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arXiv · 2312.03326

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

Marius-F. Danca
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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.

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Marius-F. Danca. 2023-12-06. Mandelbrot set as a particular Julia set of Fractional Order, echipotential lines and external rays of Mandelbrot and Julia sets of Fractional Order. https://arxiv.org/abs/2312.03326

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