<i>Ala viridis sublimis</i> : on butterflies, budgies and bicontinuous greens

Abstract Green structural colour associated with bicontinuous photonic nano structures occurs in both butterflies (Lycaenidae, Papilionidae) and birds (Chloropseidae leafbirds, Psittaculidae parrots). In butterflies and leafbirds, porous chitin or keratin single gyroids reflect green; in parrots, porous keratin disordered sponges reflect blue that combines with yellow pigment to produce green. We develop an angular–spectral framework to compute responses under biologically relevant viewing conditions. For gyroids, a spectral kernel constructed using experimentally constrained parameters and orientation statistics from Callophrys rubi serves as a generic representation across gyroid-bearing taxa, enabling computation of stereographic reflectance maps and numerical-aperture-dependent spectra as functions of crystallographic orientation distributions in polycrystalline assemblies. For disordered architectures, we introduce a random Gaussian field framework that provides a natural analytical description of bird sponges, enabling forward spectral modelling and quantitative structural characterization. Both ordered gyroids and disordered sponges represent parallel photonic strat egies converging on green through similar length scales and porosities and filtering. Gyroid-bearing species vary through orientation distributions yet maintain similar structural parameters across distantly related taxa. The analytical frameworks enable direct comparison of ordered and disordered bicontinuous structures across butterflies and birds. This article is part of the theme issue ‘Geometry, materials and the imagination’.