Convergence of Newton's method for approximating square roots

Complex plane, sequence, convergence, fractal structure, Newton's Method for Approximating Square RootsUse the controls to vary the position of the starting point in the complex plane. Coloring each point in the plane according to whether the sequence with that initial point converges to the positive (pink) or negative (green) root yields an intricate fractal structure. A part of this structure can be seen by checking the fractal background checkbox. However, do not attempt to manipulate the controls with this option checked unless you are using a very fast computer. The blue points belong to the so-called Julia set of the fractal. Close to these points convergence of the sequence becomes unpredictableComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic