Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!uakari.primate.wisc.edu!samsung!cs.utexas.edu!asuvax!ncar!unmvax!ariel!xochitl!jupiter!cheeks 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> Sender: news@xochitl.UUCP Reply-To: cheeks@edsr.eds.com Followup-To: comp.graphics Organization: EDS Research Lines: 30 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 Brought to you by Super Global Mega Corp .com