Seismic faults are known to exhibit a high level of spatial and temporal complexity, and the causes and consequences of this complexity have been the topic of numerous research works in the past decade. In this paper, we investigate the origins and the structure of this complexity by considering a numerical model of laboratory earthquake experiment, where we introduce a fault with homogeneous mechanical properties but allow it to evolve spontaneously to its natural level of complexity. This is achieved by coupling the elastic deformability of the off-fault medium (and therefore allowing for heterogeneous stress fields to develop) and the discrete degradation and gouge formation at the fault plane (and therefore allowing for structural heterogeneity to develop). Numerical results show the development of persistent stress, damage, and gouge thickness heterogeneities, with a much larger variability in space than in time. Strong positive correlations are found between these quantities, which suggest a positive feedback between local normal stress and damage rate, only mildly mitigated by the mobility of the granular gouge in the interface. For a wide range of confining stresses, after a sufficient number of seismic cycles, the fault reaches a state of established disorder with a constant roughness, a certain amount of periodicity at the millimetric scale, and a power law decay of the Power Spectral Density at smaller spatial scales. The typical height-to-wavelength ratio of geometrical asperities and the correlations between stress and damage profiles are in good agreement with previous field or lab estimates. Earthquakes occur on faults in the Earth curst, and these faults are known to be highly complex, both from a geometrical and structural point of view. This complexity is now introduced artificially in many numerical and theoretical models of faults in order to derive meaningful knowledge related to earthquake mechanics. There is little knowledge, however, about the way this complexity develops. In this paper, we employ a numerical model to observe the spontaneous development of this complexity, in order to understand its origin, its structure, and its evolution. A coupled discrete-continuum model of laboratory earthquakes allows the spontaneous development of fault complexity along seismic cycles Fault heterogeneity is persistent in space and time, with a strong positive correlation between normal stress, damage, and gouge thickness Stress fields exhibit a millimetric periodicity and a self-affinity at smaller scales, in quantitative agreement with previous estimates