A defining characteristic of the normal development of the enteric nervous system (ENS) is the existence of an enteric neural crest (ENC) cell colonization wave, where the ENC cells form stable chains often associated with axons and near the vascular network. However, within this evolving neural network, the individual ENC cell elements constantly move, change direction and appear to act independently of neighbors. Three possible hypotheses are investigated. The simplest of these postulates that the ENS follows the vascular network as a template. We present evidence which does not support this hypothesis. Two viable alternatives are either that (i) the axons muster the ENC cells, providing the pattern for the chain migration or (ii) ENC cells form chains and the axons follow these paths. These two hypotheses are explored by developing a stochastic cellular automata model, where ENC agents follow simple rules, which reflect the underlying biology of movement, proliferation and differentiation. By simulating ENC precursors and the associated neurons and axons, two models with different fundamental mechanisms are developed. From local rules, a mesoscale network pattern with lacunae emerges, which can be analyzed quantitatively. Simulation and analysis establishes the parameters that affect the morphology of the resulting network. This investigation into the axon/ENC and ENC/ENC interplay suggests possible explanations for observations in mouse and avian embryos in normal and abnormal ENS development, as well as further experimentation.