Newton-Mandelbrot set and Murase-Mandelbrot set

TL;DR

This paper introduces extended Newton and Mandelbrot methods derived from traditional Japanese Wasan mathematics, revealing their interconnectedness and the formation of a unified extended Mandelbrot set.

Contribution

It presents new extended Newton and Mandelbrot recurrence formulas from Wasan mathematics and demonstrates their unification into a single connected set.

Findings

Extended Newton's methods derived from Wasan mathematics.

Extended Mandelbrot recurrence formulas lead to a unified set.

The unified set is connected and closed.

Abstract

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.