Newton fractal

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.

Illustrations

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  ${}_{z^{3}-1}$
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  ${}_{z^{3}-2z+2}$
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  ${}_{z^{3}-2z+2}$
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  ${}_{z^{3}-2z+2}$
  closeup
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  ${}_{z^{3}+(\lambda -1)z+\lambda }$
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  ${}_{z^{3}+(\lambda -1)z+\lambda }$

Zoom

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Iterations

• z → z³ − 2z + 2
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  n = 0
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  n = 1
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  n = 2
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  n = 3
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  n = 4
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  n = 5
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  n = 6