Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!samsung!brutus.cs.uiuc.edu!apple!sun-barr!newstop!sun!coherent!dplatt From: dplatt@coherent.com (Dave Platt) Newsgroups: comp.graphics Subject: Re: Excluding Mandelbrot set Message-ID: <40443@improper.coherent.com> Date: 27 Nov 89 18:17:44 GMT References: <3544@quanta.eng.ohio-state.edu> <480003@hpsad.HP.COM> <380@fsu.scri.fsu.edu> <4233@celit.fps.com> Reply-To: dplatt@improper.UUCP (Dave Platt) Organization: Coherent Thought Inc., Palo Alto CA Lines: 40 In article <4233@celit.fps.com> billd@fps.com (Bill Davids_on) writes: >I seem to recall mention of a theorem that extrememely few numbers >will "blow up" if they haven't already within 1000 iterations. >By experiment, I've found most numbers that diverge, do so well >before hitting 100. The gain in non-Mandelbrot points from 100 >to 256 is fairly small. The gain from 256 to 1000 is even smaller. >(often there is no difference depending on resolution and sample >space). Numerically, this is true... only an extremely thin "border" around M itself has dwells which lie above 256 (for example). If you're looking at a magnification-1 overview of M, there's not much sense in setting the dwell limit much above 256. However... things are very different if you're looking at high- magnification zooms. Many _very_ interesting and highly-detailed patterns can be found very close to M itself, at high magnifications (say, 10^12 or more). The points in these patterns tend to have very high dwell values... 2000 or more is not unusual, and I've seen some images that required a dwell limit of 32765 (which is as high as my program will go at the moment). Needless to say, these images take a _long_ time to resolve. I calculated an image a few months ago which required more than 36 hours on a dedicated Mac II, using a hand-coded 68881 instruction loop for the iterations. It was 1500 pixels wide by 1000 high, examined an area of M's border at a magnification of about 10^12, and had a dwell limit of 4095 or so (I think... it's been a while). I recently had a slide made from this data, and then had it printed on Cibachrome transparency material... fantastic pseudo-stained-glass imagery courtesy of a fractal formula! -- Dave Platt VOICE: (415) 493-8805 UUCP: ...!{ames,apple,uunet}!coherent!dplatt DOMAIN: dplatt@coherent.com INTERNET: coherent!dplatt@ames.arpa, ...@uunet.uu.net USNAIL: Coherent Thought Inc. 3350 West Bayshore #205 Palo Alto CA 94303 Brought to you by Super Global Mega Corp .com