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2017 New approximations for the area of the Mandelbrot set
Daniel Bittner, Long Cheong, Dante Gates, Hieu Nguyen
Involve 10(4): 555-572 (2017). DOI: 10.2140/involve.2017.10.555

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 (1992) 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 Nguyen. "New approximations for the area of the Mandelbrot set." Involve 10 (4) 555 - 572, 2017. https://doi.org/10.2140/involve.2017.10.555

Information

Received: 5 October 2014; Revised: 19 September 2016; Accepted: 17 October 2016; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 1361.37049
MathSciNet: MR3630303
Digital Object Identifier: 10.2140/involve.2017.10.555

Subjects:
Primary: 37F45

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 4 • 2017
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