Finite Element Modeling and Analyses on Pattern Formation of Butterfly Wings
Date Issued
2006
Date
2006
Author(s)
Wu, Che-Wei
DOI
zh-TW
Abstract
ABSTRACT
One of the elementary processes in morphogenesis is the formation of a spatial pattern of tissue structures. It has been shown that relatively simple molecular mechanisms based on auto and cross catalysis can account for a primary pattern of morphogens to determine pattern formation of the tissue. This study simulates and analyses butterfly wing pattern by using Turing system. The simulated wing patterns include Satyrinae and Papilionidae butterflies. We focus on the effect of key factors such as parameter values for mode selection, wave number, wing shape and boundary conditions. We express the stability and the tendency by constructing 2D and 3D parameter plane, and we discuss the boundary conditions of the system effect on pattern formation. Elementary patterns of butterfly wings are simulated by the source-sink, source-source and diffusion-reaction methods. This study utilizes five kinds of different Turing systems to simulate butterfly wing patterns. These systems are Joakim Linde Turing system, Dilão Turing system, Gierer-Meinhardt Turing system, Gray-Scott Turing system, and Schnakenberg Turing system. The finite element software FEMLAB was used for the simulation and analyses. Judging from their similar rate of convergence, Dilão and G-M systems were used to simulate wing patterns of Lethe butler and Lethe sinorix butterfly. We also used Dilão, G-M and Schnakenberg systems to simulate wing patterns of Lethe Helena Leech butterfly. In this study we found that wing pattern formation simulation is affected by two major factors of boundary condition and wave number parameters. The parameters are adjusted iteratively until the simulated pattern error is under a threshold. In contrast to simulate wing patterns of simple shape and using single Turing system, this study expands the scope to simulate whole butterfly wing patterns using composite Turing systems. As a result, more realistic butterfly wing patterns can be simulated and visualized.
Keywords: Turing system, Biological Pattern Formation, Diffusion Reaction
Subjects
涂林系統
生物斑紋形成
擴散反應方程式
Turing system
Biological Pattern Formation
Diffusion Reaction
Type
thesis
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