Uniform approach to reproduce the Mandelbrot set, some of its inner structure as well as its complement with high sensitivity using Fourier phases

Alberto Isaac Aguilar-Hernández, Carlos Antonio Marin-Mendoza, Rogelio Valdez and Markus F. Müller

Chaos, Solitons & Fractals, 2025, vol. 198, issue C

Abstract: Here, we propose a unified approach to reproduce the Mandelbrot set, some inner structures of the period bulbs, and the complement of the Mandelbrot set. The special feature of the method is not only that all these structures are visualized with a single algorithm but also that it distinguishes mechanism that act on different time scales and, furthermore, its exceptional sensitivity, which approaches the computer accuracy. We investigate this exceptional sensitivity with sequences that are derived in close proximity to the Feigenbaum parameter on the real axis.

Keywords: Mandelbrot set; Fourier phases; Determinism; J index (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005880

DOI: 10.1016/j.chaos.2025.116575

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