From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #483 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Friday, July 7 2000 Volume 01 : Number 483 ---------------------------------------------------------------------- Date: Thu, 29 Jun 2000 23:39:30 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD, 30-06-00 (Un-named [5]) FOTD -- June 30, 2000 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal has no name. It lacks a name because I lacked the mood to invent one. But the fractal does not lack merit. The image shows a rather sinister little midget surrounded by sharp, angular, knife-like elements such as might me used for the cover of a horror novel. The formula that created the image is 2.45(Z^0.9-Z^1.1)+C -- nothing out of the ordinary, except in the fractal it draws. The parameter file takes 2-1/2 minutes to finish. If that's too long to wait to see the picture, the 640x480x256 GIF image file can be downloaded from: or from: The day's fractal weather was partly cloudy and mild, with thunder in the area this evening, but no rain. The temperature of 81F (27C) was perfect for the cats and the people as well. The profound philosophy went nowhere today, though I posted a little less-than-profound philosophy to the philofractal list earlier this afternoon. I'll try again tomorrow. For now it's time to shut down the fractal shoppe and call it an evening. Until tomorrow, take care, and the fractals just keep coming. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Un-named { ; time=0:02:23.30 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-5.16646549738710400/+1.58947089666920000\ /5976.393/1/45 params=1/0.9/-1/1.1/1.45/0 float=y maxiter=1200 inside=0 logmap=34 periodicity=10 colors=000r_B<3>vXcwWjwWq<2>BGHOHK_IMiJOzRQiOIXRA<3>\ Bi66n51r53n65j6Ff6Kb6<4>UJ6WF6<6>ia8kd8mg8<2>tp8vs8x\ tBzuD<3>nwLkxNhyP<2>hzV<3>XzjVznPyh<2>8wS<9>SnDUnBWm\ A<3>bj4UiILiW<3>BaQ9`P7ZO<2>0UK<3>8VQAVRCVSEVT<9>QZM\ R_MS_L<3>W`J<8>HXKFXKDWK<3>7VK<2>fa4g`6<3>hdBieDifEj\ gGjhHjiI<6>bpEaqD`rD<3>XvB<3>2zB<7>HzbJzeLzi<3>Szv<3\ >rzXxzRozV<3>Izi<4>UzmXzmZzn<3>gzp<5>_zjZziYzh<3>Tzd\ <8>FzpEzqCzr<3>7zwDzUJz0<2>ezs<3>SzB<5>Pz7Pz6Oz6<3>N\ z4<3>NzLNzPNzTszE5z5<2>IzBmzE } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 1 Jul 2000 01:07:05 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD, 01-07-00 (A Midget in Lilac [3]) FOTD -- July 01, 2000 (Rating 3) Fractal visionaries and enthusiasts: Today's fractal is another quickie. In fact it's the first midget I came upon in my brief 5-minute exploration this evening. The image was found in such haste because I spent most of my fractal-hunting time this afternoon thinking profound philosophical thoughts and replying to the profound philosophical thoughts of others. The formula that drew the image is a whimsical one that was calc- ulated by the M-Mix4 formula, Z^(-1.618)+1.618Z^(-16.*)+(1/C). The midget in the picture is located toward the center of a shallow valley that divides the main bud of the parent fractal. I named the picture "A Midget in Lilac" because of the color scheme, which features pastel green and lilac hues, arranged around the central midget in an unusual pattern filled with circular disks. The parameter file renders in exactly 2 minutes on a P200, plus 2/100ths of an extra second, which will never be noticed. The GIF image file has been posted in all its meager glory to the Usenet group and to Paul's site on the W.W.W. at The fractal weather today was perfect, with a deep blue sky, cottonpuff clouds, gentle breeze, low humidity, and a temperature of 80F (27C), which made the fractal cats ecstatic. Too bad it won't last. As for me, the day has ended, the cats are hungry, and I'm growing tired. That means it's time to shut down the shoppe and call it an evening. But I'll return tomorrow with fractal and philosophy. Until then, take care, and long live fractals. