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File:Newton-lplane-Mandelbrot.jpg

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Description
English: Computergraphical study of the critical point 0 of some polynomials under Newton's method in the complex -plane
Date
Source Own work
Author Georg-Johann Lay
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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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Summary

English: Fate of zero, one of the critical points of for polynomials from the family

in the complex plane. denotes the Newton operator

For in the black part of the plane, the critical point 0 of does not converge to a zero of . This means that the set of start values for which Newton's method does not converge to a zero of is a set of full measure. The black set is

The center of the region is at about .

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11 April 2008

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Date/TimeThumbnailDimensionsUserComment
current14:26, 11 April 2008Thumbnail for version as of 14:26, 11 April 20086,000 × 4,800 (2.66 MB)Georg-Johann-
12:20, 11 April 2008Thumbnail for version as of 12:20, 11 April 20082,000 × 1,600 (351 KB)Georg-Johanncrop
12:00, 11 April 2008Thumbnail for version as of 12:00, 11 April 20082,000 × 2,000 (326 KB)Georg-Johann{{Information |Description= |Source=self-made |Date={{2008-04-11}} |Author= Georg-Johann Lay |Permission={{PD-self}} |other_versions= }}

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