Wow! I have been making these for over 40 years. These take hours to create and render. I just use iterations of the Mandelbrot function Z=Z*Z+C. Where C is the complex number of "i" or square root of -1 with "i" being the Y axis and the real component the X axis. Z is iteration up to 500 million times starting with 0 to see if the C point is a member of the set. If a member it is painted black and if it is not it is painted a color based upon when it escapes to infinity. If bounded it is a member of the set. :-)