I have the following task: draw a discrete approximation of the Mandelbrot set for the quadratic family on the complex plane. I need to do this with a list-based implementation.
I have already created a plot of the Mandelbrot set for the quadratic family on the complex plane, but I couldn't manage to create a discrete approximation. Here's my code in Wolfram Mathematica for the plot of the Mandelbrot set:
ArrayPlot[Table[Length@NestWhileList[#^2 + x + I*y &, 0, Abs[#] < 2 &, 1, 100], {y, -1.2, 1.2, 0.002}, {x, -2, 0.5, 0.002}], ColorFunction -> "Pastel", PlotLegends -> Automatic]
How can I create a discrete approximation of the Mandelbrot set?