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From: putnam@steinmetz.UUCP (jefu)
Newsgroups: net.math
Subject: Re: Is the Mandelbrot set a fiction??
Message-ID: <273@steinmetz.UUCP>
Date: Thu, 19-Sep-85 07:54:35 EDT
Article-I.D.: steinmet.273
Posted: Thu Sep 19 07:54:35 1985
Date-Received: Sat, 21-Sep-85 05:11:37 EDT
References: <418@aero.ARPA> <646@petsd.UUCP>
Reply-To: putnam@kbsvax.UUCP (jefu)
Organization: GE CRD, Schenectady, NY
Lines: 30

Some questions on the mandelbrot set -- but not necessarily having anything
to do with it being a fiction.

The Sci. Am. article mentioned that there is an 'amazing theorem' that the
Mandelbrot set is connected.  I dont expect to be able to do this myself, 
but was wondering if anyone would like to sketch out the basic ideas for
the proof.

Is the complement of the set connected (im pretty sure that the 
answer to this one is yes, but again, wouldnt know how to prove it
without a (or many) hint)?

Is there some sort of minimal nice closed bounding curve for the set?
(nice meaning continuous and derivatives of all orders existing)
(minimal meaning minimum area in the curve, but not in the set) ?

Lacking the above, what would a minimum bounding convex polygon look like?
(That is, what are the extreme points)

What is the area of the set?  (I would guess that it is measurable.)

Has anyone tried looking at the 3-d surface generated by iterating the
process until the |z| > m (m not necessarily 2) and drawing this?



-- 
               O                      -- jefu
       tell me all about              -- UUCP: edison!steinmetz!putnam
Anna Livia! I want to hear all....    -- ARPA: putnam@kbsvax.decnet@GE-CRD


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