Among the many fractals, there is Collatz Fractal based on a complex extension of:
def f(x):
if x % 2 == 0:
return x / 2
return 3 * x + 1
To generate the fractal, you pick a bunch of points and repeatedly apply f over and over again a large number of times. Morally, f(f(f(f(....f(x)....)))). In this case, however, it is not a real number x but instead a complex number (often denoted z). The end result is plotted by giving it a color that "corresponds" to the resulting magnitude.
Heavily modified variant of the Mandelbrot example given here.