{
  "id": "1410.1212",
  "version": "v1",
  "published": "2014-10-05T20:53:03.000Z",
  "updated": "2014-10-05T20:53:03.000Z",
  "title": "New Approximations for the Area of the Mandelbrot Set",
  "authors": [
    "Daniel Bittner",
    "Long Cheong",
    "Dante Gates",
    "Hieu D. Nguyen"
  ],
  "comment": "12 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-05T20:53:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45"
    ],
    "keywords": [
      "mandelbrot set",
      "approximations",
      "area remains unknown",
      "series formula",
      "complement inside"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.1212B"
    }
  }
}