Vol. 10, No. 4, 2017

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New approximations for the area of the Mandelbrot set

Daniel Bittner, Long Cheong, Dante Gates and Hieu D. Nguyen

Vol. 10 (2017), No. 4, 555–572
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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Keywords
Mandelbrot set, sum of digits
Mathematical Subject Classification 2010
Primary: 37F45
Milestones
Received: 5 October 2014
Revised: 19 September 2016
Accepted: 17 October 2016
Published: 7 March 2017

Communicated by Kenneth S. Berenhaut
Authors
Daniel Bittner
Department of Mathematics
Rowan University
Robinson Hall
201 Mullica Hill Road
Glassboro, NJ 08028
United States
Long Cheong
Department of Mathematics
Rowan University
Robinson Hall
201 Mullica Hill Road
Glassboro, NJ 08028
United States
Dante Gates
Department of Mathematics
Rowan University
Robinson Hall
201 Mullica Hill Road
Glassboro, NJ 08028
United States
Hieu D. Nguyen
Department of Mathematics
Rowan University
Robinson Hall
201 Mullica Hill Road
Glassboro, NJ 08028
United States