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Midget_in_Lilac { ; time=0:02:00:02 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.92588928983815400/+0.00024206172436048\ /1137618/1/124.999 params=1/-1.618/1.618/-16.8/0/0 float=y maxiter=1200 inside=0 logmap=32 periodicity=9 colors=000RSV<3>Zfd`ifbmidqkftm<3>Ij4qls<3>m`mlYlkVj\ <2>hMfgJefIc<4>bGXaFVaFU<3>ZDO<4>WTNWWMVZM<2>UgMUjMW\ iL<3>ciJehJghI<2>mhH<7>RONOLOMJP<3>B9R<3>ZTf<8>EQqCQ\ rAQt<3>1Px<3>A`TCbLDaLD_KDZK`Hl<3>WIoVIoTJl<3>PLcOMa\ NNZFRHMNX<3>IQOHQLGRJJ8Y<3>HFRHHQGJO<3>FQIfmF<7>S`HQ\ _HOYH<3>GSH`ALWEKx4W<3>`2JV1GP1DSQLVmSE3t<3>VDeZGabI\ ZfLVjNSL7V<2>u6l<2>qcM<2>tqluuttoetiStcE<3>UWFNUFHTF\ GSGZdZMNrLOn_XGeaCje9mjDooH<7>TmRQmSNlT<3>ClX<3>YVPb\ RNhMLmIJrEI<3>eOObRQ_TR<2>R_V<3>`_cb_ed_g<2>k_m<8>QF\ ROCPLAM<3>C1D<5>POS } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 2 Jul 2000 00:22:49 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD, 02-07-00 (Galactic Minibrot [4]) FOTD -- July 02, 2000 (Rating 4) Fractal visionaries and enthusiasts: Between holiday weekend activities, writing my philosophy, and completing a little leftover work, I had almost no time today to search for a proper fractal. In desperation I turned to the MandelbrotMix4 formula, entered the parameters 1, -1.25, 1, - -5.33, 1/C, and let her rip. The parameters did produce a fractal, and the fractal does have midgets in it. The midget in today's picture is just one of an infinity of midgets lurking in the parent fractal. The image can rate no more than a 4, and considering the lack of effort, even that is a liberal rating. I named the picture "Galactic Minibrot" because of the four galaxy-like spirals that surround the midget. The parameter file renders in a little under 8 minutes -- far too slowly for an image of below-average worth. But the picture is worth at least a trip to the Usenet group: or Paul's web site at: where the GIF image file is waiting to be downloaded. The fractal weather today was a repeat of yesterday, except that the temperature was a few degrees warmer at 83F (28C). The ideal conditions brought out the best, (or worst), in the fractal cats. The philosophy was also quite active today, and can be seen in several other articles that I posted earlier to the philofractal list. As for my present condition -- it rates a 2 on the 0-to-10 energy scale. The only cure is to settle in front of the TV and watch an episode of Dr. Who. Until next time, when the energies will hopefully be restored, take care, and when tension strikes, take a fractal or two. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Galactic_Minibrot { ; time=0:07:51.81 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.41583652310222700/-0.15553310911297980\ /13842.18/1/27.499 params=1/-1.25/1/-5.33/0/0 float=y maxiter=1200 inside=0 logmap=54 periodicity=10 colors=000<16>000000000000000<3>300400501<2>82493584\ 6<79>8Xu8Xv8Yv<2>8Zx8Zy7Yz<37>NksNlsOls<2>PmsPmsNnp<\ 8>CqVBqSArQ<2>6sI5sG2vD<3>9rEBqECpEEoEGnF<6>RmGTmGVm\ GWmGYmG_mG_mI<5>cmAdm9em8em7fm6gm3<42>`mb } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 02 Jul 2000 10:40:46 -0700 From: Mark Christenson Subject: Re: (fractint) FOTD, 28-06-00 (Boo [3]) At 11:36 AM 6/29/00 GMT, you wrote: >... >Yep. That's definitely the one. The real reason I wanted it was for >animation... Anyone know of some good utilities for chaining GIFs into an >anim? GIF Construction Set, by Alchemy Mindworks Inc.. You can download their shareware at http://www.mindworkshop.com Good luck with your project. I have only done one animation, a little 18-frame number, but have other projects in mind. Several actually. As always, it's a matter of finding the time... Regards, Bud - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 02 Jul 2000 13:59:25 -0400 From: Mike Traynor Subject: Re: (fractint) FOTD, 28-06-00 (Boo [3]) Mark