Mandelbrot set as a particular Julia set of Fractional Order, echipotential lines and external rays of Mandelbrot and Julia sets of Fractional Order

2023/12/06 by Marius‐F. Danca, Danca, Marius-F.
Mathematics · #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2312.03326

Abstract

In this paper it is shown analytically and computationally that the Mandelbrot set of integer order are particular cases of Julia sets of Caputo s like fractional order. Also the differences between the fractional-order Mandelbrot set and Julia sets from their integer-order variants are revealed. Equipotential lines and external rays of Mandelbrot set and Julia sets of fractional order are determined.

Related

• Mandelbrot set and Julia sets of fractional order
• Higher Order Mandelbrot Sets and their Varying Shapes
• Julia sets appear quasiconformally in the Mandelbrot set
• Correspondence and translation principles for the Mandelbrot set
• Internal addresses in the Mandelbrot set and Galois groups of polynomials