Synthetic biology provides an opportunity for the construction and exploration of alternative solutions to biological problems - solutions different from those chosen by natural life. To this end, synthetic biologists have built new sensory systems, cellular memories, and alternative genetic codes. There is a growing interest in applying synthetic approaches to multicellular systems, especially in relation to multicellular self-organization. Here we describe a synthetic biological system that confers large-scale de novo patterning activity on 2-D and 3-D populations of mammalian cells. Instead of using the reaction-diffusion mechanisms common in real embryos, our system uses cadherin-mediated phase separation, inspired by the known phenomenon of cadherin-based sorting. An engineered self-organizing, large-scale patterning system requiring no prior spatial cue may be a significant step towards the construction of self-assembling synthetic tissues.