New approximations for the area of the Mandelbrot set

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)555-572
Number of pages18
JournalInvolve
Volume10
Issue number4
DOIs
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics

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