Numerische Mathematik

, Volume 61, Issue 1, pp 59-72

First online:

The area of the Mandelbrot set

  • John H. EwingAffiliated withDepartment of Mathematics, Indiana University
  • , Glenn SchoberAffiliated withDepartment of Mathematics, Indiana University

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We obtain upper bounds for the area of the Mandelbrot set. An effective procedure is given for computing the coefficients of the conformal mapping from the exterior of the unit circle onto the exterior of the Mandelbrot set. The upper bound is obtained by computing finitely many of these coefficient and applying Green's Theorem. The error in such calculations is estimated by deriving explicit formulas for infinitely many of the coefficients and comparing.

Mathematics Subject Classification (1991)

30-04 30C50