逃逸时间算法生成的Julia集在纺织图案设计中的应用研究

发布时间：2018-07-08 21:33

本文选题：分形 + Julia图像　；参考：《苏州大学》2009年硕士论文

【摘要】： Julia集是在二十世纪初法国数学家G.Julia和P.Fatou分别研究过的一种多项式和有理函数的迭代图像。Julia图像具有精细的结构和强烈的视觉冲击效果,可作为艺术图像在纺织印染、广告印刷、工业设计、邮票制作、服装设计及计算机教学研究等方面有着广泛的应用,其经济效益和社会效益均具有广阔的应用前景。逃逸时间算法生成的Julia图像的形状与很多参数紧密相关,如:逃逸时间极限、逃逸半径极限、吸引子虚部和收敛区域半径等。以上任何参数的变化都会令Julia图像产生变化,但到目前为止,这些影响参数与图像间的具体变化规律还不明了,使得Julia图像的快捷设计还有一定的障碍。Julia图像具有精细的结构和层状渐进的色彩渲染效果,其作为图案一般用印染较多,而作为纹样用于织造中正处于一个不断的研究探索阶段。本文采用灰度共生矩阵的能量和熵分析由不同逃逸时间极限、逃逸半径极限、吸引子虚部和收敛区域半径生成的Julia图像的纹理变化规律,为分形图像的快捷设计提供了依据。通过分析,得到逃逸时间极限和逃逸半径极限越大,则Julia图像越精细,但是图像生成时间也越长,综合考虑,逃逸时间极限和逃逸半径极限各自取70,150。吸引子虚部为互为相反数时,两图像的灰度共生矩阵互为转置。各高次Julia图像的r-能量曲线的走向基本相同,即r增大,图像的能量先减小,再增加,再则趋于平缓,但各曲线达到最小能量时的r值则不同。图像达到最精细时,各高次Julia图像的C值中p~2/q~2的值基本各不相同。本文基于Julia图像的层状渐进及精细结构这两个特点,通过组织的有序变化、杂点全经(纬)化及合理的纬重数的选择,借助于织造,把Julia图像通过组织点充分地展示在提花织物上。
[Abstract]:Julia set is an iterative image of polynomial and rational function studied by French mathematicians G. Julia and P. Fatou in the early 20th century. Julia image has fine structure and strong visual impact effect. It can be used as art image in textile printing and printing. Industrial design, stamp making, clothing design and computer teaching and research are widely used, and its economic and social benefits have broad application prospects. The shape of Julia image generated by the escape time algorithm is closely related to many parameters, such as escape time limit, escape radius limit, attractor virtual part and convergence region radius, etc. Any change in the above parameters will cause the Julia image to change, but so far, the specific rules of change between these parameters and the image are not clear. The quick design of Julia image has some obstacles. Julia image has fine structure and layered and progressive color rendering effect, which is generally used for printing and dyeing as a pattern. As patterns used in weaving is in a continuous stage of research and exploration. In this paper, the energy and entropy of gray level co-occurrence matrix are used to analyze the texture variation law of Julia image generated by different escape time limit, escape radius limit, attractor virtual part and convergence region radius, which provides the basis for the quick design of fractal image. Through analysis, the larger the escape time limit and the escape radius limit, the more fine Julia image is, but the longer the image generation time is, the more comprehensive consideration is, the escape time limit and escape radius limit are 70150 respectively. When the imaginary part of the attractor is the opposite number, the gray level co-occurrence matrix of the two images is transposed. The direction of the r-energy curve of the high-order Julia images is basically the same, that is, when the r increases, the energy of the image decreases first, then increases, and then tends to be flat, but the r values of the curves reach the minimum energy level is different. When the image reaches the most fine, the value of p~2/q~2 in the C value of each high order Julia image is basically different. In this paper, based on the two characteristics of stratified progressive and fine structure of Julia image, through the ordered change of the structure, the selection of the whole warp (weft) and the reasonable weight of the weft of the clutter, and by means of weaving, The Julia image is fully displayed on the jacquard fabric through the texture point.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2009
【分类号】：TP391.41

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