Christenson wrote: > > At 11:36 AM 6/29/00 GMT, you wrote: > >... > >Yep. That's definitely the one. The real reason I wanted it was for > >animation... Anyone know of some good utilities for chaining GIFs into an > >anim? > > GIF Construction Set, by Alchemy Mindworks Inc.. > You can download their shareware at > > http://www.mindworkshop.com > > Good luck with your project. I have only done one animation, > a little 18-frame number, but have other projects in mind. Several > actually. As always, it's a matter of finding the time... I've found that on a fast machine you can actually do a reasonable animation as large as 640x480x256 unsing the slideshow feature of LviewPro and bmp format images (makes loading quicker). Crude but then so are my animations. Mike - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 2 Jul 2000 11:10:32 -0700 From: "John Wilson" Subject: Re: (fractint) FOTD, 28-06-00 (Boo [3]) > > >Yep. That's definitely the one. The real reason I wanted it was for > > >animation... Anyone know of some good utilities for chaining GIFs into an > > >anim? > > > > GIF Construction Set, by Alchemy Mindworks Inc.. > > You can download their shareware at > > > > http://www.mindworkshop.com > > > > Good luck with your project. I have only done one animation, > > a little 18-frame number, but have other projects in mind. Several > > actually. As always, it's a matter of finding the time... > > I've found that on a fast machine you can actually do a reasonable animation > as large as 640x480x256 unsing the slideshow feature of LviewPro and bmp > format images (makes loading quicker). Crude but then so are my animations. What about Paint Shop Pro 6.0 from JASC? You can do the whole job with the built-in Animation Shop. John W. - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 2 Jul 2000 13:14:53 -0700 From: "John Wilson" Subject: (fractint) Fractal Animations Inspired by the recent messages, I tried an animation using Paint Shop Pro 6.0's "Animation Shop". It was a trivial task, taking about 10 minutes, to form a 21-frame zoom into a part of the Mandelbrot set. The results are great, if a little jerky...I didn't zoom in equal increments. PSP assembled the whole thing into a 176 KB file, optimizing the whole mess before saving it. I'm impressed. John W. - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 2 Jul 2000 23:55:12 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD, 03-07-00 (Galactic Minibrot [6]) FOTD -- July 03, 2000 (Rating 6) Fractal visionaries and enthusiasts: It's a holiday week-end here in the USA -- the Fourth of July week-end -- the time of year we celebrate with fireworks and parades our country's independence from the British. Most fireworks are now illegal, except at professionally presented displays, but in some areas sparklers are still permitted. I would have preferred something more exciting in today's fractal, such as a cherry bomb or hammerhead, but being a law-abiding citizen, I settled for a relatively safe sparkler. I wasn't too disappointed, for the sparkler rates a 6. For today's image I took Z^32 and added its reciprocal, Z^0.03125. To complete the expression I added 1/C and let it iterate. When the iterating was done, I was left with today's image. I named the picture "Holiday Sparkler" because of the sparkling effect of the many filaments radiating from the always- present midget at the center. The parameter file renders in just under 8 minutes on an aging Pentium 200mhz. The GIF image file downloads in less than 1/4 of that time. For those who desire the download, the image may be found posted to the Usenet binary group: and to Paul Lee's web site at: The fractal weather was another repeat today, though the humidity was a bit higher, and the air a bit more hazy. The temperature of 84F (29C) was ideal for the two fractal cats, who due to attacks of sleepiness, took almost no advantage of the perfect conditions. It's now 11;30pm and I'd like to write at least one philosophical reply to the philofractal list before the day ends. So until next time, take care, and always wax philosophical. