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From: pell@isy.liu.se (P{r Emanuelsson)
Newsgroups: comp.graphics
Subject: Re: Excluding Mandelbrot set -- Summary
Message-ID: <1989Nov25.174444.8953@isy.liu.se>
Date: 25 Nov 89 17:44:44 GMT
References: <3544@quanta.eng.ohio-state.edu> <3586@quanta.eng.ohio-state.edu>
Sender: news@isy.liu.se (Lord of the News)
Organization: Dept of EE, University of Linkoping
Lines: 31

Michael T. Davis:
>	Many replies included variations of the following theme from Dave
>Platt (dplatt@coherent.com), who wrote a program called MandelZot for the Mac
>(available via ftp at SUMEX-AIM.Stanford.Edu):

>>There are a couple of algorithms that people have developed to speed things
>>up.  These algorithms work by entirely avoiding the iteration on many points.
>>One algorithm is the Mariani/Silver "Eat my dust!" divide-and-conquer
>>algorithm... it assumes that if all of the points lying on the border of a
>>rectangle have the same dwell (the same number of iterations prior to
>>divergence), then all points in the interior of the rectangle can be marked as
>>having the same dwell...

This is of course not mathematically correct, but it's a useful assumption.
Especially if you take, say, every fifth point on the rectangle borders.
Sure, the images will start to look a bit strange but it's useful if you
want to have a quick peek at what things look like.

But if you take *every* point on the border and the image is very complex (:-),
as is often the case at higher magnifications, the standard Mandelbrot
algorithm is actually faster.

Region search is another method which can be quite fast. You label the
areas with equal dwell and then fill in the right color in a raster-scan
fashion. I might release some programs that implement this, but I don't
have anything ready yet. Don't ask me: I will announce here.

       /Pell
--
Dept. of Electrical Engineering	                         pell@isy.liu.se
University of Linkoping, Sweden	                    ...!uunet!isy.liu.se!pell