Complex Newton Iteration for a Cubic Polynomial

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The color at a point indicates in which region of the complex plane it lies after iterations of the map . This is Newton's method for finding the complex roots of .

Contributed by: Eric Rowland (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: After zero iterations, each point lies in its original region.

Snapshot 2: Nested structure can be seen after three iterations.

Snapshot 3: Intricate patterns develop for higher iterations.

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