Models of gene regulatory networks (GRN) have proven useful for understanding many aspects of the highly complex behavior of biological control networks. Randomly generated non-Boolean networks were used in experimental simulations to generate data on dynamic phenotypes as a function of several genotypic parameters. We hypothesized that the topological component of network genotype could be an obstacle to the discovery of mathematical formulas that can predict certain phenotypic parameters. Our data support that hypothesis. We quantitated the effect of topological genotype (TGE) and determined its influence on a number of dynamical phenotypes in simple and complex multi-gene networks. For situations where the TGE was low, it was possible to infer formulas to predict some phenotypes with good accuracy based on number of network genes, interaction density, and initial conditions. In addition to formulation of these mathematical relationships, we found a number of dynamic properties, including complex oscillation behaviors, that were largely dependent on genotype topology, and for which no such formulas were determinable. For integrated measures of gene expression state, we observed a variety of oscillation patterns, including stable, periodic cycling with a wide variety of period length, aperiodic cycling, and apparent chaotic dynamics. It remains to be determined if these results are applicable to biological gene regulatory networks.