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| View Original: | Newton z3-2z+2 iterates R.png (1043x440) | |||
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| Keywords: Newton z3-2z+2 iterates R.png Color coded analysis of the dynamics of Newton's method for the polynomial <math>z\mapsto z 3-2z+2</math> on the real axis in the range from <math>-4</math> to 4 Each row shows the color-coded value of z after n-fold applying of the method The uppermost line n<nowiki> </nowiki>0 shows the colors of the numbers <math>-4</math> to 4 themselves This polynomial has one real root at z ‰ˆ-1 8 whose color code is medium blue Other colors code for <math>-1</math> cyan zero black one red infinity white etc Examples starting from any z less than <math>-1</math> left part of the image converges to the real root medium blue Starting at z<nowiki> </nowiki>0 produces an endless cycle between 0 and 1 black red black red own original text eigene Arbeit 1 2008-04-09 Georg-Johann Lay Complex color plots Newton fractals Real number line | ||||
