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arXiv · 1410.1212

New Approximations for the Area of the Mandelbrot Set

Daniel Bittner·Long Cheong·Dante Gates·Hieu D. Nguyen
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Abstract

Due to its fractal nature, much about the area of the Mandelbrot set $M$ remains to be understood. While a series formula has been derived by Ewing and Schober to calculate the area of $M$ by considering its complement inside the Riemann sphere, to date the exact value of this area remains unknown. This paper presents new improved upper bounds for the area based on a parallel computing algorithm and for the 2-adic valuation of the series coefficients in terms of the sum-of-digits function.

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Daniel Bittner, Long Cheong, Dante Gates, Hieu D. Nguyen. 2014-10-05. New Approximations for the Area of the Mandelbrot Set. https://doi.org/10.2140/involve.2017.10.555

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