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Holiday_Sparkler { ; time=0:07:56.10 -- SF5 on a p200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-4.0775785029129250/-8.163508424429640/2.\ 394443e+007/1/-172.499 params=1/32/1/0.03125/0.05/0 float=y maxiter=3000 inside=0 logmap=152 symmetry=none periodicity=10 colors=0000EE0EE0GG2II5KK<2>DQSGSVJTYMU_<3>XXj<3>ejp\ gnqiqskutmxu<9>QeZOdXMbV<3>DWM<3>TdEXfC`hAdj8hl6a_BW\ OGKCKJ0KN0T<3>`0dd0gh0jk0m<3>d1ec1da1b`1`<3>R1QP1NM1\ KK1J<3>Y3L`4Md4M<3>m6Lo7Lr7Kt8Kv8KdVBOq3Lt6Jv9HxC<5>\ EoFEnFDlG<3>CgH<3>iKWqEZWPQA_H7bF5dDMIk<3>OLYOLUVMCP\ MRPNNQNKQOGStg<4>RfVRcSQ`P<3>QQFfPD<3>YODWODUODSODIG\ S<3>LJMMKLPJYeXN<3>VZ_TZcQZf<2>J_o<3>c_r<3>fLWgHQgEL\ <2>dAf<2>T7H<3>kHDpJCtLBuJAvIFwHKxGNyFQ<2>zCZzBazCc<\ 4>zHhzIizJjzKkzLl<3>zPmzQmzRmzSmzTm<5>zUmzUmzUmzUmzU\ m<8>zUuzUvzUwzUxzUy<21>zUz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 2 Jul 2000 23:57:51 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD, 03-07-00 (Holiday Sparkler [6]) FOTD -- July 03, 2000 (Rating 6) Fractal visionaries and enthusiasts: It's a holiday week-end here in the USA -- the Fourth of July week-end -- the time of year we celebrate with fireworks and parades our country's independence from the British. Most fireworks are now illegal, except at professionally presented displays, but in some areas sparklers are still permitted. I would have preferred something more exciting in today's fractal, such as a cherry bomb or hammerhead, but being a law-abiding citizen, I settled for a relatively safe sparkler. I wasn't too disappointed, for the sparkler rates a 6. For today's image I took Z^32 and added its reciprocal, Z^0.03125. To complete the expression I added 1/C and let it iterate. When the iterating was done, I was left with today's image. I named the picture "Holiday Sparkler" because of the sparkling effect of the many filaments radiating from the always- present midget at the center. The parameter file renders in just under 8 minutes on an aging Pentium 200mhz. The GIF image file downloads in less than 1/4 of that time. For those who desire the download, the image may be found posted to the Usenet binary group: and to Paul Lee's web site at: The fractal weather was another repeat today, though the humidity was a bit higher, and the air a bit more hazy. The temperature of 84F (29C) was ideal for the two fractal cats, who due to attacks of sleepiness, took almost no advantage of the perfect conditions. It's now 11;30pm and I'd like to write at least one philosophical reply to the philofractal list before the day ends. So until next time, take care, and always wax philosophical. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Holiday_Sparkler { ; time=0:07:56.10 -- SF5 on a p200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-4.0775785029129250/-8.163508424429640/2.\ 394443e+007/1/-172.499 params=1/32/1/0.03125/0.05/0 float=y maxiter=3000 inside=0 logmap=152 symmetry=none periodicity=10 colors=0000EE0EE0GG2II5KK<2>DQSGSVJTYMU_<3>XXj<3>ejp\ gnqiqskutmxu<9>QeZOdXMbV<3>DWM<3>TdEXfC`hAdj8hl6a_BW\ OGKCKJ0KN0T<3>`0dd0gh0jk0m<3>d1ec1da1b`1`<3>R1QP1NM1\ KK1J<3>Y3L`4Md4M<3>m6Lo7Lr7Kt8Kv8KdVBOq3Lt6Jv9HxC<5>\ EoFEnFDlG<3>CgH<3>iKWqEZWPQA_H7bF5dDMIk<3>OLYOLUVMCP\ MRPNNQNKQOGStg<4>RfVRcSQ`P<3>QQFfPD<3>YODWODUODSODIG\ S<3>LJMMKLPJYeXN<3>VZ_TZcQZf<2>J_o<3>c_r<3>fLWgHQgEL\ <2>dAf<2>T7H<3>kHDpJCtLBuJAvIFwHKxGNyFQ<2>zCZzBazCc<\ 4>zHhzIizJjzKkzLl<3>zPmzQmzRmzSmzTm<5>zUmzUmzUmzUmzU\ m<8>zUuzUvzUwzUxzUy<21>zUz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 4 Jul 2000 01:18:33 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD, 04-07-00 (More than a Midget [4]) FOTD -- July 04, 2000 (Rating 4) Fractal visionaries and enthusiasts: What could be better for the fourth of July than a fractal that rates a 4? Well, perhaps a fractal that rates a 6 or 8 would be better, but we'll ignore those technical details and consider today's image just the thing for our national Independence Day holiday here in the USA. The image was created by Andrew's MandelbrotBC (Branch Cuts) formula, which draws the more remote parts of the fractals with fractional exponents. I wandered a rather considerable distance away from ground level in the Z^2.006+C Mandeloid to find today's midget, which is close to a larger midget. I named today's picture "More than a Midget" because the midget at the center is just a bit more complex than the standard Z^2+C midget. It is quite a bit more complex in fact, for it is split right down the negative tail by one of those branch cuts, as well as surrounded by cut-off bits of filament. A close examination will reveal 8 plus a fraction elements around the midget. This is only to be expected in a fractal with an exponent of 2.006. In fact there are 8.072 (2.006^3) elements circling the midget. The parameter file renders in a relatively fast 3 minutes on a Pentium 200 machine. If this is too slow, the GIF image file may be found ready for downloading at: and at: The day's fractal weather was partly cloudy and humid, with a temperature of 88F (31C) that was perfect for the fractal cats, who enjoyed the afternoon on the porch. After dark a mild thunder-shower passed over, which cooled things down for the night. Until tomorrow, take care, and see you in 22 hours. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ More_than_a_Midget { ; time=0:02:50.98 -- SF5 on a p200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-1.05309114080759600/-0.00068667328146814\ /3.069438e+008/1/-92.5 params=2.006/0/233/0 float=y maxiter=1000 inside=0 logmap=94 periodicity=10 colors=000JHsODoTEsTFuSNnMVeGbYAkP5qH9lEDfBGZ8KS5OH2\ RA0VI9_QIeXQkdZokfpfgvahqXimSjcNkYIlXDmX8nX4oY5mZ5lY\ 6jX6iX6gY7f<3>V8`U9ZT9YS9XaRPthHzz9vwDstGnrK<5>ebcd_\ fbXj<3>YNwa6v<3>MPwIUxEYxAbx6fx<9>8VT8UQ8TN<3>8PB<3>\ Ycddgkjjr<8>_NtZKtYHu<3>U7u<3>Zjm_slVof<3>EcK<3>GfJG\ gJHhI<3>IjI<5>YPb`LecIi<3>m4v<8>ZWZYZWWaT<3>QmJ<5>Xd\ AZc8_a7<3>cX1<3>YNbXKkWIt<3>bgLdnCet4<3>iwIjxMjxP<3>\ jwN<3>XwUWwW<2>Zw`_wa`wbawcbwd<3>fwigwjhwk<9>rwmswnt\ wn<3>xwnywk<3>zwczw`zwZ<3>zwRzw`zwi<3>zwNzwHzwCzw6zw\ 1<3>zwZ<5>zw`zwQzwOzwg } frm:MandelbrotBC = { ; by Andrew Coppin e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 5 Jul 2000 00:24:00 EDT From: JimMuth@aol.com Subject: (fractint) FOTD 05-07-00 (Skewed Sweethearts [7]) FOTD -- July 05, 2000 (Rating 7) Fractal visionaries and enthusiasts: After an active day celebrating and philosophizing, I found little time for fractaling. But in that short time I managed to find a fractal that rates a 7, a rating that has been notably absent lately. The expression (1/Z)-Z+(1/C) wouldn't be expected to create much of a fractal, but fractals rarely do what's expected of them, and today's fractal is a prime example of this fractal stubbornness. I named the picture "Skewed Sweethearts" because the midget's pattern is a bit askew, and the sweethearts part of the name will pique the curiosity of the ladies. The parameter file takes 6-1/2 minutes to render, making the download from: or from: the better choice. The fractal weather today was partly cloudy and warm, with a temperature of 86F (30C), which was perfect for the cats. But due to the fireworks going off in the neighborhood, the cats stayed indoors, hiding most of the day in the hall closet. I reached philosophical exhaustion this afternoon, so there will be a rather lengthy break before the next outburst. But the break before I return with the next fractal will be only 24 hours. Until then, take care, and be serene. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Skewed_Sweethearts { ; time=0:06:31.89 -- SF5 on a p200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.00005213775768595/+0.35587124080399530\ /2.951152e+007/1/5 params=1/-1/-1/1/0/0 float=y maxiter=1400 inside=0 logmap=92 periodicity=10 colors=000r0V<2>r0Rr0Qr0Qr0Or0Nr2Mq2Kq3Jq4Jq6Iq6Hq7F\ q8EqAEqBDoBBoDAoE8oF7oH7<2>pJ3uK2zM0uM0pK2mJ4jI7<3>_\ BIYAKV8NS7QR3RR4RP6R<3>N8RNBRMASMDRKDSKERJFSJFRIHSIH\ RHITHIQFKQFJSELQELQDMQDMQBNQBNQAOQAOQ8PQ<2>7QQ6RR6RQ\ 6TQ6TQ7U87z08z0Az0Aw0Bu0Br0Do0Dm0Ej2Eg3Fe3Fb4H_6<3>J\ QBJNDKKEKIEQKJUNNYQRaRVfUZjXbnZfr_jwbnzerzgvzizzjqyk\ iukaukbvmc<2>wngwoiyqk<3>zsqzsrzuszvzzuursmjreaqXUoO\ KnHDn8BmABmBAmDAkDAkE8kF8jH<3>6iK6iK4gM4gN4gO3fO3fQ2\ fR2fR2eS0eU0eV0cV0cX<2>0bZ0b_0aa0ab0ab0_c0_e0_f0Zf0Z\ g0Zi0_j<5>0Zi0Zi0Yi<2>0Yi0Yi2Yg<3>4Xg4Xg6Xg6Xg7Xg7Xg\ 8Yg8ZgA_fBafBbfDcf<3>FifFjfHkf<3>JqeJreJseJseKsc<2>K\ scKscMsb<6>NsaNsaNsaOs_Os_Os_Os_QsZ<11>SsXSsXSsXUsV<\ 2>UsVYsYVs_UsVSsQSsHssX } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 5 Jul 2000 23:04:51 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD 06-07-00 (A Deep-down Midget [6]) FOTD -- July 06, 2000 (Rating 5) Fractal visionaries and enthusiasts: The magnitude of today's fractal is 2e+14, making it most likely the deepest I have yet gone with the MandelbrotMix4 formula. True, the image is a bit past Fractint's limit of resolution, but UltraFractal's more precise math routine should resolve it. I had to set the math tolerance to /1 to reach such a magnitude in Fractint, but the little midget is unusual enough to be worth the effort. The breakdown of resolution actually adds a rather artistic effect to the picture. I named the picture "A Deep-down Midget" because the central midget lies so deep down in its parent fractal. The formula that created the image is (-1/Z)-(Z^1.1)+(1/C) -- another formula that does more than it's appearance would suggest. The render time is a nominal 6 minutes on a P200; the download time is an even more nominal 1 minute or so. That download may be found on the Usenet network at: and on the Worldwide Web at: The fractal weather today was perfect, with blue skies, a few clouds, and no noisy fireworks. The temperature of 86F (30C) lured the fractal cats into the yard, where they enjoyed as nice a romp as nine-year-old cats can manage. The philosophy sleeps while I recharge my philosophical energies. The charge cycle might be a lengthy one, so be patient fans of wisdom, and eventually your patience will be rewarded. That's it for today, but tomorrow is near, and it will bring a new and greater fractal. And it's also about time I returned to one of my favorite diversions -- higher dimensions. So tomorrow could be interesting. Check then to find out. Until next time, take care, and stay solidly grounded in the third dimension. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Deep-down_Midget { ; time=0:06:01.96 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.12844758295825350/+0.02991434375250009\ /1.993294e+014 params=-1/-1/-1/1.1/0/0 float=y maxiter=300 bailout=25 inside=0 logmap=123 symmetry=none periodicity=10 mathtolerance=/1 colors=000bWn<3>j_ol`pnapobp<4>M9SG3O<3>CPdBUhAZl<2>\ 8nx<6>LOhNKfOGd<3>V1XPNGKg0<7>IaJI`LH_N<3>HYW<3>nHL<\ 3>b9V_8YX6_<2>P1f<3>r4K<3>hGIfIIdLH<3>WWG<3>gSPiSRlR\ T<2>tPZ<3>aXLXZIS`FObC<3>bNLeJNiFPlBR<4>TGH<3>RTh<3>\ OeVOhSNkPNnLMqIMtF<9>O`HOZHOXH<3>OPH<8>VRAWR9XR8<3>Z\ R6c4v<3>Ij_RnT<3>SpWSqWSqX<3>SsZ<4>PWbOSbONc<2>M9eM5\ eN7f<6>TLjUNkUPk<3>XXm<3>UMhTJgSHfREeRCd<4>PQOPSLPVI\ <3>Od5<5>OW7OU7OT8OR8OQ8<10>WDDXBEXAE<3>_6GKUb4pxOlZ\ fhAnoQuud<10>eVU } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 7 Jul 2000 00:35:31 EDT From: JimMuth@aol.com Subject: (fractint) FOTD, 07-07-00 (Ferndale [6]) FOTD -- July 07, 2000 (Rating 6) Fractal visionaries and enthusiasts: I named today's fractal "Ferndale". I gave it that name not because the image contains anything like a fern, and not in honor of any town of that name, but because the word just came to mind while I was studying the image trying to decide what to name it. The iterated formula is 10Z^(-10)+Z+(1/C). Such a formula would not be expected to make much of a fractal . . . well, maybe that's no longer true, since I've been making quite a few interesting fractal images with such formulae lately. The image, which rates a 6, features the standard midget at the center, surrounded by a pink and turquoise pattern of dark and light spots arranged in inwardly spiralling arms. The GIF image was souped up in a graphic program to give it a little added zip before I posted it to: The image is also available on the web at: The parameter file renders in 2 minutes or so, making it a toss-up as to which way of viewing the image is the more efficient. The fractal weather was once again perfect, with deep blue skies, low humidity, and a temperature of 82F (28C), which was perfect for cats. Unfortunately, when the fractal cats went outdoors, they were harassed most of the afternoon by a blue jay, who must have thought they were after its babies. But those angel cats would never harm the bird -- they just want to eat the birds. My philosophical musing returned to my old favorite, the abstraction of the fourth dimension, this afternoon. I tried for a few minutes to visualize double revolution and a surface of double revolution. I failed miserably. But even though I failed to visualize this four-dimensional object, that does not stop me from thinking about it. I may ponder the imponderable again tomorrow, but regardless of the outcome, I'll have the next fractal ready. Until then, take care, and the formula for the hypervolume of a five-dimensional hypersphere is 8/15*PI^2*r^5. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Ferndale { ; time=0:02:12.42 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-3.15202487684002900/+1.00536788746322700\ /6611.272/1/-25 params=1/1/10/-10/0.15/0 float=y maxiter=1200 inside=0 logmap=27 periodicity=10 colors=000000CDE<5>IJK<3>MNOOOPQPQ<3>YTU_UVbVW<2>kYZ\ nZ_q_ZtbZwd_zdZwd_t`YqXVrTS<2>uJIvGFwDA<2>u40t10s00r\ 00f16XAMLKaAUrTcz0hz6mzAcxFUsJToOXjSYfX`cac_fdV<2>sl\ IxoDzpAxlDsgFocIj_JfVM<3>PDVL9XG3XI4YI4YI4_I4_I6`<2>\ J6aJ7aJ7cJ7cL7cL9dL9dL9fL9fL9fJ9iGAlFAmCCpACr7Du19y6\ DvAGuFJsIMrMQpQToVXlY_jaaiffgjifmldroavr`zv_zyY<2>zz\ TzzSzzSzzSzzQzzQ<2>xzPuzPsyPpyPozOlzOjzOpzD<3>OzrGzz\ 9zzAzzCzzCzzDzzFzzFzzGzzIzzIzzJzzLzyLzxMzvOzuOzsPzsQ\ zrQzpSzoTzmTzlVzjXziXziYzg_zf<2>azaaz`cz__zVcz_gzalz\ f<2>yzpzzszzxzzvzzuxzs<5>YzjTziPzg<3>7zaCzc<3>OziSzj\ Vzj<3>gzpjzrmzspzsszuxzvzzxzzy<2>zzzzzzzzyzzvzzu<2>x\ zmuzjrzgozfmzcjz`gz_fzXczT`zSYzPXzMTzLQzIPzFMzDJzAGz\ 7Fz6Cz39z00z07z0<2>Yz1fz1oz3xz3CzQ7zO4zM1zJ0zI0zF } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 07 Jul 2000 14:16:33 GMT From: "Andrew Coppin" Subject: (fractint) FotD's Hi Jim. Just wanted to say: Ferndale (and the one 2 days before that...) rate about 8 on my fractal scale! PS. Edge-and-corner construction of a hypercube is beyond my intelligence quotiant. I am now attempting to construct one from the intersection of planes instead. Basically I will re-write my raytracer to work with 4D vectors and points and see what (if anything) comes out. Will let you know... PPS. Never mind the hypervolume of a hypersphere... what's the formula for a double rotation?!?! 