- Fractint - mailman.xmission.com

FOTD 08-07-04 (Cube-Root of 2-Two [7])
by Jim Muth 08 Jul '04

08 Jul '04

FOTD -- July 08, 2004 (Rating 7) Fractal visionaries and enthusiasts: We had a flood in Fractal Town on Wednesday, but the fractal basement remained dry. I attribute the dryness to the mystical power of fractals. Only unknown magical forces could have kept the water out of the basement, and fractals are the closest things to magic that I know of. My next task is to put the fractal magic to work on the work backlog. :-) Today's quickie image returns us to the same area of the same fractal that gave us yesterday's image. The viewer must again take my word that a midget lies at the center of the conver- gence, for the midget lies far beyond resolution. In fact, the image itself is of such a high magnitude that I needed to in- sert the 'mathtolerance' entry in the parameter file to assure that it renders at the correct magnitude. I named the image "Cube-Root of 2-Two" for catalog purposes. I rated it at a 7 because I feel that it is a bit better than yesterday's effort. The render time of 10 minutes gives the whole thing an overall value of 69. There is not much more to say about the image other than to report that it is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very hot 92F 33C day on Wednesday was cooled to 72F 22C by a very heavy late afternoon thunder-shower, which sent the dynamic duo scurrying for cover. By the time the rain ended, the sun was setting and the day had come to a close. The duo emerged from hiding shortly after nightfall, having totally forgotten that their day in the yard had been cut short. Today is start- ing partly sunny and slightly cooler. This is good for cats and humans alike. Unless the unexpected happens, as it sometimes does, I will return in 24 hours with the next FOTD. Until then, take care, and remember that V+F always equals E+2. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cube-Root_of_2-Two { ; time=0:10:04.34--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 mathtolerance=/1 center-mag=-1.225559316846377/+0.7079657188513047/\ 5.162144e+011/1/42.5/0.003731481390342 params=1.26\ /0/-70/100 float=y maxiter=1200 periodicity=10 colors=000aVIaTIaTIaTGaTGaTGaTG`SG`SG`SG`SF`SF`QF`\ QF`QF`QF`QF`QFaPDaODaODaMDaMDaLDaLDcJDcJDcIDcIDcGD\ cGDcFDdFDdDDdDDdCDdCDdADdADMzvOzuOzsPzrPxpQvoQumSr\ lSpjToiTmgTjfVidVgcXdaXc`Ya_Y`Y_YX_XV`VT`SS`QQaPPa\ MO_LMYJLWIJUFISDGQCFzkXzhVzeTzbSy_QxXPvVPuSOsQMpPL\ oMJmLJlIIjGGiDFgCD0TG0SF3QF7PFAOFFMFILFMJDPIDTGDXF\ D`DDcCDz7mz9jz9iz9gz9dz9cz9az9_y9Yx9XuATsASrAQpAOo\ AMlALjAIiAGgAFdzafz`fz_fz_fzYfzXfzXfxVfuVfsTfpSfmS\ flQfiQfgPfdOfaOf`MfYMfVLfTJfQJfOIfMIfJGfGFfFFfCD0z\ x1zu3zs4yr6xp7uo9smArlCoiDmgFjfGidIfcJdaLc`O`YP_XQ\ XVSVTTSSVQQXPPYMM_LL`IJaGIcDGdCF4d07a09`0C_0DY0FX0\ IV0JT1LS1OQ3PO4SM6TL6VJ7YI9_GA`FAcDCdCDCzSDzQFzQFz\ QGyQGxPIvPIuPJsPJrOLpOLoOMmOMlMOjMOiMPgMPfLQdLQcLS\ aLT`JT_JVYJVXJXVIXTIYSIYQI_PG_OG`MG`LGaJFaIFcGFcFF\ dDDdCDfADczvdc_Yxy_vx_uv_su_rs_ps_pr_op`mo`lm`jm`j\ l`ij`gi`fiadgadfacdaaca`c } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

Fractal Creations OCR
by Tim Wegner 08 Jul '04

08 Jul '04

Re scanning Fractal Creations 2nd Edition: John Wilson did what in my opinion is a very successful experiment scanning the first few pages of Fractal Creations 2nd Edition (FC2). With a quick spot check of his results, I couldn't see any obvious typos. I expected much worse. John, could you tell us what OCR software you used? And thanks to John for his effort in this regard. John initially posted his results on his web site and I may have embarressed him because I was a bit panicked that I hadn't thought through my policy on allowing book drafts on the internet, and I asked him to take the web site down. He graciously did so and emailed the files to me so I could look at them. I've now thought about the policy for publically posting FC2 and this is the result. My concern is that I don't want poor quality or incomplete copies spread around without a clear statment of the legal status of the copies. I don't anticipate trying to make another commercial publication of FC2, and I certainly favor "publishing" a free copy in electronic form. I'll need to give some thought to the legal status of the eventual complete copy. I'll want to retain the copyright in some form. I would like any working copies of FC2 to be posted only with my permission, and with the following readme: <start README start:> 1. These files represent a work in progress of a volunteer effort to scan the book "Fractal Creations Second Edition" with the permission of the author and copyright holder Tim Wegner, who does not give up his rights by the posting of these files. 2. Because these files represent a work in progress, they necessarily have a short life and will be replaced with better/more complete versions, they should not be posted elsewhere without permission of Tim Wegner, twegnerATfractint.org. <end README> I hereby grant John Wilson permission to post the FC2 files he has already created and any others he cares to create. I'll extend the same permission to anyone else who wants to contribute work to this effort and post the results, but please ask me first so we can keep the effort reasonably centralized. I don't mind if the files are publically viewable on the internet as long as the README above is present. I've had offers of FTP access with login for a few team members, but I don't think this degree of security is needed. On the other hand, I don't think we should publicize this effort more broadly than this list until it's done. Followups to the FC2 OCR discussion and the related "Fractint CD" topic should be on the fractdev list, since the discussion will only be pertinent to those who actually want to contribute, and would be wasted bandwidth for others. So if you want to discuss or lurk, you should join that list. Tim

1 0

FOTD 07-07-04 (The Cube-Root of 2 [6])
by Jim Muth 07 Jul '04

07 Jul '04

FOTD -- July 07, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "The Cube-Root of 2". The reason is simple -- the exponent of Z is 1.26, which is approximately the cube root of 2. I have complicated things a bit by drawing the fractal as it exists 70 levels down the hyper-something created by multi-valued complex-logarithms. (This something might or might not be an actual spiral.) The parent fractal is the nearly shapeless thing that would be expected to be created by exponents in this low range. Its most interesting part lies on its west border, where a nest of filaments appear to be trying to form a theme. Today's image lies near a node in this nest of loosely-organized filaments. Filaments. This is one thing that fractals in this range have an abundance of. They are easy sources of midgets, but the mid- gets have a tendency to all look the same -- like spiny undersea creatures. Today's midget, if that is what a theoretical but invisible object at the center of the image can be called, is surrounded by filaments different enough to almost create a theme pattern. The effect is striking enough to make the image worthy of being declared FOTD for July 7. The rating of a 6 and render time of four minutes (on my tired old fractal machine) combine into an overall value of 146. It is up to the individual fractalist to decide whether to run the attached parameter file and wait a couple minutes or to download the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was 95F 35C hot here at Fractal Central, until a brief heavy thunder-squall cooled things notably at 6pm. Tuesday was sunny and cooler, but the strong sun and high temperature of 88F 31C still made things uncomfortably warm. The cats made the best of the conditions. Today is starting sunny and warmer. It looks like another day of overheated cats. For me, it looks like a lot of work, so my intuition tells me it's time to get started working. Until next FOTD in a day or a few, take care, and be fair. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Cube-Root_of_2 { ; time=0:04:07.00--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-1.46\ 8655458749068/+0.9535213132151095/2446642/1/75/1.16\ 947064154049318e-005 params=1.26/0/-70/100 float=y maxiter=1200 inside=0 periodicity=10 colors=000nNrf_qcXqaVqZSqWPqTMqRKqOHqLEqKAsJCqJEoJ\ GnJIlIKkIMiIOhIQfISdHUcHWaHY`H_Z7fPHaYRYe`UmgOwiQu\ jSskUqlWomYnn_loajpchqefrgesictkaum_voYwqXxpWxpWxo\ WxoWynVynVynVymVymVzlUzlUzkUzkUzkUxjSvjQtiOriNphLn\ hJmgIkgGifEgfCeeBce9ad7`d6ab7aa8a`8a_9aZAaYAaWBaVB\ aUCbTDbSDbREbPEbOFbNGbMGbLHbKH`MGZNFYOFWPEUQETRDRS\ DQTCOUCMVBLXBJYAHZAG_9E`9Da8Bb89c78d76e64h35f65e86\ dA6bD7aF7`H8_K8AY8A_9Aa9AcAAeAAgBAiBAkBAmCAoCBqDCs\ DDuEEwEFvEGzCFfBHQDKSFNUHQWJTYLWaOZeQaiTdmVgqYjs`m\ uboweqxhszkuzmwzpxzryztzznqwnpwnovnnuomuoltoksojso\ irphqpgqpfppeorcqpdoodnndmmdkldjkdijdgidfheegecfeb\ eeade_ceZbeYcdVaeX`eZ_e_ZfaYfbWfdVgfUggTgiSgjQhlPh\ nOhoNiqMirKitJjvIjwHjy5gzGjzRmzapzYjtUdoQZjMTeHL`I\ N`JP`JR`KT`KV`LX`LY`M_`Ma`Nc`Ne`Og`Oi`Pj`Pl`Qn`Qp`\ Rr`Rt`Sv`Sw`LvVEuQ7tK1sF4qI7oKAmMCkOFjQIhTLfVNdXQb\ ZTa`W_cYYe`WgcUifTkhRnkPp } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 05-07-04 (Funny Filaments [6])
by Jim Muth 05 Jul '04

05 Jul '04

FOTD -- July 5, 2004 (Rating 6) Fractal visionaries and enthusiasts: I am using the holiday today to try to get caught up in some of the work, so this discussion must be brief. Today's quickie image takes us to a filament of the Z^1.3+C Mandeloid, when it is iterated 20 levels down the logarithmic hyper-spiral. I named it "Funny Filaments". The reason for the name will become obvious when the image is seen. The rating of a 6 combines with a render time of 3 minutes to give an overall value of 201. The value can be greatly increased by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Independence Saturday was near perfect here at Fractal Central, with brilliant sun, a temperature of 86F 30C, and happy cats. Independence day itself -- Sunday -- was less than perfect. The clouds that hung around all day released enough rain to keep the cats indoors. But the rain stopped before sunset, permitting the many area fireworks displays to go off on schedule. This disturbed the cats, who do not like the noise of fireworks. This morning is starting sunny, and it is turning quite hot. The cats are giving thanks, but will it stay dry?. I'll give thanks when I catch up on the work. And from the way things are going, that may be a while. Until next time, which will be somewhere between one and three days, take care, and where did yesterday go? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Funny_Filaments { ; time=0:02:59.33--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.0\ 0838093874183538/+2.876159505818618/1.535874e+007/\ 1/10/-2.265799798e-007 params=1.3/0/-20/100 float=y maxiter=12000 inside=0 logmap=90 periodicity=10 colors=00076G98FA9FCAEDCEFEEGEDIGDJHDLICMKCOLBPMBR\ OBSPAUQAVRAXUDZWG_ZIa`LccOdeQfgThjWilYko`mqcnseptg\ quisuktvmuwowwqxxsyxuvtpsqlpmhmjdjf`gcXd_TaXPZTLWQ\ HTNDRQHQTKOWNNYQL`UKcXIe_HhbFkfEmiCplBsoAurAzrEpsH\ fsLXsONtSDtV3tX5jZ6``7Rb8Hd98fCHhEPjHXlJd`LgPNjDPm\ 2Qp9SmFTjLUgSVdYWacXZiYWgU_eQccNgbJj`GnZCrY9uVAnTA\ gRAaQH_PNZOUXN_WMfULlTLrSKpTKoTJnUJmUIlVIkVIjWHiWH\ hXGgXGfYFeYFdZFcZJ``MYbPVcSSeVPgYMh`JjcGkZHeUH_PHU\ KHOFHIAHC5H60H18M8GQENVLVZRbcYigcffbcfbafaZfaWe`Ue\ `Re_Pe_MeZJgZHiYEkYCmYDoZEq_Fs`Gu`HwaIzbJzbKzcLzdL\ zdAzT0zj8zmGzoOzqWzsczujzwhzugztfzrdzqczobzn`zm_zk\ ZzjXzhWzgVzfXzcYz`ZzY_zW`zTazQbzNczLdzIezFfzCgzAbz\ ZYzvXzsWzqWzoVzmVzkUziUzgTzeTzcWzZYzU_zQgzXezXczXa\ zXbzVbzUbzTbzSbzRczQczPczOczNczMdzLdzKdzJdzIdzHdzG\ azG_zGYzGWzGUzGSzGQzGOzGMzGKzGIzGGzGEzGGzGIzGJzGLz\ GMzGRzIWzK`zMezOsz0tz0Wz8 } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 03-07-04 (Fourth Dimension [5])
by Jim Muth 03 Jul '04

03 Jul '04

FOTD -- July 03, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image takes us into the fourth dimension of space, an abstract world where time is the fifth dimension. We should not be too shocked by a fourth spatial dimension. According to the latest theories, our apparently three-dimensional world really has 11 dimensions, and maybe as many as 26. It's too bad that we can fit only two of these dimensions onto our screens, but take heart. Two dimensions are infinitely better than none. The scene is located on a filament on the east side of the large midget on the negative X-axis of the Mandelbrot set. A midget lies at the center of the image, though when viewed from this angle, it has been reduced to no more than a thin slit. To add a little extra life to the scene, I rendered it with the outside set to 'real'. I named the image "Fourth Dimension" because, with so much work in front of me, I did not want to take time to think of a better name. The rating of a 5 is perfectly average. The render time of 43 seconds is unusually fast however, and raises the overall value to an impressive 694. But a download of the completed image is still the simplest way to view the scene. The download may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 90F 32C, Friday was a bit too warm for the dynamic duo, who spent the afternoon in the deepest shade they could find. When evening came, they returned inside without complaint. Today looks like a repeat, which will be no problem for the cats. With another load of work to tackle, I'll have a repeat also. Until next FOTD in a day or two, take care, and be kind to homeless fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fourth_Dimension { ; time=0:00:43.39--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 float=y center-mag=0/0/1.258572e+010/0.06057/-118.638/-50.\ 33767867 params=33/-110/2/0/-1.751877555332056/0.0\ 16071035804529/-1.751877555332056/0.016071035804529 maxiter=600 inside=0 outside=real periodicity=10 colors=000NAgPCgSEhUGhWIhZKi`MibOieQjgSjjUklWknYkq\ _lsaluclseiqggoidnkblm`joYiqWgsTeuRdvPOq`8llITVRAE\ TDFUGGVIHWLIXNIIM2JN4KN5LO7MO8NOAOPBPPCQPERQFSQHTQ\ IURKVRLVRMUgITxEUtIVpLVmOWiRXfUXbXY__YWbZSe_Ph_Lk`\ InaEqaBtb7wb4zc8xdCweGvfJugNshRriUqjYpkanldmmhlnlk\ ooipshqwgqzfnvcks`hpZflWciT`fRYbOW_MTXJQTGNQELNBIJ\ 8FG6CD3AA1LJAVRJd_Sng`pcaq`arXasUatQavNawJaxGayCaz\ 9aoHdePfWWhVTfUReUPcTNbTLaSJ_SHZREYQCWQAVP8UP6SO4R\ O2Qe3Qv4Qo8RiBRcESYISSLTMOTGRTJQQLPONOMPNKRMHTLFVK\ DXKBUNDSQEPSFNVGLXHI_IGbJDdKBgL9iMDkVGlcJmlMnuVhlc\ bclXVYMZKCb62f8Bd9JcASaB_`ChZDpYExXFxVGxUIxSJxRKyP\ LyOMyMOyLPyJQyIRyGSyFTpCUgAVZ8WQ6XI4TQ7QX9McBHkAJj\ DKiGMhJNgLPfOQfRReUTdWUcZWbaXadcinYafSUZNNRZI_jDhv\ 6pu9ptBpsDprFpqHppJppLpoOpnQpmSplUpkWpjYpmYsj_pgan\ eblbdj`ehYgeWicTjaRl_OmYMoVJqTHrREtPCuNGtMJsLNsKQr\ JTqJXqIrTSqSZpRdoQkoPqK7f } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

1 0

Re: [Fractint] Viewsonic's new 3,840 x 2,400 monitor
by gnome＠hawaii.rr.com 01 Jul '04

01 Jul '04

That's a full-page print at 300dpi. Someone buy me one, please, and the video card(s) to support it? ;-) David gnome(a)hawaii.rr.com ----- Original Message ----- From: "Lee H. Skinner" <skinner(a)thuntek.net> Date: Wednesday, June 30, 2004 12:01 pm Subject: [Fractint] Viewsonic's new 3,840 x 2,400 monitor > http://www.trustedreviews.com/article.aspx?art=533 > > Pricewatch lists vendors selling the 9.2Mpixel resolution > ViewSonic > VP2290b TFT display monitor starting at a bit more than $6,000 -- > video > card is extra. > > That's 4 times a 1920x1200 image. This is an 8:5 aspect ratio. > > I'd love to see some fractals on that screen! > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

1 0

FOTD 01-07-04 (Pi in Sight [7])
by Jim Muth 01 Jul '04

01 Jul '04

FOTD -- July 01, 2004 (Rating 7) Fractal visionaries and enthusiasts: In today's short discussion I will not wax philosophical, nor will I wax political. I will wax fractal. After all, we're here because we enjoy fractals, and not to give our opinions of world events. Today's quickie shows a midget that is located on a surprisingly long and straight filament extending from the main body of the Z^1.314159...+C Mandeloid when this fractal is calculated 62 levels up the logarithmic spiral. I rated the image at a 7, mostly because of the striking colors, which I found almost totally by chance. I named the image "Pi in Sight". A closer examination of the exponent of Z will reveal the reason for the name. The parent fractal appears to hold several other interesting areas. If I find the time, I will do further investigating and present anything of interest I might find as a future FOTD. When the render time of 23 minutes is factored into the rating system, the overall value equals a 31. That value can be made higher by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another in an unending string of near perfect 84F 29C days gave the fractal cats little to complain about on Wednesday. I could complain a bit about the work that is yet to be done -- but I won't. Hopefully, what I will do is return in 24 hours or so with the next FOTD. Until then, take care, and are fractals necessary for life? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Pi_in_Sight { ; time=0:22:55.28--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+7.0\ 092422286503/+5.547921277829/9.579319e+008/1/15/1.\ 92347512060556114e-005 params=1.314159265358979/0/\ 62.85/0 float=y maxiter=120000 inside=0 logmap=63 periodicity=10 colors=0004004005105205305405505608\ 71B81D91GA1JB1MC1PD1SC1VA1Y91`81c71e61g51i41k31m84\ oD6qI9sMBuREwWGt`IqdLniNknQZsSUwUUpRUjOWfIYbD_bFab\ HcbIebKgbLibNkbOmbQobRqbTsbUu_awYhygbwfctbCfYEfbF`\ aDW`BR_9MZ7HY5CX4GV9JUDNTIQSMURQXPV`OZcNcgMgjLkbMf\ VMaOMXGMS9MO8KR8JT7IW7HY6G_6Fb5Ed5Df5Ci4Bk4An39p38\ r27u26w25y39w4Du5Gs6Kq7No8Rm9UkAYiBagCdeDhcEkaFo_G\ rYHvWIyUKxTMwSOvRQuQStPUsOWrNYqM_pLaoKcnJemIglHikG\ kjFliELdCHSJDFQ93WDAUGGSJMQNSOQYMTcKXiI_oGbuEckDdb\ CeTBeKAhLGjLMlMSnMYpNcrNhmOeiOceOe`OhXOkTOnOOqKOtG\ OwcEzz5zx8zwBzvEzuGxtJzsMzrOzlRzfTzaVzWXzR_zLazGcz\ Aez5gz8czB`zEXzHUzKQzNNzQJzTGzWCzZ9za6z`5z_5zZ5z`7\ za8zb9zcAzeCzfDzgEzhFzjHzkIzlJzmKzlMzlNzkOzkPzjQza\ ZzjRzjTziUziVzhWzhXzKezMdzOczQczSbzUazWazY`z_`za_z\ cZzeZzgYz6czAbzEazHazL`zO`zS_zV_zZZzaZzeYzCKzGMzKO\ zNPzRRzVSz6Az29z3Az3Bz3Cz3Cz3Dz4Ez4Fz4Fz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

Fractint collection
by John Wilson 30 Jun '04

30 Jun '04

I've started to place the more-or-less raw OCR records of "Fractal Creations", 2nd Edition, page by page at http://www3.telus.net/JohnW/Fractint. Hopefully the quality and quantity will improve with time! John W.

2 2

FOTD 30-06-04 (A Myriad and Unity [6])
by Jim Muth 30 Jun '04

30 Jun '04

FOTD -- June 30, 2004 (Rating 6) Fractal visionaries and enthusiasts: The news on the radio this morning is that the electromagnetic radiation from cell phones apparently reduces sperm-cell count in men. The evidence that EMR is harmful to not only sperm cells, but to the brain cells of test animals continues mount- ing, yet we continue in our state of denial, claiming that the harm has never been demonstrated in humans. And why not deny it? Cell phones and computer monitors are not only convenient, they are fun. We say the radiation harms only test animals? Do we not use test animals to determine if something is harmful to humans? I wonder how long it will be before we suddenly realize that the increased electromagnetic radiation in our modern world has been harming us, and rush to bring class-action law suits against the evil, greedy phone companies and cell-phone manufacturers, who will replace the evil, greedy tobacco companies in the future. And while we're at it, let's not forget the computer monitor manufacturers. Those old-style CRT monitors are also prodigious radiation emitters. Do not be deceived by today's image. It emits no electromagne- tic radiation. (The monitor emits the radiation.) Nor does the image lie on the X-axis. It is actually a scene in the fractal that results when Z^(-1) is subtracted from 1/10000 part of Z^10000, and 1/C is added. I named the image "A Myriad and Unity", a name that is rather deceiving, since Z^(-1) is not unity but rather 1/Z. The typical high-order features are prominent in the image, which renders in a speedy 7 minutes and combines with the rating of a 6 to give an overall value of 84. The most efficient way to view the image is to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download it from there. Perfect weather both Monday and Tuesday here at Fractal Central gave the cats a chance to do anything they wanted in the yard. In fact, we have had so many perfect days lately that the cats are actually becoming a bit bored with life in their own yard. I spotted them Tuesday afternoon exploring three yards up the hill, where the neighborhood alpha tomcat hangs out. Luckily, the bully cat was off somewhere else, and the dynamic duo made it back without a scratch. Today looks to be perfect again for the fractal cats. For me, there is still a lot of catching up to do. Until next FOTD, take care, and if the earth rotated in the opposite direction, the sun would move in the opposite direc- tion in the sky. Would this put North America in the Southern Hemisphere and Australia in the Northern Hemisphere? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Myriad_and_Unity { ; time=0:07:07.57--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.499841076927818/-0.000000321473714/\ 8.357877e+008 params=0.0001/10000/-1/-1/0/0 float=y maxiter=1400 inside=0 logmap=138 periodicity=10 colors=00061FAJUDYgGpuIipJbkKXfLQaMJXNDSO6NP0IV6ZS\ S`PlbHefAZj3TmEXkO`iYdggheqkcnhelfgjdihbjf_ldYoaWr\ _UtYRvWPxUNzSLzQJyVRxZYwcdvgkuimudlqYfmS`iLWeFQa8K\ Y2FUGPOTZJehDyr8uqBrpDopGloIhnLenNbmQ`lSYlVWkXUj_S\ jaRhZRfXQeVQcSQbQP`OP_MOYJOXHOVFNUDNSAMR8MP6MO4NP8\ OQCPRGPSKQTNRURRVVSWZTXbTXeUWfVWfWWfXVgXVgYVgZUh_U\ h_Uh`TiaTibTibTiaSbaRXaQQaPKaPE_SGYUIWWJUYLT_MRaOP\ cPNfRLhSKjUIlVGnXEpYCr_Bt`EsZGsYIsWKsVMsTOsSQsQSsP\ UsNWsMXpNXnOXkPYiQYfRYdRZaSZ_TZXU_VV_SW_QWZPVSCHTB\ KUBNVBQVATWAWXAZY9aZ9dZ9gWDeTGcQKaNN_KQYHUWEXUB_TF\ YQJWONUMQSJUQHYOF`ND1aX5cV9dUDeTHfRLgQPiPTjOXkM`lL\ dmKgnJdlLajN_iOXgQUfSSdTPcVMaXK`YHZ_EYaCWc9We6Yg4_\ iQakjcmicohcqgcsfcufbweaxd`yc_zcZzb_zb_za`zaaz`bz`\ bz`dz_dz_ezZfzZgzYgzYizYizZjzZjz_kz`lzamzbnzbozapz\ `qz_rzZqzYtzXuzWvzVwzUxzTzzSzzSzzTyzTzzUzzUzzVzzVz\ zTzzSzzRzzPzzOzzNzzMzz9zz } 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==================================

1 0

Re: FractInt Collection -- Volunteer Project ??
by Jim Muth 28 Jun '04

28 Jun '04

At 11:05 AM 6/28/04 -0700, John Wilson wrote: <snipped> > . . . However, my OCR software, ABBYY, is >coughing and choking over some of the "artsy" >pages. Somebody decided to print the text >*over* faint fractal backgrounds, and the >software has trouble resolving these "unknown >characters"!. . . John: Welcome to the frustration group. Similar problems are very familiar in my line of work. If you can work out ways to speedily solve such unexpected and frustrating problems, you might find yourself half-way to becoming a graphic designer like I am. It's this kind of stuff that keeps putting me behind. Jim M.

