Abstract
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.
Highlights
Fractal geometry is often used to describe irregular things in nature. e well-known Euclidean geometry describes objects composed of points, straight lines, common polygons and curves in two dimensions, and boxes and surfaces in three dimensions [1, 2]
Many natural objects in nature cannot be described by conventional geometric figures, such as clouds and coastlines [3]. e emergence of fractal geometry provides a new perspective for describing natural objects
The Jacobian matrix function takes the extreme value. e Jacobian matrix function takes the minimum value on the left side of the point and the maximum value on the right side, but the value of the Jacobian matrix function remains unchanged. erefore, when the Gauss-Newton iteration method is used to solve the problem and when the initial value and the real calculation result are in the same range, the optimal solution can be obtained after several iterations
Summary
Fractal geometry is often used to describe irregular things in nature. e well-known Euclidean geometry describes objects composed of points, straight lines, common polygons and curves in two dimensions, and boxes and surfaces in three dimensions [1, 2]. E emergence of fractal geometry provides a new perspective for describing natural objects. Mandelbrot set, and Newton fractal set adjust the number and shape of petals in clothing design and extracted texture information of different flower types, focusing on analyzing the relationship between Julia set flower types and various parameters [11]. Four Newton iterative transformation forms are proposed to produce different shapes of graphics, which can affect the texture effect of the fractal art graphics surface. Mathematical morphology processing of Newton’s iterative graphics with the help of MATLAB makes the pixel points of the graphics directly correspond to the tissue points, making them directly into fractal art graphics and presenting a variety of special texture effects, and we design experiments with the help of electronic Jacquard machines.
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