I felt like trying something new, so I wrote a Python script to plot Newton’s fractal.
This graphic shows the time to convergence for solving z^4+1 = 0 using Newton’s Method. The solution to this equation is one of four possibilities, which are represented using the colors red, blue, green, and yellow. The solution that Newton’s Method returns depends on the initial guess. I plotted the final solution for initial guesses in the range 0-1 (real, horizontal axis) and 0j-0j (imaginary, vertical axis). Color depth represents faster convergence to a particular soltion (i.e., brighter pixels represent initial guesses that converge to a solution faster).