The area of the Mandelbrot set

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1992 English Publisher:Springer Science and Business Media LLCJournal:Numerische Mathematik, volume 61, pages 59-72 (issn: 0029-599X, eissn: 0945-3245,

Copyright policy )

Authors: Ewing, John H.; Schober, Glenn;

doi: 10.1007/bf01385497

The area of the Mandelbrot set

- Summary
- Subjects
- Metrics

Abstract

The Mandelbrot set \(M\) consists of the complex numbers \(c\) for which the Julia set of \(z^ 2+c\) is connected. The set \(M\) is compact and connected and there is a conformal map of the form \(z+b_ 0+b_ 1z^{- 1}+b_ 2z^{-2}+\dots\) from \(| z|>1\) to the complement of \(M\). The authors compute the first 240000 coefficients \(b_ k\) recursively and note that these satisfy \(-1

Related Organizations

DigiZeitschriften
Germany
Indiana University
United States
DePaul University
United States

Keywords

Software, source code, etc. for problems pertaining to functions of a complex variable, Julia set, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, computation of coefficients, Article, 510.mathematics, Coefficient problems for univalent and multivalent functions of one complex variable, area estimates, Mandelbrot set

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	16
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average