Biological development is a remarkably complex process. A single cell, in an appropriate environment, contains sufficient information to generate a variety of differentiated cell types, whose spatial and temporal dynamics interact to form detailed morphological patterns. While several different physical and chemical processes play an important role in the development of an organism, the locus of control is the cell's gene regulatory network. We designed a dynamic recurrent gene network (DRGN) model and evaluated its ability to control the developmental trajectories of cells during embryogenesis. Three tasks were developed to evaluate the model, inspired by cell lineage specification in C. elegans, describing the variation in gene activity required for early cell diversification, combinatorial control of cell lineages, and cell lineage termination. Three corresponding sets of simulations compared performance on the tasks for different gene network sizes, demonstrating the ability of DRGNs to perform the tasks with minimal external input. The model and task definition represent a new means of linking the fundamental properties of genetic networks with the topology of the cell lineages whose development they control.