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Newton's Method Fractals
This visualization shows the "basins of attraction" for finding roots of a complex equation using Newton's method. Each pixel is a starting point on the complex plane. The color of the pixel is determined by which root the method converges to, and the brightness is determined by how quickly it converges. The intricate fractal boundaries are the points that fail to settle on a single root.
Method
z_new = z - f(z) / f'(z)