# 6f: What is the area of the Mandelbrot set?

## Description

This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by
others.

# 6f: What is the area of the Mandelbrot set?

Ewing and Schober computed an area estimate using 240,000 terms of the

Laurent series. The result is 1.7274... However, the Laurent series

converges very slowly, so this is a poor estimate. A project to measure the

area via counting pixels on a very dense grid shows an area around 1.5066.

(Contact mrob@world.std.com for more information.) Hill and Fisher used

distance estimation techniques to rigorously bound the area and found

the area is between 1.503 and 1.5701.

1. J. H. Ewing and G. Schober, The Area of the Mandelbrot Set, _Numer.

Math._ 61 (1992), pp. 59-72.

2. Y. Fisher and J. Hill, Bounding the Area of the Mandelbrot Set,

_Numerische Mathematik_, . (Submitted for publication). Available by

ftp: legendre.ucsd.edu:/pub/Research/Fischer/area.ps.Z ..

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