I understand that proof that the Mandelbrot Set is connected is not easy to follow and requires mathematical tools an Engineer probably doesn't have. But I got to wondering if there was a more accessible proof of the softer assertion, that the region $ |z_n(c)| < 2 $ is connected, where $z_n = z_{n-1}^2 + c$ and $ z_0 = c $. Then one just needs to accept that this holds in the n -> Infinity case.
Is there such a proof?
I found this old discussion, and someone suggested exactly what I thought of, but they didn't show HOW to prove that.
