From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #90 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Thursday, January 29 1998 Volume 01 : Number 090 ---------------------------------------------------------------------- Date: Sat, 24 Jan 1998 01:35:23 -0600 From: "Justin A. Kolodziej" <4wg7kolodzie@vms.csd.mu.edu> Subject: Re: (fractint) Duplicate messages (DUPLICATE) Gedeon Peteri wrote: > These past couple of days I received approximately 20 messages which > were duplicates of postings I already received once several days ago. > And they keep coming; two just this morning. The duplicates do not bear > current dates, but those of the original posting. Is anyone else > experiencing this phenomenon? > Gedeon Yep, this is a duplicate. Here's my new theory now that the Netscape one is shattered... "I repeat myself when under stress I repeat myself when under stress I repeat myself when under stress I repeat myself when under stress I repeat myself when under stress" -King Crimson, "Indiscpline" > - > ------------------------------------------------------------ > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@xmission.com > Get Commands: majordomo@xmission.com "help" > Administrator: twegner@phoenix.net > Unsubscribe: majordomo@xmission.com "unsubscribe fractint" - -- Justin A. Kolodziej Why pay for an OS when you can get a clearly superior one for free? Justin Kolodziej is 4wg7kolodzie@vms.csd.mu.edu Marquette University is www.mu.edu - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 17:11:34 -0600 From: "Tim Wegner" Subject: (fractint) Hi Folks - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 15:46:08 -0800 From: "Jay Hill" Subject: (fractint) Is this still a great list or what? Hi Fractintiers, You can still follow the adventures of Dr. J, the mad scientist of fractal space at http://home.san.rr.com/jayrhill/FotN/FotNindx.html Last we heard he may have over consumed on some beverage after the FractoBowl Game. Hopefully there are some useful formula hints there from someone who is also learning about this from this list. Enjoy Jay - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 18:59:38 -0500 From: Gedeon Peteri Subject: (fractint) gravijul formula Mark Christenson wrote: > Enjoy, and please post interesting results (I already have about > 20 of my own) ! > > - Bud Bud, I liked your formula and played around with it a good bit - that "super-generalization" you spoke of offers a lot of choices. I posted the first four pars a few days ago, but the list was down and it did not seem to get through. Since then I added two more. I hope you'll find them interesting. Gedeon ================================== Here is Mark Christenson's formula: gravijul { ; r^(-2) Mark Christenson 1/25/98 ; defaults: p1 = (1,0) p2 = (0,0) p3 = (4,0) z = pixel: w = fn1(z) z = fn3(p1/fn2(w*w)) + p2 |z| < p3 } and six of my pars: gp-gj09-01 { ; Mark Christenson's formula ; Gedeon Peteri, Jan 25, 1998 ; Wizzle deeps2 map reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/cotan/asinh passes=b center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498 params=4/0/0/0/2.95/0 float=y inside=epsiloncross outside=atan colors=000EXU<4>0IE<15>kuz<10>K0S<10>zzm<22>L29<18>\ wwm<4>pmenkcmjblha<20>O88N76M55K33K36K29K2DK1GK0K<9>\ cru<15>00P<7>cru<16>V3WU0US0U<9>C0U<6>c0U<18>60u40w40t\ <11>7CI7DF7EC8F8AIBCLE<13>fzz<9>HZX } gp-gj09-02 { ; Mark Christenson's formula ; Gedeon Peteri, Jan 25, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/sin/atanh passes=b center-mag=1.21207/-0.721783/8.83661/1/27.5 params=1/0/0/0/2.95/0 float=y outside=atan colors=0007O0uQB<16>X1wW0zX1w<22>zW0JOP<13>bfgchhbgg\ <14>JOP00z<22>z0z<23>00zNMK<6>jjh<7>NMK0G0<6>Nh1<7>\ 0G0WWz<21>yW3zW0yW2<22>WWzV8R<6>pQk<7>V8RLLL<14>llm\ <15>LLLzW0yU2xT5 } gp-gj09-03 { ; Mark Christenson's formula ; Gedeon