Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uflorida!stat!fsu!geomag!prem
From: prem@geomag.fsu.edu (Prem Subrahmanyam)
Newsgroups: comp.graphics
Subject: Re: Excluding Mandelbrot set
Message-ID: <380@fsu.scri.fsu.edu>
Date: 22 Nov 89 20:58:50 GMT
References: <3544@quanta.eng.ohio-state.edu> <480003@hpsad.HP.COM>
Sender: news@fsu.scri.fsu.edu
Reply-To: prem@geomag.UUCP (Prem Subrahmanyam)
Organization: Florida State University Computing Center
Lines: 23

In article <480003@hpsad.HP.COM> cj@hpsad.HP.COM (Chris Johnson) writes:
>where Z & C are complex, and successive iterations with Z starting at
>(0 + 0i), Z does not ever atain a magnitude greater that 2. This implies
>that one must, necessarily, go through some number of iterations to determine
>whether or not the magnitude of Z is going to "blow up" or stabilize. Actually,
>I'm not sure about the limit of 2, maybe it's just whether or not it blows up.

  Actually, the true definition is that the number does not "blow up" to
  infinity.  2 is chosen, as there is a theorem that was developed that proves
  that if the magnitude of a number exceeds 2, then it will "blow up" to 
  infinity very shortly afterwards, 2 is simply the smallest number at which
  it is certain that the magnitude will blow up.  FYI, there is also a theorem
  that was developed that proves that the entire Mandelbrot Set is connected,
  i.e., that between small "pockets" of Mandelbrot numbers, there also exist
  tiny "filaments" of Mandelbrot numbers that connect them, so there is no
  isolated pocket of Mandelbrot numbers within the set.  Some of the larger
  "filaments" are what create the lightning-like effects surrounding portions
  of the set.

  Oh, I forgot to mention, a Mandelbrot number is actually one that does not
  blow up to infinity after an infinite number of recursions.  Of course, we'd
  be waiting around forever to find one Mandelbrot number.
  ---Prem Subrahmanyam (prem@geomag.gly.fsu.edu)