1 0

FOTD 28-06-04 (Siegel Disks-3 [5])
by Jim Muth 28 Jun '04

28 Jun '04

FOTD -- June 28, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today we go from one of the slowest images of all time to one of the fastest, for a kind of look at a real Siegel Disk Fractal. (At least that's what the math encyclopedia calls its mirror image.) And this will be our last look of the current Siegel series. When the maxiter of today's image is raised to 100-million, the inside does start to fill with some kind of debris, but then the image takes several days to render. As a compromise between having a real siegel disk fractal that takes days to render and an almost-siegel disk fractal that renders in a more reasonable time, I lowered the maxiter to a miserly 300 and rendered today's image with the inside set to 'bof61'. When this was done, the siegel disks appeared as flowers set against a clear blue sky. This doesn't quite make the invisible visible, but it helps a bit. I named the image "Siegel Disks-3". It is the third and last in the current series of these quasi-objects. Now, if someone knows where to find Herman Rings, whatever they are, I will do the same with them. The rating of an average 5 explodes to a whopping 970 when the very short 30-second render time is figured in. In this case, the download will likely take longer than the rendering, but visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is still a very convenient way of seeing the FOTD images. With the near-perfect weather continuing Saturday and Sunday, the fractal duo found near-perfect happiness both days, hiding in the holly thicket, wondering where the cicadas went. The good weather made no difference to me, however. I spent most of the weekend trying to get the work under control. Some progress was made, but much more needs to be done before I can totally relax. Until next FOTD, take care, and we think, therefore we might exist. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Siegel_Disks-3 { ; time=0:00:30.93--SF5 on a P200 reset=2003 type=julia passes=1 center-mag=1.11022e\ -016/0/0.964 params=-0.390541/0.586788 float=y maxiter=300 bailout=9 inside=bof61 outside=1 logmap=yes symmetry=origin periodicity=10 colors=000jpz_ih`ji`jjakkallckkbllallall`mm`mm_mmZ\ nmZnnYnnYonXonWooWpoVpoVpoUqpUqpTqpSrqSrqRrqRsqQsr\ PsrPtrOtrOtsNusMusMusLvtLvtKvtIvwKvtMvrOvpPvnRvkTv\ iUvgWveYvb_v``vZbvXdvUevSgvQivOkvLlvJnvHpvFpyCqvDq\ sDqqDqnDqlDriDrfDrdEraEr_ErXEsUEsSEsPEsNFsKFtHFtFF\ tCFtAFajnbincgmcfldeleckfbjgajh_ihZhiYhjXgkVflUflT\ emRdnQdoPcpNbqMbqLarJ`sI`tH_uFZuEZvDYwBXxAXy9Wy8Wx\ 9Xw9Xv9Xu9Yt9Ys9YrAYqAZpAZoAZnAZmA_lA_kB_jB`iB`hB`\ gB`fBaeBaeCadCacCbbCbaCb`Cb_CcZDcYDcXDdzDdVDdUDdTD\ eSEeREeQEePEfOEfNEfMDgNEfOFfPGfQHeRIeSIeTJeUKdVLdW\ MdXNdYNcYOcZPc_Qc`RbaRbbSbcTbdUaeVafWagWahX`iY`iZ`\ j_`k__l`_ma_nb_ocZpdZqdZreZsfYtgYuhYwj_uhYsgXqfVod\ UmcSkbRi`Ph_OfZMdXLbWK`VIZTHXSFWREUPCSOBQN9OL8MK6K\ J5JI4KJ5KK6LL7LL8MM9MNAMNBNOCNKDOKEOMFONGPOHPPIQRJ\ QRKRTLmmMRVNSWOSYPTYQT_RT`SUaTUbUVdVVdWVfXWgYWhZXi\ _Xk`Zkazmbznczodzpezrfzrg } END PARAMETER FILE=========================================

1 0

FOTD 26-06-04 (Siegel Disks-2 [5])
by Jim Muth 26 Jun '04

26 Jun '04

FOTD -- June 26, 2004 (Rating 5) Fractal visionaries and enthusiasts: No, there is no mistake in the 14-hour render time of today's parameter file. It is the slowest in several years, and close to the slowest of all time. This is an unintentional tribute to the speed of Fractint's type=julia fractal. The scene is identical to that of the most recent FOTD, with one tiny but very important exception -- it has been sliced in a direction 0.0019 degree removed from the Julia direction. To do this, I had to use one of my own formulas, which is the main reason that today's image is so slow. This tiny rotation makes a world of difference to the image. Some of the Siegel Disks are still there; some are gone, but now, looking into the background, we can actually see the relation of the Julia set to the Mandelbrot set. The orange part of the image is a hugely enlarged view of the shore of the M-set. The orange valley is not a familiar one. It is an extremely tiny one, which has been enlarged over 30,000 times until it overfills the entire Julia set. The center of symmetry of the Julia set locates the exact corresponding point of the M-set. I named the image "Siegel Disks-2", and rated it at a 5. When the render time of over 14 hours is considered, the overall value rates a pathetic 0.6, the lowest rating of all time. It goes without saying that the image has been sent on ahead to Paul, who will post it to the FOTD web site, from where it may be downloaded and 14 hours of computer time saved. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday here at Fractal Central was partly cloudy with a high temperature of 84F 29C -- perfect conditions for cats. The dynamic duo spent several hours in the yard; the not-so-dynamic individual spent most of the day trying to get the work done. When the day ended, the cats were happy, but the individual had accomplished less than he had intended. By contrast, Friday was cloudy and oppressive, with a lively thunder-shower in the late afternoon. Luckily, by the time the rain arrived, the cats had been outside long enough to become satisfied, and they dashed indoors eager to stay dry and eat. This morning, the rain has moved out, it is cooler, and a clearing is on the horizon. I expect happy cats. For me, much more work waits to be done. The third and final Siegel Disk fractal will appear in a day or two. Until then, be patient and think fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Siegel_Disks-2 {; time=14:02:45.68--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/0/3.453802/1/-10/3.885780586\ 1880479e-016 params=90.0019/89.9981/2/0/0/0/-0.543\ 268/0.564772 float=y maxiter=10000000 inside=0 logmap=yes periodicity=10 colors=000PSeQTfRUgSVhTWiUXjVYkWZlX_mY`nZao_bp`cqa\ drbes`etaftbgtbhtchtcitditditeiteitfjtfjtgjtgjthkt\ hktiktiktjktjltkltkltlltllthkrejpcipbhoagn`fm_elZd\ kZcjYciXciWchVcgVcfUceTcdSccRcbQcdRcbRcaR`_SZZSWXS\ UWTRUTPTTMRX77TKQP0cL0cH0cE0aATQ7OE6PH6QJ6RL6RN6SQ\ 6TS6UU6UW6VZ6W`6Wb6Xd6Yf6Zi6Zk6_m6`o6ar6at6bv6cx6c\ z5dy5ex5fw5fv5gu4ht4it4is4jr4kq3lp3lo3mn3nn3om2ol2\ pk2qj2ri2ri3qj4qj5qk6qk7qk8ql8ql9qmAqmBqmCqnDqnEqo\ EqoFqoGqpHqpIqqJqqJmqEilAag6Ub2MY4OT5HO7IJ8LEAN9BP\ 4GQ3KS3OT3SV3XW3`X3dY3hZ3m_3qa3uc3yd3xc4xc3xb2x`1x\ Y0wW0wU0wS0wR0wP0wO0vN0vM0vK0vJ0vI0vG0uE0uC0uA0uA0\ uA0wA0uA0tA0rA0qA0oA0nA0mA0mA0mA0mA0mA0mA0mA0mA0mA\ 0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0m\ A0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0\ mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA\ 0mA0mA0mA0mA0mA0mA0mA0mA0 } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 23-06-04 (Siegel Disks-1 [5])
by Jim Muth 23 Jun '04

23 Jun '04

FOTD -- June 23, 2003 (Rating 5) Fractal visionaries and enthusiasts: The graphic work is still pretty far behind, but I decided to slip in a fractal quickie for today. Today's average-rated image shows a screen full of almost-Siegel Disks. These disks appear in the Julia sets that correspond to points on the exact egde of the Mandelbrot set, where the peri- odicity is infinite. As far as I can determine, a siegel disk consists of infinitely many tendrils going in circles around the central point. This number of tendrils is not achieved in today's fractal, nor could it be achieved in any finite fractal, making the orange areas of today's image not quite siegel disks. Luckily, Fractint's type=julia fractal is very fast. If it were not, today's image, with its maxiter of 10-million, could take many hours to render. I named today's image "Siegel_Disks-1". I have two more fractals ready that will continue the almost-Siegel theme. I rated the image an average 5, which combines with the render time of under 15 minutes to give an absolute value of 34. To see the disks in quicker time, download the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Things here at Fractal Central have been quite pleasant for the dynamic cats for the past several days. But it has been very busy for me. I still have quite a load of work to catch up on, so it's time to get started. Until the next FOTD, which will appear in a few days, take care, and how many bytes of informa- tion could a siegel disk hold? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Siegel_Disks-1 { ; time=0:14:48.25--SF5 on a P200 reset=2003 type=julia passes=1 center-mag=0/0/3.534818/1/-10/3.885780586188e-016 params=-0.543268/0.564772 float=y maxiter=10000000 inside=255 logmap=yes periodicity=10 colors=000PSeQTfRUgSVhTWiUXjVYkWZlX_mY`nZao_bp`cqa\ drbes`etaftbgtbhtchtcitditditeiteitfjtfjtgjtgjthkt\ hktiktiktjktjltkltkltlltllthkrejpcipbhoagn`fm_elZd\ kZcjYciXciWchVcgVcfUceTcdSccRcbQcdRcbRcaR`_SZZSWXS\ UWTRUTPTTMRX77TKQP0cL0cH0cE0aATQ7OE6PH6QJ6RL6RN6SQ\ 6TS6UU6UW6VZ6W`6Wb6Xd6Yf6Zi6Zk6_m6`o6ar6at6bv6cx6c\ z5dy5ex5fw5fv5gu4ht4it4is4jr4kq3lp3lo3mn3nn3om2ol2\ pk2qj2ri2ri3qj4qj5qk6qk7qk8ql8ql9qmAqmBqmCqnDqnEqo\ EqoFqoGqpHqpIqqJqqJmqEilAag6Ub2MY4OT5HO7IJ8LEAN9BP\ 4GQ3KS3OT3SV3XW3`X3dY3hZ3m_3qa3uc3yd3xc4xc3xb2x`1x\ Y0wW0wU0wS0wR0wP0wO0vN0vM0vK0vJ0vI0vG0uE0uC0uA0uA0\ uA0wA0uA0tA0rA0qA0oA0nA0mA0mA0mA0mA0mA0mA0mA0mA0mA\ 0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0m\ A0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0\ mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA0mA\ 0mA0mA0mA0mA0mA0mA0mA0mA0 } END PARAMETER FILE=========================================

1 0

Re: [Fractint] No FOTD for a few days
by gnome＠hawaii.rr.com 21 Jun '04

21 Jun '04

----- Original Message ----- From: Jim Muth <jamth(a)mindspring.com> Date: Monday, June 21, 2004 6:20 am Subject: Re: [Fractint] No FOTD for a few days > At 07:11 PM on 6/18/04, David Jones wrote: > > >And some day such work will fund the provision > >of a much faster Fractal generating box, to > >speed your FOTD searches! > > It's noon of Monday, June 21, and things are > still hectic here at F.C. The FOTD delay is > not due to a slow machine. I have four fast > computers. The problem is that when the work > gets as heavy as it is now, I am busy up to 16 > hours a day, and lack the time to even boot up > Fractint, much less search for interesting > fractals and write the discussion. Right now, > it looks like I'll be caught-up around Thursday, > and the next FOTD will appear then, but that is > no promise. Oh, I wasn't thinking of that, I was thinking more in terms of rendering times. I noticed some lengthy rendering times in some of your discussions, and figured that you probably weren't devoting your fast machines to Fractint. Of course, is Fractint dwelling on its own machine? If so, you could just leave it up all the time and do fractal stuff more frequently ... > Jim M. > > P.S. The fractal cats are doing well. I'm not sure but that our two cats aren't also fractal. They're four years apart in age, the older one weighs roughly twice that of the younger, both are black and arrived in completely random ways (one found in our local shopping center's parking lot, one found at my daughter's high school library's parking lot) ... and as they've iterated through the years, they're getting more and more self-similar ... David gnome(a)hawaii.rr.com

1 0

Re: [Fractint] No FOTD for a few days
by Jim Muth 21 Jun '04

21 Jun '04

At 07:11 PM on 6/18/04, David Jones wrote: >And some day such work will fund the provision >of a much faster Fractal generating box, to >speed your FOTD searches! It's noon of Monday, June 21, and things are still hectic here at F.C. The FOTD delay is not due to a slow machine. I have four fast computers. The problem is that when the work gets as heavy as it is now, I am busy up to 16 hours a day, and lack the time to even boot up Fractint, much less search for interesting fractals and write the discussion. Right now, it looks like I'll be caught-up around Thursday, and the next FOTD will appear then, but that is no promise. Jim M. P.S. The fractal cats are doing well.

1 0

Fractint version 20.03 patch 2 now available
by Jonathan Osuch 21 Jun '04

21 Jun '04

Fractint version 20.03 patch 2 is now available at www.fractint.org. What's new: Fixed the inability to reload a PAR created from an arbitrary precision fractal with a large magnification. Fixed the problem with a left mouse click not bringing up the zoom box after an image is completed. Incorporated Gerald Dobiasovsky's fix for the julibrot type when used with quat and hypercomplex. Fixed the display of subdirectories in Xfractint. Replaced control characters in realdos.c with the equivalent ascii values to quiet complaints by CVS. Jonathan

2 1

No FOTD for a few days
by Jim Muth 19 Jun '04

19 Jun '04

Fractal visionaries and enthusiasts: Due to an unexpected large job that has arrived, I will be unable to post the FOTD for the next few days. I will resume the daily fractals as soon as I put the work behind me. Hopefully this will be around the middle of the coming week. In the meantime I will continue reading the lists. Until the fractals re-appear, take care, and do not be concerned. Fractals will be with us always. Jim M.

2 1

Re: [Fractint] FOTD 17-06-04 (Spirit Murmur [6])
by gnome＠hawaii.rr.com 19 Jun '04

19 Jun '04

When I go to the Spirit Murmur page, only about a third of the image comes down ... Then the browser says done. 8-( David gnome(a)hawaii.rr.com ----- Original Message ----- From: Jim Muth <jamth(a)mindspring.com> Date: Thursday, June 17, 2004 5:21 am Subject: [Fractint] FOTD 17-06-04 (Spirit Murmur [6]) > > FOTD -- June 17, 2004 (Rating 6) > > Fractal visionaries and enthusiasts: > > I see that the idea of the Fractint CD is still floating around, > along with suggestions of what such a disk might contain. Some- > one, I forget who, has suggested that the Fractint CD might > include the 7-year series of FOTD parameter files. This seems > like a good idea, since my own FOTD-CD has been bogged down for > several years. The FOTD parameter files, along with the discus- > sions, take up about 8-1/2 mb of disk space in text format, and > I would be willing to include them on the disk at no charge, as > long as the disk were distributed at no cost. I have long since > realized and accepted that there would be no financial profit in > such a disk. > > To find today's fractal scene I ventured into the Seahorse > Valley area of the Z^(2+0.2i) Mandeloid. Perhaps I should call > it the Seahorse Mesa area, for the north branch of the valley > has broadened into a plateau almost as wide as the main bud. > > This is a 'new' area, not part of the standard M-set, and 'new' > areas contain new material. The scene illustrated in today's > image is certainly new, having never before been seen by human > (or alien) eyes. Of course, if an infinity of infinite parallel > universes exist, today's image has been seen an infinite number > of times. > > I named the image "Spirit Murmur". The name has no connection > to the image, I simply like the poetic sound of the name. The > rating of a 6 appears fair. The render time of just under 9 > minutes gives an overall value of 68, which is not too bad. The > best way to see the image is to download it from Paul's FOTD web > site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > It is once again quiet here at Fractal Central. The constant > din of the cicadas is gone. True, an occasional male still > sings a lonely song, hidden is some bush or tree, but even these > stragglers will soon be gone, leaving only the discarded shells > and empty holes as a reminder that they were ever here. The > cats seem totally unconcerned. > > Heavy clouds, very high humidity, a temperature of 86F 30C and > occasional showers made Wednesday quite oppressive here at > Fractal Central. But it was oppressive only for people. The > fractal cats enjoyed the conditions, and despite the wet grass, > found time for a satisfying romp (AKA rest) in the yard. When > the heaviest shower of the day drove them indoors at 6pm, they > were ready to settle for the evening without a treat of tuna. > Today is starting the same. It looks like a repeat for the duo. > > For me, it looks like another very busy day. (Isn't success > wonderful.) Until the next FOTD, which hopefully will arrive > tomorrow, take care, and when searching for truth, be sure of > how it will be recognized when it is found. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Spirit_Murmur { ; time=0:08:52.23--SF5 on a P200 > reset=2003 type=formula formulafile=allinone.frm > formulaname=MandelbrotBC2 passes=1 > center-mag=-4.514094221782175/+2.05908763207\ > 5082/2.712345e+009 params=2/0.2/-2/0 float=y > maxiter=4200 inside=0 logmap=244 periodicity=10 > colors=000S6MV5KV5IY6LX6N`6WZ7S_7V`7Xa8_U8aZ8d`9cd\ > 9if9ke9mgDliGkkJjlNinQhpTgrXfs_eubdwfcyibzlarg_jbZ\ > cYYWTXOOWHKVIMUINTIOSIQRJRQJSPJUOJVNJWMMYOP_QRaRUc\ > TXeUZgWaiYdjZfl`inalpcnreqtftvhvwiquemsbiq_epXanUY\ > lRUkOQiLMgIIeFEdCAb96`62_34Z56Z68Z7AZ8CZ9EZAFYCHYD\ > JYELYFNYGPYHQYIdJYs4ml3oe3pZ2qS2sL1tF1uPKcZaNefTkk\ > Zrpdxuixvfxvcxv`xvYxwWxwTxwQxwNxwKxxIxxFxxCxx9xx7d\ > oEMgL3_R7aQAcPDePHgOKhONjNRlNUnMXpM`qLcsLfuKjwKmyJ\ > pzJlvQhsWdpa`lhXinTftPczMbtKboIajGaeD``B`W9_R7_M5_\ > HCZDJZ9QY5WY2Z_2``2ba2eb2gd2ie2lf2ng2ph2diKUjaJkrv\ > lbsm_qnXnoUlqRisPgtMduJbvG_wEYxBVy8Tz5Rz3Ny2Jy1Fy0\ > Cy0Et4zp8zkCzgGzbKzZOzUSzQWzO_zRczUgzXgz_gzbgzegzh\ > gzkdznbzq`ztZzwWzzUzzSzzQzzNzzLzzJzzHzzKzzMzzOzzRz\ > zTzzVzzYzz_zzazzdzzfzzhzzkzzmzzozzqzzBzzAzz9zzCzzF\ > zzHzzKzzMzzPzzRzzUzzXzzZzzazzczzfzzhzzkzzmzzhzzczz\ > _zzVzzQzzMzzHzzDzzUzzRzzP } > > frm:MandelbrotBC2 { ; by several Fractint users > e=p1, a=imag(p2)+100 > p=real(p2)+PI > q=2*PI*floor(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| > END 20.0 PAR-FORMULA FILE================================== > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

4 3

XP and Fractint
by Jonathan Osuch 17 Jun '04

17 Jun '04

Here is something to try with XP that works on my system: During windows startup press <F8> to bring up the menu selections. Select "Safe Mode with Command Prompt". Change (cd) to your Fractint directory and run Fractint. When done, exit Fractint and type logoff to return to the logon prompt. You will need to restart the computer from here to get back to the normal XP environment. Jonathan

1 0

FOTD 17-06-04 (Spirit Murmur [6])
by Jim Muth 17 Jun '04

17 Jun '04

FOTD -- June 17, 2004 (Rating 6) Fractal visionaries and enthusiasts: I see that the idea of the Fractint CD is still floating around, along with suggestions of what such a disk might contain. Some- one, I forget who, has suggested that the Fractint CD might include the 7-year series of FOTD parameter files. This seems like a good idea, since my own FOTD-CD has been bogged down for several years. The FOTD parameter files, along with the discus- sions, take up about 8-1/2 mb of disk space in text format, and I would be willing to include them on the disk at no charge, as long as the disk were distributed at no cost. I have long since realized and accepted that there would be no financial profit in such a disk. To find today's fractal scene I ventured into the Seahorse Valley area of the Z^(2+0.2i) Mandeloid. Perhaps I should call it the Seahorse Mesa area, for the north branch of the valley has broadened into a plateau almost as wide as the main bud. This is a 'new' area, not part of the standard M-set, and 'new' areas contain new material. The scene illustrated in today's image is certainly new, having never before been seen by human (or alien) eyes. Of course, if an infinity of infinite parallel universes exist, today's image has been seen an infinite number of times. I named the image "Spirit Murmur". The name has no connection to the image, I simply like the poetic sound of the name. The rating of a 6 appears fair. The render time of just under 9 minutes gives an overall value of 68, which is not too bad. The best way to see the image is to download it from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It is once again quiet here at Fractal Central. The constant din of the cicadas is gone. True, an occasional male still sings a lonely song, hidden is some bush or tree, but even these stragglers will soon be gone, leaving only the discarded shells and empty holes as a reminder that they were ever here. The cats seem totally unconcerned. Heavy clouds, very high humidity, a temperature of 86F 30C and occasional showers made Wednesday quite oppressive here at Fractal Central. But it was oppressive only for people. The fractal cats enjoyed the conditions, and despite the wet grass, found time for a satisfying romp (AKA rest) in the yard. When the heaviest shower of the day drove them indoors at 6pm, they were ready to settle for the evening without a treat of tuna. Today is starting the same. It looks like a repeat for the duo. For me, it looks like another very busy day. (Isn't success wonderful.) Until the next FOTD, which hopefully will arrive tomorrow, take care, and when searching for truth, be sure of how it will be recognized when it is found. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spirit_Murmur { ; time=0:08:52.23--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-4.514094221782175/+2.05908763207\ 5082/2.712345e+009 params=2/0.2/-2/0 float=y maxiter=4200 inside=0 logmap=244 periodicity=10 colors=000S6MV5KV5IY6LX6N`6WZ7S_7V`7Xa8_U8aZ8d`9cd\ 9if9ke9mgDliGkkJjlNinQhpTgrXfs_eubdwfcyibzlarg_jbZ\ cYYWTXOOWHKVIMUINTIOSIQRJRQJSPJUOJVNJWMMYOP_QRaRUc\ TXeUZgWaiYdjZfl`inalpcnreqtftvhvwiquemsbiq_epXanUY\ lRUkOQiLMgIIeFEdCAb96`62_34Z56Z68Z7AZ8CZ9EZAFYCHYD\ JYELYFNYGPYHQYIdJYs4ml3oe3pZ2qS2sL1tF1uPKcZaNefTkk\ Zrpdxuixvfxvcxv`xvYxwWxwTxwQxwNxwKxxIxxFxxCxx9xx7d\ oEMgL3_R7aQAcPDePHgOKhONjNRlNUnMXpM`qLcsLfuKjwKmyJ\ pzJlvQhsWdpa`lhXinTftPczMbtKboIajGaeD``B`W9_R7_M5_\ HCZDJZ9QY5WY2Z_2``2ba2eb2gd2ie2lf2ng2ph2diKUjaJkrv\ lbsm_qnXnoUlqRisPgtMduJbvG_wEYxBVy8Tz5Rz3Ny2Jy1Fy0\ Cy0Et4zp8zkCzgGzbKzZOzUSzQWzO_zRczUgzXgz_gzbgzegzh\ gzkdznbzq`ztZzwWzzUzzSzzQzzNzzLzzJzzHzzKzzMzzOzzRz\ zTzzVzzYzz_zzazzdzzfzzhzzkzzmzzozzqzzBzzAzz9zzCzzF\ zzHzzKzzMzzPzzRzzUzzXzzZzzazzczzfzzhzzkzzmzzhzzczz\ _zzVzzQzzMzzHzzDzzUzzRzzP } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

RE: [Fractint] Re: ChaosScope
by Franktal Gallery 17 Jun '04

17 Jun '04

I strongly recommend joining the chaoscope mailing list at http://www.freelists.org/archives/chaoscope , it's managed by Nicolas Desprez (chaoscope's author), and you can even post pictures (< 100K). -- As far as I know, what I have in my site is the Cantor Gasket.... I think the Menger cube it's quite a different animal. But I may be wrong. >>Nice pics in your gallery - I see the Menger Cube there, but I haven't >>been able to do it yet - gimme more time to figure it out. The 3d IFS parameters at the Fractint distribution kit are your friends (hint, hint) >>BTW, IMHO, Zappa sucks. Well, everybody's entitled to an opinion, and yours is wrong in this case ;-) >>But Rush Rulez! Indeed ! Thanks for checking out my site, and best regards Miguel http://www.geocities.com/franktal2002 _________________________________________________________________ Add photos to your messages with MSN 8. Get 2 months FREE*. http://join.msn.com/?page=features/featuredemail

1 0

Fractal Creations
by Barry Smith 17 Jun '04

17 Jun '04

Thanks to David and Paul for their replies. David Jones <gnome(a)hawaii.rr.com> wrote: <I have been lurking on this list for years. <From July 1991 until August 1994 I wrote a monthly column called Â‘Frenzied FractalsÂ’ in the excellent magazine published by the local users group. Then I began a new busy job and was less than impressed when the editors often arbitrarily changed what I had written, dropped illustrations and failed to return some photos that I had paid good money for." Hmm, any possibility that your interesting-sounding column (even the old issues of it) could appear somewhere on the web? David It is nearly a decade since I stopped writing the column. The articles were written in WordStar, converted to plain text and copied to 5 Â¼ inch discs along with GIF files to be DTPÂ’d (This was over ten years ago). I have put a 5 Â¼ inch drive into my current PC and have copied hundreds of diskettes with old files to my hard disc, but canÂ’t find the ones for my articles now - There are about 500 more 5 Â¼ inch diskettes that IÂ’ve not looked at for years. It would probably be easier to scan the articles, but wonder if itÂ’s worth it. The first article was basically a brief description of what fractals are (with only a little maths) and why they are interesting, together with an enthusiastic account of the main features of Fractint. I e-mailed the text of the article to Tim to check (This was before the web or modern browsers had come on the scene; if I remember correctly I had just moved up from an acoustic coupler to a state of the art 2400 bps modem at vast expense.) Later articles mainly discussed further fractal types, including the fern and other ifs, L-systems, Lyapunov and so on. I canÂ’t imagine that I covered anything not in TimÂ’s book. Paul N. Lee <Paul.N.Lee(a)worldnet.att.net> wrote: <...I tried in vain to get a copy." He went on to say that several copies were available, both hardcover and paperback, from various brokers. On 6 Jan 1999 amazon.com wrote to say Â‘At this time, we have not yet located the item that you requested. Please rest assured that we will continue searching until you let us know that you would like us to discontinue our efforts. Â‘When a match is found, we will contact you by email to request your approval of the price of the item.Â’ I have not heard from them in the last 5 years, and assumed after Tim said that it was out of print that it was unavailable. I have a Gold Visa credit card (having cancelled my Diners, Amex, Bankcard and Mastercard) and will now revisit amazon.com. My concern was about private transactions - bank drafts are expensive. Thanks again for the replies. -------------------- Barry W Smith P O Box 442, Jamison Centre ACT 2614, Australia Tel. (Home & answering machine) (02) 6251 2119 International +61 2 6251 2119 e-mail: bsmith(a)cyberone.com.au

1 0

Re: ChaosScope
by jackoftradez＠comcast.net 17 Jun '04

17 Jun '04

David (or Miguel) thanks for turning me on to ChaosScope! It is an Excellent program - I never knew about it! It is so user friendly I didn't even need the docs. The 3D rotation feature rocks - for the first time I can see what the Lorenz graph REALLY looks like. I knew sooner or later someone would beat my SAX program :( Nice pics in your gallery - I see the Menger Cube there, but I haven't been able to do it yet - gimme more time to figure it out. The Menger image on the web site makes for seriously cool wallpaper also. BTW, IMHO, Zappa sucks. But Rush Rulez! JoTz

1 0

FOTD 16-06-04 (Discus [7])
by Jim Muth 16 Jun '04

16 Jun '04

FOTD -- June 16, 2004 (Rating 7) Fractal visionaries and enthusiasts: Sorry for the lateness, but other things needed to be done. The formula behind today's fractal combines various parts of negative Z^(1.1) and Z^(-0.9), then adds (1/C). The resulting parent fractal is a reasonably pure Mandelbrot set, with numerous slices of fractal debris to the southwest. Today's fractal scene is located in one of these slices. It is rare to see such a near-perfect circle of elements surrounding a midget, unless one dives to an extreme magnitude. I have emphasized the circular elements of the scene and named the image "Discus". The image is unusual enough to earn its rating of 7. When the render time of 3-3/4 minutes is figured in, the overall value equals a very respectful 183. As always, the completed GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another sunny and very warm (92F 33C) day kept the fractal cats inside until late in the afternoon. The few drops of rain that fell in the early evening did not deter them from their enjoymemt. They came inside at sunset fully satisfied. Today is so far a repeat. The work for me is still quite heavy. If I hope to stay ahead, I had best get started. Until next fractal, take care, and listen to the fractal murmur. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Discus { ; time=0:03:49.26--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.21897898384365270/-0.398175616577568\ 90/9.754347e+010/1/-130/-0.000605764010912487882 params=-1.2/1.1/0.9/-1.2/0/0 float=y maxiter=375 inside=0 logmap=78 periodicity=10 colors=000VL0aGAfDKkBUm9cs7ew5fvCktIpTX72j7cmCfpHm\ rMrtRzzWwz_rxXmtUhsScpPZmNUkKUpIcwCmz7rz8mw9crAUmB\ KhBGdOJa`MZmPXzL_tIaoFciBfd8hZ5jU2lP9jUFhYLfbRdfYb\ kc`oiZtoYxpZzq_zsbzvezzfzzgzzjzzmzp`qlXrhTsdPt`LuX\ HvWEwYPl_UaaURcUGeV_g5ri6lk6fk7aj7Wi7Qh8Lg8Ff8AiAF\ lCKnDPeGUYJYQLbHOf9Rk1To9RjGQeOP`VOWaNRWSPQWNK_LEd\ J8hH3lG5mM7nR9oWBo`DpeFqjHqoInlJkiKifLfdMdaMaZNYWO\ _UPaRQcOReLRgJPiNOkQMmTLoWJqZIsbGueFwhDykCzn9zW7zE\ 8zG9zI9zJAzLcz8bz9azA`zB_zBYzGWzKUzOSzSQzWPz_RzEOz\ HLzKIzNFzPCzS9zV6zX`zCbzFdzIfzLhzNezJczFazC_z8Yz5V\ zBSzHPzNMzTJzZGzdEz`CzXAzU8zQ6zM4zJ2zF0zC4zN8zYBzh\ JzkRzmZzofzqmzslznkzijzdiz`hzWgzRgzNhzMizLjzKkzJlz\ IgzRbzZZzfUznQzvLzpHzjDzd8zZ4zT0zOFzJUzEhz9wz5vzYv\ zyiz9izKizUizcizmizwlznnzepzYrzPtzHtzItzKszMszNszP\ szRszSrzUrzWrzXrzZrz_oz`lz`izafzaczb`zbYzcVzcSzcTz\ eUzfVzgVziWzjXzkXzmYznLzS } 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==================================

1 0

Re: [Fractint] Re: Multiple Boot for FractInt Users
by Stephen Stafford 16 Jun '04

16 Jun '04

It would appear this didn't get there first time because the address I posted it from wasn't subscribed (I think). ----- Forwarded message from Stephen Stafford <ssta(a)clothcat.org> ----- Date: Tue, 15 Jun 2004 17:31:20 +0100 From: Stephen Stafford <ssta(a)clothcat.org> Reply-To: Stephen Stafford <ssta(a)clothcat.org> Subject: Re: [Fractint] Re: Multiple Boot for FractInt Users To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com> Hi, I had a spare half hour, so I threw together a bootable iso image which uses freedos. It's a first approximation/proof of concept only, it's buggy as all hell and the UI isn't exactly great or intuitive. You can find it at: http://www.clothcat.org/scratch/fractint.iso After you boot, you'll want options 1, 1, 2 at the three menus...eventually I want to remove so many menus, that will depend on me having longer than a spare half hour though :) Then "cd FRACTINT" and run "fractint.exe" The FRACTINT directory is just a totally clean unzip of the distribution of 20.0 from spanky, it might be sane to chage that at some point. Some of the available resolutions crash the machine, although most of the testing I've done has been in VMWare, so don't take that as gospel since it does some weird funky stuff with odd resolutions. Cheers, ----- End forwarded message ----- Further to this, all resolutions which I would expect to work appear to work fine if I reboot the machine using the CD rather than trying to run it in vmware, so that seems okay. I hadn't realised before how snappy a bare DOS boot on a 1.5G machine would be. Arbitrary precision is quite fast really :) -- Stephen Stafford | Development and support consultant <stephen(a)clothcat.demon.co.uk> | http://www.clothcat.org <ssta(a)clothcat.org> | Never put off until tomorrow what you can <bagpuss(a)debian.org> | con someone into doing for you today ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program.

