The size of Mandelbrot bulbs | Zendy

A. C. Fowler | Zendy; Mark McGuinness | Zendy

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The size of Mandelbrot bulbs

Author(s) -

A. C. Fowler,

Mark McGuinness

Publication year - 2019

Publication title -

chaos solitons and fractals x

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.457

H-Index - 5

ISSN - 2590-0544

DOI - 10.1016/j.csfx.2019.100019

Subject(s) - mandelbrot set , mathematics , radius , orbit (dynamics) , parameter space , stability (learning theory) , geometry , mathematical analysis , physics , computer science , fractal , computer security , engineering , machine learning , aerospace engineering

We provide an analytic estimate for the size of the bulbs adjoining the main cardioid of the Mandelbrot set. The bulbs are approximate circles, and are associated with the stability regions in the complex parameter μ-space of period-q orbits of the underlying map z → z 2 − μ . For the (p, q) orbit with winding number p/q, the associated stability bulb is an approximate circle with radius 1 q 2 sin π p q .

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