Numerische Mathematik

, Volume 61, Issue 1, pp 59–72

The area of the Mandelbrot set


  • John H. Ewing
    • Department of MathematicsIndiana University
  • Glenn Schober
    • Department of MathematicsIndiana University

DOI: 10.1007/BF01385497

Cite this article as:
Ewing, J.H. & Schober, G. Numer. Math. (1992) 61: 59. doi:10.1007/BF01385497


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

Copyright information

© Springer-Verlag 1992