantum Hall effect. With recent advances in moiré superlattices (e.g., twisted bilayer graphene), the Hofstadter spectrum can now be observed experimentally, enabling studies of topological and fractal quantum phenomena. The internship project aims to explore a duality in the Hofstadter model within moiré crystals, which are described by continuous models rather than tight-binding ones. This duality suggests that the high-flux regime of the continuous model corresponds to an effective tight-binding Hofstadter model.