2 2

Copies of Fractal Creations
by Barry Smith 16 Jun '04

16 Jun '04

I have been lurking on this list for years. From July 1991 until August 1994 I wrote a monthly column called Â‘Frenzied FractalsÂ’ in the excellent magazine published by the local users group. Then I began a new busy job and was less than impressed when the editors often arbitrarily changed what I had written, dropped illustrations and failed to return some photos that I had paid good money for. After /Fractal Creations/, 2nd edition, came out in 1993 I tried in vain to get a copy. On 22 March 1997 I received a reply from Tim Wegner, then with a different address, saying: 'Hi Barry, good to hear from you. Â… [the 2nd edition of Fractal Creations] Great book, my best, now sadly out of print.' On 1 Jan 1999 Amazon.com confirmed my order for a second-hand copy of/ Fractal Creations//Book, CD-ROM, Disk and 3-D Glasses - Timothy Wegner, Mark Peterson; price currently unknown (Out of print; availability varies) It seems that a few copies are still around. Especially as I am now retired and have more time, I would dearly love to get a new or second-hand copy. My main problem is how to make a payment from Australia. -------------------- Barry W Smith P O Box 442, Jamison Centre ACT 2614, Australia Tel. (Home & answering machine) (02) 6251 2119 International +61 2 6251 2119 e-mail: bsmith(a)cyberone.com.au

3 2

FOTD 15-06-04 (Recursive Rosebuds [7])
by Jim Muth 15 Jun '04

15 Jun '04

FOTD -- June 15, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows what happens when 1.5 parts of Z^(-1.15) are combined with 1.5 parts of negative Z^(0.85) and (1/C) is added. The resulting parent fractal features a stretched-out main bay edged with the expected out-of-proportion buds. Today's scene is located near the tip of a filament attached to a small bud on the southern shoreline of the main bay. The scene was rendered with the outside set to 'tdis' rather than the standard 'iter'. Doing this gives interest to the otherwise large areas of flat color. The image is one of those rare ones that needed almost no color tweaking, which is a lucky break, considering how busy things are here at Fractal Central. I named the image "Recursive Rosebuds". I like the sound of the phrase, which is also a fitting description of the picture. The rating of a 7 appears justified, and, combined with the render time of 6-1/2 minutes, gives an overall value of 106. The most efficient way of viewing the image is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 88F 31C, Monday was a bit too warm for the dynamic duo. But being very bright cats, they waited until late afternoon when it grew cooler before venturing into the yard. After a pleasant evening, they came indoors at sunset, quite satisfied. This morning it looks as though the day will be a repeat, though today there is a chance that rain will spoil their outing. We'll see what happens. For me, the work is what will happen. And when the work is finished, it will be time for fractals. Until next FOTD, take care, and don't take those fractals too seriously. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Recursive_Rosebuds { ; time=0:06:36.12--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.01210822479891212/-0.300373383209480\ 30/4.494955e+010/1/142.5/0.00756951427375174291 params=-1.5/0.85/1.5/-1.15/0/0 float=y maxiter=1000 inside=0 outside=tdis periodicity=10 colors=000`dzabzb`zbZzcXzcVzdYzd`zdbzeezehyejwfmuf\ psfrqguogxmgzkhymhxohxphwrhvthvuhuwhuxhtzhszhszhrz\ hqzhqzhpzhpzelzbiz_ezXbyVZvSWsPSpMPmJLjHIgHMdHQbHU\ `HYZHaXHeVHiTHmRHqPHuNHxLKpOMhQOaTRUVTNYVF_X8aYB_Y\ EZZGYZJXZMW_OV_RT`TS`WR`ZQa`PacOaeNTLIK1DFCLBMS6W_\ 2ef7`aCWXHRSMMNLKTKIYJGbIEgHClGAqF8vE6zD4zD3zE8zFC\ vFGnGLgiP_iTTHXMMNJRDGi3Ei2Dj1CpJzpKzpLzpMznNymNqk\ NhjO`hOSgOKfOCgKOhHZhDjiAui7zj6zk6yk6vl5rl5om5lm5i\ n4en4bm4_m3Wm3Tm3Qm3Nm6Pm8QmARmDSmFTlHUkKVkMWjOXiR\ YhTZhV_gY`f_aeabeccfeeggfhigikhjmijnkkpllrmmtnnvon\ wpjxqgxrdxsaxtXwsSvsNtsIrrDor9lr8ip8fn8cl7`k7Yi7Vg\ 6Sf6Pd6Mb5Ja5G_5DY5AX77V99UACSCGREKQFNOHRNIULKYKMa\ JNdHPhGQkFPiGOgGOeGNcGNaHM`HLZHLXHKVIKTIJRIJQIKTKL\ VLLYMM_NNbONdPOgROiSPlTQnUQqVRsWRuXOn_LgaJ`cH`eE_f\ C_h6NW7PY8R_9Ta9VcAXeBZgB_h7ao3bu2dz2ez2cz7azC_zHY\ zMWzRUzXSzaQzfOzkMzpKzuIz } 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==================================

1 0

Chaoscope gallery at my web site
by Franktal Gallery 15 Jun '04

15 Jun '04

I just set up the first Chaoscope gallery at my web site, so drop everything you're doing right now and go check it out. Pleeeeease ? http://www.geocities.com/franktal2002 Regards, Miguel Fliguer - Buenos Aires, Argentina _________________________________________________________________ Add photos to your messages with MSN 8. Get 2 months FREE*. http://join.msn.com/?page=features/featuredemail

2 1

FOTD 14-06-04 (Disconnected Diversion [6])
by Jim Muth 14 Jun '04

14 Jun '04

FOTD -- June 14, 2004 (Rating 6) Fractal visionaries and enthusiasts: Things are still quite busy here at Fractal Central, but not so busy that I lack time for the FOTD. I see thoughts of a Fractint CD circulating on the list. And I see ideas about what might be included on the disk. I am fully in favor of such a disk. If one were realized, I would certainly want a copy. But I fear that if such a project were begun, even with the best intent, the project would go the way of the FOTD CD, which has been on the drawing board for at least three years, but which I have yet to finish. All I can say is 'the best of luck with the project'. I hope my outlook for the likelihood of a successful completion of the Fractint CD is wrong. Today's fractal image lies in some scattered debris near the shoreline of the main bay of its parent. It is another of my 'evaporated' fractals, with the blank screen brought to life with the 'bof61' inside fill. I named the image "Disconnected Diversion". The name has a rather pleasant sound, with a hint of the unusual. I have rated the image at a 6, mostly because of the unusually strong color effect. The overall value comes in at a respectable 122. The most convenient way to see the image is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It rained all day Friday here at Fractal Central. Saturday was sunny; Sunday was cloudy. The fractal cat duo did not know what to make of these confusing conditions, and simply tried to enjoy things the way they were. A bit of tuna was needed on Friday however to bring their moods up to average. Today could best be described as unsettled. It might turn sunny; it might rain. Who knows what the duo will make of it. For me, the work is temporarily caught up, but with a big new customer to satisfy, this could quickly change. Until next time, take care, and keep searching the sky for fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ DisconectdDiverson { ; time=0:04:54.12--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.587095958/+0.650711057/9012.137/1/50\ /-1.11942413671962e-010 params=1/-0.9/1/-6.5/0/1e+\ 100 float=y maxiter=500 inside=bof61 periodicity=10 colors=000YGr`KscOtfRuiVvlZwobxqeyrfw000tfstgqugov\ gmwhkwhixhgyiezicziaYPT65K77F78A795BE9EICHMGLRJOVN\ RZQVcUYgX`k`dpcpzgzzjVRVUTWUUXUWYTZZTc_Th_Tm`SraSw\ bSzcSzcWMMULOSLQQLSOLUMLWKLXILZHL`FLbDLdBLe9Lg7Li5\ Lk3Lm2Ln6JmAIlEHkIFjMEjQDiUBhYAga9ge7fi6em5dp4dk6`\ g7Yc8V_9SWAPSBMODJKEGGFDCGA8H74I40J1LEOeAid9lc9oa8\ r`8u_8w5QDAOFFNHafk`glZhlYilXjmWkmVlnTmnSnnRozQpzP\ qzOrzNrzMrzLrzKrzJrzIrzHszGszFszEszDszCszBszAtz9tz\ 8tz7tz6tz5tz5tz8mzBfzE`zHUzKNzNHzRKzVMzZOf`NgaMhbL\ icKjdJkeIlfHlgGmhFnjEokDplCqmBqnAro9sp8tq7ur6vs5vp\ 7um9tkBthDseFrcHr`JqZLqVJsRHtNFuKDvGBwC9x98yFCuKFr\ PIoVLl_OidSejVboY_t`XycUv`TsZTpXSnVSkSRhQRfOQcMQ`K\ PYHPWFOTDOQBNO9NRDMTGLVKLYNK_RKaUJdXIf`IhcHkgHmjGo\ mGlkJjiLhhNffPddRbcT`aVZ_XXZZVX`TVbRUdPSfNQhLPjJNl\ HLnFKpDIrBGt9Fvzm6TweSufRtfQsgPrgOqhNphMoiMniLmjKl\ jJkkIjkHilGhlP8lR8nS8pVCq } 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==================================

1 0

Re: Deep Zoom?
by jackoftradez＠comcast.net 14 Jun '04

14 Jun '04

Deep ZooMs ? I have already a couple made (full screen resolution), and am currently rendering a third. They may or may not be what you are looking for. Check out the "Universe viddies" at: http://www.fractal-animation.net/index.html My animation programs work up to a little beyond the arbitrary precision limit; beyond that I use an autokey script. However, after about E+32 the images start to jump around and get distorted. Can't go further. Wonder why that is ... Stay Amazed! ' JoTz

1 0

Re: [Fractint] Re: Fractint Boot CD ?
by Guy Marson 14 Jun '04

14 Jun '04

At 17:57 13/06/2004 +0000, you wrote: >Fractalnauts: > >Or burn CD copy and mail it? idem for me.. CD or DVD.. >Lemme know. > yes, you may let me know too.. >Long Live the Cult of Fractint ! > oh yeah!! cheers, Guy +++++++++++++++++++++++++++++++++++++++++++++ Dear friends, My new email address is <gmarson[at]mnhn.lu>. The former address <guy.marson[at]mnhn.lu> is no more valid. +++++++++++++++++++++++++++++++++++++++++++++

1 0

Re: Fractint Boot CD ?
by jackoftradez＠comcast.net 13 Jun '04

13 Jun '04

Fractalnauts: I have the books (Fractal Creations, 2nd ed., Tim Wegner & Bert Tyler, and Fractals for Windows, Wegner, Peterson, Tyler, Branderhorst) as well as the original software (CD and disk) that came with them. Also have Zillions of PAR, FRM etc. Fractint files on CD been collectiong for years. I would be happy to contribute to this project should it go foreward, but I'm not sure how to, unless I can make copies of the software and send it by email or post it on my web site. Or burn CD copy and mail it? Lemme know. Long Live the Cult of Fractint ! Stay Amazed, JoTz FYI - if anyone cares, my email is changed. B4 it was : JackOTradez(a)msn.com that is gone now. Now it is: JackOfTradeZ(a)comcast.net (broadband - gotta luvit!)

1 0

No FOTD for June 11, 12, 13
by Jim Muth 11 Jun '04

11 Jun '04

Fractal fans: Due to an unexpected work load, there will be no FOTD until June 14. Do not fret, all is well, and the FOTD will resume on schedule in 3 days. Jim M.

1 0

FOTD 10-06-04 (Perpetual Outcast [6])
by Jim Muth 10 Jun '04

10 Jun '04

FOTD -- June 10, 2004 (Rating 6) Fractal visionaries and enthusiasts: With the work falling behind again, and a potential new customer to impress, today's discussion will be very short. The image continues the same complex-powers theme of the most recent FOTD's, the major difference being that today I have rendered the scene with the outside set to 'tdis'. I named the image "Perpetual Outcast" on a whim. The result is different enough for the image to be rated a 6. The short render time of 2 minutes raises the overall value to 276. The overall value becomes meaningless when the completed image is downloaded from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With lots of hazy sun, humidity, and a temperature of 91F 37C, the Wednesday weather inclined the fractal cats to do nothing but lounge under the holly trees and enjoy life. In the evening I treated them to a dish of tuna, though it really was not necessary. Today is starting warm again, but rain is supposed to be on the way. We'll see how the dynamic duo takes these conditions. The work today is piled high, a clear sign to get busy. Until next FOTD, which might not be until June 15, take care, and be patient. The best is yet to come. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Perpetual_Outcast { ; time=0:02:10.23--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-2.3\ 335844466742/+0.2407662638893/75905.47/1/-140/4.87\ 057810749647047e-010 params=2/0.1/0/0 float=y maxiter=1800 inside=0 outside=tdis periodicity=10 colors=000a_Y`aY`cY_fZ_hZZjZZlZYnZYpZXrZXtZVp`TmaR\ jcPfdOceM`gKYhIUjGRkFOlDLnBHo9Eq7Br68sMGt`NtoUtnRs\ mOsmLslIslFskCskAsbIgUQXMYMKXNJWOIVPHVQGURFTSETTDS\ UCRVBQWAQX9PY8OZ7O_vC0p96k7Bf5Ha3MYBLUJKRRKNZJKfJJ\ gMJgOJgQJgTJgVJgXJg_JgaJgcLebNdbPcbRabT`bV_bXYaZXa\ `WabUadTaeXai_elghikmfnsakoXglRahMXdHRaBMY6HU1CR5G\ U9KXCN_GRbKUeNYgRajVdmYhpakseovhpxgnugksggqgdofamf\ YkfVifRgeOeeLceHaeE_eBY`KhWSrURoSRlQQjOQgNPdLPbJP_\ HOXFOVENSCNPAMN8MK7MIBOKFQMISNMTPQVRTXSXYU__VcaXgb\ Zjd_nfaqgbxKxpQphWiaabUgVNpOFvH8zABzHmzNmzTmzZmzdm\ zjmzpmzomzomzomzomzoOhnOfnOenOcnObnOanRZmUXmWVlZTl\ `RkcPkeNkhKjkIjmGipEirChuAhw8htBiqEinHikKiiMifPjcS\ j`VjYYjW_jkY_zWPwXRuXSsXUqXVoXXmYYkY_iY`gYbeYccZea\ Zf_ZhYZiWZjZah`cgbefdhefjdhlcjnblqans`pu_rwZkt`drb\ YodSmfLkhEhj7fl1dm6`jAXgFTdJPaOLZSHWXDT`9Qd5Ne8LeB\ KeEJeGIfJHdPXcSYbUYbWYaYY } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 09-06-04 (Tickle My Fancy [5])
by Jim Muth 10 Jun '04

10 Jun '04

FOTD -- June 09, 2004 (Rating 5) Fractal visionaries and enthusiasts: A heavier than usual pile of work before me means a shorter than usual discussion. Today's image is a journey into the Mandeloid fractal that results when the formula Z^(2+0.2i)+C is iterated at the negative pi level of the logarithmic spiral. The parent fractal is shaped almost exactly the same as the curiously distorted midget that highlights today's image. The scene of today's image is located in the broad northern branch of the Seahorse Valley area of the parent. Other areas of the parent hold equally strangely shaped midgets, some of which might appear in FOTD's to come in the near future. As for the rating -- I could give the image nothing more than an average 5. But the unusual shape of the midget and reasonably short render time of 6 minutes makes it worth the effort. The overall value is a nominal 78. I named the picture "Tickle My Fancy". I actually was a bit tickled when I saw the shape of the midget. And fractal fans will also be tickled when they see the couple minutes that can be saved by avoiding rendering and downloading the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A sunny and very warm day on Tuesday, with a temperature of 84F 29C, was just what the cats needed. They spent the entire afternoon exploring the holly thicket at the bottom of the yard, dodging the falling cicadas, which are starting to die off at an increasing rate. When evening came, the duo were ready to come inside without complaint. This morning is starting sunny and even warmer. I expect a similar day. In my corner, the work is waiting before me. I always feel better when it is finished and behind me. So it's time to get started. Until next FOTD, take care, and see you when that glorious time arrives. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Tickle_My_fancy { ; time=0:06:23.49--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-4.07570601913123700/+2.189601450837599\ 00/28201.47/1/80/-7.37824690233424008e-010 params=2/0.2/-3.14159265358979/1500 float=y maxiter=1800 inside=0 logmap=95 periodicity=10 colors=000SLlQKkOJjMJiQRhUZgXefRZZLSRFLJ9EB374CF6L\ M8TTAa_CjfErmFdYJRJMD4PG9QIDRKIRMMSORTQVTS_UUcVWhV\ YlW_qXauXenehhnkbvl_umYunWunUuoSupQupOuqMurKurIusG\ utEutCurBrpBooBlmBjkBgjBdhBafB_eBXcBUbBSeHXhN`jTdm\ ZhpdmrjqupuwuysnuphrlboiXleRibLfZFcW9`YAZZAY_BW`BV\ aBUbCScCRdCQeDOfDNgDMfELfFKeGKeGJeHJdIIdJIdJHcKHcL\ GcLGdMKeNNfOQfPTgQXhR_iSbiSekJSlAEh9Jd9N`8RY8VU8ZQ\ 7bM7fJ7jHEiGKhFQgIRhKRhMSiOSiQTjSTjQVfOWcNX`LZXJ_U\ I`RGaOEcKDdHBeEAfBCeDDeEEdGFdHGcJHcKIcLJbNKbOLaQMa\ RN`TO`UP`VS_VUYUXWTZUSaTSdRRfPQiNPkMPjLOiKOhJOhIOg\ HOfGOeFOeEOdDNa6KcCNbBNbANa9N`8N_7NCcJIcKOcLUcMmUK\ kKLjELiDLgCMfBMeAMd9Mb8Na7N`6NoJsmHnkGjiKfgPbeUZcU\ VaZRAcIJcKScMBckOcZacO`cN`cN`cN`cN`cN`cNacNccNecNg\ cNicNkcNmcmoaiq_esYau_YwaUycQzemzgoziqzkszmuzmwzmx\ zmyzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

2 1

FOTD 08-06-04 (Iterative Complexity [5])
by Jim Muth 08 Jun '04

08 Jun '04

FOTD -- June 08, 2004 (Rating 5) Fractal visionaries and enthusiasts: This morning I was up early with my telescope and sun filter set up in the east-facing attic window of F.C., ready to see the final stages of the transit of Venus across the sun. Unfortunately, fog was in the air at the time the sun rose, obscuring the horizon. As a result, I saw nothing. When the sun appeared 2-1/2 hours later, the event had long since ended. Hopefully the luck will be better in 8 years, when the next transit occurs. If not, it's a wait of 122 years. I guess I shouldn't be too disappointed. Those farther west saw nothing at all. Today's fractal was created by iterating the expression Z^(2+0.1i) and examining a spurious valley of the resulting chaotic fractal. The scene is located near a larger midget in the valley. I named the image "Iterative Complexity" because I could find so little order in it. In the classic Mandelbrot set, the features are arranged around the midgets in the series 2,4,8,16... In the cubic Mandeloid the features follow the series 3,9,27,81... In Mandeloids of fractional powers, the series follows the same rule. Thus we have 2.5, 6.25, 15.625, 39.0625... But what series will a Mandeloid with an imaginary component in its exponent follow? Complex numbers are not counting numbers. As today's image shows, the result is total chaos. There is no order at all in the features surrounding the central midget. In a way this makes things more interesting. I rather enjoy an 'anything can happen' fractal. I didn't really know what kind of a rating to give to today's image. When in doubt, I always do the most likely thing, so I ended up giving the image a rating of an average 5. The render time of close to an hour holds the overall value to a modest 9, but this value can be drastically increased by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image there. But before going to the web site, give Paul a chance to render and post the image. Monday was sunny and warm here at F.C., with a high temperature of 81F 27C. It was a perfect day to keep cats happy. They spent several hours in the yard, ignoring the cicadas, which are again singing. When evening arrived, they came indoors with no complaint. Today looks to be a repeat. I expect a repeat in the cats' mood also. The work is moderate, which means about 4 hours effort will put it behind me. Then it's on to the world of fractals. If I'm lucky, tomorrow's fractal will be better than today's. If not, it will still be interesting. Until next time, take care, and hope for clear skies in 8 years. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ IterativeComplexty { ; time=0:55:48.13--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.62142028795967830/-0.363045619197981\ 00/4.570629e+010/1/-7.5/-5.02629616519895128e-005 params=2/0.1/0/0 float=y maxiter=18000 inside=0 logmap=1430 periodicity=10 colors=000bMsaNqaNp`On_OmZPlYQjXQiWRgWRfVReUScTSbS\ T`RT_QTZQUXPUWOVUNVTMVSLWQKWPKXNJXMIXLHYJGYIFZGEZF\ DYDEZEEZFFZGFZGFZHGZIGZIHZJHZKHZKIZLIZMJZMJZNJZOKZ\ OKZPLZQLZQLZRMZSMZSMZTN_UN_UO_VO_WO_WP_XP_YQ_YQ_ZQ\ __R__R_`S_aS_aS_bT_cT_cU_dU_eU_eV_fV_gV_gV_gTbiRdj\ PfkNilLkmJmoHppFrqDtrCvsCuqCtpCsnCrmCqkCpjCohCnfCm\ eClcCkbCj`Cj_CiYChWCgVCfTCeSCdQCcPCbNCaLC`KC_ICZHC\ YFCYEHZIMZMRZQW_T`_Xe_`j`co`gt`ky`nx_nwZnvYnuXntWn\ sVnsUnrTnqSnpRnoQnnPnnOnmNnlMnkLnjKniJniInhHngGnfF\ neEndDndCncBnbAna9n`8n_7n_7nV8gR8aN8WJ8QE9JA9D6972\ 914A16B17C19C1BD1CE1EF1FF1HG1JH1KH1MI1OJ1PK1RK1SL1\ UM1WM1XN1ZO1`P1aP1cQ1dR1fR1hS1iT1kU1mU1nV1pW1qW1pY\ 2pZFp_Io`LoaOobRncUndXne_mfbmgemihmjklknllqlmtknwk\ ozkpzjqzjrzjszjtziszhszhszgszgszfrzfrzerzerzdrzcqz\ crzbszbtzauzbvzcwzcxzcyzczzczzczzczzczzczzczzczzcz\ zczzczzczzczzczzczzczzczz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 07-06-04 (A Fractal Event [4])
by Jim Muth 07 Jun '04

07 Jun '04

FOTD -- June 07, 2004 (Rating 4) Fractal visionaries and enthusiasts: I named today's image "A Fractal Event". Every fractal is an event. It is not a very great event however, because I could rate it at only a 4. The image is actually a scene in the Z^2.01+C Mandeloid, 150 levels up the logarithmic spiral, rendered with the outside set to 'fmod' and the proximity set to 0.006. At this level of the spiral, the M-set has rotated until the eastern shoreline of the large southern bud lies on the negative real axis. Today's scene is located in the confusion near the big break. I think it is the overly-brilliant Renoir-like coloring that holds down the rating. Otherwise it is a rather unconventional image that somewhat reminds me of a planetary nebula surrounding an evaporating star. The bits and pieces scattered throughout the scene could easily be taken as interstellar debris. Strangely enough, the pattern around the midget appears perfectly symmetrical, even though the exponent of Z is fractional. The render time of 7 minutes and the rating of 4 combine to give an overall value of 56. The job of rendering can be avoided by downloading the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Though the sky remained cloudy all day Sunday here at Fractal Central, and the temperature never rose above 68F 20C, the cats managed nearly two hours in the yard, doing what aging cats do best -- sleeping in the brush. They did perk up briefly when a mockingbird started scolding them, but the bird soon returned to its nest and the duo returned to sleep. When the day ended, they came indoors without urging. Today is starting partly cloudy and warmer. It looks like a better day for the duo. Today will be good enough for me if I can finish the day's work by sometime early this afternoon. But to finish I must first start. Until tomorrow's FOTD, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Fractal_Event { ; time=0:07:12.38--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.67150446161930160/+0.039024030044104\ 01/232355.9/1/-90/3.88578058618804789e-016 params=2.01/0/150/0 float=y maxiter=1500 inside=0 proximity=0.006 outside=fmod periodicity=10 colors=000FOtHLsJKrMGqOCpQ9oS8nU7nW7nY6n_5ma5mb4md\ 3mf3mh2lj1ll1ln0lo0lo2ko3ko4jo6jo7jo8io9ioBioChoDh\ oEhoGgoHgoIgoKfoLfoMfoNeoPeoQeoRdoSdoUdoVcoWcoXcZZ\ RI_E1`23_45_67_89ZABZCDZDFZFGYHIYJKYLMXNOXOQXQSXST\ WUVWWXWYZWZ`V`bVbdVdeUfgUhiUikUkmTmoToqTqrTrqRqqQp\ qPoqOopNnpLmpKmpJloIkoHkoFjoEinDinChnBgnAgm9em9dm9\ cl8bl8al8`l7_k7Zk7Yk6Xj6Wj6Vj5Uj5Ti5Ri4Qi4Pj4Ok3Nl\ 3Mm3Ln2Ko2Jp2Iq1Hr1Gs1Ft1Eu1Hv1Kw1Nx1Qy1Tz1Wz1Yz1`\ z1cz1fz1iz1lz1oz1qz3pz5oz7oz8nzAnzCmzEmzFlzHlzJkzL\ kzMjzOjzQizSizThzVhzXgzYgzT`zOVzJPzFJzADz57z11z34z\ 47z5Az6Dz7Fz8Iz9LzAOzBRzCTzDWzEZzFazGdzHfzJezLdzNc\ zPbzRazT`zU_zWZzYYz_YzaXzcWzdVzfUzhTzjSzlRznQzoQzm\ RzkRzjRzhSzfSzeSzcSzaTz`TzZTzXUzWUzUUzTUzRVzPVzOVz\ MWzKWzJWzHWzFXzEXzCXzBXzGrzIqzKqzMpzOpzQpzSozUozWn\ zYnz_nz`mzbmzdmzflzhlzjkzlkznkzpjzrjzsjzqdzp_znVzm\ QznPznPzoOzoOzpOzpNzqNzqN } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 06-06-04 (A Feathery Fractal [7.5])
by Jim Muth 06 Jun '04

06 Jun '04

FOTD -- June 06, 2004 (Rating 7.5) Fractal visionaries and enthusiasts: Today's fractal is different. To start, it was created by raising Z to a complex power -- 1.3+0.08i. Then I found that the hyperparent spreads out and dissipates as we go up the logarithmic spiral, but it condenses and becomes more interes- ting at the negative levels of the spiral. The parent fractal of today's image lies 16 levels down the spiral. At the default magnitude it is a tiny shrunken thing, but when magnified it becomes a comet-like object, full of interesting places in need of exploration. Today's scene lies in the chaos edging a valley on the southern shoreline of the comet head. No special outside rendering methods were needed with today's scene. The standard equal-iteration bands did everything. Admittedly, I did help a bit with the coloring, but I did less work than the first appearance would suggest. The name, "A Feathery Fractal", captures the feeling of the image. Undecided whether to rate the image a 7 or 8, I finally decided on a 7.5, which gives an overall value of 84. This value can be raised if the task of rendering the image is eliminated by down- loading the finished GIF file from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy rain all day here at Fractal Central on Saturday and an unusually cool temperature of 59F 15C kept the cicadas quiet and the cats indoors. The cicadas clung motionless in the trees all day; the cats sulked in the window all day. Sun and warmer temperatures will make the cicadas happy, but a sizable treat of tuna was needed to put the cats back in a good mood. Today is starting cloudy. The rain appears to have moved on. All we need is sun. I'm going to try to take it easy today. If I succeed, I'll consider it quite an accomplishment. Maybe I'll start writing that story I've been thinking about for at least three years. Maybe not. Until tomorrow's FOTD, take care, and be prepared at least for an outburst of philosophy. It has been building for several days and could break loose at any time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Feathery_Fractal { ; time=0:08:55.58--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.0\ 0050914586947115/-0.00033084146774130/5188497/1/-2\ 7.5/4.6970816125e-011 params=1.3/0.08/-16/0 float=y maxiter=4500 inside=0 logmap=153 periodicity=10 colors=000TOLTLMTNNTPOSRQSTRSUSSVTSWURXVRYWRZXR_YQ\ a_Qb`QdaQebPgcPhdPjePkfPlgOjeNhcNfaMe`McZLaXK`WKZU\ JXSJVQIUPHSNHQLGPKGNIFLGFIFEHIDGKDFMCEOBFQBGSAGU9H\ W9IY8J_7Ka7Lc6Ne6Og8Rh9UhAXhB_hCbiDeiFhiGkiHnjIqjJ\ tjKwjLzjPzmUzoZzqczshzumzwsAUs5Ts7Ts8Sq9RoBRmCQkDP\ iFPgGOeHNeJNeKMeLLgMKiOKkPJlQImSInTHoUGpWGqXFrYEr_\ Es`DtaCubCmaEcaFc`Hd`Id_Ja_L_ZMXZNUYPRYQPXRMXTJWUH\ WVJTYKR_MPaNNcPObQPbQPbPQbPQbORbTRbQSbTSbVTbXTb_Ub\ aVbdVbfWbiWbkXbmXbnYbpYbqZbrZbm_`i__e`Za`XYaWTaVPb\ ULbSHcRDcQ6eQ9ePBhPDeOFeOHZNKUNMSMOOMQULSTLURKXQKZ\ PJ`NJbMIdLIfKIiQFlVDo`Bre9vl5tj7ri8ph9nfKleOjdRicU\ gaXe`_c_baZe_XhZWkXVnVUqTStRRwPQzOPzPSzPUzQWzRYzU_\ zXaz_czbeze_zhQzkSznUzqWztYzw_zzbzzdzzfzzhzzjzzlzz\ jzzhzzfzzdzzbzz`zzZzzXzzVzzTzzRzzPzzNzzLzzJzzHzzFz\ zEzzHzzKzzMzzPzzSzzUzzXzz_zzazzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 05-06-04 (Curse of the Creature [7])
by Jim Muth 05 Jun '04