8-]) ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 7 Jul 2000 22:54:04 -0400 (EDT) From: Jim Muth Subject: (fractint) FOTD 08-07-00 (A Midget in Blue [7]) FOTD -- July 08, 2000 (Rating 7) Fractal enthusiasts and visionaries: Today's fractal rates a 7 -- the second above average fractal with such a rating in a week. But before getting to the image, I must finish what I started yesterday. In yesterday's FOTD I mentioned the surface of double revolution, while neglecting to tell what it is. That oversight will now be corrected. A surface of double revolution is a curved two-dimensional surface, which exists in the three- dimensional boundary of a four-dimensional hypersphere. It consists of the points lying at a given distance from a given great circle of the hypersphere, and so at the complementary distance from the polar, or completely perpendicular, great circle. A surface of double revolution is also the path traced by points of the hypersphere when it is subjected to a double revolution. A double revolution is a type of motion possible only in spaces of four or more dimensions. It is comprised of two simple but completely perpendicular rotations applied simultaneously to a single object, each rotation taking place in two separate dimensions. The surface of double revolution is of importance in the theory of functions with two complex variables. Nested surfaces of double revolution could serve to measure the latitude of a four-dimensional hyperplanet. In this case, they would start at the equatorial great circle of the planet, where they would resemble the torus or doughnut-shape of three- dimensional space. But they would undergo an impossible-to- visualise transformation before they converged, as inside-out doughnuts, on the polar great circle of the planet. It is the shape of this surface of double revolution when it measures 45 degrees of latitude that has me puzzled. But there is no puzzle about today's FOTD, which turned out unexpectedly good. The formula behind the image is 0.3Z^(-1.05)+Z^(1.05)+(1/C). The parent fractal is another of those strange figures that appear when Z and 1/Z, or values close to this are combined in various ways. Adding 1/C instead of C merely adds to the interest. I named the picture "A Midget in Blue" when I noticed the deep blue haze surrounding the central midget. The colors of today's picture blend together unusually smoothly. In fact, the image must be examined closely to be sure that it is not in true-color. The parameter file is unusually slow, taking almost 1/2 hour to render on an average Pentium. But as always, the GIF image has been posted to the Usenet binary group: and to Paul Lee's web site at: The fractal weather today was absolutely perfect, with deep blue skies, puffy clouds, low humidity, a gentle north wind, and a temperature of 80F (26.5C). The cats must have approved, as they spent the better part of the day sleeping on the porch and keeping out of the blue jay's way. The fractal philosophy is still on hold, and likely will remain so for several weeks yet. But fear not, for the four- dimensional muse is once again stirring, giving me much to think and write about. And the impossible things that are possible in four dimensions make the illusions of the world's greatest magicians look like nothing. For now, the time to shut down the fractal shoppe has arrived. The cats need to be evicted and fed, and I need to settle in front of the TV to doze off trying to watch a junky old movie. But I'll be back in 24 hours, so until then, take care, and don't let those higher dimensions make you hyper. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A Midget_in_Blue { ; time=0:27:15.63 -- SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-4.919970039353122/+1.649879877881105/1.8\ 42739e+010/1/-34.997 params=0.3/-1.05/1/1.05/0/0 float=y maxiter=3600 inside=0 logmap=511 colors=000P9T<3>SAQTBPUBO<19>mL_nM`oMa<3>rOcrPdsPdsQ\ esRd<38>tkitkitli<3>tnisohtni<35>uimuhmuhm<2>uhmuhmv\ jn<22>_N_ZMZYLY<3>UHXTGXSFWREWQDW<3>MHXLIYKJZJK_KJZK\ IYKHXKGUKFSLEQLCPLAMLBQLCPMDN<17>PPHPPHQQH<3>QTGPRH<\ 20>hqBirBjsB<3>mxAkxBjyB<3>ezBdzBczB<3>ZzBQz`<11>bzT } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ End of fractint-digest V1 #483 ******************************