Peteri, Jan 25, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/cotan/asinh passes=b center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498 params=4/0/0/0/2/0 float=y inside=epsiloncross outside=atan colors=000BWN8SJ4NF00c<6>0Wz<7>00cV5H<6>uVg<7>V5H0G0\ <6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk<7>0008LM<6>Pkl\ <7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>L5ZW00<6>z00<7>W0000W\ <6>0zz<7>00WS24<6>wRT<7>S24L5Z<6>fQu<5>O8aL5ZG0W<6>\ zWz<7>G0WIF7<6>mfU<6>MIAIF7G00<6>z00<7>G004NF<6>Wti<4>F_R } gp-gj09-04 { ; Mark Christenson's formula ; Gedeon Peteri, Jan 25, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/atanh/atan passes=t center-mag=-3.55271e-015/1.77636e-015/0.3743325/1/20 params=1/0/0/0/2/0 float=y inside=period outside=atan decomp=256 colors=G00M00G004NF<6>Wti<7>4NF00c<6>0Wz<7>00cV5H<6>\ uVg<7>V5H0G0<6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk\ <7>0008LM<6>Pkl<7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>\ L5ZW00<6>z00<7>W0000W<6>0zz<7>00WS24<6>wRT<7>S24L5Z\ <6>fQu<5>O8aL5ZG0W<6>zWz<7>G0WIF7<6>mfU<6>MIAIF7G00\ <6>z00<4>Y00M00 } gp-gj09-05 { ; Mark Christenson's formula ; Gedeon Peteri, Jan 26, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=flip/flip/log passes=b center-mag=1.77636e-015/-6.21725e-015/0.1813158 params=2/-1.5/0/0/8/0 float=y outside=atan colors=000N5B<17>wwm<4>pmenkcmjblha<20>O88N76M55\ K33K36K29K2DK1GK0K<9>cru<15>00P<7>cru<16>V3WU0US0U\ <9>C0U<6>c0U<18>60u40w40t<11>7CI7DF7EC8F8AIBCL\ E<13>fzz<7>MdbKa_HZXEXUBUR8RO<2>0IE<15>kuz<10>K0S\ <10>zzm<22>L29 } gp-gj09-06 { ; Mark Christenson's formula ; Gedeon Peteri, Jan 26, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/cotan/asinh passes=b center-mag=-4.44089e-016/-1.55431e-015/0.9432784/1/27.499 params=4/0/0/0/2.95/0 float=y maxiter=1023 fillcolor=255 inside=epsiloncross outside=atan invert=0.596820086519159/0/0 colors=000M00<5>z00<7>G004NF<6>Wti<7>4NF00c<6>0Wz\ <7>00cV5H<6>uVg<7>V5H0G0<6>WzW<7>0G0S24<6>wRT<7>S2\ 4000<6>kkk<7>0008LM<6>Pkl<7>8LMJN4<6>ntS<7>JN\ 4L5Z<6>fQu<7>L5ZW00<6>z00<7>W0000W<6>0zz<7>00WS24\ <6>wRT<7>S24L5Z<6>fQu<5>O8aL5ZG0W<6>zWz<7>G0WIF7\ <6>mfU<7>IF7000 } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Mon, 26 Jan 1998 11:56:15 -0500 From: Gedeon Peteri Subject: Re: (fractint) hearts and flowers Mark Christenson wrote: > Enjoy, and please post interesting results (I already have about > 20 of my own) ! > > - Bud Here is Mark's formula: gravijul { ; r^(-2) Mark Christenson 1/25/98 ; defaults: p1 = (1,0) p2 = (0,0) p3 = (4,0) z = pixel: w = fn1(z) z = fn3(p1/fn2(w*w)) + p2 |z| < p3 } and four of my pars: gp-gj09-01 { ; Mark Christensen's formula ; Gedeon Peteri, Jan 25, 1998 ; Wizzle deeps2 map reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/cotan/asinh passes=b center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498 params=4/0/0/0/2.95/0 float=y inside=epsiloncross outside=atan colors=000EXU<4>0IE<15>kuz<10>K0S<10>zzm<22>L29<18>\ wwm<4>pmenkcmjblha<20>O88N76M55K33K36K29K2DK1GK0K<9>\ cru<15>00P<7>cru<16>V3WU0US0U<9>C0U<6>c0U<18>60u40w40t\ <11>7CI7DF7EC8F8AIBCLE<13>fzz<9>HZX } gp-gj09-02 { ; Mark Christensen's formula ; Gedeon Peteri, Jan 25, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/sin/atanh passes=b center-mag=1.21207/-0.721783/8.83661/1/27.5 params=1/0/0/0/2.95/0 float=y outside=atan colors=0007O0uQB<16>X1wW0zX1w<22>zW0JOP<13>bfgchhbgg\ <14>JOP00z<22>z0z<23>00zNMK<6>jjh<7>NMK0G0<6>Nh1<7>\ 0G0WWz<21>yW3zW0yW2<22>WWzV8R<6>pQk<7>V8RLLL<14>llm\ <15>LLLzW0yU2xT5 } gp-gj09-03 { ; Mark Christensen's formula ; Gedeon Peteri, Jan 25, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/cotan/asinh passes=b center-mag=4.44089e-016/-3.10862e-015/0.4026667/1/27.498 params=4/0/0/0/2/0 float=y inside=epsiloncross outside=atan colors=000BWN8SJ4NF00c<6>0Wz<7>00cV5H<6>uVg<7>V5H0G0\ <6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk<7>0008LM<6>Pkl\ <7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>L5ZW00<6>z00<7>W0000W\ <6>0zz<7>00WS24<6>wRT<7>S24L5Z<6>fQu<5>O8aL5ZG0W<6>\ zWz<7>G0WIF7<6>mfU<6>MIAIF7G00<6>z00<7>G004NF<6>Wti<4>F_R } gp-gj09-04 { ; Mark Christensen's formula ; Gedeon Peteri, Jan 25, 1998 reset=1960 type=formula formulafile=*.frm formulaname=gravijul function=recip/atanh/atan passes=t center-mag=-3.55271e-015/1.77636e-015/0.3743325/1/20 params=1/0/0/0/2/0 float=y inside=period outside=atan decomp=256 colors=G00M00G004NF<6>Wti<7>4NF00c<6>0Wz<7>00cV5H<6>\ uVg<7>V5H0G0<6>WzW<7>0G0S24<6>wRT<7>S24000<6>kkk\ <7>0008LM<6>Pkl<7>8LMJN4<6>ntS<7>JN4L5Z<6>fQu<7>\ L5ZW00<6>z00<7>W0000W<6>0zz<7>00WS24<6>wRT<7>S24L5Z\ <6>fQu<5>O8aL5ZG0W<6>zWz<7>G0WIF7<6>mfU<6>MIAIF7G00\ <6>z00<4>Y00M00 } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 19:20:22 EST From: Nature102 Subject: Re: (fractint) Reuse of previous zooms In a message dated 1-28-98 6:01:39 PM Central Standard Time, EPA@datcon.co.uk writes: << For example, if the zoom box is half as wide and half as high as the old image, then one in four of the pixels in the new image have already been calculated. Using some kind of guessing algorithm, most of the others could be worked out very quickly. This would make zooming into fractals a great deal faster. >> Well, yah, but I personally zoom in with the box as small as possible. It's true that if you were to use a relatively big box, there would be a major speed increase, but for small boxes, the speed increase would be negligible ::Shrugs:: Oh well. It's a cool idea. Let's bomb the Fractint people with it. :-) BTW, does anyone know about how long it is between versions of Fractint on the average? I just got into the fractal world with 19.6, so I don't really know how often it gets updated. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 04:19:52 -0500 From: davides Subject: (fractint) Re: simple par Posting only a simple par; for whatever reason I rather like the colors in this - something of a quiet fractal. Forward flames to your local tax collection agency... :) pastel_blue2 { ; (c) Copyright David Shanholtzer, 1998 reset=1960 type=phoenixcplx center-mag=0.45827/0.312116/6.94316/1.2136 params=0.2/0/0.3/0/0 maxiter=5000 inside=255 logmap=75 decomp=256 colors=rqvnourqv<62>6Ia5I`4H`4H`4Ia4Jb<31>CmrDnsEnr<8>TgoUgoWhp<13>vvw<1\ 5>UUhVVhWXhYZh<43>omspnspnsqotpmrokp<11>cRTZ00<11>mfjoinpmrrqvrnv<14>m0m\ 3Km<8>Ycraerdgsgjtklu } davides@pipeline.com Back up my hard drive? How do I put it in reverse? - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 19:46:01 -0800 From: Peter Jakubowicz Subject: (fractint) 2 Dumb ?? 1)What does the Farey series have to do with the Mandelbrot set? 2)How long is the coast of the Mandelbrot set? Thank you. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 16:52:11 -0800 From: "Jay Hill" Subject: Re: (fractint) Re: simple par David wrote >Posting only a simple par; for whatever reason I rather like the colors in >this - something of a quiet fractal. The image seems a little pale, so I panned down to this pastel_blue2a { ; (c) Copyright David Shanholtzer, 1998 ; nearby image reset=1960 type=phoenixcplx center-mag=0.491675/-0.344382/3.471483/1.2137 params=0.2/0/0.3/0/0 maxiter=5000 inside=255 logmap=75 decomp=256 colors=rqvnourqv<64>4H`4H`4Ia<32>CmrDnsEnr<8>TgoUgoWhp<13>vvw<15>UUhVVhW\ XhYZh<45>pnsqotpmr<12>cRTZ00<11>mfjoinpmrrqvrnv<14>m0m3Km<9>aerdgsgjtklu } Jay - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 19:56:14 EST From: Nature102 Subject: Re: (fractint) 2 Dumb ?? In a message dated 1-28-98 6:52:10 PM Central Standard Time, pfjakub@earthlink.net writes: << 1)What does the Farey series have to do with the Mandelbrot set?