05 Jun '04

FOTD -- June 05, 2004 (Rating 7) Fractal visionaries and enthusiasts: To find today's image we ventured into the depths of the fractal that results when 0.2 parts of Z^(-8.25) are combined with one part of Z^(-1.65), and (1/C) is added. Like so many fractals that are created by combining negative exponents of Z, this fractal is indescribable. Like the familiar Mandelbrot set, it has bays and valleys, but the inner detail of these features is totally unlike anything found in the M-set. Today's scene is located on the north edge of a valley on the positive real axis of the parent. An unusual feature of the scene is that it is not there. The scene has been 'evaporated' by raising the escape radius so high that all points are trapped. The trapped points are not dead however. They still have freedom to move around, and this motion has been made visible by the 'bof61' inside fill, which colors the points according to which iteration takes them closest to the origin. The image so produced appears as today's FOTD, which earns its rating of a 7 quite honestly. I have named it "Curse of the Creature" in recognition of those not-so-great old movies that they just don't seem able to make any longer. There might be some kind of creature lurking somewhere in the image. If I looked long enough, I'm sure I could find one. But the image is good enough as it is. We'll keep the creatures where they belong -- in the old movies. The render time of just under 14 minutes combines with the rating of 7 to give an overall value of a neat 50. And if the image is downloaded from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> the rendering will be eliminated and the value will rise. A cloudy cool day here at Fractal Central on Friday turned into light rain in the evening, but the cat duo got in enough yard time before the rain began to keep them reasonably happy. Only a little tuna was needed to make their day complete. Today is starting with clouds, cool temperatures and rain. Hopefully, it will turn dry in time for the cats to have their outdoor romp. With me, the work is mostly caught up, and the next FOTD fractal will appear in approximately 24 hours. Until then, take care, and be lucky. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ CurseOfTheCreature { ; time=0:13:57.77--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.37819276581849900/+0.001714053513647\ 82/1.158226e+007/1/152.5/-1.09526888978292436e-005 params=1/-1.65/0.2/-8.25/0/1e+100 float=y maxiter=1700 inside=bof61 periodicity=10 colors=000x99sEEnJIjNMeSQaWUX`YSeaOieJniFrmGonGmnG\ joGhoGepGcpG`qGZqGWrGUrGSrCVg8XX4ZM6TO8OQAJRCETE9V\ F4WUOKhg9feAecAdaAb`AaZB`XBZWBYUBXSBWQCUPCTNCSLCQK\ CPIDOGDNEDLDDKBDJ9EH8EG6EF4EE3EG5DI6DK8CM9COABQCBS\ DAUFAWG9YH9_J8aK8cL7eN7gO6iQ6kR5mS5oU4qV4sW4n_MidT\ ehZamdYqjWmfUjcTf_RcXQ`UPZTOYTOWTNVSMTSMSSLQSKPRKN\ RJMRIKQIJQHHQGGQGEPFDPEBPEAOD8OC7OC6O96J76EBAFEDGI\ HHLKIONJSRKVUKZYLa`MdcNhgOkjPnmPedWXWaONhFFnIIoLLo\ NOoQQoTToVWpYZp``pbcpefpghp9ckEaiI_gMYeQWdUUbYS`aQ\ _eOYiMWmLVnSUnZUneUnlUnsUnzUoxRowOpuLptJqsGqqDrpAr\ o8rp7rq7rr6rs6rt6ru5rv5rw4rx4rx4ow8mwCjvGhvJeuNcuR\ auUcrSeoQflOhiNjgLkdJmaHoZGpWErUCtRAuO9wL7yI5zG4vH\ 8sHCpHGmIKiIOfIScJW`J_XJcUKgRKkOKoLKrKMiKN`KPSKQJK\ RBJUAIWAHYAG_AFaAEd9Df9Ch9Bj9Al9An9Gj9Lf9Qb9WZ9`V9\ eR9kN9pJ9uF9uIBuLCuOEuQFuTHuWIuYKu`LucNueOuhQukRum\ TupUusWjAJmAIo9Gq9Et9Cv9A } 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==================================

1 0

FOTD 01-06-04 (Scene of Discovery [5])
by Jim Muth 04 Jun '04

04 Jun '04

FOTD -- June 01, 2004 (Rating 5) Fractal visionaries and enthusiasts: Believe it or not, today's image is a view of the chaos along the shoreline of what remains of Seahorse Valley of the Z^(2.01,0.03)+C Mandeloid. For some reason known only to the higher authority, the buds have choked off and changed into distorted quadratic midgets, while curious new open areas have appeared, in the form of round holes connected by tooth-like spirals to infinity. I have named the image "Scene of Discovery". After all, it is at least a minor discovery. The two circular areas in the left half of the image, along with the tooth-spiral connecting them, form one of the more unusual hole complexes I have found in the world of fractals. Even with the maxiter of 15000, the edge of the valley, on the upper right, is not fully defined. But the render time of 48 minutes is already unreasonably long, so I decided to be satisfied with less than full definition. Since I can see nothing really above average in the artistic aspect of the image, I have rated it at a 5. The slow render time reduces the overall value to an unexceptional 10. Considering all this, the best way to view the scene is to let Paul render it and post it to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Clouds, cool temperatures in the 60'sF (around 18C), and occasional light rain kept the fractal cats indoors and the cicadas quiet here at Fractal Central on Monday. The cats cheered up in the evening when they had their treat of tuna; the cicadas cheered up this morning when they saw the sun and warmer temperatures. I'll cheer up when the latest pile of work is behind me. Until next FOTD, take care, and don't be too busy to enjoy the fractal side of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Scene_of_Discovery { ; time=0:48:19.02--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 logmap=24 center-mag=-0.7088779767/-0.2550825285/255.7718/1/\ 25/-2.66779653923521209e-013 params=2.01/0.03/0/0 float=y maxiter=15000 inside=0 periodicity=10 colors=000QYUSYUTZUUZTW_TX_SY`S_`S`aRaaRcbQdbQebQg\ cPhcPidOkdOleOmeNofNpfMqgMsgMthLuhLvhMvhLsfKpdKmbJ\ m`ImZImXHmVHmSGmQFmOFmMEmKDmIDmGCmBDmECmHCmKBmNBmQ\ AmTAmW9mZ9ma8md8mg7mj7mm6mp6ms5mv5mx5mw6lv6ku6jt6j\ s7js7jr7jq7jp8jo8jn8jn8jm9jl9jk9jj9jiAjiAjhAjgAjfB\ jeBjdBjdBjcCjbCjaCj`Ci_Bj`Cj`Cj`Cj`Dk`Dk`Dk`Ek`Ek`\ ElaElaFlaFlaFmaGmaGmaGmaHmaHnbHnbHnbInbIobIobJobJo\ bJobJnaMn`Om_Qm_SlZVlYXkYZkX`jWbjVeiVgiUihTkhTmeWk\ bYi`_gYaeWddTfbRh`OjZLlXJoWGqUEsSBuQ9wPEuNJsMNqLSo\ KXmI`kHeiGjgFneEmeFmeGaZbbYbcXbcWadWadVaeUafTafT`g\ SahRbhQciPdiPejOfkNgkMhlMimLjmKknJlnJmoInpHopGpqGq\ rFrrEssDttEusDvrCwrBxqAyp9zp9zo8zn7zn6zm5zl4zm0zl4\ zl7zlBzlEzkIzkLzkOzkSzkVzjZzjazjezjhzmszkozjkzigzh\ czf_zeWzdSzcOzcGzbIzbKzaLzaNz`Oz`Qz_Rz_TzZVzZWzYYz\ YZzX`zXazWczWezVfzVhzUizUkzFpzNnzUlz`jzghznfzlgzkg\ zjgzigzhhzghzfhzehzdizciz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

2 1

Re: [Fractint] No FOTD for June 4
by Jim Muth 04 Jun '04

04 Jun '04

At 10:03 AM 6/4/04 -0400, you wrote: >Jim Muth wrote: >> >> Fractal visionaries and enthusiasts: >> >> Due to an unexpected rush here at F.C., >> there will be no FOTD for June 4. The >> FOTD will return on schedule on June 5. > >I want my money back! :-) I give double your money back to all unsatisfied readers. BTW, the FOTD would be a bargain at half the price. :-) Jim M.

2 1

No FOTD for June 4
by Jim Muth 04 Jun '04

04 Jun '04

Fractal visionaries and enthusiasts: Due to an unexpected rush here at F.C., there will be no FOTD for June 4. The FOTD will return on schedule on June 5. Jim M.

2 1

FOTD 03-06-04 (Blueberry Pie [6])
by Jim Muth 03 Jun '04

03 Jun '04

FOTD -- June 03, 2004 (Rating 6) Fractal visionaries and enthusiasts: When the time came to name today's fractal, I was in the mood for a slice of blueberry pie, so I named it "Blueberry Pie". Unfortunately, giving the fractal such a name did not make it edible, but I have left a note to pick up a blueberry pie on the next visit to the market. The parent fractal of today's scene was created by combining positive and negative portions of the golden ratio. It is not a single object, but rather an assortment of Mandeloids and other holes. There are two main Mandeloids, one of them fairly normal, the other all cut off, as though it were too close to an escape radius. Today's scene is located in a tiny spiral in the remnants of the East Valley of this cutoff Mandeloid. After a moment's indecision, I rated the image at a 6, which is the highest rating in several days, and, when the render time of 7 minutes is considered, gives an overall value of 83. The task of rendering may be avoided entirely by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Between rain squalls, Wednesday was a fair enough day, with lots of sun and a temperature of 82F 28C. But even while the sun was shining, the trees were dripping water, making things too wet for the delicate ears and paws of the dynamic duo. They ventured onto the porch but never made it to the grass. A minor treat of extra tuna was needed to end their day satisfactorily. This morning is starting slightly chilly, but it is sunny, and no rain is in sight. I expect the cats will have a better day. For me, the work is still heavy and everyone wants his job at once. This means another busy day, so until next FOTD, take care, and button down the hitches. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Blueberry_Pie { ; time=0:07:14.29--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.86260395598377170/-1.536571085905906\ 00/2.040066e+009/1/7.5/6.43303208599371734e-006 params=-1/-1.618034/1/1.618034/-0.4/0 float=y maxiter=1500 inside=0 logmap=138 periodicity=10 colors=000_eTXbSU_RSXRPUQNRQKOPILPFIODFOACN89N56M3\ 3M48L5CK5GK6LJ7PI7TI8YH8aH9eGAjFAnFBrEBvEOfPrCpnCi\ iDddD``DWXESTENPEJLFEHFADF5AF1EH3HI5LJ7OK8SMAVNCZO\ EaPF`RA`T6bV7cW8dY9eZAf_BgaChbDidEjeFkfGfiZ`lp`gp`\ cp`Zp_VpZXkZZiZ_fZbmZekYgjXjgameeobir`mtZrp`mlbhhd\ cefZahUYjPUlKRnFOpALr5Jt2Nr2Qp2Tn2Wm3Zk3ai3dg3gfNq\ hfzicyjaxjZwjXwjUvjSujPujNtkKskIrkFrkDqkApk8pkBmhD\ kfGidIfbLd_NbYQ_WSYUVWRXTP_RNaPLcNJaQH_SGYUFWXDVZC\ T`BRbAPe8Ng7Mi6Kk5In3Gp2Er1Dt0Jm6PgCVaI`WOfQUkK_lN\ ZmPZnSYoUYpXXqZXraWscWtfVuhVujVolZimacneYohSqlMroG\ ssAtv4uy5qx5mx6ix6ex7bx7Zw8Vw8Rw9Nw9KwAGvACvB8vB4v\ B1vE6tHArKEpNIoQMmTQkWUjZYhaafdeefbbg__hXXjUVkRSlO\ PnMNoPKpUHrZFscCth9um7lt8dw9Wz9OzAFzB7zB9zGBzKCzOE\ zTGzXHz`JzeLziMzmJznJzhFzlCzo8zs5zw2zz5zx7zw9zuCzt\ EzsGzqJzpLznNzmQzlSzjUziXzgZzf`zeYzaVzZSzVPzSNzOKz\ LHzHEzECzBGzAKzA_zY_zW_zU } 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==================================

1 0

FOTD 02-06-04 (Reckless [5])
by Jim Muth 02 Jun '04

02 Jun '04

FOTD -- June 02, 2004 (Rating 5) Fractal visionaries and enthusiasts: As is happening more frequently lately, the amount of work waiting to be done means that the discussion will be short. Today's fractal, which combines the positive and negative square-roots of 2, is filled with so much detail that it is downright reckless. This is why I named it "Reckless". The over-detailed effect was produced by rendering the scene with the outside set to 'summ' rather than the usual equal-iteration bands. The excess detail actually clutters the scene and holds the rating to an average 5, though those who prefer their fractals teeming with detail might consider a higher rating. The rating of 5 combines with the coincidental render time of 0:06:06.06 to give an overall value of 82. Those who would rather not render may find the finished GIF image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 81F 27C, brilliant sun, deep blue sky, gentle winds and puffy white clouds, the weather here at Fractal Central on Tuesday would have been perfect were it not for the violent thunder-storm that suddenly arose at 3:30pm and sent the dynamic duo scurrying for cover. Fortunately, they weathered the storm safely in the closet, and came out for their comfort shortly after the sun re-appeared. Today is again starting perfectly, but I hear of more storms on the way. We'll see how it goes. I plan on finishing my work as early as possible. The local electric company has a hard time keeping the juice flowing when the weather acts up. I don't want to be caught with work to do and the power down. If all goes well, I'll return in 24 hours with the next in the apparently endless series of FOTD images. Until then, take care, and batter down the hutches. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Reckless { ; time=0:06:06.06--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.68688328765946660/+0.774924960077894\ 20/217914.6/1/35/2.83901438469236211e-009 float=y params=1/1.414213562373/-1/-1.414213562373/-0.15/0 maxiter=1800 inside=0 outside=summ periodicity=10 colors=000lOFlOFmNGnNHoNIpMIqMJrLKsLLsLLqIJoFImCHl\ 9Fj6Eh3Dg0Cf2De4De6Dd8Dd9EcBEbDEbFEaHFaIF`KF_MF_OG\ ZQGZRGYTGXVHXXHWZHW_HZWJ`TKbQLdNNgKOiHPkERmBSo8TpA\ UpBUpCVpEVqFWqGWqIWqJXqKXrLYrNYrOYrPZrRZsS_sT_sU`s\ W`sX`tYat_at`btabtbbbTXMKRHKPCKO7KM2KL7JNBJPGJQKJS\ PITTIVYIXaIYfH_jH`oHbsHcoG_kGWgFScFO_FKWEGSECOE9QH\ ASJAULBVNBXQCZSC`UCaWDcYDe`EgbEhdFjfFmhFpkGrmGuoHx\ qHzsHwqItpJqnJnmKjlKgjLdkMblM`lNYoNWrOUvOSzPQwQNrQ\ LmRJhRHcSFZSHURJSRLRRNRRPQRRPRTPRVORXNRYNQ_MQaLQcL\ QeKQgJQiJQkIQmHQnHQdMOVQMLUKBYJPLWa8ha9iaAiaBiaCia\ DiaEiaFiaFiaGiaHiaIiaJiaKjaLjaMjaMjaNjaOjaPjaQjaRj\ aSjaTjaTj_VhYXgWYfV_dT`cRbbQcaOe_MfZLhYJiXHkVGlUEn\ TCoSBqQ9rP7tO6uN8tP9sRBsTCrVErXFqZGp`IpbJodLofMnhN\ mjPmlQlnSlpTkrUks``tgRtePrcOqbNp`LoZKmYJlWIkUGjTFh\ REgPCfOBeMAcK9bJ7aH6`F5ZE3YC2XA1W90VA3SB5PB8NCAKCD\ IDFFDHDEJEELFENFEPGEQHESH } 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==================================

3 2

FOTD 31-05-04 (Not Quite Insane [6])
by Jim Muth 31 May '04

31 May '04

FOTD -- May 31, 2001 (Rating 6) Fractal visionaries and enthusiasts: To create today's image I added a small, (0.03), imaginary part to the exponent of the Z^2.01+C Mandeloid, and stood back to see what would happen. What happened is that the Mandelbrot set suffered a total breakdown, both in its macroscopic and micro- scopic aspects. The real axis split completely apart, especially on its negative side. Seahorse Valley dissolved into two vague disconnected valleys, and East Valley broke apart as though an earthquake fault had appeared and slipped down its center. To find today's image I examined the southern side of East Valley, or more accurately, what is left of East Valley. I found the valley totally changed, a whole new world waiting to be explored. I chose a narrow sliver of chaos to examine, and there I found today's scene, which for some crazy reason I named "Not Quite Insane", and rated at a 6. I have no idea why I have so rarely used complex exponents in my fractals. Perhaps I am keeping things a bit too simple. But now that I have seen what complex exponents can do, I will be using them more often. In fact, I have already found several additional interesting scenes in today's parent fractal, which I will be presenting in the days to come. Today's image, with its very fast render time, has an overall value of a whopping 337. Those who prefer their fractals pre- cooked may find the completed GIF image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of clouds, with some sun and a temperature of 75F 24C, kept the dynamic duo happy under the holly trees most of Sunday afternoon. When evening arrived, they came indoors without complaint. Unfortunately, this morning is threatening rain. I fear the good day will not be repeated. My ever-present graphic-design work is heavy but bearable. One of these days I'll collect my million dollars from one of those international lotteries. I have won at least 100 of them, but never collected my winnings. Then I'll be able to devote all my time to fractals. But today is not that day, so it's time to get to work. Until next FOTD, take care, and those who enjoy fractals are the richest on earth. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Not_Quite_Insane { ; time=0:01:46.56--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=+0.2966005299\ 4884770/-0.01118730711845938/6.463393e+007/1/-75/1\ .8412302334180897e-007 params=2.01/0.03/0/0 float=y maxiter=950 inside=0 logmap=71 periodicity=10 colors=0009R85R64T84V94XA4ZC4`D3bE3dF3fH3hI3jJ3kK7\ jOBiRFiUJhXNg_RgbVffZeibelfdojcrmcuhWocOjZGeU8`P1W\ R4YT7ZV9_WC`YEa_Hb`KcbMddPeeRfg9AfBDfDFfFIfHKeJMeL\ PeNRePTaMQYKOUILQFJMDGIBEE8BA696477EB8NE8WI9eLAnPA\ wSDvRGvRJvRMuQPuQSuQUuQXtP_tPbtPesOhsOksOmsOgrPbrQ\ XrRSrSMqTHqUBqV6qVAoXDmZGl`JjbMhdQgfTehWcjZbla`nd_\ p`WnXSlTPjPLhLIgINjGRlDVnBZp9_j8`d7aZ5bU4cO3dI2eDP\ b6Nd7Mf7Lh7Kj7Jl7In8Hp8Gr8Ft8Ev8Dw8CuBBtDAsG9rI8pL\ 7oN7nQ6mS5kV4jX3i_2ha2gc7f`CfZHeXMeVQeTi8nfChcGbaK\ YZOSWSMUWHTXJSXKRYLRYMQZNPZOP_PO_QN`RN`SMaTLaULbVK\ bWJcXJcYOffSioRliQodTmeVkfXif_ggaegccheahh_ijYilWj\ nUjgTfaSbVR_PQWJPSCOP6NL0NI2MM3MP4LS5MV6NY7O`8Pd9Q\ gASjBUmCWpDYsE_vDatCcrCepBgnBilAkjAmi9og8qe8sc7ua7\ w_6xY6yX8zZAz`BzbDzdFzfGzhIzjJzkLzgNzcPz_RzWTzSVzO\ XzKZzG`zCbz8dz4ez0fz2gz4gz6ezEdzLczSazZ`ze_zlZzs`z\ paznbzkczidzfezdNzHIzEEzB } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 30-05-04 (Midget on the Mount [5])
by Jim Muth 30 May '04

30 May '04

FOTD -- May 30, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image reminds me of one of those probably fictional hermits who sits in total isolation on a mountain top, meditating on the mysteries of existence and dispensing wisdom to any with the fortitude to struggle all the way to the top of the mountain to receive it. I have never heard how the hermit could be expected to survive without assistance on the exposed mountain top for the 20 or 30 years it takes for him to reach his enlightened state. I guess it's a miracle. I have named today's image "Midget on the Mount" and rated it at a 5. The unexceptional coloring brings down the rating. If I had put a little more work into the coloring, the image could have rated a 6. But all is not lost. With a render time of only 2 minutes, the image is a fast one. And that speed boosts the overall value to a respectable 239. The parent fractal is a close relative of yesterday's parent, with just a bit more 'i' added. I must experiment more along this line. Complex exponents do interesting things to fractals. As always, today's image is available for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was nearly perfect here at Fractal Central on Saturday. The dynamic cats took full advantage of the perfection by spending the entire afternoon by the holly trees at the bottom of the yard, thoroughly enjoying the warm sun and temperature of 73F 23C. Even the noisy cicadas failed to disturb their repose. When the sun went down and the cicadas stopped singing, the dynamic duo came inside for their treat of tuna. Today is starting nearly the same, but it's unlikely that the duo can have two perfect days in a row. As for me, I'm going to trim a small plot of overgrown grass, and then settle down to ponder the mysteries of the universe. When I finish pondering, I'll take a trip to fractal land. If I find anything of worth there, it will appear as tomorrow's FOTD. Until then, take care, and one mystery leads to another. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ MidgetOnTheMount { ; time=0:02:05.45--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+2.36224752783415900/+7.021481211098950\ 00/1646.061/1/90/3.88578058618804789e-016 params=1.4142/0.08/-1/0 float=y maxiter=1800 inside=255 logmap=38 periodicity=10 colors=000dbVbaU`_U_ZTYXSWVRVUQTSQRRPQPOOONMMMLLMJ\ KPIJRHIUGIWFHYEG`DFbCFdBEgADi9Cl8Cn7Bp6As59u49w5Ct\ 6Er7Gp8Jm9LkANiBQfCSdCUcHWcLXcPYcTZcX`c`acdbchccld\ cheedfg`giXhkTimPjoLkqHltDmwAmzCnzEozGozIpzKpzMqzP\ qzUrzZrzcszeszgozikzkgzmczo_zqXzsTzuPzwLzxHzyEzzDz\ zCzzBwzArz9mz9hzGczNZzTUz_PzfKzlIwsHuyHstFroEpkDoo\ CnqBls9ku8iw7hx6gy5ezEczMazV_zbYzkXzsazmezgiwamwWq\ uQusKyqEzoLzmRzkXzibzg_zeYzcWzcUzcSzcPzcNzcLzcJzcH\ zcFzcIzcLzcOzcRzaUz_XzY_zWbzUezShzQkzOnz0qz0tz0wz0\ yz2zz4zz6zz8zzAzzCzzEzzDzzCzzDzzEzyFzxGzwHzvIzuJzt\ KzsLzrMzqNzpOzoPznQzmRzmSzmTzmUzmVzlWzlXylYxlZwl_u\ k`skaqkbokcmkekkhihkgenecqc`tcZwcWzHTzGRzEOzCRzBUz\ KXzT_zabziezchzckzcnzcqzctzcwzczzjzzkzzkzzlzzlzzmz\ zmzznzznzzozzozzpzzpzzkzzgzzczz_zzWzz`zzezzizznzzs\ zzwzzjzzZzzNzzMzzLzzLzzKzzJzzJzzIzzIzzHzzGzzGzzFzz\ FzzCzz9zz6zz3zz8zzYzzXzzz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 29-05-04 (Fractal Study-Two [7])
by Jim Muth 29 May '04

29 May '04

FOTD -- May 29, 2004 (Rating 7) Fractal visionaries and enthusiasts: It seems as though every time I ponder the question, 'What is the world made of?' the answer is different. In my lifetime I have seen it made of atoms, sub-atomic particles, probability waves, energy, quarks, multi-dimensional strings and membranes, holograms, information, thought, and even nothing. Of course, all of these things are inventions, the result of trying to reduce something beyond our understanding to the level of everyday experience, and they are all a little right but mostly wrong. We could keep inventing the basic stuff of existence for a million years, and we would never find an answer that totally works. The universe is actually a fractal, and fractals are made of numbers. (BTW, I cannot prove this.) The universe is made of numbers. As for the constitution of numbers, well, they are most likely made of God, or whatever non-offensive word Atheists choose to use. And as to the nature of God . . . I refuse to speculate. There are an infinity of numbers however, and this leads to the question of which of the infinity of numbers are the basic building blocks. My guess is that the whole numbers, positive and negative, are the building blocks, with the positive number 'one' being by far the most common. Of course, I could always be wrong. ;-) Today's image pictures a midget in the Z^((sqrt(2))+0.03i)+C Mandeloid. I rarely use complex exponents in my fractal explorations, but decided to try it today anyway. Adding just 0.03 part of 'i' went a long way, totally changing the shape of the parent fractal. I'll have to do this more often. I named the image "Fractal Study-Two", though I could just as easily have named it "Kilroy Was Here". The central midget is shaped suspiciously like that character with the oversized nose who was seen peeping over every fence during the time of the Second World War. Yesterday's image took almost 4 hours to render, and even then rated only a 5. Today's image renders in only 2 minutes, and rates a 7. This gives it an overall value of 326, a vast improvement over yesterday's rating of a miserable 2. Regardless of ratings or render time, the FOTD images are always available for download from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A partly cloudy day here at Fractal Central on Friday, with a temperature of 79F 26C, gave the fractal cats several pleasant hours in the yard. When the day ended, they came indoors without complaint. Today is starting sunny and cooler. These are conditions that promise the best for the dynamic duo. I must clear away more of the backed-up work before I start thinking again of fractals, and the time to start is now. Until next time, take care, and fractals are neither real nor unreal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Study-Two { ; time=0:02:09.02--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.47098430823224210/+2.838089870359976\ 00/2135.219/1/-65/-3.95622423710051407e-012 params=1.414213562373/0.03/-1/0 float=y maxiter=1800 inside=0 logmap=50 periodicity=10 colors=000B0NB0OB0RB0VB0YB0aB0bB0fB0iB0lB0pA0qE0lI\ 0iM0fQ2bV8_`DXfITlLQrQNyVJzaGzgDzm9zr6zv2zdBzTIzGQ\ x4Xq0dl0kn0lp0lq0ns0nt0pw0px0qz0qz0sz1sz2tz6tz8wz9\ wzDxzExzGzzIzzLzzNzzOzzQzzOzzzpzzztzzwzzwzzwzxwzpw\ zgwzawzTwzLwzEwz6wz0sz0pz0lz0kz0gz0dx0at0_s0Xq0Tn0\ Ql0Ok0Li0Ii0Ei0Di0Gi0Ji0Li6OiDRiJTiRXiY_idaikdiqfi\ xdizdizdizbizbizbizqifziGzi0zi0zi0zi0zi0zi0zi1zi2z\ i4xi6wi8tiBqiDpiEliGkiIgiJfiLbiNaiO_iQYiOXiOViNTiN\ RiNXiIaiDfi8ii2ki6li8li9niBniDpiEqiIqiJsiLsiNtiOti\ QwiTxiVxiXziYzi_ziazibzifxigwiitiltinsipqiqpitpiwn\ ixlizkizkiziizgizfkzflzdnzbpzaqzaszftzgwzixzkzzlzz\ nzwpzsqzpszntzkwzixzgzzdzzbzzazzYzzXzzVzzRzzQzzOzz\ LzzJzzIzzEzzDzzBzz8zz6zz4zzDzzLzzTzzazzizzpzzgzzaz\ zVzzNzzGzz9zz1zz0zz0zz0zz0zz0zz1zz8zzEzzLzzRzzYzzd\ zzkzzqzzxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzxzzwzztzz8zz9zzDzzGzzJ } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 28-05-04 (A Fractal Study [5])
by Jim Muth 28 May '04

