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From: gwyn@smoke.BRL.MIL (Doug Gwyn)
Newsgroups: sci.math.num-analysis,sci.math,comp.graphics,comp.terminals.tty5620,comp.theory
Subject: Re: How much precision does Mandelbrot need
Message-ID: <12282@smoke.BRL.MIL>
Date: 4 Mar 90 00:40:13 GMT
References: <8602@cbnewsh.ATT.COM>
Reply-To: gwyn@brl.arpa (Doug Gwyn)
Followup-To: sci.math.num-analysis
Organization: Ballistic Research Lab (BRL), APG, MD.
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In article <8602@cbnewsh.ATT.COM> wcs@cbnewsh.ATT.COM (Bill Stewart 201-949-0705 erebus.att.com!wcs) writes:
>How much precision does it take to calculate Mandelbrot sets correctly?

That depends on the algorithm and on the resolution.
With the most straightforward method, over thousands of iterations,
I get the right results even at fairly high enlargements using normal
double-precision floating-point hardware.  If you think about the way
that rounding errors would accumulate, that's not too surprising.

>Since Mandelbrot sets depend very strongly on initial conditions,
>it would seem that loss of precision would quasi-randomly cause
>different results near any boundaries.

It doesn't have a noticeable effect on the images, though.

I would think that the software floating-point emulation of the 630
CCS would suffice.  While I'm a fan of scaled fixed-point for such
systems, I haven't tried applying that to Mandelbrot image generation.
It would probably work, though.