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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
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Abstract |
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Due to its fractal nature, much about the area of the Mandelbrot set remains to be understood. While a series formula has been derived by Ewing and Schober (1992) to calculate the area of 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. |
Keywords
Mandelbrot set, sum of digits
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Mathematical Subject Classification 2010
Primary: 37F45
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Milestones
Received: 5 October 2014
Revised: 19 September 2016
Accepted: 17 October 2016
Published: 7 March 2017
Communicated by Kenneth S. Berenhaut
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Authors |
| Daniel Bittner | |
| Department of Mathematics Rowan University Robinson Hall 201 Mullica Hill Road Glassboro, NJ 08028 United States |
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| Long Cheong | |
| Department of Mathematics Rowan University Robinson Hall 201 Mullica Hill Road Glassboro, NJ 08028 United States |
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| Dante Gates | |
| Department of Mathematics Rowan University Robinson Hall 201 Mullica Hill Road Glassboro, NJ 08028 United States |
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| Hieu D. Nguyen | |
| Department of Mathematics Rowan University Robinson Hall 201 Mullica Hill Road Glassboro, NJ 08028 United States |
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