Organismal phenotypes emerge from a complex set of genotypic interactions. While technological advances in sequencing provide a quantitative description of an organism's genotype, characterization of an organism's physical phenotype lags far behind. Here, we relate genotype to the complex and multi-dimensional phenotype of an anatomical structure using the Drosophila wing as a model system. We develop a mathematical approach that enables a robust description of biologically salient phenotypic variation. Analysing natural phenotypic variation, and variation generated by weak perturbations in genetic and environmental conditions during development, we observe a highly constrained set of wing phenotypes. In a striking ex-ample of dimensionality reduction, the nature of varieties produced by the Drosophila developmental pro-gram is constrained to a single integrated mode of variation in the wing. Our strategy demonstrates the emergent simplicity manifest in the genotype-to-phenotype map in the Drosophila wing and may represent a general approach for interrogating a variety of genotype-phenotype relationships., 32 pages, 5 figures, 8 supplementary figures