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From: hatcher@INGRES.BERKELEY.EDU (Doug Merritt)
Newsgroups: comp.sys.amiga
Subject: Re: Amgia World Ray-tracing article...
Message-ID: <8704250732.AA21568@ingres.Berkeley.EDU>
Date: Sat, 25-Apr-87 02:32:52 EDT
Article-I.D.: ingres.8704250732.AA21568
Posted: Sat Apr 25 02:32:52 1987
Date-Received: Sun, 26-Apr-87 19:57:52 EDT
Sender: daemon@ucbvax.BERKELEY.EDU
Organization: University of California, Berkeley
Lines: 34
Summary: doubts about 5 sec Mandelbrot

In article <448@applix.UUCP> scott@applix.UUCP (Scott Evernden) writes:
>The first Mandelbrot generators I saw on my Amiga would take almost 2 minutes
>to plot the entire set.  But recently, a PD demo copy of MANDFXP would do the
>same set (presumeably using the same arithmetic) in about 5 seconds!!  Doesn't
>this suggest that one could invest some effort in improving the math used and
>realize some radical improvements?

What!? 5 seconds for a full Mandelbrot on an Amiga without hardware floating
point is incredible! It's probably not impossible, but the issues involved
in speeding it up that much go far beyond "improving the math" used (if
what you mean is smarter arithmetic). It would indeed involve "improving
the math" in the sense of either some very deep analysis or a very clever
algorithm that does not actually compute the set in the usual ways.
(Where can I get this MANDFXP???)

I am inclined to think that you are simply misremembering the numbers,
or that there was a trick involved. The first mandelbrot on the Amiga that
I saw took about 30 minutes for low quality mode, and much more for high
quality. More recently I've seen them speeded up to somewhere between
45 seconds and 3 minutes (I wasn't timing). That was Crystal Rose software;
I talked to the author and he did indeed have some pretty good insights
into the nature of the problem, and had come up with some heuristics for
avoiding some of the arithmetic some of the time. 

He had originally gotten it down to about 5 minutes by very careful attention
to use of integer arithmetic and by tight coding. This I found very
believable from my own experiences with implementing mandelbrots.

The radical improvements that you are looking for do not come as easily as
you imply; obvious methods are slow. When you optimize them, you get
medium speed. To make something really blindingly fast you generally need some
kind of deep insight into the problem. Improving the arithmetic is necessary
but not sufficient. This is as true of ray tracing as it is of mandelbrots.
	Doug Merritt		ucbvax!ingres!hatcher