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Hello, Oscar! I was introduced to fractals back in the early 2010s (2012, maybe?), and the first fractal that I saw was the Mandelbrot set. Years later, numerical analysis and root-finding algorithms (such as Newton, Halley, Muller, Householder and Steffensen) allowed me to make more amazing fractals. I used very fast and intuitive software such as Kalles Fraktaler, FractInt, Ultra Fractal and ChaosPro to make explorations of such fractals. With Ultra Fractal, and your videos, I progressed, and even managed to make multidimensional Newton fractals (so far I only did the two-dimensional variant), and I plan on doing Broyden's method, Jenkins-Traub and Lehmer-Schur. These methods may be a little bit more difficult, but it's always a fun challenge. Ultra Fractal also allows you to use different coloring algorithms, such as binary decomposition, exponential smoothing and triangle inequality average. Here are fractals that I generated with Newton-Bisection and standard Newton's method for the function |
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