>> Umm... They both have standard scientist names that aren't exactly normal human names like Smith or Jones? They both involve plus signs? I give up. :-P (What IS the Farey series, for that matter? :-P) << 2)How long is the coast of the Mandelbrot set? >> Ooh, ooh, I know! It's really long! Infinite, to be exact! Same length as the coast of anything! (Hmm... Iraq's border is infinitely long. Bet that would boost our friendly mad dictator with weapons of mass destruction's ego some. :-P) - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 17:06:39 -0800 From: "Jay Hill" Subject: (fractint) 2)How long is the coast of the Mandelbrot set? What measure would you like to use? There is the boundary of the Cardoid with the attached buds. In this case, it is a fractal whose dimension I measured a few years ago. I calculated the circumference as a function of limiting bud size. These is also the boundary around all of the set. I measured this using the arc length of the contours. There may be even other measures. I don't have the numbers handy. Jay - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Mon, 26 Jan 1998 18:57:27 -0600 From: "Tim Wegner" Subject: Re: (fractint) Astrophysical Lunacy Mark wrote: > Geez, I almost wish you hadn't pointed that out, but I guess > it's best I know the ugly truth. I should have been suspicious > of integer artifacts from the nearly-hyperbolic "biomorph" spikes > in ap-102. Sadly, I find that all of the half-dozen images I > genned from jul1-138 lose their best features when generated > in their "true" form, which means they're not really fractals. From a philosophical point of view, images that depend on integer artifacts can still be fractals. Fractals can be generated from discontinuous functions with strange rounding and multiple cases as easily as from iterating simple, elegant, differentiable nonlinear functions. To take the point further, one of the points of fractal theory is to break the prejudice that prefers the well behaved, smooth functions of elemntary calculus, and sneers at the others as unimportant counter examples. Perhaps we have just pushed the same prejudice one level deeper when we acknowlege highly "ill behaved" fractal functions as long as they are defined by iterating nice, friendly, smooth, well-defined functions like z^2+c. That's my view as a philosopher, but not my view as a programmer. A good programmer takes backwards compatability very seriously, because the alternative is to create huge problems for users every time a new software version is released. Integer artifacts give programmers fits when they happen accidently, because they are hard to control. I would prefer that artists use floating point and the various rounding functions, because then the software behaves more robustly when the internals change. Perhaps we need some new functions proposed that satisfy those who enjoy exploring artifacts. Integer math surely is going to be removed from fractint. We're just not sure how soon. Tim - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 21:21:05 -0800 From: Peter Jakubowicz Subject: Re: (fractint) 2)How long is the coast of the Mandelbrot set? At 05:06 PM 1/28/98 -0800, you wrote: > >What measure would you like to use? > >These is also the boundary around all of the set. I measured >this using the arc length of the contours. That's what I want to know. What did you do about the arc length of the contours to determine the boundary? BTW, thanks for those FOTNs. Good exercise for both halves of the brain. Unfortunately, the March Astronomy is not out in my part of the world. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 18:40:11 -0800 From: "Jim sellers" Subject: (fractint) Virus This was received from a friend and it sounds important. Jim Sellers > > > Subject: > > > Date: Fri, 23 Jan 1998 10:52:17 -0500 (EST) > > > Message-ID: > > > > > > VIRUS WARNING > > > If you receive an email titled "JOIN THE CREW," DO NOT open it. It will erase everything on your hard drive. Forward this letter out to as many people as you can. This is a new, very malicious virus and not many people know about it. This informatio n was announced Wednesday morning from IBM; please share it with everyone that might access the internet. Once again, pass this along to EVERYONE in your address book so that this may be stopped. Also, do not open or even look at any mail that says "RETURNED OR UNABLE TO DELIVER." This virus will attach itself to your computer components and render them useless. Immediately delete any mail items that say this. AOL has said that this is a very dangerous virus and that there is NO remedy for it at this time. Please practice cautionary measures and forward this to all users. > > > > > > Gloria Litteral > > > Administrative Assistant to the Dean > > > Dean of Students' Office > > > The College of Wooster > > > Galpin Hall > > > Wooster, Ohio 4469l > > > Telephone: 330-263-20ll > > > FAX: 330-263-2594 > > > e-mail: GLitteral@acs.Wooster.edu > > > > > > --------- End forwarded message ---------- > > Received this from a friend, and have no reason to doubt it. I've > > already had a couple of messages that were returned that should have > > gone through. > > > > Pat Cline - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 21:19:28 -0600 (CST) From: 4wg7kolodzie@vms.csd.mu.edu Subject: Re: (fractint) Reuse of previous zooms On Mon, 26 Jan 1998, Edward Avis wrote: > If you zoom in to a fractal there is potential for part of the old image to > be used to calculate the new one. > > For example, if the zoom box is half as wide and half as high as the old > image, then one in four of the pixels in the new image have already been > calculated. Using some kind of guessing algorithm, most of the others > could be worked out very quickly. > > This would make zooming into fractals a great deal faster. Yes, it would... IF you zoom in by half. If you zoom in by, say, making the zoom box .084637745656 as wide and .084637745656 as high (random numbers), there is a very high likelyhood that NONE of the pixels will have been calculated already. You would have to limit zooming in to simple rational numbers, like 1/3, 1/4, 1/10... for it to work. Justin A. Kolodziej - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 21:32:15 -0600 From: Bob Margolis Subject: Re: (fractint) Virus (There is none!) Jim sellers wrote: > > This was received from a friend and it sounds important. > Jim Sellers > > > > Subject: > > > > Date: Fri, 23 Jan 1998 10:52:17 -0500 (EST) > > > > Message-ID: > > > > > > > > VIRUS WARNING The virus you're talking about is the message you're sending. E-Mail messages don't spread viruses; software programs do. You've sounded an alarm for nothing. Bob Margolis - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 21:41:15 -0600 From: "Tim Wegner" Subject: Re: (fractint) Virus > > > > VIRUS WARNING > > > > If you receive an email titled "JOIN THE CREW," DO NOT open it. Please don't post messages like this to the fractint list!!! ONLY post messages to this list that have to do with fractals. The "virus" message was a fraud, but even if it weren't a fraud, this is not a virus discussion list! Sorry to bother everyone with this, but I felt this message needed a response. Also, folks, if you see off topic messages, you don't need to personally take care of it by posting a response; as list administrator, I will. (Feel free to email me personally if yopu think I missed something.) Thanks for your patience, and glad to see things are getting back to normal. back to fractals! Tim - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 21:54:37 -0600 From: "Paul N. Lee" Subject: Re: (fractint) Virus Jim sellers wrote: > > This was received from a friend and it sounds important. > Jim