Biological morphogenesis has inspired many efficient strategies to diversify material structure and functionality using a fixed set of components. However, implementation of morphogenesis concepts to design soft nanomaterials is underexplored. Here, we study nanomorphogenesis in the form of the three-dimensional (3D) crumpling of polyamide membranes used for commercial molecular separation, through an unprecedented integration of electron tomography, reaction-diffusion theory, machine learning (ML), and liquid-phase atomic force microscopy. 3D tomograms show that the spatial arrangement of crumples scales with monomer concentrations in a form quantitatively consistent with a Turing instability. Membrane microenvironments quantified from the nanomorphologies of crumples are combined with the Spiegler-Kedem model to accurately predict methanol permeance. ML classifies vastly heterogeneous crumples into just four morphology groups, exhibiting distinct mechanical properties. Our work forges quantitative links between synthesis and performance in polymer thin films, which can be applicable to diverse soft nanomaterials.