Re: [math-fun] Mandelbrot's Conjecture (as mentioned in this video interview)

Suddenly two definitions of the Mandelbrot set come to mind, the first one I learned (I), and the much more common one (II): For any c in C, define f_c(z) as z^2 + c. I. The set of c in C for which the Julia set of f_c is connected. (See < http://en.wikipedia.org/wiki/Julia_set >.) II. the set of c in C for which the orbit of 0, under (forward) iteration of f_c, is bounded. I've never seen a proof that these definitions are equivalent, though I haven't looked very hard, either. (In II, it seems to me that considering the orbits of 0 rather than of any other point is somewhat arbitrary.) --Dan Sometimes the brain has a mind of its own.