# Galois Theory and Ricci Flow Curvature Applications for Generating the Mandelbrot Set

## Keywords:

Mandelbrot set, Ricci flow, fractal, Riemannian metric, Euclidean metric## Abstract

In this paper, an application of Galois theory is presented through Ricci flow curvature in Mandelbrot set. The Mandelbrot set is analyzed over Ricci flow equation for generating the fractal set simply. Although, the fractal set is generated as the points in the complex plane connected to the Julia set and approaches to infinity. This paper proposes an efficient method of fractal set generation based on onto-one correspondence between Ricci flow manifold and the Mandelbrot set over the Riemanninan curvature. First, the Mandelbrot set transforms into the vector and then each element of the Mandelbrot vector corresponds to the n-dimension curvature tensor. The Mandelbrot set is formed by _finite interval and sequence of time instead of infinite interval and without sequence of time. Riemannian metric approach generates the fractal set faster than the Euclidean metric.