28 May '04

FOTD -- May 28, 2004 (Rating 5) Fractal visionaries and enthusiasts: The combination of an unusually heavy work load and a balky computer has once again put me behind in my work, so today's discussion will again be brief. For today's fractal I decided to move in close-up to study a midget of the order 1.5. The parent fractal is an unimpressive thing that appears to spiral around the origin, with a prominent discontinuity along the positive real axis. The shoreline of this parent is lined with irregular buds. Today's scene is located on the inside of the northern branch of the valley of a small bud on the eastern edge of the parent. To be sure I captured all of the midget, I raised the maxiter to 500,000. Even with such an extreme maxiter, it still appears that the midget is not quite fully defined, but with a render time approaching 4 hours, the present maxiter will have to suffice. The midget itself is typical of midgets in this range, showing little tendency to develop the semi-chaotic patterns around it that make quadratic midgets so attractive. In fact, there is almost a feeling of 'anything can happen' about the scene. An orbit check shows that the entire scene has a periodicity of 3, with but minor variations in the different areas of the midget. I have not checked the Julia aspect of today's scene, though it is certainly equally disorganized. I named the picture "A Fractal Study" because that's what it is. Actually, I studied the image very little. I simply started it going and let it calculate for four hours while I worked on the balky machine. The rating of a 5 could be a gift or a robbery, depending on one's view. The extreme render time drags down the overall value to an abysmal 2. But all is not lost, for I have sent the finished GIF image on ahead to Paul, and it will soon be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> ready for immediate download. Both Wednesday and Thursday were quite warm here at Fractal Central, with brief showers both evenings. On both days the fractal cats managed to hold off the hordes of cicadas long enough for a few restful hours in the shade of the holly trees. Today is starting partly cloudy and slightly cooler. The cats have not yet decided what kind of day they will have. If I catch up in the work, today could be restful for me, but that will take quite a bit of effort. Until next FOTD, take care, and despite all appearances to the contrary, we could all be part of a big hologram. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Fractal_Study { ; time=3:43:15.29--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=t center-mag=+1.32928740683383100/+0.164093949176507\ 60/76478.92 params=1.5/0/0/0 float=y maxiter=500000 inside=0 logmap=1040 periodicity=10 colors=000WOVa`Ub`Uc_UdZTeZTfYTfZSgYTgXUgWVhVWhUXh\ TYiSZiS_iR`jQajPbjOckNdkMekLflLglKhlJimIjmHkmGlnFm\ nEnoFmnEnnDnmDnmCnlCnkBnjBniAnh9ng9nf8oe8od7oc7oc6\ ocUUccUccUccUccUcOUcUUccTccScUScURcURcPQccQccPccPc\ UOcUNcUNccMccMccLccLcKKcKKccJccIcbIbaHa`H``G`_G_ZF\ ZYFYXEYXEWVHUTJSRLQPNONPNLRLJTJHVHFXFDZ97gEC`IHVMM\ PRRJVWD``6Z_7YZ7XY7WX8VW8TW8SV8RZ9QT9PS9OS9QTCRTFS\ UHTUKVUNWVPXVSYVVZWX`W_aXabXdcXgdNifYlgYohZqiZtlYx\ jZviZthZrfZpeZnd_lc_ja_h`_f__dZ`bX``W`ZV`XU`VSaURa\ SQaQPaONaMMbKLbIKbGIbEHbCGcAFc8Dc6Cc4BcAAeKBgUAiaA\ kaAmaAo`Aq`Fs`Ku`Pv_Uv_Zu_cu_huZmuZrtZwtZwtYwsYwsY\ wsYzrXzrXzrXzrXzqZzp_zo`znazmczldzkezjfzihzhizgjzf\ kzemzdnzcozbpzarz`sz_tzZuzWwzYvz_vzawzcxzeyzfzzhzz\ jzzlzzmzznzzozzpzzqzzrzzszztzzuzzvzzwzzxzzyzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

MyFOTD
by M J Benkers 28 May '04

28 May '04

Dear fractallovers, Because Jim is very busy, I send you a picture from my fractal collection. A simple, nice Julia. Here in Dutch Fractal Centre things are not going as they should. I am just recovering from the flu and I am a little bit shaky. But the weather is very nice today, so I hope I will feel better. Last week it was cold, with a cold wind blowing. Just the right weather for influenza. The old fractal dog is sleeping; as usual. Mary START FORMULA FILE twinspiral { reset=2003 type=julia center-mag=-0.000483746/0.859679/7.983634 params=0.258919/1.76951e-007 float=y decomp=256 colors=000006<3>00800900A<9>K04M04O03<2>U01W00W00<10>d00e00f00<14>u70v70\ w80x80z90<79>zm0zm0zn0<43>zx0zy0zy0zy0zy0<68>zzz } END FORMULA FILE The older I grow the more I distrust the familiar doctrine that age brings wisdom. H. L. Mencken

1 0

Re: [Fractint] FOTD 26-05-04 (Little Joe [6])
by gnome＠hawaii.rr.com 27 May '04

27 May '04

FWIW, a few minutes after sending that note, I reloaded the main index page, and everything was as it should be ... must've been the menehunes feeling bored again. David gnome(a)hawaii.rr.com ----- Original Message ----- From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> Date: Thursday, May 27, 2004 5:23 am Subject: Re: [Fractint] FOTD 26-05-04 (Little Joe [6]) > David <gnome(a)hawaii.rr.com> wrote: > > > > Problem - went to Paul's site, but there > > is no link for May 2004! And here it's > > almost JUNE!!!! > > > > That is curious, especially since the May 2004 webpage has been > visitedover 950 times already, which averages out to about 36.15 > visits per day > this month. A little bit below what is "normal", but only by > about 10% > or 15%. > > If the 'Main Index Page' is not showing the May 2004 link correctly, > then I first suggest refreshing your cache, followed by contacting > yourInternet provider. If that fails, then just use the > following: > > http://home.att.net/~Paul.N.Lee/FotD/FotD_04-04.html > > The actual Monthly webpages all follow the same naming convention: > FotD_97-04.html 1997, May > FotD_00-12.html 2000, December > FotD_04-01.html 2004, January > > And the days of the month are very similar, but are grouped by three > years worth on to different shared sites. > > > Sincerely, > P.N.L. > ------------------------------------------------- > http://home.att.net/~Paul.N.Lee/PNL_Fractals.html > http://www.Nahee.com/Fractals/ > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com

1 0

No FOTD for May 27, 2004
by Jim Muth 27 May '04

27 May '04

Fractal enthusiasts: Due to technical difficulties, which have not yet been solved, there is no FOTD for May 27. If all goes as well as hoped, the FOTD will return on schedule on May 28. If not, then it will return on the 29th or 30th. Jim M.

1 0

Re: [Fractint] FOTD 26-05-04 (Little Joe [6])
by gnome＠hawaii.rr.com 27 May '04

27 May '04

Problem - went to Paul's site, but there is no link for May 2004! And here it's almost JUNE!!!! David gnome(a)hawaii.rr.com ----- Original Message ----- From: Jim Muth <jamth(a)mindspring.com> Date: Wednesday, May 26, 2004 6:14 am Subject: [Fractint] FOTD 26-05-04 (Little Joe [6]) > > FOTD -- May 26, 2004 (Rating 6) > > Fractal visionaries and enthusiasts: > > Another busy day means another brief discussion. > > There is not much to be said about today's image, which was > found in the same way as yesterday's. To add a bit of interest, > I rendered the scene with the outside set to 'fmod' and the > proximity set to the default 0.01. > > The midget at the center is another shapeless thing, though not > quite as shapeless as the midget in yesterday's image. > > For some reason now forgotten, I named the image "Little Joe". > I rated it at a 6 because blue is one of my favorite colors. > The render time of 13 minutes results in an overall value of 45. > > The image is available, already rendered, on the FOTD web site > at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > Sunny very warm weather here at Fractal Central on Tuesday gave > the cats a pleasant afternoon in the yard. The temperature > reached 88F 31C, then at 7pm, a whopper of a thunder-storm moved > in, but by that time the cats were inside for the evening. They > took shelter in the closet until the noise passed, then came out > for their evening treats. Today is starting cloudy and very > humid, with more storms due. The cats are already checking the > outdoor conditions. > > I have quite a bit of work to finish before I turn to fractals, > so I had best start working. Until next FOTD, take care, and be > decisive. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Little_Joe { ; time=0:13:17.96--SF5 on a P200 > reset=2003 type=formula formulafile=allinone.frm > formulaname=MandelbrotBC2 passes=1 > center-mag=+0.1814731907900935/-0.0169584462205538\ > 5/8693.298 params=1.5/0/2.5/0 float=y maxiter=16000 > inside=0 outside=fmod logmap=60 periodicity=10 > colors=0006vy7ux7tw8sv8ru9rt9qsAprBoqBnpCmoCmnDlmD\ > klEjkEijFhiGhhGggHffHeeIddIccJccKbbKaaL``L__MZZMZY\ > NYXNXWOWVPVUPUTQUSQTRRSQRRPSQOTPNTPMUOLUNKVMJVLIWK\ > HXLFWKHWKIVKJVKKUKLUKMUJOTJPTJQSJRSJSSJTRIVRIWQIXQ\ > IYQIZPI_PHaOHbOHcOHdNHeNHfMGhMGiMGjLGkLGlKGmKFoKFp\ > JFqJFrIFsIFtIFuIHtIIsIJsIKrILqIMqINpIOpIPoIRnISnIT\ > mIUlIVlIWkIXkIYjIZiI_iIahIbgIcgIdfIefIfeIgdIhdIicJ\ > ldIjcIhbIfaHd`Hb_H`ZGZYGXXGVWFTVFRUFQTFOSEMREKQEIP\ > DGODENDCMCALC8KC6JD3IC4JC5JC6JC7JC7JB8JB9JBAJBBJBB\ > JACJADJAEJAFJAFJ9GJ9HJ9IJ9JJ9JJ8KJ8LJ8MJ8NJ8NJ7OJ7\ > PJ7QJ7RJ7RJ6SJ6TJ6UJ6VJ6VJ9SKBQLDOLFMMHJNJHNLFONDP\ > PAPR8QT6RV4RW5SX5SX5TY5TY5TZ5UZ5U_5U_5V`5Va5Va5Wb5\ > Wb5Wc5Xc5Xd5Xd5Ye5Yf5Yf5Zg5Zg5Zh6_h6_i6_i6`j6`k6`k\ > 6al6al6am6bm6bn6bn6co6cp6cp6dq6dq6dr6er6es6es6ft6f\ > u5ht6fs7er7dr8cq8bp9ap9`oAZnBYKlNJmQInTHnVGoYFp`Eq\ > cDqfCriBskAtn9tq8ut7vw5wz } > > frm:MandelbrotBC2 { ; by several Fractint users > e=p1, a=imag(p2)+100 > p=real(p2)+PI > q=2*PI*floor(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| > END 20.0 PAR-FORMULA FILE================================== > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

2 1

http://ecn.ab.ca/~brewhaha/FRACTINT/params.zip
by SherLok Merfy 27 May '04

27 May '04

This is the omnibus archive of parameters and maps that I'm particularly proud of, but the maps are all external to the parameters and a few other insignificant changes like orientation and symmetry assertions might distinguish them from the first time that I posted them. There are a few unposted goodies in there that are just waiting for the appropriate context. Neither fractint.frm nor fractint.par are in the file. I did some marketing in person, yesterday. Maybe that's the kind of thing that occupies Mister Muth on occasion, or maybe his cats do the marketing and his wife takes stuff out for production. All that I know is that my own context is small business. In a health-food store, she showed me a fridge with a 71 by 15 inch illuminated frame. I gave her a page of 4x3 "thumbnails" to choose from and gave her an estimate of what my costs and labour were to cover the frame with transparencies. It's a custom job, and her part is to narrow the selection, although I'm open to "all" and some specifications for orientation. I didn't colourize any more than were already colourized. I gave her only grayscales, because I might leave some of them that way or make them into a simple pattern of monochrome (a map for the arctanjent view that goes from black to yellow to white is monochrome to my way of thinking). (I wasn't going to do any more labour than I had to before her husband agreed to the rate for labour, and it wouldn't hurt to hear them discuss a scheme for colour). My rate for labour is a seventh of what what Nordraft down the avenue is charging for desktop publishing, but I don't hav a store front, and this would be my first order. Referrals are a big part of sales. They say it's not what you know, but who you know. I say it's more like switching gears to understand people.

1 0

FOTD 21-05-04 (Splash [3])
by Jim Muth 27 May '04

27 May '04

FOTD -- May 21, 2004 (Rating 3) Fractal visionaries and enthusiasts: The discussion for today must once again be brief. The shelves here at F.C. are filled with work waiting to be done. Today's quickie image takes us to the fractal that results when the expression Z^(sqrt(2))+C is iterated. I use the square root of two because this value causes the midgets to reveal their presence by the 2-way symmetry that often surrounds them. The existence of a midget in today's image must be inferred. The actual midget at at the center lies far beyond resolution. The fragmented, sharply angular features radiating from the unseen midget are typical of midgets in fractals created by exponents of Z between 1 and 2. The scene itself actually lies in the 'East Valley' area of a larger midget. Seeing little of interest in the image, I rated it at another lowly three, and named it "Splash". One look at the finished image will justify the name. When the 7-minute render time is considered, the overall value comes in at an unimpressive 40. The render time and value become meaningless when the completed GIF image is downloaded from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With light sprinkles of rain continuing through the day Thurs- day, the duo had little opportunity to get outside. A generous treat of tuna eased their disappointment. Today is starting cloudy, and we have already had one thunder-shower. It does not look good for the duo. For me, it will look better when the customers are satisfied. Until next time, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Splash { ; time=0:07:34.56--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-0.3372158749\ 447071/+1.146008548386008/3.684655e+011/1/115/-0.3\ 303244820299197 params=1.414213562373/0/0/0 float=y maxiter=1500 inside=0 logmap=355 periodicity=10 colors=000`v_`r_`nZ`jZ`fY`bYaZXaVXaRWaNWaJVaFVY0_a\ BVdLRgVNkdInnEox4qxArxGsxMtxRuxXvxbwxhsrzxxmyrnymn\ yhoycoyYpyTpyOqyJqvImsHjpGgmFdkEahDZeCWbCS_BPYAMV9\ JS8GP7DM6AE58K67P67V67_76e76k53j76j89j9CjBFiCIiDLi\ EOiGRiHUhIXhK_hLbhMekQghNhfLicJjaHk_FlXDmVBnJB7T9n\ QGjNNgKUcI``FgXCnU7wPAuRCtSFrTHqVJpWMnXOmZRk_Tj`fx\ PViaxZxJWmKXoKXpKXqKXrLXsLXtLYuLYvMYwMYxMYyMYzO_yP\ `xQbxRcwSdvTfvUguViuWjtXksYmsZnrZst_or_lq`ip`foacn\ a_lbXkbUjcRigNucOh`OXXPKYR9UP8RO8NN8KM8GL7DK79J74F\ 66I77L79N8AQ8CT9BV1DV9UyFFVGwRC00G3AH6JI9TJBaJC`MD\ `PE_SE_VFZXGZ_GZbHYeIYhJXjJXmKWpLWsLWuKXrJYoIYmHZj\ GZhF_eE`cD``CaZBaWAbU9cR8cP7dM1cM7dKDeJJfHPfGVgE`h\ DfhBliArj8yi3xj7xjBxjExjIxjLxjPwkSwkWwkZwkbwkewkiw\ kloegg`c`W_TQWLLSEGOIFMLFKPFJSFHVEGZEEaEDdEBhE9kD8\ nD6rD5uD3xD2uH3rK3pN4mR4jU5hX5e`6bc6ae1`f6_fA_gEZg\ IZgMYhQYhUXhYWia_yZYyi_z` } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

2 1

FOTD 26-05-04 (Little Joe [6])
by Jim Muth 26 May '04

26 May '04

FOTD -- May 26, 2004 (Rating 6) Fractal visionaries and enthusiasts: Another busy day means another brief discussion. There is not much to be said about today's image, which was found in the same way as yesterday's. To add a bit of interest, I rendered the scene with the outside set to 'fmod' and the proximity set to the default 0.01. The midget at the center is another shapeless thing, though not quite as shapeless as the midget in yesterday's image. For some reason now forgotten, I named the image "Little Joe". I rated it at a 6 because blue is one of my favorite colors. The render time of 13 minutes results in an overall value of 45. The image is available, already rendered, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunny very warm weather here at Fractal Central on Tuesday gave the cats a pleasant afternoon in the yard. The temperature reached 88F 31C, then at 7pm, a whopper of a thunder-storm moved in, but by that time the cats were inside for the evening. They took shelter in the closet until the noise passed, then came out for their evening treats. Today is starting cloudy and very humid, with more storms due. The cats are already checking the outdoor conditions. I have quite a bit of work to finish before I turn to fractals, so I had best start working. Until next FOTD, take care, and be decisive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Little_Joe { ; time=0:13:17.96--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.1814731907900935/-0.0169584462205538\ 5/8693.298 params=1.5/0/2.5/0 float=y maxiter=16000 inside=0 outside=fmod logmap=60 periodicity=10 colors=0006vy7ux7tw8sv8ru9rt9qsAprBoqBnpCmoCmnDlmD\ klEjkEijFhiGhhGggHffHeeIddIccJccKbbKaaL``L__MZZMZY\ NYXNXWOWVPVUPUTQUSQTRRSQRRPSQOTPNTPMUOLUNKVMJVLIWK\ HXLFWKHWKIVKJVKKUKLUKMUJOTJPTJQSJRSJSSJTRIVRIWQIXQ\ IYQIZPI_PHaOHbOHcOHdNHeNHfMGhMGiMGjLGkLGlKGmKFoKFp\ JFqJFrIFsIFtIFuIHtIIsIJsIKrILqIMqINpIOpIPoIRnISnIT\ mIUlIVlIWkIXkIYjIZiI_iIahIbgIcgIdfIefIfeIgdIhdIicJ\ ldIjcIhbIfaHd`Hb_H`ZGZYGXXGVWFTVFRUFQTFOSEMREKQEIP\ DGODENDCMCALC8KC6JD3IC4JC5JC6JC7JC7JB8JB9JBAJBBJBB\ JACJADJAEJAFJAFJ9GJ9HJ9IJ9JJ9JJ8KJ8LJ8MJ8NJ8NJ7OJ7\ PJ7QJ7RJ7RJ6SJ6TJ6UJ6VJ6VJ9SKBQLDOLFMMHJNJHNLFONDP\ PAPR8QT6RV4RW5SX5SX5TY5TY5TZ5UZ5U_5U_5V`5Va5Va5Wb5\ Wb5Wc5Xc5Xd5Xd5Ye5Yf5Yf5Zg5Zg5Zh6_h6_i6_i6`j6`k6`k\ 6al6al6am6bm6bn6bn6co6cp6cp6dq6dq6dr6er6es6es6ft6f\ u5ht6fs7er7dr8cq8bp9ap9`oAZnBYKlNJmQInTHnVGoYFp`Eq\ cDqfCriBskAtn9tq8ut7vw5wz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 25-05-04 (A Hot Midget [5])
by Jim Muth 25 May '04

25 May '04

FOTD -- May 25, 2004 (Rating 5) Fractal visionaries and enthusiasts: I have been doing some pondering since the last FOTD. Yesterday I received in the mail a special report from 'Scientific American' magazine with the title "Are You a Hologram?" At one place the article states that the three-dimensional world we see around us might be an illusion that we are creating, that in reality we are two-dimensional somethings. There is an illustration showing a two-dimensional woman imagining that she is three-dimensional. This revelation nearly knocked me flat! I thought that the assumed number of dimensions in our universe was increasing, not decreasing. And if we really are two-dimensional, then it must be possible to imagine more dimensions. So what is keeping us as 2-D beings from imagining four dimensions. Finally, I wonder about the nature of the 2-D things that are having the illusion of three-dimensional space. It is all so complex. I like things simple. Complexity brings confusion; simplicity brings ease of understanding. At least that's the way it's supposed to work. Of course, it often happens that things which at first appear quite simple turn out to be surprisingly complex. And nowhere is this unexpected complexity more evident than in the world of fractals. The iterated expression behind today's image is Z^1.5+C, as simple an expression as one could hope to run into in the arcane field of mathematics. Yet it has an infinity of infinite worlds hidden within it. Today's parent fractal is but one of these infinity of worlds. It is a shapeless thing with bits and pieces of itself lying scattered to the west of the main bay. This bay has a rudimentary East Valley, and today's scene is located in the chaos along the southern shoreline of this valley. (In this case, the northern shoreline is entirely different.) I named the image "A Hot Midget" because to me at least, the midget at the center looks overheated. It is a curious midget, almost giving the impression that it cannot decide what shape to take, and has decided to try to take all shapes. There is an obvious smaller midget lying on the midget's main filament. I have already checked this smaller midget and found it to be both less interesting and far slower to render. After carefully considering the situation, I rated the image at a 5, which is not good and not bad. After all, this is the kind of stuff I was doing 12 years ago. Back then it would have rated a 7 or 8. Nowadays, the 5 is all I could give it. When the render time of 22 minutes is considered, the overall value rates a 22 also. With images of such mediocre worth, perhaps the wisest way to view them is to download them from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another very warm and sunny day here at Fractal Central, with a temperature of 90F 32C, was acceptable for the dynamic duo, who spent an hour in the yard, fighting off the cicadas that were threatening to overwhelm them. Actually, I think the ear-split- ting singing of the bugs disturbs the duo more than the bugs themselves. The singing masks the warning sounds of approaching threats. Today is starting sunny but less warm. The singing is very loud however, and it remains to be seen how the duo will react. As usual, my day will be much improved when the work is finished. Until next FOTD, take care, and see you in the fractal vicinity. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Hot_Midget { ; time=0:22:32.59--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.16011719832039840/-0.003322865380414\ 47/305474.1 params=1.5/0/2/0 float=y maxiter=18000 inside=0 logmap=290 periodicity=10 colors=000XNQYORZOS_PT`PUaQVbQWcRXdRYeSZfS_gT`hTai\ UbjUckUelUfmUhnUigUjaUjVVjPTmIQoCNm5Dl6Ej6Ei7Eh7Eg\ 8Ef8Ee9Ec9EbAEaAE`BE_BEZBFYAHWAKUALT9OR9QQ9RO8SN8T\ L8UK7VI7WH7XF6YE6ZC6_B5`95a85b63c25d56e87eB8dE9cGA\ bJB`MC_PDZSFYUGXXHW_IUbJTeKSgLRjMQmNPpOOrPNsPMsPMs\ PLsQLsQKsQJsQJsRIsRIsRHsRGtRGtSFtSFtSEtSDtTDtTCtTC\ tTBtTBtRDpPEmNFjLGgJHdHIaFJZDKWBLT9MQ7NN5OK3PH1QE5\ RH9RKDRNGSQKSTOSWSSXRRYRRWRQURPSRORRNPRMNQLLQKJQJI\ QIGQHEQGCQFAQE9RDASDATCAUCAVCAWBAXBAYBAZAA_AA`9Aa9\ Ab9Ac8Ad8Ae8Af7Ag7Af5Bg7Ah9AiAAjC9kD9lF9mG8mI8nJ8o\ L7pM7qO7rP7sR6tS6tU6uV5vX5wY5xZ4yZ4z_4z_4wa8tbBqcF\ neIlfKkgLkhLkiLjjMjkMjlMjmNioNipNiqOjrOktOluPmvQov\ UqwYrwasxetxiuymvymwzmxzmyzmzzmzzmzzmzczz`zz_zzZzz\ ZzzYzzYzzXzzWzzWzzVzzVzzUzzUzzWzzYzz_zz`zzbzzdzzez\ zgzzizzjzzlzznzzozzqzzszztzzpzzlzzhzzdzz`zzXzzVzzU\ zzTzzRzzQzzOzzNzzLzzMzzGz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

Franktal Gallery update
by Franktal Gallery 24 May '04

24 May '04

Franktal Gallery update (two updates in a month.... unbelievable !) - Couple of new Nature Fractals - A new IFS gallery Set your course to http://www.geocities.com/franktal2002 And don't be scared by those Geo@%#cities "bandwidth exceeded" messages, just try again later. Thanks for visiting ! Best regards, Miguel _________________________________________________________________ The new MSN 8: advanced junk mail protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

1 0

FOTD 24-05-04 (Fun in the Sun [5])
by Jim Muth 24 May '04

24 May '04

FOTD -- May 24, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image is something different. It has no midget at the center, and it has been created by one of the built-in formulas -- the manzpower. To find the image, I drew the Z^(998.1)+C Mandeloid and examined it in the area of the negative real axis. Fractals of such a high order are normally very dull objects, appearing as circles with a multitude of identical tiny bays lying along the perimeter. The inner detail of these bays has a similarity that makes exploration boring. But today's image was drawn with a fractional power of Z, and that fractional part makes the difference. Most of the parent fractal consists of the expected identical bays. The difference lies along the negative real axis, where the fractal is splitting apart and new scenes are springing into existence. It is in this area that today's image lies. In today's image the view window has been rotated 90 degrees. East is up and north is left. The X-axis runs up and down the center of the screen. The magnitude of the scene is a nominal 2x(10^8), the maxiter an unimpressive 1500. The resulting image reminds me of a fantastic tree set against an alien sky, with smoky globules of light scattered among the branches. For reasons not recalled, I named it "Fun in the Sun". The tree itself is unlike anything that could be found on earth, but if one of the leading quantum theories is correct, and an infinity of alternate universes does exist, then this exact scene not only exists, but exists an infinity of times. The rating of a 5 is a fair representation of the image's worth. I found it almost automatically and spent very little time in rendering or coloring it. When the render time of 2 minutes is considered, the overall value is an exciting 226. For fractal convenience, the parameter file of the image has been rendered and the finished image posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday was a repeat of Saturday here at Fractal Central. The temperature reached 91F 33C under lots of sun, and the cats spent several hours in the yard, watching cicadas and occasion- ally eating one that fluttered too near. In the evening they came inside and settled down without complaint. Today looks as though it will be another repeat. In my corner of F.C. the work is piling up, so I had best get started. Until next FOTD, which will most likely, but not certainly, appear in 24 hours, take care, and be kind to all types of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fun_in_the_Sun { ; time=0:02:12.70--SF5 on a P200 reset=2003 type=manzpower passes=1 bailout=10 center-mag=-1.00064242478037900/0/2.137563e+008/1/\ 90/3.88578058618804789e-016 params=0/0/998.1/0 float=y maxiter=1500 inside=bof60 outside=real periodicity=10 colors=000F2LD3JC4IB5G96F87D78B59A4\ A82B63C73D73E73F73G74H74I74J84K84L85M85N85O85P81Q7\ 3R85S87T98U9AVACWAEXAFYBHZBJ_CL`CMaDObDQcDSdETeEVf\ FXgGZhH_iIajJckKdlMemOgnQioSkpUkqWmrYos_osapscprep\ qgppippkpompnopmqplrplsoktojunivnhwngxnfyoezodzocz\ ocztbStaTt`Tt_TuZUuYUuXVuWVuWWuVWuUWuTXvSXvRYvQYvP\ YvOZvNZvN_vM_wL`wK`wJ`wIawHawGbwFbxFawFbwFbvFbvFbu\ FbuFbuFctFctFcsFcsFcsFcrFdrFdqFdqFdqFdpFdpFeoFeoFe\ oFenFenFemFemFflFflFflFfkFfkFfjFgjFgjFgiFgiFghFghF\ hhFhgFhgFhfFhfFhhBmgDjfFhfHfeJdeLbdM`cOYcQWbSUbUSa\ WQcYRbXPaXO`XN_XMZXLYXKXXJWXIWWGVWFUWETWDSWCRWBQWA\ PW9PW8RVBSVDUUFVUHWTJYTLZSN_SPaRRbRTdQVeQXfPZhP`iO\ bjOdlNfmNhnNjnMkoMkoLlpLmqKmqKnrJnrIosIosHptHpuGqu\ GqvFrvFrwEswEsvFrqNquGruHrtIrtJrsJqsKqrLqrMqqNqYiO\ ZhPZhPZhQ_gQ_gR_gR_fR`fS`fS`eTaeTaeUadUadUbdVbcVbc\ WXSeVRcUQbSQ`RPZQOYONWNMVMLTKLRJKQIJOGIN } END PARAMETER FILE=========================================

1 0

FOTD 23-05-04 (Z-Eexponent-Pi [3])
by Jim Muth 23 May '04

23 May '04

FOTD -- May 23, 2004 (Rating 3) Fractal visionaries and enthusiasts: Unless I am mistaken, today's image is the third consecutive one with a rating of a lowly 3. FOTD quality seems to be slipping. The work rush here at F.C. is taking its toll. There is an infinite family of 'zexpe' fractals with an exponent of epsilon, so why not a family of 'zexpi' fractals with an exponent of pi? In fact, there is a family of 'zexpi' fractals, (I just decided there is), and one of its infinite number serves as the source of today's image, which I have named Z-Exponent-Pi. The scene of the image is very near the negative real axis of its parent, in an area filled with discontinuities. The render time of 4-1/2 minutes gives an overall value of 65, which, depending on the individual fractalist, may or may not be worth the effort. The simplest and quickest way to see the image is to view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was quite warm and sunny here at Fractal Central. The high temperature of 90F 32C was near perfect for both fractal cats and cicadas. The cats watched from the yard while the cicadas sang in the trees, and as far as I could tell, everyone was happy. When evening arrived, the cicadas stopped singing and the dynamic duo came indoors for their treat. Today is starting the same. I'm going to take it as easy as possible today. It looks like a very busy week coming up. Until next FOTD, which I still hope to have ready in 24 hours, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Z-Exponent-Pi { ; time=0:04:34.96--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.44889489820032070/-0.008655752583507\ 26/1687871/1/-80/1.02041138039243862e-009 params=3.14159265358979/0/0/0 float=y maxiter=1400 inside=0 logmap=114 periodicity=10 colors=000VMGIIDFF9BB8S84O400002604D06F29G4BG6DI8F\ I9P`O`qaeyghzlauhVhcPZZIMTG6GDBO9GT6MZ4Pc0Vh0`n0es\ 0Mw0hy0sz0zz0jw0Rs08p00n0DZ0aK0gR0jX2nc8shBwpFzuIq\ sMjsPcqRXqVPqZGp`9pc2ng0nh0n6az2`z0Zz0Xz0Vz0Tz0Rz0\ Pz0Zz0Oz0KzBFzMBzZ6zh2zs0zz0zz0yz0wz2uz8szFqzKpzPn\ zXlzalzgjznhzsgzyezzczzazz`zz`zzZzzXzzVzzVzzTzwRzs\ RzpPzlOzgMzcMz`KzXIzTIzPMzMPzKTwGXuF`qBcp9gl6hh2lg\ 0pc0sa0wZ0zX0zT0zR0zT0zV0zX0zZ0z`2z`4zyVzzuzzzgjzK\ Xz0Tz0Pz0Oz0Kz0Gz2Fz4Bz69z66z82z90zB0zB0zD0zF0zG0z\ F0zG0zG0zG4zIBzIGzIOzKTzKZzKezMjzMqzMwzOzzOzzOzzIz\ zOzzTzzZzzczzhwzlsyqpwwlszhpzelzlczajzTqzKyzBzu2zn\ 0zg0z`0zZ8yZKlXV`XgMXq9Vz0Vz0Vz0cz0jz6qzDyzKzzRzzV\ zzXzzZzzZzzZzz`zz`zz`zzazzazzazzczzczzczzezzczzazz\ `zzZzzZzzXzzVzzTzzRzzRzzPzzOzzMzzMzzIzzGzzFzzDzzDz\ zBzz9zz8zz8zz6zz4zz4zz6zz8zz9zzBzzDzzFzzGzzGzzIzzK\ zzMzzOzzPzzRzzTzzTzzPzz0z } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 22-05-04 (Hexafault [3])
by Jim Muth 22 May '04

