Wolfram Demonstrations Project

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

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.

Contributed by: Eric Rowland

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Complex Newton Iteration for a Cubic Polynomial