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From: sinclair@aero.ARPA (William S. Sinclair)
Newsgroups: net.math
Subject: Is the Mandelbrot set a fiction??
Message-ID: <418@aero.ARPA>
Date: Mon, 9-Sep-85 15:25:14 EDT
Article-I.D.: aero.418
Posted: Mon Sep  9 15:25:14 1985
Date-Received: Sun, 15-Sep-85 11:38:51 EDT
Reply-To: sinclair@aero.UUCP (William S. Sinclair)
Organization: The Aerospace Corp., El Segundo, CA
Lines: 15


I have been looking at the error propagation properties of the Mandelbrot formula,
e.g. z=z*z+c. The error grows without bound in a very small number of  iterations. The implication on a finite precision machine is that for the exact same
number on two different machines, you are going to get different results.
In fact, on the SAME machine, using two different precisions, the results will
be different. I have verified this on the CDC Cyber 176.
 
The gist of this is: For points near the Mandelbrol set boundary, without an infinite
precision machine, you can't determine whether or not the point really does belong in the set.
 
                                    Bill Sinclair   213/647-1753


P.S.  I tried integer and fractional  arithmetic, but in both cases,
the numbers grow without bound, and have to truncated at some point.


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