The living cell encodes information in the state and organization of its constituent molecules. The organization and flow of molecules and information is regulated by energy-consuming processes in the cell. These active energy consuming processes result in a dynamic patterning of molecules within the cell -- here we will focus on the active organization of molecules at the surface of living cells, which separate the inside of the cell from the outside. This has profound implications for the spatiotemporal regulation of chemical reactions, optimization of information processing and computation on the cell surface. This will bring together two apparently unconnected seminal papers of Alan Turing.