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Mathematical Modeling and Simulation

  • Mathematical Modeling and Simulation of Compound Eyes

    In this project we design a three dimensional geometric model of compound eye with flexible parameters and a model of compound eye evolution using computer simulation. During the process we investigate the geometric open problem “Distribution of Points on the 2-Sphere” and the various algorithms proposed by mathematicians and scientists to solve the problem. 

    By manipulating variant parameters of the geometric model, we can see the overall change of the eye structure and how it will affect its optical properties. With the evolution model, we will observe and predict evolutionary changes in compound eyes due to different lifestyles and habitats of animals. The outcome of the evolution will then be demonstrated by the geometric model.

    Applied Math Figure 3

    Figure 3: Compound eye of a dragonfly and eye structure

    Applied Math Figure 4

    Figure 4: A coarse simulation