Path: unixg.ubc.ca!vanbc.wimsey.com!scipio.cyberstore.ca!math.ohio-state.edu!uwm.edu!hookup!olivea!uunet!mr.net!dawn.mmm.com!newsdist.tc.umn.edu!news.d.umn.edu!ub.d.umn.edu!dfinton From: dfinton@ub.d.umn.edu (david finton) Newsgroups: sci.fractals Subject: A deep-zoom fractal contest? Date: 15 Mar 1995 03:49:19 GMT Organization: University of Minnesota, Duluth Lines: 29 Message-ID: <3k5o40INNo1g@news.d.umn.edu> NNTP-Posting-Host: 131.212.134.2 X-Newsreader: TIN [version 1.2 PL2] I've been fooling around with the deep zooming mode available on Fractint v 19.0 and I love it. I've been able to view pictures that I couldn't have possibly seen on my computer before I got it. While it takes a little while longer to calculate the images, they are well worth it. Tim Wagner proposed a deep zooming fractal contest. I want to submit the following .par file to the contest. It's not a very deep picture (It took only two hours to calculate on a Pentium), but I like it and I want to share it anyway. Here it is: ---- Cut Here --------------------------------------------------------- Flower { ; Swirls within swirls, ad infinitum ; (When is anything in the Mandelbrot set NOT ; ad infinitum?) reset=1900 type=mandel passes=t corners=-1.74731064714761698304/-1.74731064714761683396/-5.5936523e-17/5\ .5936523e-17 params=0/0 float=y maxiter=20000 inside=0 logmap=-1050 symmetry=xaxis colors=000<5>I00L00O20<5>fE0jG0kI0<14>zz0<7>W00<4>C00<9>z00<16>000<7>00z\ <62>W51X60X60X70<59>yxFyyFzzGzzH<44>zzz0z0z00 } ----- Cut Here ----------------------------------------------------------- Enjoy! Path: unixg.ubc.ca!nntp.cs.ubc.ca!newsxfer.itd.umich.edu!agate!tcsi.tcs.com!uunet!in1.uu.net!ankh.iia.org!birdseh From: birdseh@iia.org (Henry Birdseye) Newsgroups: sci.fractals Subject: 10^233 magnification Date: 5 Jul 1995 00:26:50 GMT Organization: International Internet Association. Lines: 29 Message-ID: <3tcm8a$koe@ankh.iia.org> NNTP-Posting-Host: iia.org X-Newsreader: TIN [version 1.2 PL2] Here is a huge magnification .par file I've been zooming for a while. Cut here ---------------------- 233 { ; mag = 10^233 ; This takes a while ; Henry Birdseye - birdseh@iia.org ; Mail me your deep .par files reset=1920 type=mandel passes=2 center-mag=-0.7320299298281361984552930152710573055695167223049229392827\ 649564115771810297845444840812404043441296278932140339697145134072822677\ 086003318252081469770916042159178755967032000445188081331280125432690897\ 715003022308347206188135908325909287/0.362254943051205664189634244517662\ 428237917023435025634249637350403140930892080222768288921485422473252016\ 083128169244094674454003420702120965466655270667981376175896195517699326\ 5252623488386153939460345614941145789560489349509360628096195/1.306558e+\ 233 params=0/0 float=y maxiter=999990 colors=000zbO<3>zv4wz0<4>7z00z3<4>0zs3wz<6>w3zz2x<8>zlEzt6zy1qz0<4>2z00z\ 9<4>0zx7sz<4>kFzs7zz0z<7>zeLzjGznCzt6zy1qz0<4>2z00z9<4>0zx7sz<4>kFzs7zz0\ z<7>zeLzjGznCzt6zy1qz0<4>2z00z9<3>0zn60t<6>z00z60<6>zy0tz0<4>Hz0Ex5<4>0g\ Z0Sh0Jn08u20x<6>v04z20<5>zm0zu0xz0<3>Tz0Lz0Fy2<4>2jW0bb0Sh0Jn08u20x<6>v0\ 4z20<5>zm0zu0xz0<3>Tz0Lz0Fy2<4>2jW0bb0Sh0Eq03x60t<6>z00z60<6>zy0tz0<4>Hz\ 0Ex5<4>0gZ0Ye0Nk0Eq03x60t3wz<6>w3zz2x<5>zYT } ------------------------- END Let's see some more deep zoomers! -- Henry B. Path: unixg.ubc.ca!vanbc.wimsey.com!news.cyberstore.ca!math.ohio-state.edu!howland.reston.ans.net!news.sprintlink.net!gryphon.phoenix.net!news From: Twegner@phoenix.net (Tim Wegner) Newsgroups: sci.fractals Subject: Re: 10^233 magnification Date: Thu, 06 Jul 1995 15:08:29 GMT Organization: Phoenix Data Systems Lines: 86 Message-ID: <3tgu9h$5ag@gryphon.phoenix.net> References: <3tcm8a$koe@ankh.iia.org> Reply-To: twegner@phoenix.net NNTP-Posting-Host: dial56.phoenix.net X-Newsreader: Forte Free Agent v0.55 birdseh@iia.org (Henry Birdseye) wrote: >Here is a huge magnification .par file I've been zooming for a while. This is an impressive accomplishment, and I commend you for your diligence. However, you too have now joined the "Deep Zoom Whirlpools of Similarity Victims Club", of which David Chapman and I are charter members, The problem with relatively blind deep zooming is that there is a danger of creating deep zoom images that are essentially similar to much shallower zooms. The appeal of deep zooming is at least partly the hope of discovering some new images not visible at shallower depths. If this is your motivation, then you must strive to avoid the dreaded "whirlpools of self-similarity" that are legion in the Mandelbrot. The only technique I know for avoiding this horrible fate is to search for baby Mandelbrots and leap from baby Mandelbrot to baby Mandelbrot while zooming. This technique is unfortunately much more time consuming than the easier (but more dangerous for those fearing whirlpools) technique of zooming into any "fractally" looking area. My procedure for testing the condition of being trapped in such a whirlpool is as follows. First, I generate the deep zoomed image at as low a resolution as possible to save time, requiring only enough detail to see the main structure. Then I make a copy of the deep zoom PAR entry in center-mag form, and edit the magnification to bring it within range of normal double precision (usually about e+14 or so). I generate the much-shallower-zoomed image, and look for structures resembling the deep zoom. After framing the structure as accurately as possible, I then rotate the colors to get an approximate match. This whole procedure usually takes only a few minutes after generating the deep zoom, which is the sloweest step. Such quick success at finding similar structures at such vastly different magnifications (greatly exceeding the ratio of the size of the visible Universe to tiny sub-atomic quantum effects which is a mere 1.0e+61) is pretty good evidence of self-similarity. The results for the "233" zoom are as follows. The PAR below includes a copy of your deep zoom as well as my shallower zoom. I have only tried to match the framing and colors enough to convince myself of self-similarity; I'm sure a better match could be achieved with a little care. I challenge Henry and other sci.fractals readers to produce a zoom this deep (e+233) that is *not* a self-similar copy of a much shallower image at the same location. Keep on deep zoomin'! Tim 233 { ; mag = 10^233 ; This takes a