Another Chaotic search

Newton’s Method

 Newton’s method is a more simple way of finding a root.   The formula is

x_{n+1}=x_n - \frac{f^{'}(x)}{f(x)}

 However, the behavior of the algorithm in finding roots is anything but simple.  Above, I display the behavior of this algorithm on the complex interval where the real part of and the imaginary part of each complex number if between -1 and 1.  The coloring scheme is identical to the previous post.

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