Fig. 4. General interface patterning can be achieved with just four adhesins, providing an engineering platform for applications such as smart biomaterials and human-readable molecular diagnostic devices.

a, Generating regular triangular, square and hexagonal tilings requires one to two adhesin pairs. Scale bars, 3 mm (left) and 9 mm (middle and right). b, Generating Voronoi tessellation with four doublet elements is guaranteed by the four-colour theorem (Supplementary Video S8). Scale bar, 9 mm. c, Schematic of how a non-Voronoi tessellation can be realized by solving for the associated Voronoi pattern and hiding the added interfaces. d, Definition of closed, open, visible and hidden interfaces. General open interface patterns can be realized using only the four doublet elements and the null element. e, A three-step algorithm for sequentially identifying seed configurations on regular triangular lattices enables arbitrary interface patterning using only two adhesin pairs (Supplementary Video S9). Scale bar, 9 mm. f, Complex curved interface patterns generated with differential expansion rates and seeding densities (green indicates the Nb3-1 strain). Scale bar, 9 mm. g, Thin sheets with interface patterns can be cut out and handled, shown here floating in a PBS bath. Scale bar, 1 cm. h, Surface wettability of biomaterials can be patterned owing to differential hydrophilicity of interface patterns. PBS added to an interface pattern shows that the liquid surface closely tracks the patterned interface (Supplementary Fig. S29). Scale bar, 1 cm. i, Liquid droplets can be captured in regularly tiled squares (Supplementary Fig. S29). Scale bar, 5 mm. j, Demonstration of an environmentally dependent patterning and molecular diagnostic application in which a human-readable indicator (‘\’ or ‘X’) is formed, depending on whether a molecular inhibitor against the Nb2 adhesin (EPEA¹⁰, Fig. 2d) is present or not. Scale bar, 2 mm. k, Implementation of the common 16-segment digital display, programmed to write ‘U of A’, demonstrates complex combinatorial patterning with human-readable output (Supplementary Video S8). Colour codes defined in Fig. 3d; for continuum simulations of b and j, see Supplementary Fig. S27. Scale bar, 9 mm.