while ; Henry Birdseye - birdseh@iia.org ; Mail me your deep .par files reset=1920 type=mandel passes=2 center-mag=-0.7320299298281361984552930152710573055695167223049229392827\ 649564115771810297845444840812404043441296278932140339697145134072822677\ 086003318252081469770916042159178755967032000445188081331280125432690897\ 715003022308347206188135908325909287/0.362254943051205664189634244517662\ 428237917023435025634249637350403140930892080222768288921485422473252016\ 083128169244094674454003420702120965466655270667981376175896195517699326\ 5252623488386153939460345614941145789560489349509360628096195/1.306558e+\ 233 params=0/0 float=y maxiter=999990 colors=000zbO<3>zv4wz0<4>7z00z3<4>0zs3wz<6>w3zz2x<8>zlEzt6zy1qz0<4>2z00z\ 9<4>0zx7sz<4>kFzs7zz0z<7>zeLzjGznCzt6zy1qz0<4>2z00z9<4>0zx7sz<4>kFzs7zz0\ z<7>zeLzjGznCzt6zy1qz0<4>2z00z9<3>0zn60t<6>z00z60<6>zy0tz0<4>Hz0Ex5<4>0g\ Z0Sh0Jn08u20x<6>v04z20<5>zm0zu0xz0<3>Tz0Lz0Fy2<4>2jW0bb0Sh0Jn08u20x<6>v0\ 4z20<5>zm0zu0xz0<3>Tz0Lz0Fy2<4>2jW0bb0Sh0Eq03x60t<6>z00z60<6>zy0tz0<4>Hz\ 0Ex5<4>0gZ0Ye0Nk0Eq03x60t3wz<6>w3zz2x<5>zYT } 233-shallow { ; Arrgggh! A much shallower copy of Henry Birdseye's ; "233" image. Self-similarity strikes again. ; Tim Wegner reset=1920 type=mandel center-mag=-0.7320299298280675908/0.3622549430511640843/1.1816e+014 params=0/0 float=y maxiter=999990 colors=000Q0`<3>v04z20<5>zm0zu0xz0<3>Tz0Lz0Fy2<4>2jW0bb0Sh0Jn08u20x<6>v0\ 4z20<5>zm0zu0xz0<3>Tz0Lz0Fy2<4>2jW0bb0Sh0Eq03x60t<6>z00z60<6>zy0tz0<4>Hz\ 0Ex5<4>0gZ0Ye0Nk0Eq03x60t3wz<6>w3zz2x<5>zYTzbOzgJzlEzq9zv4wz0<4>7z00z3<4\ >0zs3wz<6>w3zz2x<8>zlEzt6zy1qz0<4>2z00z9<4>0zx7sz<4>kFzs7zz0z<7>zeLzjGzn\ Czt6zy1qz0<4>2z00z9<4>0zx7sz<4>kFzs7zz0z<7>zeLzjGznCzt6zy1qz0<4>2z00z9<3\ >0zn60t<6>z00z60<6>zy0tz0<4>Hz0Ex5<4>0gZ0Sh0Jn08u20xA0pI0h } Path: unixg.ubc.ca!news.bc.net!info.ucla.edu!library.ucla.edu!agate!news.duke.edu!godot.cc.duq.edu!newsfeed.pitt.edu!dsinc!netnews.upenn.edu!mipg.upenn.edu!dewey From: dewey@mipg.upenn.edu (Dewey Odhner) Newsgroups: sci.fractals Subject: Re: 10^233 magnification Date: 10 Jul 1995 13:08:41 GMT Organization: University of Pennsylvania Lines: 15 Distribution: world Message-ID: <3tr8op$gk1@netnews.upenn.edu> References: <3tcm8a$koe@ankh.iia.org> <3tgu9h$5ag@gryphon.phoenix.net> NNTP-Posting-Host: mipgsun.mipg.upenn.edu In article <3tgu9h$5ag@gryphon.phoenix.net>, Twegner@phoenix.net (Tim Wegner) writes: |> I challenge Henry and other sci.fractals readers to produce a zoom this deep |> (e+233) that is *not* a self-similar copy of a much shallower image at the |> same location. Horiz.Hold { ; by Dewey Odhner. Public domain. reset=1920 type=mandel center-mag=-1.9999999999999999999999999999999999999999999999999999999999\ 999999999999999999999999999999999999999999999999999999999999996416785918\ 148134530430458843562012392471211940405947277366380516671161895619483871\ 9021305389817240974903756614325041160443974/0/3.3e+242 params=0/0 float=y maxiter=3000 inside=0 } Path: unixg.ubc.ca!info.ucla.edu!library.ucla.edu!agate!howland.reston.ans.net!news.sprintlink.net!gryphon.phoenix.net!news From: Twegner@phoenix.net (Tim Wegner) Newsgroups: sci.fractals Subject: Re: 10^233 magnification Date: Tue, 11 Jul 1995 