Magnetic flux emerges from the solar surface as dark filaments connecting small sunspots with opposite polarities. The regions around the dark filaments are often bright in X-rays and are associated with jets. This implies plasma heating and acceleration, which are important for coronal heating. Previous two-dimensional simulations of such regions showed that magnetic reconnection between the coronal magnetic field and the emerging flux produced X-ray jets and flares, but left unresolved the origin of filamentary structure and the intermittent nature of the heating. Here we report three-dimensional simulations of emerging flux showing that the filamentary structure arises spontaneously from the magnetic Rayleigh-Taylor instability, contrary to the previous view that the dark filaments are isolated bundles of magnetic field that rise from the photosphere carrying the dense gas. As a result of the magnetic Rayleigh-Taylor instability, thin current sheets are formed in the emerging flux, and magnetic reconnection occurs between emerging flux and the pre-existing coronal field in a spatially intermittent way. This explains naturally the intermittent nature of coronal heating and the patchy brightenings in solar flares.