This is repeated as many times as necessary. But the problem with this equation is that it never stops growing. To get the type of pattern one desires from a fractal equation, one needs a twist on the formula, take, for example, our earlier formula. However, with the use of simple numbers one does not get exciting results. It is only when the x represents complex numbers.
Complex numbers contain two parts, a real part, and an imaginary part.
They are only named this for historical reasons, and could be named Jack and Jill, without any serious repercussions. Each complex number can be represented as a point on a two-dimensional plane. When x becomes a complex number, the formula can produce the Mandelbrot set. If the equation starts heading off into infinity, the computer stops the equation with that point. The point is then labelled chaotic, and is assigned a colour, depending on how quickly it broke out from stability.