22 May '04

FOTD -- May 22, 2004 (Rating 3) Fractal visionaries and enthusiasts: I'm still far behind in the work, so the discussion will once again have to be brief. I think it was Lee Skinner who named the Z^(2.1828...) fractal the 'Zexpe' fractal. To create today's image, I have taken the 'Zexpe' fractal, and with the MandelbrotBC2 formula, calculated it at a different level to produce a different yet similar fractal. This fractal is indescribable, basically a Mandeloid standing on its nose, with branch cuts and irregularities everywhere. Several jagged spirals lie on the northwest part of this fractal; today's scene is rather deep in one of these spirals. I named the image "Hexafault", because the midget at the center is sliced almost perfectly symmetrically by six major branch cuts, or fault lines. It is rare to see such fault-line symmetry in a fractional-power fractal. Unfortunately, I gave almost no effort to the coloring, not that it would have made much of an improvement if I had. As a result, the rating is another lowly 3. But the very fast render time of 33 seconds raises the overall value to a very respect- able 534. Those who prefer to avoid rendering may download the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was pleasant enough here at Fractal Central on Friday, with some sun and a temperature of 81F 27C, but the cats had to be escorted as they took their daily walks in the yard, to keep them from overstuffing themselves with those easy-to- catch cicadas that are flying around by the millions. Today is starting sunny and quite warm, and the cicadas are quite active. It looks like another chaperoned day for the duo. For me, it looks like I'm going to try to get caught up. If I make reasonable progress in the work, the next FOTD will appear in 24 hours. If not, it might be 48 or 72 hours. Until next FOTD, take care, and who will be first to realize that the universe is a great fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hexafault { ; time=0:00:33.67--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=-1.3193191562\ 43292/+0.2253921211100132/1952924/1/-165/-5.999734\ 35516655e-009 params=2.71828182845905/0/0/0 float=y maxiter=1000 inside=0 logmap=23 periodicity=10 colors=000AMQ8OH6Q9DUAKXBR_CYbDdeEkhFrkGphIofKncLm\ aNkZPjXQiVShSUgQVeNXdLZcI_bGaaEbbHdcKfdNheQjfTlgWn\ hZpiarjdtkgvliwkkvjlujnuiotiqthrsgtrgurfwqfxqbsp_o\ pXkpTfpQbpNZpM`oLbnLcmKelJgkJhkNdgQ`cTY`WUX_RTbNQe\ KMhGIkDFlCIlBLlBOlARlAUl9Wm8Zm8am7dm7gm6jm6lk7EjCH\ iHKhMNgRPfWSe`VdeYcj_`hXYgUVeRTdPQcMNaJK`GI_EGaDEd\ CCfAAh98k86m74o68m7Bk8Fi9IgALeBPcCSaDV_EZYFaWGeUHh\ SIkQJoOKrMLuKMnPOgTP`XRU`SNeTGiV9mW3qX4rZ5r`6sa7sc\ 8se8tf9thAtiBukCumCvnDvpEvrFwsGwuGwvEtsDqqCqnArl9s\ i8tg6ud5vb4w_3xY2y_2za2zc1ze1zg1zi0zk0zm0zo0zp4zl7\ ziBzfEzcIz`LzYOzVQzTTzQVzOYzL_zJbzHdzEgzCiz9lz7nz5\ pz7rz9tzBvzDwzEdzaMzxMzwMzwMzwMzwMzwMzwMzwMzwMzwMz\ wMzwMzwMzwMzwQztTzqWznZzlazidzfgzdezcczbazb_zaZzaX\ z`Wz_UzZTzZRzYQzXOzWNzWCzN2zF8zKEzOKzSQzWVz_`zdfzh\ lzlrzpwztqzokzjfze`z`VzXQzSKzNEzI9zECzKFzQIzWLzaOz\ fEz3Iz5Lz7JzjIzmIzoFzfDzY } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

A fractal showing the fractional power Mandeloid "fault line" phenomenon (fractal "SierpinskiUnwoven")
by Hiram Berry 21 May '04

21 May '04

A few days ago I asked if anyone on this forum was familiar with the phenomenon whereby a Mandeloid, even when done as a union of the sets produced from all its critical points, ends up showing straight or smoothly curved lines on the boundary between inside and outside points, or else in the outside iteration zones in a discontinuous way (eg. smoothly sided polygons of iter=7 bordering a region with iter=15). I didn't get any answers on this, as to whether this is a genuine effect or not-- one doesn't see this in the classic M-set, nor as far as I have been able to tell in Mandeloids of integer power, but on encountering it once more and unintentionally, I am more confident that it is a genuine effect. Today though I came across an example of this phenomenon (accidentally) that was so thorough that the smooth lines actually extend on down fractally-- infinitely more such regions as the scale gets smaller. A couple of days ago Jim M. mentioned a Mandeloid using exponents 0.15 and -0.15, commenting that all the points were inside points (ie. there was no attraction to infinity to generate an outside). It got me thinking about the possibility of having the attractor for outside points being something other than infinity for fractals like this where the generator itself can't possibly go to infinity. So, on the way to writing a .frm that could display many orbits of outside points, I needed a sentry value to put in one of the parameters to indicate it was an orbit fractal and not the usual bailout kind; the number e came to mind since it would not likely be hit accidentally during the nonorbit iteration. I accidentally put this in the place for the exponent of the Mandeloid instead-- being a good approximation for an irrational number, an interesting thing happened on the _non_ orbit screen: the fractal generated had the "fault lines" all over one side of the fractal. Zooming in, they become so numerous in some areas that they become the dominant visual theme. One particular area is very reminiscent of the Sierpinski triangle-- with the triangles slightly rearranged and etched away, but trailing down into the infinitesimal (while blue-shifting as they get smaller). It can be generated by this .frm-.par pair: Sincerely, Hiram =================PAR BEGIN===================== SierpinskiUnwoven { ; The fault lines from fractional order Mandeloid powers ; proliferate @ exp=e. The torn triangles in fractal dimen ; sion remind me of the Sierpinski triangle with its parts ; distorted rearranged and partially covered. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=orbit_mandeloid passes=1 center-mag=-0.65861073150000000/+0.17502501600000000/86.33309/1/-47.5590\ 028298907441/0.159744895096057493 params=2.71828182845905/0/2.71828182845905/0/4/0 float=y maxiter=10000 inside=0; colors=(a)spectrm3.map colors=000oC8<7>uM4vO3vP3<2>yT1zV0zY0<3>xj0xm0wp0ws0vw1<3>hxHdxL`xPXyU<1\ 6>WyoWypWyq<2>WyuVzwWww<3>cgwdcwf_whWwjSw<4>e8wd4wc0w<9>Y0kY0jX0h<2>V0eU\ 0cU0c<118>TQTTQTTRT<3>SSS000000zzzc00<6>n00o00p00<3>w00<7>nE9mGAlIB<3>fP\ GeRHdTI<9>xU2 } ==================END PAR======================= ==================BEGIN FRM===================== Orbit_Mandeloid{ ; p1=A in z->z^A+C,p2=(sentry to do orbit,radius), ; p3=(bailout for nonorbit,angle subdivisions for orbit) IF(isinit==0) isinit = 1 A = p1 lim = real(p3), anglediv = trunc(imag(p3)), angle = 2*pi / anglediv sentry = real(p2), radius = imag(p2) rotfactor = cos(angle) + flip(sin(angle)) orbititer = trunc( (maxit - 1) / anglediv ) ENDIF isorbit = ( real(pixel) == sentry ) IF(isorbit) C_ct = 0 ; count C values on the radius i_ct = 0 ; count iterations per C value C = radius ; set initial C position to radius along +real axis continue = 1 ; the "do not bail out" flag ELSE C = pixel ENDIF z = 0 ; in either case z starts at 0 : IF(isorbit) IF(C_ct >= anglediv) ; should terminate continue = 0 ELSE ; normal iteration for orbit screen z = z^A + C i_ct = i_ct + 1 IF(i_ct >= orbititer) ; go to the next C value C_ct = C_ct + 1, i_ct = 0 z = 0 C = C * rotfactor ; rotate C-value around the circle ENDIF ENDIF ELSE z = z^A + C continue = ( |z| <= lim ) ENDIF continue } =================END FRM=========================

1 0

FOTD 20-05-04 (A Tangle of Points [3])
by Jim Muth 20 May '04

20 May '04

FOTD -- May 20, 2004 (Rating 3) Fractal visionaries and enthusiasts: I have another very busy day ahead of me, so I must again be brief. Today brings another 'nothing' fractal, worth only a lowly 3. The low rating reflects the disappointment I feel with it. I have named the image "A Tangle of Points" because it reminds me of a tangle of vines. It is part of the larger fractal that is created when portions of Z^(-0.8) and Z^(-7.5) are combined and (1/C) is added. The image has been 'evaporated', and therefore consists totally of 'inside' points made visible by the 'bof61' inside fill. Other fills might have done better, but I had no chance to try them. The rating of 3 and render time of 7 minutes combine into an overall value of 41. All this becomes meaningless when the completed image is downloaded from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Clouds hung tough all day Wednesday here at Fractal Central. Combined with occasional light rain and a temperature of 82F 28C, the lack of sun kept the fractal cats safely ensconced indoors. They were only mildly annoyed however, and spent the afternoon sleeping by the window. Today is again starting cloudy, but at least it is dry. The cats are still sleeping. It is too early to predict what kind of day they will have. As usual, I have a lot of work to do. Unless the unexpected happens, the next FOTD will appear here in 24 hours. Until then, take care, and where is the world going, other than around the sun? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Tangle_of_Points { ; time=0:07:17.42--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+15.30615106164459000/+1.23468727139517\ 000/5.37212e+009/1/157.5/-0.00641920475950448488 params=1/-0.8/0.2/-7.5/0/1e+100 float=y maxiter=750 inside=bof61 periodicity=10 colors=000r_IvbYydmwcjvbgtbesabq``p`Yn_Wm_TlZQjYOi\ YLgXJfWGdWEcVBbV9_REXOIULMRIQOEULBYI8aF5eEAbEF`EJZ\ EOXETVEXTEaREfPEjNEoLEtJExH7vZ0tp4sf8rYCqPGqGQ0YT0\ ZV0_Y0``0ab0be0cg0dj0el0fo0gq0go3cm5`k7Yi9VgBSeDPc\ FMgBTj7_n3fq0mm6kjBjfHhcMg`SeXXdUbbRgaNm_KrZHwY9va\ 2vd6rd9ndCjdFfdJbdMZdPWdSSdVOdZKdaGddCdg8dj5dh9cgD\ cfHceLcdPccTbbXba_b`cb_gbZkaYoaXsaWwaVzahzLuz4sx6r\ w7qu8ot9nrAmqBgjJbcRYYZSRfNKnIEuPNlVVdUU`TTXSSUSRQ\ RQNQPJPOGPNCOM9NL5NL2SSDWZN_eXY`TWWQURNSMKQHHOCEM8\ BKGEIOGGWIEcKCkMAsO8zQDvPIrONnNSkMXgLacKf_JjXJX_UJ\ bd5do6ap6_q6Yr7Wr7Us7St8Qt8Ou8Lv9Jv9Hw9FxADxAByA9z\ A7z9Hl8RZ7`L6j78g6Ae5Bb5D`4EY4GW3HT3JR2KO2MM1NK1PJ\ 5QJ8RJBSJFUIIVILWIPXISZHV_HZ`HaaHd_GfZFgYFhWEiVEjU\ DlTDmRCnQCoPBpOBrMAsLAtK9uJ9v_LAZG8ZB6_E5_G5_J4`L4\ `N4`Q3aS3aV2aX2bZ2ba1bc1cf0ch0cj0ek1gk1ik2jk2lk2nk\ 3ok3qk4sk4tk4rg3qc3o_2nX2 } 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==================================

1 0

FOTD 19-05-04 (Decorated Minibrot [4])
by Jim Muth 19 May '04

19 May '04

FOTD -- May 19, 2004 (Rating 4) Fractal visionaries and enthusiasts: I am still lagging behind in my regular work, so I must be brief. Z^(0.15) does not make a fractal; nor does Z^(-0.15). And combined they do not make a fractal. They make a blank screen consisting of trapped 'inside' points, but just as with the 'evaporated' images, these points can be brought to life by rendering them with an active inside fill. In today's case, the bof61 fill works best, though the main action lies just beyond the left border of the default screen. Hiding almost invisibly there lies the scene of today's image, which pictures a strange Mandeloid with unusual decorations. I named the image "Decorated Mandeloid". The rating of 4 combines with the render time of just under 2 minutes to give an overall value of 205. That value might be raised by downloading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather here at Fractal Central on Tuesday was fair enough, with a temperature of 82F 28C. It was fair enough that is until it started thundering around 6pm. But by that time the fractal cats had long since come inside. The dynamic duo has taken a liking to the cicadas, which are in unlimited supply in the area. The bugs are good to eat and easy to catch, but the duo doesn't know when to stop catching and eating them. I guess the aging cats feel good about once again being able to catch prey at will, but I will likely have to limit their outdoor time until the cicadas are gone, which will be in about a month. I do not want the duo overstuffing themselves with wings. When the cicadas started singing, I thought there was a faucet running somewhere in the house, but now that I know what it is, I find the song rather enjoyable. It has a diffuse, direction- less, far-away quality about it that always raises feelings of nostalgia. The last time I heard it I had just discovered fractals, and had not even dreamed of leaving my designer position at the print shop to see what I could do on my own. A lot can happen in 17 years. If I don't fall too far behind in the work, the next FOTD will appear in 24 hours. Until then, take care, and search for the source of dark energy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ DecoratedMandeloid { ; time= 0:01:57.10--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=t center-mag=-1.998748343088183/0/1139.953/1.1658 params=1/0.15/1/-0.15/0/0 float=y maxiter=256 inside=bof61 symmetry=xaxis periodicity=10 colors=000L2OD0ND1OB6T9BX8Ga6Ld4Qi1Tl0Yq0bt0gz0lz0\ qz0tz0uz2qz8qzEpzJpzOnzTlz_lzdkzikzniztgzzgzzfzzfz\ zgzzizwizskzpksklkgladnT_nJXpBTp2Rn6Qn8Qn9OlBNlDNl\ ELlGJkIJkJIkLIkNLVQQRaTQkYOwaNznTzzYzzbwzfzpizdlzT\ pzJszBzz2zz0zxtzzzfzzdzqbzgbz_awRanJdzDfz4iz0kz9gz\ LdzXazgYzsVqzTkdkgEzf0zd0za4z_DtYJkXRbVYVTdbqiiznp\ zQObz0zz0zz0zzDzzQztbznnzszzwzzzzzzzzxzzszwnzqizld\ zg_wbVpYRkT_p_ftfnzktzqzzxzzzzzzqzwgst_kqQdpIYl9Rk\ 8Tl6Vl6Xl4Yl2_l2al1bl1bl8kqEqtJzxQzzVzzzEfkEbXE_IE\ X2ET4zg6sl8lq8fw9_zBTzBNzDGzD9zLDzRGz_JzfNzwbxzssz\ znzzqzztqzxfzzTwzItzIwzIwzIxzIxzLzzOzzRzzVzzXzz_zx\ bzxfzwiztkztnzsqzqtzqzzkxzpzznzznzzlzzk19T8EVDJXIN\ YNR_RX_X_aadbgidllfqqfwwgzzizzkqxzszzszzszztzztzzt\ zzwzzwzzwzzxzzxzzxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzxzzwzzwzztzzszzqzzqzzpzznzznzzlzzkzzRzz\ VzzXzzYqgxkaqfVkaNfVG_Q9V } 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==================================

1 0

how do I generate a file par
by Alessandro Flamini 19 May '04

19 May '04

Hi, I've just started to use Fractint and I don't know how to create a new fractal starting from scratch. My understanding is that I should create a file.par and a file.frm (the second with wordperfect) which contain the code, am I right? Furthermore, how do I generate a par file? Thanks in advance. Alex

2 1

Project Euler
by Paul N. Lee 19 May '04

19 May '04

Greetings, The following was taken from another fractal related group, thought it might be of some interest to a few individuals here as well. ________________________________________________________________________ Project Euler Leonhard Euler (1707-1783) Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. Please be warned that the problems are challenging and you are unlikely to make much progress if you have no knowledge of programming. Having said that, this is both the perfect environment and opportunity to learn new techniques and refine your programming skills. In order to track your progress it is necessary to setup an account and have Cookies enabled. If you already have an account and would like to login, click here: http://www.mathschallenge.net/index.php?section=project&ref=login To setup a new account click here: http://www.mathschallenge.net/index.php?section=project&ref=register When new problems are added to the database they are initially worth 20 points. However, each time a problem is solved by a registered user, it reduces slightly in value. As a result, easy problems, which will be solved by most users, quickly become low scoring problems. Conversely, truly difficult problem will remain high scoring. Your overall score is not fixed and will change if any of the problems that you have already solved change in value. It is hoped that this entirely dynamic and original scoring system will, on the one hand, add an extra dimension of interest to solving problems, but on the other hand, will lend itself to users of all abilities. That is, it should allow beginners to identify the easier problems to get started with, and advanced users to target the more difficult and challenging problems. Please note that each problem is designed according to a "one-minute rule", which means that although it may take several hours to design a successful algorithm with more difficult problems, an efficient implementation will allow a solution to be obtained on a modestly powered computer in less than one minute. Of course solving a problem is the ultimate goal, but if you consider yourself a skilled programmer/problem solver you may like to retry some of the challenges that took longer to solve on your first attempt. http://www.mathschallenge.net/index.php?section=project&ref=problems ________________________________________________________________________ Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

1 0

RE: need some help...
by carenp 18 May '04

18 May '04

.2. the operating system is win2k, but may be using XP (ickypoo) within 6 months... .4. downloaded... that's exactly what i was looking for, as long as the gallet and REB formulae are in there... .ManPWin. handled image size fine, but couldn't read the PARs worth a darn... .overall. THANX! :) Subject: Re: [Fractint] need some help... Caren K. Park wrote: > .2. does anyone know how to make fractint understand a newer nVidia video card, specifically in 1600x1200 mode? What operating system are you using?? > .4. FRMs are problematic, too... does anyone have a collection of FRMs fromthat time period, up to say 1997ish? Have you looked through what is available in this latest updated collection that I have been taking care of: http://home.att.net/~Paul.N.Lee/OrgForm.html > > i've tried chaos pro and..... > i've also looked at winfract 20.2.... I have not tried Paul's "ManPWin" for higher resolutions, but that might be an option: http://www.deleeuw.com.au/

5 4

MFOTD
by M J Benkers 18 May '04

18 May '04

Dear Fractallovers, Again I found a nice picture in my big fractal collection. I saved all my fractint-pictures on a iomega-zipdisk. When I made the fractals, long, long ago; the hard-disks were small and cd-romburners didn't exist. The only way to save a lot of pictures was on a zip-disk. So I buyed a zipdrive to save all my artwork. Nowadays I never use it, so I had to install the bloody thing again. Then I had some trouble to make a par-file. But after much trying and thinking I succeded in making a par-file that really works. Greetings, Mary BEGIN PARAMETER FILE horsetail { reset=2003 type=lambdafn function=cos center-mag=0.760521/1.17913/1.364392/1/60.077870103739734/-2.37641987192\ 727111e-007 params=-1.029754638671875/0.670745849609375 float=y inside=bof60 colors=Lls<20>5IW4HV4FU<2>1BR09P19Q<8>FHbGIcIJe<2>MMiONkQPk<8>kktmmuppv<\ 2>wwyzzzzwx<8>zOazK_zGX<3>z0N<8>Q0AL08H07<3>000<8>8JC9MEAOF<3>EXLCYLA_K<\ 8>dnhhpkkrm<3>zyyzzz<25>nTnnRnmQm<3>kKk<9>niYnlXnoV<2>owRpzPoxP<16>UGLTE\ LSBK<2>O3KM0JM0K<13>90i80k70m<2>40r30t00v10x00z<23>KizKkzLmz<3>Puz<3>Mpv\ 000kkk } END PARAMETER FILE The older I grow the more I distrust the familiar doctrine that age brings wisdom. H. L. Mencken

1 0

FOTD 18-05-04 (Random Shapes [*])
by Jim Muth 18 May '04

18 May '04

FOTD -- May 18, 2004 (Rating *) Fractal visionaries and enthusiasts: The time has come for the next FOTD to appear, but I am still behind in my work. I do not wish to disappoint, so I have gone to Fractal Land and taken the first thing I found, which in this case, not surprisingly, turns out to be a midget. The fact that it is not quite a quadratic midget is a bit more surprising. The generating expression is Z^(2.03)+C, which means that, when the MandelbrotBC2 formula is used, the resulting image can be of many different shapes. In this case however, since the exponent is so close to 2, most fractals will be a rotated version of the traditional Mandelbrot set, with a bit of distortion thrown in to make things interesting. In today's case, the parent M-set is rotated only slightly clockwise. The main bud has come apart, with near total chaos in the area between the two competing remnants. Today's image lies in this chaos.. I gave the image a wild-card rating. I put too little effort into it to consider a firm rating. In fact, I am not even certain it is worthy of being a FOTD. I named the image "Random Shapes" which is basically a full description. The render time of under 3 minutes makes it almost worth the effort of running the included parameter file. I still have quite a bit of work to do, plus drifts of cicada shells to sweep away, so if I miss a FOTD or two in the coming week or so, don't be concerned. I merely will be still trying to catch up in the work. The image, for what it is worth, is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather has been pleasant here at Fractal Central since the last FOTD, with the exception of Monday afternoon, when an intense thunder-storm moved in, with 2 inches (5cm) of rain, 1 inch (2.5cm ) diameter hail, terrifying (at least for some) lightning and thunder, and winds of 65mph (100kph). Needless to say, the cats dashed into hiding, and were not seen for several hours. Today is looking to be a repeat. We'll see how it goes. I'm still a bit behind in my work, so the thing for me to do is start working. Until next FOTD, take care, and do dare. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Random_Shapes { ; time=0:02:51.59--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-1.19187521524887300/+0.035312902072153\ 03/422.451/1/-127.5/-1.03011349450454759e-012 params=2.03/0/0/0 float=y maxiter=1200 inside=0 logmap=26 periodicity=10 colors=000diNfkLglKinIkpGlqFnsDotChmBbgAXa9RW9LQ8F\ K79E74FA7GCAHFDIHHJKKKMNLPQLRUMTXNW_OYbP`fQbiRelSg\ oSilTgjUehVcfWadX_bYY`ZWZ_UX`SVaQTbORcMPdKNdIPeHRe\ GTfGVfFXfFZgE`gEbhDdhDfhChiCjiBljBnjApjAT4WS3YR3_Q\ 2`P2bP1cO1eN0fM0hM0iC2d23`ABcIJfQQiYYleeollqUmhBn_\ Aka9ic9gd8df8bg7`i7Yj6Wl6Um5Ro5Pp4Nr4LsBOmHQhNScTU\ Z_WUeYPk_KqaFoZGnWHmUHlRIkOJjMJiJKhHKlOGpVCs`8tWFu\ SMvOTwK_xGfyCmxDjwEhwFfvGduHbuI`tIYtJWsKUrLSrMQqNO\ qNMaROMVQ6ZS9UWCPZFKaIFdLAgO5jQ0mgIpx_sF1vG7wHCxII\ yINwSPw`RwiSwiPwiNwiLwiIwiGwiEwiBwi9wi7wi5wCDwDEwD\ EwEFwEFwFFwFGwGGwGGwHHwHHwIHwIIwJIwJIzXNzjRzkPzkNz\ kMzlKzlJzlHzlGzmFznEznDzoCzoBzpAzp9zq8zq7zr6zr5zsC\ zsIztPztVzuazuczvczvcztczrczpcznczlczjczhczg`zeZzc\ WzaUz_SzYPzWNzVKzTIzRGzPDzNBzL8zJ6zI4zG6zF8zEAzCCz\ BEzAGz8Iz7Kz6Mz4Oz3Qz2SzKQz`PzqOzoPznPzmPzlPzkPzjP\ ziPzgQzfQzeQzdQzcQzEfzFgz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

MyFractalOfTheDay
by M J Benkers 18 May '04

18 May '04

Dear Fractal Lovers, Because Jim is very busy, I searched in my big fractal picture collection for a nice fractal. I did find something and I hope you like it..... The fractal weather in Holland is very nice, after a cold week with clouds and a cold wind blowing, so my fractal dog Moppie and I made a long walk in the park. Moppie is now gnawing on a bone, and I am writing this message nibbling on a rice cake. I am addicted to that stuff. I hope you have a nice day and I will send you tomorrow a new fractal from my collection, if Jim is still busy. Until then, take care, and keep cool, Mary PARAMETER FILE: squidgie { reset=1730 type=spider passes=b center-mag=-0.088536/0.175075/28.73344/1/-90/3.88578058618804789e-016 params=0/0 float=y maxiter=1000 fillcolor=200 inside=bof60 outside=mult invert=0.229998/0/0 decomp=64 periodicity=4 colors=000Puz<26>5IW4HV4FU<2>1BR09P19Q<8>FHbGIcIJe<2>MMiONkQPk<8>kktmmup\ pv<2>wwyzzzzwx<8>zOazK_zGX<3>z0N<8>Q0AL08H07<3>000<8>8JC9MEAOF<3>EXLCYLA\ _K<8>dnhhpkkrm<3>zyyzzzzyz<26>DOGBNE9LD<3>1F5<8>VeHZhIakJ<3>oxP<16>UGLTE\ LSBK<2>O3KM0JM0KL0MK0OJ0Q<25>o0Rp0Rq0R<3>w0S<9>`XlZ`oXcq<3>NqzOsz } END PARAMETER FILE The older I grow the more I distrust the familiar doctrine that age brings wisdom. H. L. Mencken

2 1

need some help...
by carenp 17 May '04

17 May '04

hello, fractographers... some of you might remember me from the "good ol' days" as an artist with the stone soup group back in the 80s and 90s... i was wondering a few things yesterday: .1. does anyone happen to have archived a copy of my pars, specifically from 1601 to 1700? i have the earlier ones, but for some reason cannot find those... .2. does anyone know how to make fractint understand a newer nVidia video card, specifically in 1600x1200 mode? .3. on a related subject, does anyone know why i can't save a disk video of my creations in fractint 20.3? i'd like to push some out as far as 6000 x 4500, and i have the disk space and the processor to handle most of them... .4. FRMs are problematic, too... does anyone have a collection of FRMs from that time period, up to say 1997ish? those formulae must also have died in the great crash a few years ago (don't ask; i'm still grieving)... i'd be especially grateful for sylvie's and the REBs... i've tried chaos pro and it worked well for one of my old collection (one that didn't require an external FRM), but crashed badly on another (same one that when it worked, it didn't recreate correctly at all)... i've also looked at winfract 20.2, and it refuses to handle large images (among other issues)... i'm looking for as inexpensive an option as possible, as i'm broke trying to get my new photography business up and running... thanx, folks ;) 00 caren http://www.parkgallery.org

