Many experimental studies have reported that in-vitro neuronal networks develop into a critical state. Potential mechanisms for such development have been suggested by modeling studies, such as short-term and long-term synaptic plasticity, the balance between excitatory and inhibitory neurons, or the network topology. However, it remains unclear how these mechanisms are orchestrated in physical space where network connectivity and propagation delays are constrained. Here, we simulated a leaky integrate-and-fire neural network located in two-dimensional space with three types of plasticity: excitatory and inhibitory long-term spike-timing dependent plasticity, and short-term depression. From an initial state with zero weights, the network received stochastic inputs and self-organized into a structured network. The network exhibited a temporary supercritical state and settled into a critical steady state with power-law distributed neuronal avalanches. This dynamic development closely mirrors findings in neuronal cultures. To examine how physical constraints on inhibitory connectivity affects the critical state development, we fixed the excitatory network and manipulated the inhibitory network by controlling the probability and the maximal distance of inhibitory connections. We found that the constraints of the inhibitory connections determined whether the network will develop into a subcritical, supercritical, or critical state. In the poster, we will further discuss how the physical range of the inhibitory connections affects the network dynamics.