Path: utzoo!attcan!uunet!snorkelwacker!bloom-beacon!eru!luth!sunic!liuida!isy!pell
From: pell@isy.liu.se (P{r Emanuelsson)
Newsgroups: comp.graphics
Subject: Re: Excluding Mandelbrot set
Message-ID: <1989Nov25.172130.8759@isy.liu.se>
Date: 25 Nov 89 17:21:30 GMT
References: <3544@quanta.eng.ohio-state.edu>
Sender: news@isy.liu.se (Lord of the News)
Organization: Dept of EE, University of Linkoping
Lines: 29

Michael T. Davis:
>	if (InMandelbrot(point(x,y)))
>	    /*ignore*/
>	else
>	    /*calculate distance*/

>The basic idea is to avoid running through the "maximum" number of iterations
>for each point in the Mandelbrot set.  Is this possible, or alternately, is
>there a more acceptable algorithm in terms of speed?

It is possible, but you have to do it while calculating the usual formula.
Mandelbrot points "converges" by going into "loops" (or "cycles"). Thus, as
soon as you detect a loop you can conclude that the point is in the set
and move on.

Unfortunately, it's not that simple to detect a loop. You have to store
old iteration values and search for a match and undoubtedly this will take
some time. I'm currently supervising a master's project and the students
report that the gain was insignificant. Maybe this is because at larger
magnifications there are usually not *that* many set-points in the region
of interest but the extra calculation has to be performed for every point.

There are, however, other faster algorithms, especially if you want to have
a rough-n'-fast outline of what you're looking at. More about this later.

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