The butterfly Papilio dardanus is well known for the spectacular phenotypic polymorphism in the female of the species. We show that numerical simulations of a reaction diffusion model on a geometrically accurate wing domain produce spatial patterns that are consistent with many of those observed on the butterfly. Our results suggest that the wing coloration is due to a simple underlying stripe-like pattern of some pigment-inducing morphogen. We focus on the effect of key factors such as parameter values for mode selection, threshold values which determine colour, wing shape and boundary conditions. The generality of our approach should allow us to investigate other butterfly species. The relationship between these key factors and gene activities is discussed in the context of recent biological advances.