Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!ll-xn!ames!amdahl!orandy From: orandy@amdahl.amdahl.com (Kevin Clague) Newsgroups: comp.sys.amiga Subject: Re: The Interior Mandelbrot Message-ID: <8021@amdahl.amdahl.com> Date: Fri, 5-Jun-87 13:34:41 EDT Article-I.D.: amdahl.8021 Posted: Fri Jun 5 13:34:41 1987 Date-Received: Tue, 9-Jun-87 07:23:10 EDT References: <710@hao.UCAR.EDU> Organization: Amdahl Corporation, Sunnyvale, CA 94086 Lines: 85 Keywords: Yawn; Strange Attractors In article <710@hao.UCAR.EDU>, hull@hao.UCAR.EDU (Howard Hull) writes: > Recently, there was Yet Another Mandelbrot Program, titled MandelVroom, posted > to the net by one Kevin Clague at Amdahl. I considered calling it YAMP. It is shorter than MandelVroom, but not as much fun to say ;-) > He added a Motorola floating point > section that he claimed would give much improved resolution over the previously > available Mandelbrots, though I haven't checked that out in detail yet. One Umm... I'm not sure where you think I claimed greater resolution, maybe you misunderstood. I did not intend to make such an inaccurate claim. If you use the fixed point generator, or the floating point generator, you will be using 32 bit variables. The only other kind of resolution I can think of is graphics resolution. Needless to say, all you get is what the Amiga hardware provides. > thing that Kevin did make a note about in his code is the "Ring Detector" for > ponderous points in the inner lobes of the Mandelbrot interior exo-set. This > code detects non-migrating orbits for rotating points and escapes to more > productive duty, setting the cell count to max on the way out. However, > another thing it is capable of doing, so it turns out, is acting as a strange > attractor contour generator of sorts. It doesn't do a perfect job of this, > (in fact, I am wondering why it works at all) in that some places where there > are inflections in the contour, (See Note 1. below) it just gets "noisy". I detect 'non-migrating orbits' using a 32 entry trace table. I calculate and record the value of Z until I've filled the trace table. Then I compare the current value against the trace table. If I find a match, I know I've hit Mandelbrot. The points in the Mandelbrot set slowly converge to a stable orbit. Your patch shows how many iterations (divided by 32) it took for MandelVroom to detect stability in orbit. > Howard includes a patch to get interior colored. > If you make the patch, remember to select FFP in the Generator item submenu > after opening the EDIT menu. For those with no Manx, I'll post a .uue that > has this done for you, (along with an optimized color register set) in a > following article. You can make a similar patch to the fixed point generator. I think you did for the executable you posted. I will add an option to show data in the interior of the Mandelbrot set to MandelVroom. There are other things that can be shown on the interior of the Mandelbrot set. > ----------------------------------------------------------------------------- > Note 1: See contour map, Fig 33 p.60, "The Beauty of Fractals" by > H.-O. Peitgen - P.H. Richter, Springer-Verlag (Berlin, New York,...) > ----------------------------------------------------------------------------- There are a few things to note: 1. I can only detect orbits that are up to 32 iterations long. 2. The closer you get to the edge of the Mandelbrot set, the less effective this method is. 3. This method slows down points that do not bail out because of orbital stability. 4. This method works best on pictures of the main Mandelbrot set. Trace table orbital detection is discussed in the August 1985 issue of Scientific American's Computer Recreation column. It says that for N iterations, a trace table method could cost you N squared comparisons to detect these orbits. My method will not detect all orbits, but is on the order of N penalty instead of N squared. I could also produce pictures like Figure 34 on page 61 of "The Beauty of Fractals". Would anyone be interested in this feature in MandelVroom? Does anyone else use it? Kevin -- UUCP: orandy@amdahl.amdahl.com or: {sun,decwrl,hplabs,pyramid,ihnp4,seismo,oliveb,cbosgd}!amdahl!orandy DDD: 408-737-5481 USPS: Amdahl Corp. M/S 249, 1250 E. Arques Av, Sunnyvale, CA 94086 [ Any thoughts or opinions which may or may not have been expressed ] [ herein are my own. They are not necessarily those of my employer. ]