Understanding how neural circuits in the brain wire up during development is important for the implementation of numerous functions in adulthood, but also for the prevention and treatment of many neurological disorders that result from bad wiring. Before the onset of sensory experience, spontaneous activity in the developing brain organizes and refines circuits. Hence, alterations in spontaneous activity can lead to severe deficits in wiring. One such alteration occurs in the Fragile X mouse model, where a single genetic mutation reduces cortical inhibition and increases the number of neurons recruited in spontaneous activity. The mechanisms behind the generation of spontaneous activity remain unclear, especially regarding how genetic mutations affect spontaneous activity. To address this, we investigated how biologically realistic spontaneous activity can emerge in recurrent networks with excitatory and inhibitory neurons and background input representing the sensory periphery. We find that our model successfully captures two distinct types of spontaneous activity, local (L-) and global (H-) events, that match experimentally characterized activity originating in the sensory periphery or the cortex. During local events strong inputs from the sensory periphery result in dominant inhibition which limits lateral spread of activity. Conversely, during global events intrinsically triggered inputs produce dominant excitation which spreads laterally without restriction. We next analyzed calcium imaging data from the developing cortex of Fragile X mice revealing spontaneous activity with an increase of global and decrease in local events. Finally, we explored two plausible mechanisms that lead to this altered activity: weakened feedforward connectivity vs. reduced inhibitory recurrent connectivity. These alternatives make different experimentally-testable predictions for the relative ratio between local and global events. Our model allows us to investigate the role of connectivity profiles, intrinsic excitability, and correlations in shaping normal and genetically-altered spontaneous activity, and the implications for receptive field refinements in development.