Multicellularity enables the growth of complex life forms as it allows for the specialization of cell types, differentiation and large-scale spatial organization. In a similar way, modular construction of synthetic multicellular systems will lead to dynamic biomimetic materials that can respond to their environment in complex ways. To achieve this goal, artificial cellular communication and developmental programs still have to be established. Here, we create geometrically controlled spatial arrangements of emulsion-based artificial cellular compartments containing synthetic in vitro gene circuitry, separated by lipid bilayer membranes. We quantitatively determine the membrane pore-dependent response of the circuits to artificial morphogen gradients, which are established via diffusion from dedicated organizer cells. Utilizing different types of feedforward and feedback in vitro gene circuits, we then implement artificial signalling and differentiation processes, demonstrating the potential for the realization of complex spatiotemporal dynamics in artificial multicellular systems.