During embryogenesis, homogenous groups of cells self-organize into stereotypic spatial and temporal patterns that make up tissues and organs. These emergent patterns are controlled by transcription factors and secreted signals that regulate cellular fate and behaviors through intracellular regulatory circuits and cell-cell communication circuits. However, the principles of these circuits and how their properties are combined to provide the spatio-temporal properties of tissues remain unclear. Here we develop a framework to explore building-block circuits of developmental programs. We use single-cell gene expression data across developmental stages of the human intestine to infer the key intra- and inter-cellular circuits that control developmental programs. We study how these circuits are joined into higher-level hyper-motif circuits and explore their emergent dynamical properties. This framework uncovers design principles of developmental programs and reveals the rules that allow cells to develop robust and diverse patterns.