It's quite easy to see how simple 3D objects could be created using the principle. For example, if the solution were only applied to the edges, only they would shrink when heated, and the disc would form a bowl-shaped object. But more complex "chemical origami" would need an intricate application pattern, and it is difficult to predict 2D patterns that will accurately translate into the 3D objects desired.

The problem is that surfaces in 3D do not follow the same "Euclidean" geometry as those in 2D. In non-Euclidean geometry, the angles of a triangle do not add to 180°, and parallel lines are not straight but curved. This is why, for example, it is impossible to draw a map of the Earth on a flat sheet of paper without compressing the polar regions – in other words, the grid formed by the lines of latitude and longitude has squares that become distorted in size. What engineers would be keen to do, however, is the opposite: design a structure as a grid on a flat 2D object and then "activate" the third dimension by giving each grid square the right amount of a certain stimulus.

Eran Sharon and colleagues from the Hebrew University of Jerusalem have now done just that by calculating a "metric" – a tensor that characterizes how local distances ought to vary over a surface when activated. Using this metric as a blueprint, the physicists applied the monomer solution N-isopropylacrylamide (i.e. the stimulus) in varying spatial concentration over the surface of the disc. When the disc was then heated over 33 °C, the regions of higher concentration shrunk more (in other words, local distance was reduced) and hence created deeper bends under the resultant stress.

Sharon's team created a range of structures varying in complexity, from slightly wavy crisp-like objects to those that look like a sombrero. Randall Kamien, a physicist from the University of Pennsylvania, told Physics Web that the technique could be used in the engineering of prototypes. "You could imagine a printer that prints a metric into a flat sheet, which you heat, and it forms the desired 3D object," he said.