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From: cheeks@edsr.eds.com (Mark Costlow)
Newsgroups: comp.graphics
Subject: Re: Excluding Mandelbrot set
Message-ID: <234@xochitl.UUCP>
Date: 27 Nov 89 17:57:07 GMT
References: <7106@ficc.uu.net> <3544@quanta.eng.ohio-state.edu> <480003@hpsad.HP.COM>
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In article <7106@ficc.uu.net>, peter@ficc.uu.net (Peter da Silva) writes:
> One thing that can be done to speed up calculations of the mandelbrot set is
> to use memory. After you have determined that a point is in the set, you know
> that all the other points visited in determining that are in the set as well,
> so you can mark them black. Similarly, if you determine a point is not in the
> set you know that all the other points you visited are not in the set
as well,
> so you can mark them white (or whatever colors you're using). This is
a pretty
> safe optimisation.
>
Hmmm ... maybe I'm missing something here, but that doesn't seem to be a
valid algorithm. Since the Mandelbrot algorithm is Z(n+1) = Z(n)^2 + C, then
each iteration for a given C defines a "path" through the plane, stopping
at several (possibly infinite) discrete points. But, isn't the path different
for each different C? I mean, just because you saw point P when iterating
with C1, doesn't mean that if you see point P when iterating on C2 that
the C2 iteration will behave identically to the C1 iteration.
Well, I didn't word that pretty well, but I think you can see what I mean.
So, am I missing something?
> `-_-' Peter da Silva .
> 'U` -------------- +1 713 274 5180.
> "The basic notion underlying USENET is the flame."
> -- Chuq Von Rospach, chuq@Apple.COM
Mark Costlow
cheeks@edsr.eds.com