Fractal art graphics are the product of the fusion of mathematics and art, relying on the computing power of a computer to iteratively calculate mathematical formulas and present the results in a graphical rendering. The selection of the initial value of the first iteration has a greater impact on the final calculation result. If the initial value of the iteration is not selected properly, the iteration will not converge or will converge to the wrong result, which will affect the accuracy of the fractal art graphic design. Aiming at this problem, this paper proposes an improved optimization method for selecting the initial value of the Gauss-Newton iteration method. Through the area division method of the system composed of the sensor array, the effective initial value of iterative calculation is selected in the corresponding area for subsequent iterative calculation. Using the special skeleton structure of Newton’s iterative graphics, such as infinitely finely inlaid chain-like, scattered-point-like composition, combined with the use of graphic secondary design methods, we conduct fractal art graphics design research with special texture effects. On this basis, the Newton iterative graphics are processed by dithering and MATLAB-based mathematical morphology to obtain graphics and then processed with the help of weaving CAD to directly form fractal art graphics with special texture effects. Design experiments with the help of electronic Jacquard machines proved that it is feasible to transform special texture effects based on Newton's iterative graphic design into Jacquard fractal art graphics.

中文翻译：

---

分形艺术图形设计的改进牛顿迭代算法

分形图形是数学与艺术融合的产物，它依靠计算机的计算能力来迭代地计算数学公式，并以图形方式呈现结果。第一次迭代的初始值的选择对最终的计算结果有更大的影响。如果没有正确选择迭代的初始值，则迭代将不会收敛或收敛到错误的结果，这将影响分形图形设计的准确性。针对这一问题，本文提出了一种改进的优化方法，用于选择高斯-牛顿迭代法的初值。通过由传感器阵列组成的系统的区域划分方法，在相应区域中选择迭代计算的有效初始值以进行后续迭代计算。利用牛顿迭代图形的特殊骨架结构，例如无限精细地镶嵌链状，散点状构图，并结合图形辅助设计方法，我们进行了具有特殊纹理效果的分形艺术图形设计研究。在此基础上，通过抖动和基于MATLAB的数学形态学处理牛顿迭代图形，以获得图形，然后在编织CAD的帮助下直接处理具有特殊纹理效果的分形艺术图形。在电子提花机的帮助下进行的设计实验证明，基于牛顿定律变换特殊纹理效果是可行的。