Newton-Mandelbrot set and Murase-Mandelbrot set
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915974570049536 |
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| author | Horiguchi, Shunji |
| author_facet | Horiguchi, Shunji |
| contents | We obtain four extended Newton's methods and three extended Mandelbrot's recurrence formulas from the Wasan (Japanese mathematics in the Edo period (1603-1868)). Furthermore, two extended Newton's methods relate to one of the extended Mandelbrot's recurrence formulas. We lead four types of extended Mandelbrot recurrence formulas. Next, we show that these become the same extended Mandelbrot set, and connected, closed set. These show the originality of Wasan. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_14872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Newton-Mandelbrot set and Murase-Mandelbrot set Horiguchi, Shunji General Mathematics 37F16, 49M15 We obtain four extended Newton's methods and three extended Mandelbrot's recurrence formulas from the Wasan (Japanese mathematics in the Edo period (1603-1868)). Furthermore, two extended Newton's methods relate to one of the extended Mandelbrot's recurrence formulas. We lead four types of extended Mandelbrot recurrence formulas. Next, we show that these become the same extended Mandelbrot set, and connected, closed set. These show the originality of Wasan. |
| title | Newton-Mandelbrot set and Murase-Mandelbrot set |
| topic | General Mathematics 37F16, 49M15 |
| url | https://arxiv.org/abs/2502.14872 |