The most vibrant and striking colours in living organisms are often caused by a combination of pigments and nano-scale transparent architectures, which interact with light to produce so-called structural colours. These colours are the result of light interfering with the nanoscale structures that are present in the materials. Such colour-producing structures are not perfect, and irregularities in the arrangements (disorder) are present in many organisms. However, disorder in natural structures is not detrimental but functional, as it allows a broader range of optical effects. This chapter reviews and attempts to classify structurally coloured organisms, highlighting the influence that disorder has on their visual appearance. It also showcases how photonic systems, such as the blue Morpho butterfly and the white Cyphochilus beetle, are capable of obtaining optical properties (long-distance visibility and whiteness, respectively) where disorder seems to be highly optimized, indicating that disorder is important for obtaining complex visual effects in natural systems.

The chapter first introduces the mathematical concepts required for analysing disordered systems, such as the Fourier transform and the structure factor. Then, ordered and disordered natural photonic systems are reviewed. This is followed by examples of completely disordered structures responsible of white appearances. Finally, we review the possibilities of hierarchical organisation and pixelated surfaces to widen the range of optical appearances.