A recent theory has suggested that populations of migrating and proliferating cells can create network structures by responding to strain cues associated with the cell density variations that arise during network formation. Unlike prior theories of network formation, the strain-cue mechanism leads to nonfractal networks, consisting of closed loops rather than tree-like morphologies. In this paper, the possibility is suggested of developing a synthetic process for fabricating networks that mimic the mechanisms present in the theory. Such a biomimetic process should replicate three phenomena: (1) the extension of the existing network domain should be governed by the strain field that exists just outside the existing domain, rather than the strains within the domain; (2) the process should be stochastic; and (3) a relaxation mechanism must be present by which the strains that induce network extension at any location will fade with time. Simulations imply values for the key parameters of these mechanisms to achieve useful networks. Possible routes to realizing a biomimetic system are discussed.