Mathematical Modeling of Pattern Formation in Butterfly Wings
Date Issued
2005
Date
2005
Author(s)
Yeh, Cheng-Feng
DOI
zh-TW
Abstract
This study combines L-system and Turing system for the research of the mathematical modeling of pattern formation in butterfly wings. In the part of L-system, we develope a program includes some features to realize the objective of reconstruct and describe butterfly veins by L-system strings. Furthermore, the number of different points between the original image and reconstruction of auto sectioned is lesser than the one of non-sectioned by 4 times. There are two problems solved in this process, 1. The line width of vein image is not 1 pixel. 2. Unable to find or extract all of the veins from image completely. We use the method of lower down the resolution and the method of spiral searching from every cross-point to solve these problems. In the part of Turing system, the program developed by this study provides four kinds of Turing system, including activator-inhibitor system (Joakim Linde), eyespot system, G-M Turing system, and Schnakenberg Turing system. On the hand of boundary condition, it could be inputted by the format of bitmap or L-system string file. We compare and discuss the coefficient effects to the formation of patterns and find out the combinations of coefficient which will form patterns meaningful. Finally, we combine the vein reconstructed by L-system strings and Turing system to do the research of pattern formation in butterfly wings with different coefficients and boundary condition described by reconstructed veins. When the boundary condition described above applied, we found that there’s almost no influence on pattern styles, however, influence on pattern distribution.This study can simulate concentric eyespot and wave stripe along the boundary of wing in Nymphalidae, besides, we can also simulate smaller and non-regular wave pattern which distributes over the wing. By this study, we figure out the patterns on the butterfly wings can be classified into two types, global patterns belong to the background, and local eyespot patterns according to the wing cell midline, furthermore, our study simulates these patterns by computer simulation.
Subjects
L系統
涂林系統
生物斑紋形成
影像處理
L-system
Turing system
biological pattern formation
Type
thesis
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