6 5

Polymorphic Julia Sets and the Spacebar Toggle
by Hiram Berry 16 May '04

16 May '04

[note: repost; on checking the archive and finding it absent, again I suspect that my post of last night was not received] "Gerald K. Dobiasovsky" <gerald.dob(a)aon.at> wrote: > > Hiram Berry wrote: > > > But how is the "cursor position" variable communicated to the > > program? I see how one may use an IF/ELSE to take differing execution paths > > in the generation of the fractal, but for it to work the cursor position > > from before the toggle must be known after the toggle. How is that done? I > > have an inkling that the cursor position might be put into the parameter p1 > > That's exactly how it works. > > Fract200.par and fract200.frm (both distributed with Fractint) > are the files to look into. There are two example image pars > "image_demo_julia" and "image_demo_mandel" calling an example > formula contained in the formula file. > Thankyou Gerald, for confirming this. On the strength of that, I went ahead and altered the "bimandeloid" formula (generalized z->z^A+k*z^B+C iteration) to enable space bar toggling to the Julia set corresponding to the cursor position. In the midst of doing so it occurred to me that the meaning of what a corresponding Julia set meant could be interpreted in more than one way. As I understand it we make the "C" part of the iterator constant and then vary over the screen the initial z value in order to generate the Julia sets, but it seems to me the choice of the z_init parameter for screen variation is somewhat arbitrary: it is after all just one of several reasonable parameters that could be variable in the generating formula. I use the term "k" in the bimandeloid formula rather than separate coefficients on each of the terms because as I showed in a reply to Jim Muth earlier, a simple change of variable allows one to normalize the leading coefficient and get a fractal that is geometrically similar to the first one-- which I consider the same fractal. So, the coefficient "k" would seem an obvious choice to vary across the screen instead of z_init. The other one I thought reasonable was to vary the exponents A and B; since they are both real the form A+Bi suggests itself for the screen. Now its necessary to communicate which type of Julia set is to be toggled from the bimandeloid main set, so I do this as a flag in the real part of parameter p5 in the formula: 0=usual sort of Julia set, of z_int, 1= k-variant Julia set, 2= power Julia. The nice thing about these is that one may toggle into the first type of Julia from the bimandeloid, then use the z-screen to go to the other types without changing the C-value put into p1 by the toggle. These alternative Julia sets are very interesting! The k-variant one looks much like a hybrid between Mandelbrot and Julia sets, though the Mset parts look complete (not with the eroded surface of perturbed sets), while the power Julia set looks _very_ different from what we usually think of as Julia sets, with areas of connected smooth disks and areas of almost random chaos. In any event, here are some results in case anyone cares to have a look at this system of multiple types of Julia set. Regards, Hiram ==================.pars using bimandeloid formula BEGIN================== Bimandeloid_Main { ; A Biomandeloid-- the main M-set like view of the set ; generated by z->z^4+(0-1.5i)*z^7+C. Note the trilateral ; only symmetry (not bilaterally symmetrical on the arms). ; Decided by real(p5),<sp>toggles goes to 1 of 3 Julias. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=bimandeloid3 ismand=y passes=1 center-mag=0/0/0.6666667 params=0/0/4/7/0/-1.5/400/4/0/0 float=y maxiter=10000 inside=0; colors=(a)speccyc1.map colors=000zV0<6>yi0yk0xn0<2>xt0ww0vw1<9>exKcyLayN`yPZyRXyT<17>WyoWypWyq<\ 2>WyuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SS\ S000000zzzc00<6>n00o00p00<3>w00<8>mGAlIBjJC<3>eRHdTIfTG<8>xU2 } BimandeloidJulia1 { ; The usually defined Julia set from a cursor point in the ; Bimandeloid z->z^4 + (0-1.5i)*z^7 + C (varies the ; initial z value as screen position). Generated by the ; space bar screen toggle from the bimandeloid. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=bimandeloid3 ismand=n passes=1 center-mag=0.0194201/-0.0147727/0.9576667/1/90/-1.23373533611470521e-014 params=-0.1505376344086022/0.8663624511082139/4/7/0/-1.5/400/4/0/0 float=y maxiter=10000 inside=0 colors=000zV0<6>yi0yk0xn0<2>xt0ww0vw1<9>exKcyLayN`yPZyRXyT<17>WyoWypWyq<\ 2>WyuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SS\ S000000zzzc00<6>n00o00p00<3>w00<8>mGAlIBjJC<3>eRHdTIfTG<8>xU2 } BimandeloidJulia2 { ; A "k-variant" Julia set from a cursor point in the ; Bimandeloid z->z^4 + (0-1.5i)*z^7 + C (ie. the -1.5i ; term is no longer constant, but varies with screen pos) ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=Bimandeloid3 ismand=n passes=1 center-mag=0.51448/-2.17995/0.3370987/1/90/3.88578058618804789e-016 params=-0.1505376344086022/0.8663624511082139/4/7/0/-1.5/400/4/1/0 float=y maxiter=10000 inside=0; colors=(a)spectrum.map colors=000zzzc00<7>o00p00r00s00u00w00<9>lIBjJCiLD<3>dTI<4>nTApU8rU7<2>xU\ 2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<8>fxIexKcyL<2>ZyRXyTXyU<16>WyoWypWyq<2>W\ yuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SSS00\ 0000 } BimandeloidJulia3 { ; The third type "Power Julia" set from a cursor point in ; Bimandeloid z->z^4 + (0-1.5i)*z^7 + C (the exponents ; 4 and 7 are replaced by real,imag screen position) ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=Bimandeloid3 ismand=n passes=1 center-mag=0.0194201/15.5171/0.02551012/1/90/-1.23373533611470521e-014 params=-0.1505376344086022/0.8663624511082139/4/7/0/-1.5/400/4/2/0 float=y maxiter=10000 inside=0; colors=(a)PwrJulia.map colors=000DQA8R8<3>a6ji0tj7t<3>n_wofxpmyruznpzijy<3>knhlpdlq`<3>ovJ<4>T_\ VOWXJR_<3>08i<3>HEaMF_QHY<3>gNQYSZ<3>fiQimOkrMnwJ<6>q_RqXSrTU<3>tFZ<7>tS\ PtUNtWM<2>t`IubGubTuaev`s<4>oSYmQTlOP<2>gIBeG6eI6<5>dW8dY9d_9<2>dfAciBdf\ B<3>hU8iR7jO7kL6mH5cIFUJP000zzzc00<7>o00p00r00s00u00w00<9>lIBjJCiLD<3>dT\ I<4>nTApU8rU7<2>xU2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<8>fxIexKcyL<2>ZyRXyTXy\ U<16>WyoWypWyq<2>WyuVzwWww<3>cgwebvgXtiRslLqoRWsYA<3>SMNLJQEGT6CX<2>lkMs\ PWz2f<3>X3HQ3AI43<4>_PJ<3>IQC } BimandeloidJ_Insid { ; A Julia set generated by space-bar toggling a point in ; the generator Mset of z->z^4+(0-1.5i)*z^7+C. The point ; was just on the inside of the set-- the relation of ; inside pt(M)->connected(J) seems to hold for Bimandeloid ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=bimandeloid3 ismand=n passes=1 center-mag=0/0/0.6666667 params=-0.6666666666666666/0.1779661016949153/4/7/0/-1.5/400/4/0/0 float=y maxiter=10000 inside=0; colors=(a)speccyc1.map colors=000zV0<6>yi0yk0xn0<2>xt0ww0vw1<9>exKcyLayN`yPZyRXyT<17>WyoWypWyq<\ 2>WyuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SS\ S000000zzzc00<6>n00o00p00<3>w00<8>mGAlIBjJC<3>eRHdTIfTG<8>xU2 } BimandeloidJ_Power { ; Part of the Power Julia from the same C point as ; BimandeloidJ_Insid. Black is _inside_ color. ; ; ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=bimandeloid3 ismand=n passes=1 center-mag=-2.39484/-0.818481/1.253133/1/4.99999999999999822/-5.05012698\ 326368081e-014 params=-0.6666666666666666/0.1779661016949153/4/7/0/-1.5/400/4/2/0 float=y maxiter=10000 inside=0 colors=000zzzc00d00f00tw3<3>m00<3>s00u00w00<9>lIBjJCiLD<3>dTI<4>nTApU8rU\ 7<2>xU2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1tw3w00qw7<5>fxIexKcyL<2>ZyRXyTXyU<1\ 6>WyoWypWyq<2>WyuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQ\ TTQTTRT<3>SSS000000 } =================END .pars===================================== ===============Toggling bimandeloid .frm BEGIN=========================== Bimandeloid3{ ; toggles with 3 different kinds of corresponding Julia sets ; generator z->z^A+k*z^B+C, main screen varies C, first Julia varies z_init ; second Julia varies k, third Julia varies exponents as A+Bi. ; Flag Jf: 0=first Julia type, 1=second Julia type, 2=third Julia type ; p2=(A,B)[reals],p3=k[complex],p4=(bailout-4,#critical points),p5=(Jf,0) ; Main screen and second Julia type start iterations on critical points IF(isinit==0) ; image-wide initialization section isinit = 1 maxit = maxit ; forces fp Jf = real(p5) IF( ismand || Jf!=2 ) ; cases where A,B constant A = real(p2), B = imag(p2) ENDIF Jf = real(p5) IF( ismand || Jf==0 || Jf==2 ) ; cases where k is constant k = p3 ENDIF bailout = real(p4) + 4 IF( ismand || Jf==1 ) ; case where critical points used cps = trunc(imag(p4)) IF(cps<=0) ; give a default value for entry of 0 cps = 1 + ceil(abs(A - B) ) ; works for integers only ENDIF diff = (A - B), angle = 2 * pi / diff rotfactor = cos(angle) + flip(sin(angle)) IF(ismand) ; case where cps are constant over screen principal = (-B * k / A) ^ (1/diff) ENDIF ENDIF ENDIF IF(ismand) C = pixel ; Mandelbrot-like type ELSE ; initialize C and variable non-z for Julias C = p1 ; one of Julia-like types IF( Jf==1 ) ; Julia type which screen-varies k k = pixel principal = (-B * k / A) ^ (1/diff) ELSEIF( Jf==2 ) ; Julia type which screen-varies A,B A = real(pixel), B = imag(pixel) ENDIF ENDIF IF( ismand || Jf==1 ) ; initialize z for cases which use cps z = currcp = 0, cpctr = 1 ; first critical point is z = 0 isdiv = isalldiv = 0 ; flags for current cp and all cps divergence ELSEIF( Jf==0) ; case which screen-varies z_init z = pixel ELSE ; otherwise start z at 0 z = 0 ENDIF : IF( ismand || Jf==1 ) ; cases that use cps IF(isdiv) ; last critical point diverged cpctr = cpctr + 1 IF(cpctr > cps) ; finished, with all cps diverging isalldiv = 1 ELSEIF(cpctr == 2) ; second cp is the principal value z = currcp = principal, isdiv = 0 ELSE ; rotate the last cp by angle on the complex plane currcp = currcp * rotfactor z = currcp, isdiv = 0 ENDIF ENDIF IF(isalldiv != 1) z = z^A + k*z^B + C ; main iteration isdiv = ( |z| > bailout) ENDIF ELSE ; cases that do not use cps z = z^A + k*z^B + C ; main iteration isalldiv = ( |z| > bailout) ENDIF isalldiv == 0 } ================END .frm===========================

1 0

Re: [Fractint] Re: FOTD 07-05-04 (Rocket [6])
by Jim Muth 16 May '04

16 May '04

At 12:25 PM 5/7/04 -0500, Paul Lee wrote: >I guess I should have checked back a few more years before renaming to a >#2 version, since it appears that there are several versions already. I simply used the version of the formula that was included in the original 1997 par file. I'll rename it JimsCompMand4. Having several versions of the same formula always creates problems. Jim M.

3 2

Another break
by Jim Muth 14 May '04

14 May '04

Disappointed fractal fans: Due to a log-jam in my other work, I will be unable to post the FOTD until Tuesday, May 18. I'm sorry for the let-down, but some things are simply unavoidable. I will however continue reading the lists and adding brief comments whenever I have something worthwhile to say. Jim M.

1 0

How may one write .frms that enable Julia/Mandelbrot toggling?
by Hiram Berry 13 May '04

13 May '04

When we run an explicitly Mandelbrot or Julia fractal in fractint, space bar toggling lets us generate the reverse type corresponding to a point on the screen represented by the cursor. I know that the "ismand" boolean variable is supposed to help implement that behavior when writing formula type fractals. But how is the "cursor position" variable communicated to the program? I see how one may use an IF/ELSE to take differing execution paths in the generation of the fractal, but for it to work the cursor position from before the toggle must be known after the toggle. How is that done? I have an inkling that the cursor position might be put into the parameter p1 (which would overwrite anything in there before) due to an accident; I ran this "image" version of the M-set (to see the image of attractor points -- I put the value of the attractor in p1), but then when playing around with it while looking at the orbit screen hit the space bar (ismand isn't in the formula and no attempt was made for it to have a toggle counterpart, but...) which caused the same fractal to be rendered, but the location of the image points changed. So I'd appreciate it if someone more experienced with writing .frms would confirm/deny/explain what happens with the space bar toggle. Thanks, Hiram ===================BEGIN=================================== img of pt in 3bud { ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=MsetImages passes=1 center-mag=0/0/0.6666667 params=-0.1700879765395894/0.7607561929595827/0/10/0.01/0 float=y maxiter=2000 inside=zmag outside=0 periodicity=0; colors=(a)spectrum.map colors=000zzzc00<7>o00p00r00s00u00w00<9>lIBjJCiLD<3>dTI<4>nTApU8rU7<2>xU\ 2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<8>fxIexKcyL<2>ZyRXyTXyU<16>WyoWypWyq<2>W\ yuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SSS00\ 0000 } MsetImages{ ; inside=zmag renders closest approach to given point ; p1=target point p2=(bailout-4,begin scan pass) p3=(bullseye granularity,0) ; color=1 shows points which hit < granularity from p1. periodicity=0. ; Roughly shows the image of points with p1 as an attractor. IF(isinit==0) bailout = 4 + real(p2) isinit = 1 IF(imag(p2)<1) scan = 1 ELSE scan = trunc(imag(p2)) ENDIF gran = real(p3) targ = p1 ENDIF z = zp = 0 iter = 1 C = pixel : IF(iter == scan) ; start tabulating closest distance closest = cabs(zp-targ) ELSEIF(iter > scan) ; compare to see if new closest dist = cabs(zp-targ) IF(dist < closest) closest = dist ENDIF ENDIF zp = sqr(zp) + C iter = iter + 1 IF( iter==maxit && iter>=scan ) ;last pass-- render inside ins_col = 1 + trunc( closest/gran ) z = sqrt( ( ins_col*2 - 1 ) / maxit ) ENDIF |zp| <= bailout } =======================END=====================

2 1

Re: [Fractint] Strange result when rendering "bimandeloid"
by Hiram Berry 13 May '04

13 May '04

[note: I sent this msg to the list last night, but it appears not to have been registered in the archive, thus the resend.] Lee H. Skinner <skinner(a)thuntek.net> wrote: > The horizontal lines are periodicity effects. Set periodicity=no. > Thankyou, Lee. That's exactly what the lines were-- your remedy totally eliminated them. On closer examination I noticed that there was something else wrong with the second fractal. Areas of the inside to outside border appeared to have the visual quality of perturbed sets, implying that I had not initialized those areas on all the critical points of the generator expression. I found that I had made a mistake in the formula where calculating the principal value of the root that sets the modulus of the nonzero critical points, and had used an exponent of diff instead of 1/diff. Fixing that as well caused the second fractal to render properly. I wish that setting periodicity=0 had changed the result of the first .par as well, but it did not. It rendered substantially the same, with the straight horizontal border between outside and inside sets along the negative real axis, so that conundrum remains. Changing the exponents in the terms so that they differed by an integer, but were themselves rational nonintegers, changed the position of the puzzling behavior but not the fact of its existence. In the following case (with the revised .frm) the exponents are 5.5 and 3.5 instead of 5 and 3.5, and a section of the main body's border in the third quadrant is shown. It doesn't look like the perimeter of an M-set at all; it is smooth and the outside points which usually show the direction of a gradient are divided up into many facets without an apparent gradient direction. I have to wonder if this is a mathematical effect related to taking a fractional power-- I had thought that the sets would vary continuously as the exponents were varied, but this effect suggests discontinuity instead, if it is not spurious. Regards, Hiram ================BEGIN PAR & FRM===================== OddThirdQuadrant { ; z->z^5.5+(0-1i)*z^3.5+C ;The fault line has been replaced by this faceting of the ; outside=iter points and smooth surfaced "midgets" and ; main body coastline in the third quadrant. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=bimandeloid2 passes=1 center-mag=-0.716191/-0.354303/8.788233/1/-115/-2.50563458870090017e-014 params=5.5/3.5/0/-1/400/3 float=y inside=0 periodicity=0 colors=000zzzc00<6>n00o00p00<3>w00<8>mGAlIBjJC<3>eRHdTIfTG<3>nTApU8rU7<2\ >xU2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<9>exKcyLayN`yPZyRXyT<17>WyoWypWyq<2>W\ yuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SSS00\ 0000 } Bimandeloid2{ ; vary C over the screen in z->z^A+k*z^B+C ; p1=(A,B)[reals],p2=k[complex],p3=(bailout-4,#critical points) IF(isinit==0) ; image-wide initialization section isinit=1 A = real(p1), B = imag(p1), k = p2 bailout = real(p3) + 4, cps = trunc(imag(p3)) IF(cps<=0) ; give a default value for entry of 0 cps = 1 + ceil(abs(A - B) ) ; works for integers only ENDIF is_agtb = (A > B), diff = abs(A - B), angle = 2 * pi / diff rotfactor = cos(angle) + flip(sin(angle)) IF(is_agtb) ; principal roots of the eqn for cps principal = (-B * K / A) ^ (1/diff) ELSE principal = (-A / B / k) ^ (1/diff) ENDIF ENDIF C = pixel ; Mandelbrot-like type z = currcp = 0, cpctr = 1 ; first critical point is z = 0 isdiv = isalldiv = 0 ; flags for current cp and all cps divergence : IF(isdiv) ; last critical point diverged cpctr = cpctr + 1 IF(cpctr > cps) ; finished, with all cps diverging isalldiv = 1 ELSEIF(cpctr == 2) ; second cp is the principal value z = currcp = principal, isdiv = 0 ELSE ; rotate the last cp by angle on the complex plane currcp = currcp * rotfactor z = currcp, isdiv = 0 ENDIF ENDIF IF(isalldiv != 1) z = z^A + k*z^B + C ; main iteration isdiv = ( |z| > bailout) ENDIF isalldiv == 0 } ===================END=======================

1 0

FOTD 13-05-04 (An Extra Fractal [4])
by Jim Muth 13 May '04

13 May '04

FOTD -- May 13, 2004 (Rating 4) Fractal visionaries and enthusiasts: Today's less-than-exceptional image is an extra one, and that's what I named it. Due to an above-average amount of regular work, I have once again exhausted my cache of FOTD images, making it necessary to go with the first thing I found. Today's FOTD is the first thing I found today. I will probably have to take another short break from the FOTD in the next few days, though exactly when that will be has yet to be determined. Today's image was created by taking just plain Z, mixing 1/4 part of Z^(-0.25) into it, then adding 1/C. The parent fractal is a simple cone-shaped hole with a very narrow band of chaos along its edge. Today's scene is located in the chaos on the northern edge of the cone. The rating of a 4 is justified. The image is nothing that has not been seen a hundred times before. When the render time of 8 minutes is considered, the overall value amounts to 49. As always, the finished GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A lot of heat and humidity kept the cats at their most lethargic on Wednesday. Today is starting similarly; the cats will likely have a similar day. For me the day looks like another busy one, but I'll be back in 24 hours with another FOTD. Until then, take care, and keep cool. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ An_Extra_Fractal { ; time=0:08:13.18--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=-2.73581413851751600/+0.806553274091938\ 10/1071028/1/-144.999999941732341/1.37720104535776\ 766e-007 params=1/1/0.25/-0.25/0/0 float=y maxiter=1600 inside=0 outside=summ periodicity=10 colors=000UajZbicchichmdhnehmehlfikgijgijhiiijhijg\ jjfkkekkelkdmkcmlbnlaolaolYheUa_QWUMPNIIHECBLBDRBF\ XBGbBIhBJnBLtBMrCLqCKpDKoDJnEJmEIlFIkFHjFHiGGhGGgH\ FfHFeIEdIEcIDbJDaJC`KC_KBZLBYLAXLAZMC_ND`NFaOGbOIc\ PJdPLeQMfQNgRPhSQiSSjTTkTVlUWmUYnVZoV_mWZkXYjXYhYX\ fYWeZWc_Va_U``UZ`TXaSWaSUbRScQRcQPdPNdOMeOKfNIfMHg\ MFgLDhKChKEgJFgIGgHHgHIfGJfFLfEMfENfDOeCPeBQeBSeAT\ e9Ud8Vd8Wd7Xd6Zd5_c5`c4ac3bc2cc2R`KFY`H_XJ`ULbRMcO\ OdLQfIRgFTiCVj9Wk6Xj7Yj8Zj8_j9`j9`jAajAbjBcjCdjCdi\ DeiDfiEgiEhiFhiGiiGjiHkiHliIliIkjJkjKkjKjjLjjLjjMi\ jNijNikOikOhkPhkPhkQgkRgkRgkSglSflTflUflUelVelVelW\ elWgmVhnUjpUkqTlrTmnRnjQofOpbNqZLrVKsRItNHuJFvFEwB\ Cx7By39y08x39w59w7Av9AvBBuDBuGCtICtKDsMDrODrQEqSEq\ VFpXFpZGo`GobHndHnfH4h85fA5eB5cC5bD5aE5_F5ZG5XI5WJ\ 5VK5TL6SM6QN6PO6OP6MR6LS6JT6IU6HV6FW6EX6DY7F_7H`7J\ a7Lb7Nc7Pd8ReATfFVgKYhP_i } 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==================================

1 0

FOTD 12-05-04 (Charge Cloud [3])
by Jim Muth 12 May '04

12 May '04

FOTD -- May 12, 2004 (Rating 3) Fractal visionaries and enthusiasts: Long ago, back in my wonder years, when I was just discovering the 'true' nature of the world, I imagined atoms to be like tiny solar systems. The nucleus was the sun and the electrons were the planets. But even then I saw a problem. Since material is made of atoms, what then are the atoms made of? Of course, I never found a totally intuitive answer, for there is none, but I soon found that electrons can more accurately be imagined as charge clouds surrounding the nucleus. The stronger the charge, the more likely that the electron is there. This raised the question of what then is the 'real' electron, the cloud or the point. I had discovered wave-particle duality. I mention a bit of physics because today's humdrum image reminds me of my mental image of a charge cloud around an atom. I named it "Charge Cloud". The rating of a lowly 3 seems justified, since I can find nothing of notable interest in the image. The one good feature is the render time, which is a speedy three minutes, and raises the overall value to 96. The minor task of running the parameter file can be eliminated by downloading the completed GIF file of the image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Midsummer weather on Tuesday, with a temperature of 90F 32C, brought out the midsummer behavior of the fractal cats. We let them out into the yard early, but it was already too warm for cat comfort, and they soon found a cool spot in the shade of the holly trees, where they spent the day sleeping. No evening treat was needed. Today is starting the same. For me, the work is backing up again, so I had best get busy. Until next FOTD, take care, and be at ease. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Charge_Cloud { ; time=0:03:07.19--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.40084736494522780/+0.459932651461377\ 90/5665385/1/24.9999999674488542/-4.42219866281234\ 886e-008 params=1.3/-1.3/-1.3/1.3/-0.3/0 float=y maxiter=1000 inside=0 logmap=52 periodicity=10 colors=000QB6OB4LC3JC2GECEGLBHU9Jb7KkCMfGNcKOYPPZT\ RWXSTaTPeUNiWLnYJr_HvaFzrDxcCvbCtaCs`CqaCoaCnaClaC\ jaChbCgbCebCcbCbbCfUEiLFmILpFQtCVw9_wJWwTTwbQt`SrZ\ UpXVnVXlTZjR_hPafObcLY`JUZGPWELTBGR9CQGNQNXPUfP_pQ\ amQckQeiQgfQidQkbRm_RoYRqWRsTRuRRwPUuOWsOZqN`oNcmM\ ekMhiMjgLmeLocKraKt_JwYJyWJwUKvTKuSKtRKrPLqOLpNLoM\ LnLLlJMkIMjHMiGMhFMjGKkHHmIFnIDmKFmLGlMHlNIkOJkPKj\ QLjRNjROiSOiTPiUQhVRhWSgXTgYVfZWf_Xe`YeaZdb_dc`dda\ ceccfdbgebhfaigajh`ki`lk_ml_nm_onZpoZqpYrqYssXttXu\ uWvvWwwVwxVwyUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzU\ wzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwz\ UwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUw\ zUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzU\ wzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwz\ UwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUw\ zUwzUwzUwzUwzUwzUwzUwzUwz } 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==================================

1 0

Strange result when rendering "bimandeloid"
by Hiram Berry 12 May '04

12 May '04

I don't know a more correct name for the polynomial type mandeloids which have two power terms, such as the ones Jim Muth has lately been using for his FOTDs, so use that term to refer to them. As we know, the inside of such sets will not be completely rendered by starting the iteration sequences on a single critical point, and they always have at least two critical points. Possibly a subset of the critical points will generate the complete inside set; but the problem I've recently encountered doesn't seem to relate to that, because in each case I rendered the set with (I think) all critical points. It may be a result of my making a mistake in the formula, or maybe it is an artifact of calculation; the problems do not appear with bimandeloids with integer powers, nor usually with fractional power ones, but in the following cases the behavior is strange: in the first case a straight linear border of the inside set along a substantial portion of the negative x-axis, and in the second case suspicious horizontal lines rendered as if they were part of the inside set (color 0). These things don't seem likely to be in the actual fractals, so if anyone has seen these effects before and knows what causes them, or sees errors in my formula, please enlighten me. Regards, Hiram ===================BEGIN PARS========================= BimandWithKEq-1i { ; z->z^5+(0-1i)*z^3.5+C ; Is the "fault line" on the negative real axis genuine? ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=Bimandeloid passes=1 center-mag=-0.112597/0.0884386/0.8509822 params=5/3.5/0/-1/400/4 float=y maxiter=1000 inside=0; colors=(a)spectrum.map colors=000zzzc00<7>o00p00r00s00u00w00<9>lIBjJCiLD<3>dTI<4>nTApU8rU7<2>xU\ 2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<8>fxIexKcyL<2>ZyRXyTXyU<16>WyoWypWyq<2>W\ yuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SSS00\ 0000 } CalculationEffects { ; z->z^4(0+i)*z^2C ; Are the horizontal black lines artifacts of calculation? ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=Bimandeloid passes=1 center-mag=-1.03683/0.332464/5.806702 params=4/2/0/1/400/3 float=y maxiter=2000 inside=0; colors=(a)spectrum.map colors=000zzzc00<7>o00p00r00s00u00w00<9>lIBjJCiLD<3>dTI<4>nTApU8rU7<2>xU\ 2zV0zX0<5>yi0yk0xn0<2>xt0ww0vw1<8>fxIexKcyL<2>ZyRXyTXyU<16>WyoWypWyq<2>W\ yuVzwWww<8>lOwmKwoGw<3>w0w<9>e0kc0ja0h<2>W0eU0cU0c<118>TQTTQTTRT<3>SSS00\ 0000 } =================END PARS=============================== =================BEGIN FRM============================== Bimandeloid{ ; vary C over the screen in z->z^A+k*z^B+C ; p1=(A,B)[reals],p2=k[complex],p3=(bailout-4,#critical points) IF(isinit==0) ; image-wide initialization section isinit=1 A = real(p1), B = imag(p1), k = p2 bailout = real(p3) + 4, cps = trunc(imag(p3)) IF(cps<=0) ; give a default value for entry of 0 cps = 1 + ceil(abs(A - B) ) ; works for integers only ENDIF is_agtb = (A > B), diff = abs(A - B), angle = 2 * pi / diff rotfactor = cos(angle) + flip(sin(angle)) IF(is_agtb) ; principal roots of the eqn for cps principal = (-B * K / A) ^ diff ELSE principal = (-A / B / k) ^ diff ENDIF ENDIF C = pixel ; Mandelbrot-like type z = currcp = 0, cpctr = 1 ; first critical point is z = 0 isdiv = isalldiv = 0 ; flags for current cp and all cps divergence : IF(isdiv) ; last critical point diverged cpctr = cpctr + 1 IF(cpctr > cps) ; finished, with all cps diverging isalldiv = 1 ELSEIF(cpctr == 2) ; second cp is the principal value z = currcp = principal, isdiv = 0 ELSE ; rotate the last cp by angle on the complex plane currcp = currcp * rotfactor z = currcp, isdiv = 0 ENDIF ENDIF IF(isalldiv != 1) z = z^A + k*z^B + C ; main iteration isdiv = ( |z| > bailout) ENDIF isalldiv == 0 } ===================END FRM=========================

2 1

Re: FOTD 11-05-04 (Oak Tree by Night [7])
by Jim Muth 11 May '04

11 May '04

At 10:23 AM 5/11/04 -0500, I wrote: >> There is an old white oak tree in the Fractal Center neighbor- >> hood, standing 100 feet (30 meters) tall and broad, with a trunk >> about 6 feet (2 meters) in diameter. It has probably stood >> there for well over 100 years..... Paul Lee replied: >You may wish to contact the "Maryland State Archives" and let them know >about this tree, since it seems to be bigger than the one they have on >their web site: > >http://www.mdarchives.state.md.us/msa/mdmanual/01glance/html/symbols/tree2.… The Maryland web site is outdated. The Wye Oak, which is illustrated, no longer exists. It blew down in a storm two years ago. The measurements I gave of the tree near Fractal Central are rough estimates, likely subject to some exaggeration. One of these days I might take more accurate measurements, but today is not the day. Of more immediate concern is the impending cicada invasion. Jim M.

