Newton fractal

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English: The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial p(Z) ∈ ℂ[Z].
Deutsch: Das Newton-Fraktal ist eine Grenzmenge in der komplexen Ebene, die das Newton-Verfahren für ein fixiertes Polynom p(Z)\in\mathbb{C}[Z] charakterisiert.

[edit] Illustrations

Fractal newton.png
Newton roots stor.jpg

{}_{z^3-2z+2}
FRACT008.png
FRACT007.png
Newton-Fraktal1.png
Newtroot 1 0 m3i m5m2i 3 1.png
Newtroot 1 0 0 m1.png
Newtroot 1 0 0 0 0 m1.png

{}_{z^3-2z+2}

{}_{z^3-2z+2}
closeup

{}_{z^3+(\lambda-1)z+\lambda}

{}_{z^3+(\lambda-1)z+\lambda}

[edit] Zoom

Newton1.png
Newton2.png
Newton3.png

[edit] Iterations

z → z³ − 2z + 2

n = 0

n = 1

n = 2

n = 3

n = 4

n = 5

n = 6
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