Sellers > > > > Subject: > > > > Date: Fri, 23 Jan 1998 10:52:17 -0500 (EST) > > > > Message-ID: > > > > > > > > VIRUS WARNING > > > > Those are bogus virus email messages. If you want to know about the "real" viruses going around: ____________________________________________________________________ Welcome to the Virus Alert of the Day for Tuesday, January 27, 1998. The following new viruses are expected to activate tomorrow: PS-MPC VCL Victor Girafe Viruses scheduled to activate today are: Ah Emo-899 Demon variants Murphy variants All of the above viruses can be detected and removed with regular antiviral agents. Ongoing alerts for the month of January: Plastique Major Manzon Tentacle Ripper Baby New Year: e-mail hoax ____________________________________________________________________ The rest of the information may be obtained on a daily basis by going to the following and subscribing: http://www.tipworld.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 29 Jan 1998 17:02:49 +1300 From: "Morgan L. Owens" Subject: Re: (fractint) Astrophysical Lunacy and Integer Arithmetic At 18:57 26/01/98 -0600, Tim Wegner wrote: > >Integer math surely is going to be removed from fractint. We're >just not sure how soon. > >Tim > I've been expecting this myself for a while now - Fractint's integer arithmetic was after all introduced for the sake of speed, and I for one find that the floating-point algorithms are much _faster_ on my machine, and have been since my 486. (My 386/IIT was faster at floating point than integer for that matter). These days I only ever use integer arithmetic for deliberately introducing artefacts. The thing is, I really _like_ some of these artefacts (my Astro.frm formulae are cases in point). So when integer arithmetic is removed from Fractint (Fractfloat? Ouch...) I would like to see some sort of fossil support retained. MLO circuitry { ; It's an artefact and I don't care! reset=1950 type=unity passes=b float=n center-mag=0/0/0.25 maxiter=256 inside=255 potential=255/300/150 periodicity=0 colors=@headache.map } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 21:20:33 -0700 (MST) From: Kerry Mitchell Subject: Re: (fractint) 2 Dumb ?? The Farey series provides a convenient way to identify the disks along the cardioids in the Mandelbrot set. For review, the Farey sequence starts: 0/1, 1/1 in the first generation, followed by 0/1, 1/2, 1/1; 0/1, 1/3, 1/2, 2/3, 1/1; etc. For each subsequent level, every second term is a combination of two terms from the previous generation. For example, the 1/3 comes from (0+1)/(1+2) from the previous step. For the Mandelbrot set, let 0/1 represent the cusp (0.25,0), 1/2 is the large disk at -1, and 1/1 is back to the cusp. Looking at the third level above, between 0/1 and 1/2 is 1/3. This corresponds to the large disk at the top of the cardioid (and 2/3 is the other disk at the bottom). Between any two disks with adjacent Farey entries at generation j, the largest disk between those two has the Farey number between those two at generation j+1. In other words, the largest disk between disks 1/3 and 1/2 is disk (1+1)/(2+3) = 2/5. Aside from labelling, the Farey numbers also serve as a coordinate. Let theta = 2 * pi * m/n, where m/n is the Farey fraction for the given disk. Then, r = 0.5 * (1 - cos(theta)), x = r * cos(theta) + 0.25, y = r * sin(theta), c = x + i*y c is the point of tangency between the main cardioid and the m/n disk. Since all fractions eventually show up in the Farey series, all fractions have corresponding disks. Also, if we replace the rational number m/n with an irrational number (such as phi = 0.618034...), then the corresponding c will be a cardioid boundary point with no tangent disk. Therefore, it will have a chaotic orbit. (An easier way to get chaotic points is to use a rational number for