Complex Iteration
For examining the fundamental calculation of the Mandelbrot and Julia Sets.
The Mandelbrot set is the set of values C for which the function
f(z)=z^2+C converges when iterated starting at z=0.
a_0=0, a_1=f(0)=C, a_2=f(C)=C^2+C... a_n+1=f(a_n)
The Julia set, which can be defined for a broad class of complex functions,
has a related idea: keep C constant, a make a set based on the behavior of
iterations of a_0=z for different z in the complex plane.
This sketch shows you 22 iterations of a_0 = A, and f(z)=z^2 + C, where we
think of points (a,b) as representing the complex number a+bi.