Newton fractal for a cubic polynomial in the complex plane, rendered in real time on the GPU
Newton’s method applied to a polynomial in the complex plane produces a fractal pattern: points are colored according to which root the iteration converges to, with intricate boundaries between the basins of attraction. This program computes the Newton fractal for the polynomial z3−2z2+3 by iterating the map z↦z−f(z)/f′(z) for each pixel, coloring based on the limiting value. The view zooms in and out over time to reveal the self-similar fractal structure.
Controls: WASD to rotate, arrow keys to translate.
