The Mandelbrot set is a set of complex numbers, generated with the sequence , where and . The complex numbers in the set fulfill the following equation
In some cases, is defined as , therefore the computation is much simpler.
In this case, the Mandelbrot set is defined as
It is easier to determine, which of the numbers are not in the Mandelbrot set
This requires a iterative approach on the sequence , which determines in finite steps, if the value of gets above the threshold. I demonstrate this method in the code snippet here. The Code generates a pattern of 599999 cases and checks cases to .