04:35:33 GMT Organization: Phoenix Data Systems Lines: 24 Message-ID: <3tsv37$boe@gryphon.phoenix.net> References: <3tcm8a$koe@ankh.iia.org> <3tgu9h$5ag@gryphon.phoenix.net> <3tr8op$gk1@netnews.upenn.edu> Reply-To: twegner@phoenix.net NNTP-Posting-Host: 199.3.234.129 X-Newsreader: Forte Free Agent 1.0.82 dewey@mipg.upenn.edu (Dewey Odhner) wrote: >In article <3tgu9h$5ag@gryphon.phoenix.net>, Twegner@phoenix.net (Tim Wegner) writes: >|> I challenge Henry and other sci.fractals readers to produce a zoom this deep >|> (e+233) that is *not* a self-similar copy of a much shallower image at the >|> same location. >Horiz.Hold { ; by Dewey Odhner. Public domain. > reset=1920 type=mandel > center-mag=-1.9999999999999999999999999999999999999999999999999999999999\ > 999999999999999999999999999999999999999999999999999999999999996416785918\ > 148134530430458843562012392471211940405947277366380516671161895619483871\ > 9021305389817240974903756614325041160443974/0/3.3e+242 > params=0/0 float=y maxiter=3000 inside=0 > } This sure is weird. It looks like a bug, but I have investigated a little and can't see what it is. Maybe it is for real! If anyone has the time and computer power to make a 640x480 image of this I'd like to see it. Tim Path: unixg.ubc.ca!news.bc.net!news.uoregon.edu!newsfeed.internetmci.com!news.mathworks.com!zombie.ncsc.mil!simtel!daffy!uwvax!newssinet!news.u-tokyo.ac.jp!wnoc-tyo-news!wnoc-sfc-news!wnoc-kyo-news!kuis-news!kudpc!sakura.kudpc.kyoto-u.ac.jp!a51511 From: a51511@sakura.kudpc.kyoto-u.ac.jp (unknown) Newsgroups: sci.fractals Subject: Re:10^233 magnification Date: 21 Jul 95 09:36:44 Organization: Fukui-nct,Fukui Pref.,Sabae,JAPAN. Lines: 56 Distribution: world Message-ID: NNTP-Posting-Host: sakura.kudpc.kyoto-u.ac.jp A Dewey Odhner writes >> Horiz.Hold {: by Dewey Odhner. Public domain >> reset=1920 type=mandel My theory for the series converging to c=-2.0 can explain Dewey Odhner's picture. < Series of small M ( with period m=3,4,5,...) converging to c=-2.0 > For small M with period m ( m>>1), the location c(m) and the size d(m) are given by c(m)=-2.0+eps(m)=-2.0+(1.5*pi^2/4^m)+... d(m)=(6*pi^2/16^m)+... respectively. The value of c(m) for large m can easily be calculated by taking the above principal value as a initial value. Dewey Odhner's picture locates at relative Xctr=0.68 position, i.e. near the casp point of the small M. The period of this small M is m=202. The magnification, which makes the small M to the size of Full M, is given by 0.5/d(m). The relative branch length L(m,k) of the branch, which has the direction of (pi/2^k)*odd ( which is distorted by the cardioid like shape very near M ) and is normalized by d(m), is given by L(m,0)=eps(m)/d(m)=4^(m-1) L(m,k)=sqrt(L(m,k-1)), k=1,2,... . Therefore, the every relative branch length become longer as m increases. From these results, my theory can say: " The number of (additional) branches at the same coressponding area near small M is proportional to m." This can explain the reason that many horizontal branches appear near the casp point of small M for large m. I calculated many pictures near the small M with period m=25,50,100, 200, ( and 400). These