Fractals of the Julia and Mandelbrot sets of the Riemann Zeta Function

TL;DR

This paper explores the fractal structures of Julia and Mandelbrot sets generated from the Riemann zeta function, providing new insights and conjectures related to number theory and complex dynamics.

Contribution

It introduces the computation and analysis of these fractals for the zeta function, derives a corollary of Voronin's theorem, and proposes a scale-invariant equation for Goldbach conjecture bounds.

Findings

Properties of the Julia and Mandelbrot sets of the zeta function are characterized.

A corollary of Voronin's theorem is derived.

A conjectured scale-invariant equation for Goldbach bounds is proposed.

Abstract

Computations of the Julia and Mandelbrot sets of the Riemann zeta function and observations of their properties are made. In the appendix section, a corollary of Voronin's theorem is derived and a scale-invariant equation for the bounds in Goldbach conjecture is conjectured.