Improved Newton Iterative Algorithm for Fractal Art Graphic Design
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 t...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/6623049 |
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| author | Huijuan Chen Xintao Zheng |
| author_facet | Huijuan Chen Xintao Zheng |
| author_sort | Huijuan Chen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-eca40cb699da42cc85efaa4f28882fbe |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-eca40cb699da42cc85efaa4f28882fbe2025-02-03T00:58:51ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/66230496623049Improved Newton Iterative Algorithm for Fractal Art Graphic DesignHuijuan Chen0Xintao Zheng1Academy of Arts, Hebei GEO University, Shijiazhuang 050031, Hebei, ChinaAcademy of Arts, Hebei GEO University, Shijiazhuang 050031, Hebei, ChinaFractal 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.http://dx.doi.org/10.1155/2020/6623049 |
| spellingShingle | Huijuan Chen Xintao Zheng Improved Newton Iterative Algorithm for Fractal Art Graphic Design Complexity |
| title | Improved Newton Iterative Algorithm for Fractal Art Graphic Design |
| title_full | Improved Newton Iterative Algorithm for Fractal Art Graphic Design |
| title_fullStr | Improved Newton Iterative Algorithm for Fractal Art Graphic Design |
| title_full_unstemmed | Improved Newton Iterative Algorithm for Fractal Art Graphic Design |
| title_short | Improved Newton Iterative Algorithm for Fractal Art Graphic Design |
| title_sort | improved newton iterative algorithm for fractal art graphic design |
| url | http://dx.doi.org/10.1155/2020/6623049 |
| work_keys_str_mv | AT huijuanchen improvednewtoniterativealgorithmforfractalartgraphicdesign AT xintaozheng improvednewtoniterativealgorithmforfractalartgraphicdesign |