  The emissivity of common materials remains constant with temperature
variations, and cannot drastically change. However, it is possible to design
its entire behaviour as a function of temperature, and to significantly modify
the thermal emissivity of a surface through the combination of different
materials and patterns. Here, we show that smart patterned surfaces consisting
of smaller structures (motifs) may be designed to respond uniquely through
combinatorial design strategies by transforming themselves from 2D to 3D
complex structures with a two-way shape memory effect. The smart surfaces can
passively manipulate thermal radiation without-the use of controllers and power
supplies-because their modus operandi has already been programmed and
integrated into their intrinsic characteristics; the environment provides the
energy required for their activation. Each motif emits thermal radiation in a
certain manner, as it changes its geometry; however, the spatial distribution
of these motifs causes them to interact with each other. Therefore, their
combination and interaction determine the global behaviour of the surfaces,
thus enabling their a priori design. The emissivity behaviour is not random; it
is determined by two fundamental parameters, namely the combination of
orientations in which the motifs open (n-fold rotational symmetry (rn)) and the
combination of materials (colours) on the motifs; these generate functions
which fully determine the dependency of the emissivity on the temperature.
