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File:Bairstow-fractal 6 11 m33 m33 11 6 scale 03.png

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Summary

Description Convergence map for the en:Bairstow's method, notation following de version, similar to en:Newton fractal
Date
Source My own C program, derived from the newtroot program used for the newton fractals
Author Lutz Lehmann User:LutzL
Permission
(Reusing this file)
my own


What it is

Bairstow's method tries to find quadratic factors of polynomials, all with real coefficients. This image shows the behaviour of different initial factors for x,y in the range [-3,3]. A black point indicates no convergence after ca. 100 iterations, a white point indicates a solution after one iteration, a colored point signifies convergence to the limit point located in the basin of that color. The polynomial to be factored is

.

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
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  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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This licensing tag was added to this file as part of the GFDL licensing update.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 2.5 Generic license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.

newton braistow caclutae the appropriate meaures to be qeqippd

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6 October 2006

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File history

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Date/TimeThumbnailDimensionsUserComment
current14:44, 17 August 2009Thumbnail for version as of 14:44, 17 August 20091,201 × 1,201 (595 KB)LutzLcorrected a sign error in the horizontal direction. better white dots at locations of quadratic factors
16:12, 16 August 2009Thumbnail for version as of 16:12, 16 August 20091,201 × 1,201 (582 KB)LutzLReverted to version as of 16:08, 16 August 2009. Sorry for the double reversion, it did not show the new version after the upload.
16:09, 16 August 2009Thumbnail for version as of 16:09, 16 August 2009601 × 601 (41 KB)LutzLReverted to version as of 13:55, 6 October 2006
16:08, 16 August 2009Thumbnail for version as of 16:08, 16 August 20091,201 × 1,201 (582 KB)LutzLHaving corrected a nasty error in the source code, the basins of convergence for this example look a lot more impressive. Increased the resolution to double size, added coordinate system.
13:55, 6 October 2006Thumbnail for version as of 13:55, 6 October 2006601 × 601 (41 KB)LutzL{{Information |Description=Convergence map for the en:Bairstow's method,notation following de version, similar to en:Newton fractal |Source=My own C program, derived from the newtroot program used for the newton fractals

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