Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!rutgers!tut.cis.ohio-state.edu!ucbvax!bloom-beacon!eru!luth!sunic!draken!md85-epi
From: md85-epi@nada.kth.se (Urban Koistinen)
Newsgroups: comp.graphics
Subject: Re: Excluding Mandelbrot set
Keywords: Mandelbrot
Message-ID: <2383@draken.nada.kth.se>
Date: 23 Nov 89 15:30:47 GMT
References: <3544@quanta.eng.ohio-state.edu> <480003@hpsad.HP.COM> <380@fsu.scri.fsu.edu> <4233@celit.fps.com>
Reply-To: md85-epi@nada.kth.se (Urban Koistinen)
Organization: Royal Institute of Technology, Stockholm, Sweden
Lines: 16

In article <4233@celit.fps.com> billd@fps.com (Bill Davids_on) writes:
>I'd like to know why 2 is magic.  Why not 1.99?
Try c = -2
>
>--Bill Davidson
the initial value
z(0) = 0
the recursion formula
z(n+1) = z(n)*z(n) + c
the distance from 0 of the next value
|z(n+1)| >= |z(n)*z(n)| - |c|
this you can use to prove that if |c|>2 then |z| grows without bond.

Similarly you can prove that if |c|<=1/4 then c lies in the mandelbrot set.

--Urban Koistinen