Synthetic biology is a promising tool to study the function and properties of gene regulatory networks, and is being applied to studying patterning systems in biology. Although several patterning mechanisms have been proposed in classical developmental biology, the Turing pattern mechanism is unique in terms of self-correction, and economy of design, and has never been constructed ab initio using defined biological components. It is therefore a tantalising engineering target. However, it is difficult to bridge the gap between mathematical formulations and biological implementations of Turing patterns, even though this is necessary for both understanding and engineering these networks with synthetic biology approaches. In this talk, we will present our work on building a toolkit of mammalian components for spatiotemporal network engineering, as well as the design considerations that increase the chances of obtaining artificial Turing patterns.