Path: utzoo!attcan!uunet!lll-winken!decwrl!ucbvax!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: <1989Nov25.173416.8870@isy.liu.se>
Date: 25 Nov 89 17:34:16 GMT
References: <3544@quanta.eng.ohio-state.edu> <480003@hpsad.HP.COM> <19885@pasteur.Berkeley.EDU>
Sender: news@isy.liu.se (Lord of the News)
Organization: Dept of EE, University of Linkoping
Lines: 36

Jeff Anton:
>In one of the books about fractals there is a system of determining
>how far away a given point is from any point in the Mandelbrot set.
>From that you could write a program which could eliminate pixels from the
>set until it can eliminate no more leaveing pixels in the Mandelbrot set.
>[...]
>I think the system is not really better than traditional approach and
>is more complicated.

Perhaps not, but it's a different way! And it's fun to watch too!

The main drawback as I see it is that the algorithm only generates B/W images.

The main advantage is speed - especially when you are not interested about
details in the current magnification, but want to move on to more interesting
details.

Now, suppose you choose to use the standard Mandelbrot algorithm, but to save
time you only iterate every tenth point. Voila! The time drops to 1/100!
But the resulting image will be of no use. Instead, use the disk algorithm
mentioned above! As soon as you hit a point not in the set, the algorithm
will recursively generate disks around the set. Not 1/100, but still a
significant speedup.

If you want full resolution the disk algorithm will be slower, though.

I implemented this in February. You can get the program by anonymous FTP
from isy.liu.se (130.236.1.3), file FastMtool.tar.Z.
It's for SUN:s, but the algorithm is easy to rip out.
I think the program FRACTINT for PC:s contains this algorithm too, but
I haven't tried it.

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