Subsection 1.2.2 The iteration of complex functions
We were introduced to the idea of complex iteration back in Subsection 1.1.3 and, again, there's no reason the function we iterate needs to come from Newton's method. In the context of complex iteration we'll meet Julia sets, a few of which are shown in Figure 1.19
The Julia sets shown in Figure 1.19 all arise from the iteration of functions in the quadratic family - i.e. from the iteration of functions of the form \(f(z)=z^2+c\text{.}\) It is in this context that the famous Mandelbrot set shown in Figure 1.20 arises.