pictures support my theory. For the case of M=400, per file is made, but it is not calculated yet, because it takes very long time. The following is the par file of small M with period m=25. Zoom areas you want. I hope you can enjoy pictures and my theory. Figures can be calculated in shoter time , though number of branches is about 1/8 compared with the case of m=202. m25a1 { : by Minoru Morikawa. small M with m=25. reset=1900 type=mandel center-mag=-1.99999999999998685104553996190604824145973215854934\ /0.0/1.07e+028/1 params=0/0 float=y maxiter=10000 inside=0 } m25horz { : by Minoru Morikawa. Horiz. Lines reset=1920 type=mandel passes=t center-mag=-1.999999999999986851045539961874934/2.250452e-45/3.032787e+0\ 29 params=0/0 float=y maxiter=10000 inside=0 } i Path: unixg.ubc.ca!info.ucla.edu!csulb.edu!nic-nac.CSU.net!usc!cs.utexas.edu!swrinde!tank.news.pipex.net!pipex!news.mathworks.com!zombie.ncsc.mil!simtel!daffy!uwvax!newssinet!news.u-tokyo.ac.jp!wnoc-tyo-news!wnoc-sfc-news!wnoc-kyo-news!kuis-news!kudpc!sakura.kudpc.kyoto-u.ac.jp!a51511 From: a51511@sakura.kudpc.kyoto-u.ac.jp (unknown) Newsgroups: sci.fractals Subject: Re:10^233 magnification and 10^1000 Date: 22 Jul 95 09:28:02 Organization: Fukui-nct,Fukui Pref.,Sabae,JAPAN. Lines: 55 Distribution: world Message-ID: NNTP-Posting-Host: sakura.kudpc.kyoto-u.ac.jp Last time, I mentioned my theory for the series converging to c=-2.0, and as examples gave only par files for m=25 and forgot ones for m=50. I give here par files m25a1,m25horz(correction),m50a1,and m50horz. m25a1 { : by Minoru Morikawa. small M with m=25. reset=1920 type=mandel center-mag=-1.99999999999998685104553996190604824145973215854934\ /0.0/1.07e+028/1 params=0/0 float=y maxiter=10000 inside=0 } m25horz { : by Minoru Morikawa. Horiz. Lines reset=1920 type=mandel passes=t center-mag=-1.999999999999986851045539961874934/0.0/3.0e+029 params=0/0 float=y maxiter=10000 inside=0 } m50a1 { : by Minoru Morikawa. small M with m=50. reset=1920 type=mandel center-mag=-1.9999999999999999999999999999883213824069750497300385583139\ 2087677/0.0/1.36e+058/1 params=0/0 float=y maxiter=10000 inside=0 } m50horz { : by Minoru Morikawa. Horiz. Lines reset=1920 type=mandel passes=t center-mag=-1.9999999999999999999999999999883213824069750497300385583138\ 956/0.0/3.85e+059/1 params=0/0 float=y maxiter=10000 inside=0 } You can see that the number of branches becomes double as m becomes double. The following is an example of very deep zoom. This has no meaning except one for a test of Fractint 19.2. As a test to show that a 10^1000 magnification picture can be calculated correctly by Fractint 19.2, the well known Xctr=0.0 and Yctr=1.0 self similar case is treated. The par file is very simple and is given as follows: test1000 { : by Minoru Morikawa 10^10000 reset=1920 type=mandel center-mag = 0.0/1.0/1.0e+1000/1.0 params=0/0 float=y maxiter=100000 inside=0 } The result is nice. As expected, the pictures for for mag=1.0e+1000 are similar with ones for mag=1.0e+50 , except rotation. Time was 60 hours 24min for videomode F3 by Pentium 90. This shows Fractint 19.2 can calculate deep zoom accurately. ---- morikawa@fukui-nct.ac.jp