I believe this is what Mandelbrot was referring to. Here's another interview with him in which he talks very specifically about it: http://www.webofstories.com/play/10523 Tom Dan Asimov writes:
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.
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