## Mandelbrot Set

The Mandelbrot set is created from this very simple formula in which both Z and C are complex numbers. The formula is iterated to determine whether Z is bounded or tends to infinity. To demonstrate this assume a test case where the imaginary part is zero and focus just on the real part. In this case, the formula is trivial to evaluate starting with Z = 0. The table below shows the outcome at C=0.2 and C=0.3 and where one is clearly bounded and the other is not! Iteration C = 0.2 C = 0.3 0 0 1 0.2 0.3 2 0.24 0.39 3 0.2576 0.4521 4 0.266358 0.504394 5 0.270946 0.554414 6 0.273412 0.607375 7 0.274754 0.668904 8 0.27549 0.747432 9 0.275895 0.858655 10 0.276118 1.037289 11 0.276241 1.375968…