Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it, we construct a Turing reaction-diffusion model which generates spot patterns initially. Starting from this spotted pattern, we successfully generate patterns of adult leopards and jaguars by tuning parameters of the model in the subsequent phase of patterning.

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We simulate the patterns on the hard wings of lady beetles using a reaction-diffusion equation based on the Turing model. A part of a spherical surface is used to approximate the geometry of the hard wings. Various patterns common to lady beetles in Taiwan can be produced on this curved surface by adjusting the parameters of the model.

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