Newton’s Method & Fractals

I am constantly amazed at how Newton’s work can find fresh applications. Steven Strogatz has an excellent essay on complex numbers in today’s NYT, in which he goes from the  basic definition of i to how Newton’s Method for approximating roots can lead to a complex chaotic system. The video below is an illustration of this concept (Read the NYT article first, though, to understand what the video is about!):

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