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From: gclark@utcsri.UUCP (Graeme Clark)
Newsgroups: net.math
Subject: Mandelbrot set question
Message-ID: <2355@utcsri.UUCP>
Date: Wed, 19-Mar-86 23:33:38 EST
Article-I.D.: utcsri.2355
Posted: Wed Mar 19 23:33:38 1986
Date-Received: Thu, 20-Mar-86 09:27:15 EST
References: <886@ellie.UUCP> <641@bentley.UUCP>
Reply-To: gclark@utcsri.UUCP (Graeme Clark)
Organization: CSRI, University of Toronto
Lines: 16
Summary: 

[Balanced meal for line eater goes here.]

As you may know, the Mandelbrot set is the set of complex numbers c
such that the sequence

              2      3
    0, f(0), f (0), f (0), ...           
					 k
is not bounded, where f(z) = z^2+c, and f (z) = f(f(f(...f(z)...)))
						k
(k applications of f).  It is claimed that if |f (0)| > 2 for some
k, then the seqence blows up (in absolute value) to infinity.  Can
someone show a proof for this?

Graeme Clark -- Dept. of Computer Science, Univ. of Toronto, Canada M5S 1A4
{allegra,cornell,decvax,ihnp4,linus,utzoo}!utcsri!gclark