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From: cjh@petsd.UUCP (Chris Henrich)
Newsgroups: net.math
Subject: Re: Is the Mandelbrot set a fiction??
Message-ID: <646@petsd.UUCP>
Date: Tue, 17-Sep-85 10:26:31 EDT
Article-I.D.: petsd.646
Posted: Tue Sep 17 10:26:31 1985
Date-Received: Wed, 18-Sep-85 03:45:12 EDT
References: <418@aero.ARPA>
Reply-To: cjh@petsd.UUCP (PUT YOUR NAME HERE)
Organization: Perkin-Elmer DSG, Tinton Falls, N.J.
Lines: 31

[]
In article <418@aero.ARPA> sinclair@aero.UUCP (William S. Sinclair) 
writes:
>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.
>...
>For points near the Mandelbrot set boundary,
>without an infinite precision machine, you can't determine whether or 
>not the point really does belong in the set.

     Does the difference affect the overall appearance of the
Mandelbrot set?  In other words, are the "scrollwork" effects
so dramatically displayed in Dewdeney's article in
_Scientific_American_ artifacts?

     By the way, I think that article was mistaken in stating
that if the value of z ever got to where |z| > 2, it was sure
to go to "infinity".  It is fairly easy to show that if 
          |z| > |c| + 1
then the sequence will go to infinity.
Regards,
Chris

--
Full-Name:  Christopher J. Henrich
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