Genetic regulatory networks have the complex task of controlling all aspects of life. Using a model of gene expression by piecewise linear differential equations we show that this process can be considered as a process of computation. This is demonstrated by showing that this model can simulate memory bounded Turing machines. The simulation is robust with respect to perturbations of the system, an important property for both analog computers and biological systems. Robustness is achieved using a condition that ensures that the model equations, that are generally chaotic, follow a predictable dynamics.