theta. Since pi is irrational, that guarantees that the factor (m/n in the Farey case) will also be irrational.) The point abouve above chaotic orbits brings up another Farey connection. Each disk has a corresponding Farey number m/n, which is in lowest terms. The denominator, n, indicates the periodicity of the disk tangent to the cardioid at the point c. For example, with m/n = 1/2, the tangency point is at the disk of periodicity 2 at -1. The 1/3 and 2/3 disks are tangent to the period 3 disks at the top and bottom. These are the connections between the Farey sequence and the Mandelbrot set of which I'm aware. Any others? - ------------------------------------------------------------------------------- Kerry Mitchell lkmitch@primenet.com - ------------------------------------------------------------------------------- On Wed, 28 Jan 1998, Peter Jakubowicz wrote: > 1)What does the Farey series have to do with the Mandelbrot set? > 2)How long is the coast of the Mandelbrot set? > Thank you. > > > - > ------------------------------------------------------------ > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@xmission.com > Get Commands: majordomo@xmission.com "help" > Administrator: twegner@phoenix.net > Unsubscribe: majordomo@xmission.com "unsubscribe fractint" > - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 21:20:33 -0700 (MST) From: Kerry Mitchell Subject: Re: (fractint) 2 Dumb ?? The Farey series provides a convenient way to identify the disks along the cardioids in the Mandelbrot set. For review, the Farey sequence starts: 0/1, 1/1 in the first generation, followed by 0/1, 1/2, 1/1; 0/1, 1/3, 1/2, 2/3, 1/1; etc. For each subsequent level, every second term is a combination of two terms from the previous generation. For example, the 1/3 comes from (0+1)/(1+2) from the previous step. For the Mandelbrot set, let 0/1 represent the cusp (0.25,0), 1/2 is the large disk at -1, and 1/1 is back to the cusp. Looking at the third level above, between 0/1 and 1/2 is 1/3. This corresponds to the large disk at the top of the cardioid (and 2/3 is the other disk at the bottom). Between any two disks with adjacent Farey entries at generation j, the largest disk between those two has the Farey number between those two at generation j+1. In other words, the largest disk between disks 1/3 and 1/2 is disk (1+1)/(2+3) = 2/5. Aside from labelling, the Farey numbers also serve as a coordinate. Let theta = 2 * pi * m/n, where m/n is the Farey fraction for the given disk. Then, r = 0.5 * (1 - cos(theta)), x = r * cos(theta) + 0.25, y = r * sin(theta), c = x + i*y c is the point of tangency between the main cardioid and the m/n disk. Since all fractions eventually show up in the Farey series, all fractions have corresponding disks. Also, if we replace the rational number m/n with an irrational number (such as phi = 0.618034...), then the corresponding c will be a cardioid boundary point with no tangent disk. Therefore, it will have a chaotic orbit. (An easier way to get chaotic points is to use a rational number for theta. Since pi is irrational, that guarantees that the factor (m/n in the Farey case) will also be irrational.) The point abouve above chaotic orbits brings up another Farey connection. Each disk has a corresponding Farey number m/n, which is in lowest terms. The denominator, n, indicates the periodicity of the disk tangent to the cardioid at the point c. For example, with m/n = 1/2, the tangency point is at the disk of periodicity 2 at -1. The 1/3 and 2/3 disks are tangent to the period 3 disks at the top and bottom. These are the connections between the Farey sequence and the Mandelbrot set of which I'm aware. Any others? - ------------------------------------------------------------------------------- Kerry Mitchell lkmitch@primenet.com - ------------------------------------------------------------------------------- On Wed, 28 Jan 1998, Peter Jakubowicz wrote: > 1)What does the Farey series have to do with the Mandelbrot set? > 2)How long is the coast of the Mandelbrot set? > Thank you. > > > - > ------------------------------------------------------------ > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@xmission.com > Get Commands: majordomo@xmission.com "help" > Administrator: twegner@phoenix.net > Unsubscribe: majordomo@xmission.com "unsubscribe fractint" > - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 28 Jan 1998 22:40:13 -0800 From: "Jay Hill" Subject: (fractint) F.O.T.N. (Fractal of the Night) 29 Jan 1998 (Garden Path) F.O.T.N. (Fractal of the Night) 29 Jan 1998 (Garden Path) Finally, contact with Dr. J. He just cannot resist those technical questions. Alas, he won't answer my email questions about the FractoBowl games. Since he won't say anything, we can assume his favorite team lost. Tonight, it would seem, he has been reading his email and saw something of interest. So I'm taking a break from the sequence of panoramas, like last nights panorama. Peter Jakubowicz asked about the perimeter of the Mandelbort set lakes. I replied, in the usual way, "Been there, done that". Just kidding, got to stall somehow. But Dr. J put me to shame as only someone from that fractal space can. He just went for his evening stroll around the grounds and counted his steps. After all, isn't that the definition of a fractal perimeter. He says he can take big steps following the lower count escape contours, which should be obvious. But as he huffed and puffed around the higher iteration count contours (see Big Fatso to see why he huffs and puffs) http://home.san.rr.com/jayrhill/FotN/FotN20.html he reported he had to take steps about half as long for each contour. That is so he can follow the curves. He sent along the following picture, Figure 1, showing his garden pathways. http://home.san.rr.com/jayrhill/FotN/FotN29.html http://home.san.rr.com/jayrhill/FotN/FotNindx.html Figure 1. Dr. J's paths around the ground of his home. n perimeter 1 12.5663606457797931 2 8.8944950515498699 3 7.7383729769791320 4 7.4436432355331474 5 7.7000303808066779 6 8.1421088527093027 7 8.9862442676535721 8 9.9311532506364844 9 11.2267264962016062 10 12.7021596574680396 11 14.5645917174476154 12 16.6181359097436469 13 19.2297329357505035 14 22.1410545197811443 15 25.6606374585242084 The perimeter seems to be a function of n, the iteration count for the contour, namely, a one fifth power. P = C1*2^(n/5) Since Dr. J had to take steps half as long to insure getting around every wrinkle in the path, we know his step lengths are L=C2*2^(-n) Therefore, the dimension must be the exponent in P/L. P/L = C*2^(6/5) and the dimension is 6/5. Enjoy Jay PS. Newton's method was used to follow the contour around the MSet. Approximate halving the step size was required to prevent straying from the path. Following the path to higher order is of ever more difficulty. I have reached the limits of 80 bit floats and weekend runs on a P200. If the trend is real, the dimension using this measure is 6/5. Dr_Js_grounds { ; A simulation of Dr. Js garden pathways. reset=1960 type=mandel center-mag=-0.5/0/0.6666667 params=0/0 maxiter=16 float=y colors=@default.map } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 29 Jan 1998 05:05:30 -0500 (EST) From: ao950@freenet.carleton.ca (Paul Derbyshire) Subject: Re: (fractint) Hi Folks That's a big ten-four. - -- .*. Friendship, companionship, love, and having fun are the reasons for -() < life. All else; sex, money, fame, etc.; are just to get/express these. `*' Send any and all mail with attachments to the hotmail address please. Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ End of fractint-digest V1 #90 *****************************