Universal Mandelbrot Set as a Model of Phase Transition Theory

TL;DR

This paper proposes simplified methods for constructing Mandelbrot Sets to model phase transitions, demonstrating that adding parameters does not necessarily connect the phase diagram.

Contribution

It introduces two improvements to Mandelbrot Set construction, enabling better modeling of phase transitions with potential for more complex parameter spaces.

Findings

Simplified construction methods for Mandelbrot Sets

Adding parameters does not guarantee a connected phase diagram

Enhanced modeling capabilities for phase transition theory

Abstract

The study of Mandelbrot Sets (MS) is a promising new approach to the phase transition theory. We suggest two improvements which drastically simplify the construction of MS. They could be used to modify the existing computer programs so that they start building MS properly not only for the simplest families. This allows us to add one more parameter to the base function of MS and demonstrate that this is not enough to make the phase diagram connected