逃逸时间算法生成的Julia集在纺织图案设计中的应用研究
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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。
Julia sets are the polynomial and rational function Iterative image which have been studied separately by G.Julia and P.Fatou—French mathematicians at the beginning of the 20th century.Julia images have the fine structure and the intense visual impact effects. Those as the artistic graph have a widespread application in the textile dyeing and printing, advertisement printing,industrial designining,stamp manufacture,dress designing, computer teaching research and so on.Its economic and social benefits have broad application prospects.
The shape of the Julia image which has been generated by Escape Time algorithm is closely related with many parameters,such as:the limit of escape time,the limit of escape radius,the fictitious department of attraction,the radius of regional convergence and so on. Changing any of the above parameters would make Julia image changes,but so far,the relationship between the parameters and the Julia image has not been totally understood. The quick design of Julia image also has a certain barrier.Julia image has the fine structure and the layered evolution of color-effect.It tends to be used as a dyeing and printing,but as a pattern for weaving is at a constant research and exploration phase.
In this paper,energy and entropy from gray level co-occurrence matrix are used to analysis the texture changes of Julia sets which are generated by the different escape time limit,escape radius limit,attraction's imaginary part and the converging-region radius.It will provide the basis for the fractal image's quick design.By the analysis,The Julia image is finer and the generated time of the image is longer,when the limit of escape time and the limit of escape radius are increasing.A general consideration,the limit of escape time is 70 and the limit of escape radius is 150.The gray level co-occurrence matrixes of the two images are transposed mutually,when the fictitious departments of attraction are inverse. The trend of each r-energy traces are same,namely r increases,the image energy reduces first,then increases,moreover flatten out,however,the r value is different when each curves achieve its minimize energy.The values of p2/q2 are different when each high time Julia images achieve its precise time.
The Julia image has the fine structure and the layered evolution of color-effect.In this paper,interlacing organization's order change,miscellaneous spots are all turn into Warp interlacing point or Warp interlacing point and reasonable weft-backed renumbers are used. Julia image would have been fully demonstrated on the jacquard fabric.
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。
Julia sets are the polynomial and rational function Iterative image which have been studied separately by G.Julia and P.Fatou—French mathematicians at the beginning of the 20th century.Julia images have the fine structure and the intense visual impact effects. Those as the artistic graph have a widespread application in the textile dyeing and printing, advertisement printing,industrial designining,stamp manufacture,dress designing, computer teaching research and so on.Its economic and social benefits have broad application prospects.
The shape of the Julia image which has been generated by Escape Time algorithm is closely related with many parameters,such as:the limit of escape time,the limit of escape radius,the fictitious department of attraction,the radius of regional convergence and so on. Changing any of the above parameters would make Julia image changes,but so far,the relationship between the parameters and the Julia image has not been totally understood. The quick design of Julia image also has a certain barrier.Julia image has the fine structure and the layered evolution of color-effect.It tends to be used as a dyeing and printing,but as a pattern for weaving is at a constant research and exploration phase.
In this paper,energy and entropy from gray level co-occurrence matrix are used to analysis the texture changes of Julia sets which are generated by the different escape time limit,escape radius limit,attraction's imaginary part and the converging-region radius.It will provide the basis for the fractal image's quick design.By the analysis,The Julia image is finer and the generated time of the image is longer,when the limit of escape time and the limit of escape radius are increasing.A general consideration,the limit of escape time is 70 and the limit of escape radius is 150.The gray level co-occurrence matrixes of the two images are transposed mutually,when the fictitious departments of attraction are inverse. The trend of each r-energy traces are same,namely r increases,the image energy reduces first,then increases,moreover flatten out,however,the r value is different when each curves achieve its minimize energy.The values of p2/q2 are different when each high time Julia images achieve its precise time.
The Julia image has the fine structure and the layered evolution of color-effect.In this paper,interlacing organization's order change,miscellaneous spots are all turn into Warp interlacing point or Warp interlacing point and reasonable weft-backed renumbers are used. Julia image would have been fully demonstrated on the jacquard fabric.
引文
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