1 0

FOTD 11-05-04 (Oak Tree by Night [7])
by Jim Muth 11 May '04

11 May '04

FOTD -- May 11, 2004 (Rating 7) Fractal visionaries and enthusiasts: There is an old white oak tree in the Fractal Center neighbor- hood, standing 100 feet (30 meters) tall and broad, with a trunk about 6 feet (2 meters) in diameter. It has probably stood there for well over 100 years, surviving every storm that has assaulted it in that time. From its appearance, the tree, which is in perfect health, might stand for another 100 years. I mention this tree because the outline of a mighty oak tree is not very difficult to see in today's image. The dark blueness of the sky and hints of stars showing through the bare branches would indicate that the time of the scene is a winter night. The name "Oak Tree by Night" seems very appropriate. I found the scene by accident, while browsing the same parent fractal that produced the two most recent FOTD's. The fractal tree is located in a disconnected neighborhood in the western suburbs of this parent. The entire area is a forest of similar but not identical trees, some connected, some disconnected, and not all of them are white oaks. I rated the scene at a 7, since it is a refreshing change from my constant fare of quadratic midgets, which even to me sometimes seems boring. The short render time of under 3-1/2 minutes results in an overall value of 203. The task of rendering may be dispensed with by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It is possible to have too much of a good thing, and this is what happened Monday here at Fractal Central when the temperature reached 88F 31C. This was too warm for the sensitive ears of the dynamic duo, who came inside after less than 1/2 hour in the yard. They would have preferred to lie under an air conditioner, but I have not yet turned any on. Today is starting just as warm. I will give the duo a break, and let them outside in the morning, before it gets too hot. The work for me is normal today, but hopefully, the fractal will be as far above normal as the temperature. Until next FOTD, take care, and ponder the inner meaning of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Oak_Tree_by_Night { ; time=0:03:24.93--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-14.8903/-0.96767/36.79717/1/52.5/-4.07\ 27e-007 params=1.5/-1.24/0.19/-7.26/0/0/0/0 float=y maxiter=1200 inside=0 logmap=48 periodicity=10 colors=000RL7QL7RN7QL7QM7PL7PL9OKBOKCNJ9NJ5MI2MJ0L\ IELIFKJGKJHJKIJKJIKKIKLHKMHKNGKOGKPGKQFKRFKTEKVEKX\ DKYDK_CKaCKcBLeBMgBMiANkANm9Po9Pq8Ps8Qu7Rv7Rw6Rx6R\ y6Rz7Qz8Pz9PzAOzBOzCNzDNzDMzEMzFLzGLzHKzIKzJJzJIzK\ IzLHzMHzNGzOGzPFzPFzQEzREzSDzTDzUCzVCzVBzWAzXAzY9z\ Z9z_8z`8z`7za7zb6zc6yc5xc5wc4vc4ucAscKqcUocUmIckEc\ iEcgEceEccEcaEc_EcYEcWEcUEcSEcQEcOEcNEcMEcOEcPEcRE\ cSEcUEcWEcXEcZEc`EcaEccEceEcfEchEcjEckEcmEcoEcpEcr\ EcsEcuFcsFcqGcpGcnHcmHckIcjIchJcgJceKcdKcbKcaLc_Lc\ YMcXMcVNcUNcSOcROcPPcOPcMQcLQcJQcIScJTcKUcLWcMXcNY\ cO_cO`cPacQccRdcSecTgcUhcUicVkcWlcXmcYocZpc_qc_sc`\ tcaucbwccxcdycezcexcdvcducdscdrcdpccoccmcckccjcchc\ bgcbecbdcbbcb`ca_caYcaXcaVcaUcaVc_WcYXcWXcUYcSZcQZ\ cO_cM`cK`cIacGbcEbcCccBccBccBdcBdcBdcBecAecAecAfcA\ fcAfcAgc9gc9gc9hc9hc9hc9ic8ic8ic8jc8jc8jc8kc7kc7kc\ 7lc7lc7lc7mc6mc6mc6nc6nc6 } frm:MandelbrotMix2 {; 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)+(p4)), 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==================================

2 1

FOTD 09-05-04 (Alternate Reality [6])
by Jim Muth 11 May '04

11 May '04

FOTD -- May 09, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a very fine example of what I call a dry lake. It is a place where a midget almost appears, but doesn't quite make it to the surface. It would seem to be easy to track down the midget by varying initial Z until the midget appears, but this plan will not work. To begin, I am not sure that there actually is a midget lying nearby. Also, when initial Z is varied, the scene moves off the screen faster than it can be kept track of. Maybe the midget, if one does exist, lies in an alternate reality, where the universal laws are different. Then again, maybe it does not. Today's scene, at least as far as I tracked it, which is not very far, opens up into a symmetrical hole with no resemblance whatever to a quadratic midget. I named the image "Alternate Reality" because the midget is nowhere to be seen. And also I am fascinated by the idea of alternate realities, from the humble seven or so spirit planes of the occultists to the infinity of alternate realities that are fashionable among physicists. As a side note, I wonder why it is considered kooky and irrational for occultists to speak of a few spirit worlds, and cutting-edge science for physicists to speak of an infinity of alternate universes, where everything possible, presumably including the spirit worlds, actually does exist. While trying to understand this inconsistency, I will remind fractal fans that, even without a midget at its center, today's image rates a 6. And when the 15-minute render time is consi- dered, its overall value registers a 38. When the completed image is downloaded from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> the value increases. The weather unexpectedly turned sunny on Saturday afternoon here at Fractal Central. There was no rain, and the temperature reached a warmer-than-expected 64F 18C. As a result, the cats were happier than expected. Today is starting sunny and warmer. I expect more happy cats. There is not much for me to do today other than perhaps a bit of yard work. Those 17-year cicadas will be coming out any day now. Their countless holes and mud-turrets are under every tree. They are harmless, except for the noise they make and for the cats who eat them and stuff themselves to the bursting point. Until next time, take care, and spend a little extra time with your favorite fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Alternate_Reality { ; time=0:15:44.94--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-3.959551639/-0.15869233282/509.596/1/\ -22.5/-4.85950169e-012 params=1.5/-1.24/0.19/-7.26\ /0/0/0/0 float=y maxiter=1200 inside=zmag outside=tdis periodicity=10 colors=000zz0zz0zz0zz0yz0xy0vx0tt0ts0sq0qp0pm0nk0m\ j0mg0ke0jd0hb0g_0eY0eW0dV0bS0`Q0_P0YN0YK0WJ0VH1TE1\ SC1QA1Q92P52N42M22K14J04J04H04G05E05C05A05A05A04A0\ 2A01A01A00A00A00A00A00A00A00A00A00A00A00A00C00C00E\ 20E40G50G92HA4HC7JG9JHCKJEKMHMNJMPMNSNNTQKTTMVSMVS\ NVSNVSPWQPWQQWQQWQSWQSYPTYPTYPV`PV`PW`NW`NY`NY`N_`\ N_`M``M`aMbaMbbMdbKdbKebKebKgbKgcJhcJhdJhdJjdJjeHk\ eHkeHmeHmeHngGngGpgGpgGqgGqhEshEshEthEvhEviCvjCxjC\ xjCyjCykAzkAzkAzkAzkAzm9zm9zm9zm9zpAzn9zm9zm9zk9zj\ 9zj7yh7xg7vg7te7sd7qd5pb5n`5m`5k_5jY5hY4gW4eV4dV4b\ T4`S4_S2YQ2WP2VP2TN2SM2QM1PK1NJ1MJ1KH1JG1HG0GE0EC0\ CC0AA05C07A09A09A1A91A92C94C74E75G77G57H59H5AJ5AJ4\ CK4EM4EM2GN2HN2HP1JP1KQ1KS1MS0NT0NT0PV0QV0QW0SY0TY\ 0V_0V_0W`0Y`0Yb0_d0`d0`e0be0dg0dg0eh0gj0gj0hk0jk0j\ m0km0mn0mp0np0pq0pq0qs0sx0tt0ss0sq0qp0qn0pm0pk0ph0\ ng0ne0md0mb0m`0k_0kW0jV0j } frm:MandelbrotMix2 {; 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)+(p4)), 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==================================

2 1

RE: need some help
by carenp 11 May '04

11 May '04

jonathan, i received no error message... what i DID get was a 1024x768, no matter that i chose the 2048 option (and would have liked to try larger, but you know, my older age and memory kept me from remembering how to tweak the CFG to get it right :) 00 caren http://www.parkgallery.org Date: Sat, 8 May 2004 07:27:22 -0500 From: Jonathan Osuch <osuchj(a)avalon.net> Subject: Re: [Fractint] need some help... Caren, > .3. on a related subject, does anyone know why i can't save a disk video > of my creations in fractint 20.3? i'd like to push some out as far as 6000 > x 4500, and i have the disk space and the processor to handle most of > them... Do you get any sort of error message? Does the screen say Fractint is saving the file? I've tried this at 2048x2048 and 6000x4000 with the mandel type and had no problem. Also tried 2048x2048 and 6000x4500 with a formula type and had no problem. I don't know the effect of using an NTFS partition has on Fractint. Jonathan

2 1

Test
by JimMuth＠aol.com 10 May '04

10 May '04

This is a test to see if I am still subscribed

2 1

FOTD 10-05-04 (Ham-and-Eggs Atom [5])
by Jim Muth 10 May '04

10 May '04

FOTD -- May 10, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image lies in the same shapeless parent fractal that gave us yesterday's image. But while yesterday's image was found in a chaotic area in the western part of the parent, today's is located in a valley in the eastern part. Yesterday's image consisted of outside material rendered with the 'tdis' option. Today's is an 'evaporated' image, consisting totally of inside points rendered with the 'bof61' inside fill. I named it "Ham-and-Eggs Atom" for no good reason. Perhaps I was thinking of breakfast. I am actually starting to become a bit weary of these so-called evaporated images of mine. As a result, I could give the image a rating no higher than an average 5. I am also less than satisfied with today's coloring. The colors are strong but the balance is too far toward the magenta, and this held the rating down. The overall value, for any who might be concerned, is 35. The completed GIF image is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday passed sunny and warm here at Fractal Central, the temperature of 86F 30C leaving the cats happy. A mild thunder- shower arose late in the evening, but by that time, the cats were sleeping soundly. Today is starting sunny and warm again. The duo should again be happy. For me it will be the usual amount of work before play. Until next FOTD, take care, and fractals have been proved interesting beyond all reasonable doubt. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ham-and-Eggs_Atom { ; time=0:14:25.68--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+4.93679735683400800/-0.308310304732402\ 90/7988515/1/2.5/2.34537594498429591e-006 params=1.5/-1.24/0.19/-7.26/0/1e+100/0/0 float=y maxiter=1500 inside=bof61 periodicity=10 colors=00000y00q00k00b00WUGOzgMzeHzdCzb7zb2z`0z_0z\ _0zd0zi9znJxrTwxbtzknrlgin``oURoOJqH9r04z02zC0UO0g\ `0Wn0Kz0Gz0Cy09q77kG4bP0UY0Mg0Go0MgBT_R_TgeKxt7zlE\ zeKz_RyTYqMdk0YqGkdUwTizHxz6BGoCJiCKb9Mi7On4PrUzzG\ oz2Rx00U00z04r07g0BW4EK9H9EK0HM0GR0GU9GYKEbWEegEir\ 6CrBUxElzYlzPtzHzzBzt9zx9zy9zz9yz9tzGlrKeiP_Yzg4l_\ EUTOE_dET`EMYEGUE9RE2OE0K90EE0HJ0KO4MTBPYJTbPUgWYk\ TklYdlb_leTnkOnnHnrC20600E00M00E2J6E`0Pr0`z0_t0Yd0\ WP0YC6_0R`0kbJgR00e7dT07QEHU07V0CT0HY0MX0RY0WY0`Z0\ eb0me0rj0xl0zr0zr0zz0ztKwte_tzBtz0zbizRTzHCz70z00z\ 60zE0zM0zX0zg0zs0zw4zz7zk6wf6yV4l74l02b02b00P00J00\ E007000400700B04C4JC9YCClCHzCMzCPzEJxECoE7kG4gG0bG\ 0_G0WH0RH0OH0KH000w00q00n00k60gB0dG0`R7dbRenkgyzie\ zbOlW6dRGYTORUWMUdGWn9Yw4Yz0_6rz6kz7bz7Wz9Oz9GzB7z\ 0n06PYB0zg0WU9CHK0JC0K60M04O09P0CR0GkCOziWzzbqzROx\ H0o77We4Pg0Ji0Ek07l02n00o } frm:MandelbrotMix2 {; 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)+(p4)), 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==================================

1 0

FOTD 08-05-04 (The Golden Egg [5])
by Jim Muth 08 May '04

08 May '04

FOTD -- May 08, 2004 (Rating 5) Fractal visionaries and enthusiasts: For today's parent fractal I combined positive and negative Z^1.5 with 1/3 as much positive and negative Z^4.5, and set initial Z to -1. This parent fractal is not really a single fractal, but rather a scattering of tiny open areas, some of which are small Mandelbrot sets, while others are mere shapeless holes. The place I chose to explore was the area just east of the tiny westernmost M-set. This area holds many scattered bits and pieces of fractal debris. Much of this debris is concentrated around large central disks, like satellites circling a planet. The debris is plentiful, but only a few pieces contain midgets. Today's image shows a midget lying in this field of debris. I named the image "The Golden Egg". The golden color is obvious, but as for that egg, well, I have no idea where it might be. I rendered the image with the outside set to 'tdis'. I find I am using this option more often, since it does rather well on disconnected scenes such as today's, where the standard 'iter' rendering falls flat. I could rate the image no higher than a 5. It is not all that striking and we have seen many similar images before. But the render time is only 3-1/2 minutes, which raises the overall value to a respectable 147. Perhaps the most respectable way to see the golden egg image is to download it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday here at Fractal Central was warm and sunny enough until 2pm, when a rain squall arrived and the temperature dropped from 86F 30C to 67F 19C. When the wind arose, the cats beat a hasty retreat and spent the rest of the day on their window shelf, watching the outside activity from inside. By evening they were mildly annoyed, but only a minor treat of tuna was needed to make them happy. This morning it is cooler with lots of clouds. The duo is likely to have another less-than-perfect day. For me it's likely to be an uneventful day, that is unless the aliens arrive from space. Since I expect no aliens, I will be free to return in 24 hours with another fractal. Until then, take care, and I wonder if the aliens know about fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Golden_Egg { ; time=0:03:24.70--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=recip passes=1 center-mag=-1.54575313438937500/+0.827504998767173\ 40/3.087104e+007/1/-170/-3.94734106006627838e-006 params=1/-1.5/-1/1.5/0.333/-4.5/-0.333/4.5/-1/0 float=y maxiter=500 inside=0 outside=tdis periodicity=10 colors=000AJ08T08d06m66xC4zH4zL0zE0s80g24dARbGm`Ls\ REvJ8zC2z40z00z00z00z00z00z00z00x00u00q40o60uAEzCX\ zGqzHzzJzuRzbXzJdm0i`4ZP6PE8G2A60C00XC0oR0zd0zg0zi\ 0zm0zo0zs2zu4zx6zz8zvTssmbozNmzRbzVRzZGzb4ze0zi0zm\ 0zq0zu0zx4xzEqiHiVLbEPX0TP0XJ0RH0LH8GGGAGN4EV0Eb0E\ e4GgEHkNJmVLqdNsmPvvRxzRkxNZuJLqGAkE0gA0d60`40XEEV\ NZRXsPdgbiZomNzqEzu4zxzzXieGGG000000bECkPLs`Vzkdzv\ mzzvzdXzC8z00uZ0Zz0Cz2Lz2Vz4bz4kz4uu6zq6zm6zi4xe4d\ b2JZ20V20X60X82XCEZERZHbZJm0uE0oGAkGRgHedHmVJuNLzG\ Nz6Pz0Rz0Tz0Vzz8ozAdxCToEHdE6TG0JH08J00J06GCECVL8m\ T4z`0ze0zdCzbNz``zZkuZv6GL00e00x00s00o00k00g04d28`\ 4CX4EVbXmzozz00z00z00v08m2Ge4Lqd6zz0qzzvzvzzkzz`zz\ NzvCzq0zm0zb0zT4zJCzAJz0Rz0Zo8NXNCEd00s00m00gA0dH0\ ZR0T`0Pg0Jq0Gx2TvCduLqsVzqdzomzmdzgXzbNzZGzT6zN0zJ\ EzGTzEgxAvo8zg6z8mz0zz0zzCezTJzk0zz0kv0TsH8od0kzgR\ 0biNXzuTxs44`66N86AA80C80 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

1 0

Re: [Fractint] Franktal Gallery is back !
by Ale 07 May '04

07 May '04

Hi Miguel, long time no see! I hope everything is ok. I was browsing your site and there was a problem, which I copy/paste here: Sorry, this site is temporarily unavailable! The web site you are trying to access has exceeded its allocated data transfer. Visit our help area for more information. Access to this site will be restored within an hour. Please try again later. http://www.geocities.com/franktal2002 Also couldn\'t acces to the FZ page... :( Cheers, Alejandro Mensaje citado por: Franktal Gallery <franktal(a)hotmail.com>: > Franktal Gallery is back, and everyone\'s invited to check it out. > > http://www.geocities.com/franktal2002 > > Regards, > Miguel > > _________________________________________________________________ > The new MSN 8: smart spam protection and 2 months FREE* > http://join.msn.com/?pageþatures/junkmail > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > __________________________________ Registrate desde http://servicios.arnet.com.ar/registracion/registracion.asp?origenid=9 y participá de todos los beneficios del Portal Arnet.

1 0

Franktal Gallery is back !
by Franktal Gallery 07 May '04

07 May '04

Franktal Gallery is back, and everyone's invited to check it out. http://www.geocities.com/franktal2002 Regards, Miguel _________________________________________________________________ The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail

1 0

Re: [Fractint] need some help...
by nick.grasso＠hrads.com 07 May '04

07 May '04

Caren wrote: >>>i've tried chaos pro and it worked well for one of my old collection (one that didn't require an external FRM), but crashed badly on another (same one that when it worked, it didn't recreate correctly at all)... i've also looked at winfract 20.2, and it refuses to handle large images (among other issues)...<<< Have you tried UltraFractal? It is compatible with most Fractint formulas and you can make the fractals any size you want. It is $60 but you can download a free trial. Nick

2 1

FOTD 07-05-04 (Rocket [6])
by Jim Muth 07 May '04

07 May '04

FOTD -- May 07, 2004 (Rating 6) Fractal visionaries and enthusiasts: I have a young friend who apparently is convinced that there is an evil plot foisted by aliens from outer space. According to him, these aliens are already in control of many governments and big businesses, and are currently in the process of softening us up, making us into mentally-retarded, helpless, docile sheep, addicted to TV, viagra, computer games, cell phones and brain- dead gadgets in general. He supposes we will soon be burned-out hulks unable to mount any resistance to the coming invasion and ready to be carted off as slaves. I'll not go into the details of how the plot is supposed to work, but I must admit that after listening to him present his case and observing the craziness of the present-day world, I can see why so many are convinced that UFO's are actually alien space ships. But don't worry. I don't believe this alien-invasion nonsense . . . not yet. I named today's image "Rocket" because the dark shape in the center is vaguely shaped like a rocket ship. According to 'Smedley', the aliens are so technologically advanced that they don't need rockets. They move from their departure point to their destination instantly, without needing to occupy the points in between. Their method of travel is even better than teleportation because it is not limited by the velocity of light. Today's image, which is almost as fast as light, is based on a previous FOTD image, one that appeared many years ago. But in today's incarnation, it has been changed enough to make it virtually new. The parent fractal is a distortion of the Z^1.064 Mandeloid, created by the JimsCompMand formula, which is simply a further generalization of the 'cmplxmarksmand' formula of Fractint. In the original image, one of the two orangish streaks was the Hale-Bopp comet. I preserved the color palette of that old image, adjusting only a few registers for special effect. When all was said and done, the result was worth a 6, which is what I rated it. But that routine 6 is raised to a whopping 654 by the render time of under one minute. So forget the aliens and start rendering, or visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the finished image from there. A pleasant day here at Fractal Central on Thursday, with lots of sun and a temperature of 75F 24C, made for happy cats. After a quiet day in the yard and on the porch, they enjoyed a treat of tuna. It was as close to cat paradise as it is possible to come on the earthly plane. This morning is starting cloudy, and rain is possible this afternoon. But it is still warm. We'll see how it goes. My day will go well when the work is finished and the next fractal found. That fractal will appear as tomorrow's image. Until then, take care, and never abandon the search for the lost fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rocket { ; time=0:00:55.04--SF5 on a P200 reset=1950 type=formula formulafile=allinone.par formulaname=JimsCompMand center-mag=-1.14178850421\ 374300/0/91.1936/1/-90/-1.23373533611470521e-014 params=1.064/0/1.651/0/0/0 float=y maxiter=860 bailout=100 inside=255 logmap=27 periodicity=10 colors=000EKKDPzBPzAPz9Nw7Ns6Po5Pl4Rk2Rj1Ti0Th1Tf2\ Te3Sc4S_5R`5Q`6P`7O`8N`9M_AK_BK_CKZDKZDKZEKYFKXGKX\ HJWIKVJKVKKVKKULKUMKUNKTOLTPMTPNTQOSSPQUQPWROYSN_T\ LaUKcUJeUIgUGiVFkWEmXDoYBqZBs_Au`9wa7xb6yc8zc9zcBz\ cDzcFzcGycIxcKwcLvcNucPtdRseSrfUqgWphXoiZni`mjblkc\ klejjehieggeefeddfbcfaaf_`fZZfXXfWWfUUfTTfRRgQQgOO\ gNNgLLgLLhMMhMMiMNiMNjNOjNOkNPkNPlOQlOQmORmORnPRnP\ SoPSoPTpQTpQUqQUqQVrRVrRWsRWsYUsdRtjPtqMtpNspOroPq\ nQpnRomSnlTmlTlkUkjVjjWiiXhhYghZfg_fg`efadebcecbdd\ ace`ce_bfZagYahX`iW_jV_kUZlTYiUXgVWdWVaXU_YTXZSU_R\ S`QPaPMbOKcNHdMEeLCfK9gK7hL8iM8iM9iN9iN9iOAiOAiPBj\ PBjQBjQCjRCjRCjSDjSDjSDjQGgPIeNKbMM`KOZJQWHSUGVVGX\ XF_YEbZDd_DgaCjbBlcAodArf9tg8whBueGraIp_LoYNmVPkTS\ jRUhPWfMZeK`cIbbGbdHbeHbfIbgIq8`p9`n9`mA`lA`kB`iB`\ hC`gC`eD`dD`cE``Fa`Fa_GaYGaXHaWHaVIaTIaSJaRKaPKaOL\ aNLaMMaKMaJNbIObGObFPbzzb } frm:JimsCompMand {; Jim Muth z=c=pixel: z=z^p1*(c^(p2-1))+c, |z| <= p3+100 } END 20.0 PAR-FORMULA FILE==================================

2 2

More Mandelbrot sets????
by Raymond Filiatreault 07 May '04

07 May '04

I don't know if this is the proper forum to ask my questions. If not, may someone be kind enough to give me proper directions. Fractals have been one of my numerous hobbies for several years. Another one of my hobbies is programming. Lately, while programming another one of those zillion fractal generators (in assembly as a challenge and by curiosity), I accidently stumbled on two "fundamentally" different simple formulas which produced the exact same fractal!!! In addition, that fractal is a replica of the Mandlebrot set in approx. a quarter of its size and shifted approx. +2 on the X axis. The Julia sets are also replicas, similarly reduced in size and shifted. My questions are: 1) Have different formulas producing the same fractal been reported in the past? 2) Are there currently known formulas, other than the z^2+c, producing a replica of the Mandelbrot set? In other words, am I re-inventing the wheel? Raymond _________________________________________________________________ MSN Premium: Up to 11 personalized e-mail addresses and 2 months FREE* http://join.msn.com/?pgmarket=en-ca&page=byoa/prem&xAPID=1994&DI=1034&SU=ht…

5 5

FOTD 06-05-04 (Four-Star Fractal [6])
by Jim Muth 06 May '04

06 May '04

FOTD -- May 06, 2004 (Rating 5) Fractal visionaries and enthusiasts: I am once again fabulously wealthy. In my e-mail this morning I found that I had won not one but three international lotteries, and there are also two people in Africa who are ready to share over 50-million dollars with me. The irony is that if I had somehow found a way to eliminate all spam, I would never have realized that I have become rich. I must celebrate by finding a rich fractal. Today's fractal however is only middle class. True, it is a four-star fractal, but it is not four-star in the quality sense, such as a four-star hotel or restaurant might be. In fact, it rates only an average 5. It is four-star because it has four stars, or more accurately pentagrams, surrounding the central midget. The parent fractal, which combines diminishing portions of Z^(-1), Z^(-2), Z^(-3) and Z^(-4), is a delicate inside-out thing -- a cloud of evaporating fractal debris floating in the infinite nothingness of fractal space. Mandel buds line the outer edges of the debris cloud, with the largest two buds lying at the northern and southern extremities. Today's scene is located some distance west of the southern bud. Since the parent fractal was already evaporating when I stumbled upon it, I helped the evaporation along by raising the bailout (escape-radius) to one-googol. (no relation to the popular internet search engine) I then re-rendered the blank screen with the inside set to bof61 to produce today's image. The hum-drum average rating of a 5 and render time of over 23 minutes holds the overall value to a measly 21. But that value may be increased by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A near-perfect day here at Fractal Central on Wednesday, with lots of sun and a temperature of 70F 21C, was spoiled by a brief thunder-squall at 6pm. The cats scurried inside when the weather turned bad, but it was no great loss. They were ready to come inside anyway. Today is starting similarly. It looks like another good day for the cat duo. For me, the problem is the fractal grass, which is up again and in need of a trimming. And before I return to Fractal Land, there is some commercial work to do as well. The next FOTD will appear in 24 hours. Until then, take care, and be of fractal mind and sound body. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Four-Star_Fractal { ; time=0:23:20.54--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=recip passes=1 center-mag=+0.49379527691459430/-0.935006663699541\ 20/2585228/1/-85/1.751373456954e-007 params=2/-1/1\ /-2/0.5/-3/0.25/-4/-0.825328/1e+100 float=y maxiter=800 inside=bof61 outside=tdis periodicity=9 colors=000vl5vo5us1vq5vo8vmBvkEvjHvhLvfOvdRvbUvaXv\ _`vYcvWfvUivTlrRhoPelObiM_eKWbJT_HQXGNTEJQCGNBDK9A\ I74H87H99H9BHAEGAGGBIGCLGCNFDPFDSFEUFFWFFZEG`EGbEH\ eEIgDIiDJlDJnDKpCIuDKrELoFNlGOjGQgHRdITaJU_KWXKXUL\ ZRM_PNaMObJOcHelEwtBurDtqFspHqoJpnLomMnlOlkQkjSjiU\ hhWggXffZee`cdbbcdabf`agMlP8v6DtAIrDNpGSnJXnLWmMWm\ NWmOWmOWmPWmQWmQWmRWmSWmSWmTVlUVlVVlVVlWVlXVlXVlYV\ lZVlZVl_Vl`Vl`XkaYjaZia_ha`gaafabeacdadcaebafaag`a\ h_aiZajYakXahNhlXariUpfVndVlbVj`ViZVgXVeVVcSVaQV`O\ VZMVXKVVIVTGVSEVTGUUIUVKTVLTWNSXPSYRRYSRZUQ_WQ`YP`\ ZPa`ObbO_hNbcOd_OgWPiRPlNQlCRnJQoQPpXOxdRqcOkcMdbJ\ acFZbHXaIV`JS_KQZMOZNLYOJXPHWREVSCUT7TTAUUCVUEWUGX\ VIXVLYVNZWP_WR_WT`XVaXYbX_cYacYcdYeeZhfZjfZlg_nh_p\ i_ujeri_oiUliPihJfhEch8ah3YgAVfGReMOdSKcYHbcAYhEai\ HdjKhkNklQnmRlnSjoTioUgpVfqWdqXcrYasY`sZZt_Yu`WuaV\ vbTwcSwdQxgNydPxtd4ug4ui5 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

1 0

Re: [Fractint] FOTD 05-05-04 (The Total Distance [6])
by Jim Muth 06 May '04

06 May '04

At 09:16 AM 5/5/04 -0400, you wrote: > >FOTD -- May 05, 2004 (Rating 6) > >Fractal visionaries and enthusiasts: > >This will be a short discussion. I am falling behind in my >work and must get caught up before I find myself in another >morass. > >Yesterday's image was a meditation on the negative golden ratio; >today's is a meditation on the negative square root of 2. The >parent fractal is another grossly oversized thing with more >places to investigate than could fit in an infinite universe. > (oxymoron noted) > >Today's image was rendered with the outside set to 'tdis', which >explains the name "The Total Distance". The inside was set to >'fmod' to fill in some holes. > >Since IMO the image is a bit above the uninflated FOTD average, >I rated it at a 6. The render time of just over 6 minutes gives >an overall value of 98. > >Rendering can be eliminated entirely by downloading the finished >image from: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > >A sunny but chilly day on Tuesday limited the cats' outdoor time >to under two hours. But this was enough to keep their moods >good. Today is starting sunny and warmer, but showers are >possible later. We'll see how things go for the duo. > >For me, it looks like a normal day. Except for the left-over >sawdust, that fallen limb has been disposed of. Until next >FOTD, take care, and be at ease. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START 20.0 PAR-FORMULA FILE================================ > >The_Total_Distance { ; time=0:06:04.00--SF5 on a P200 > reset=2003 type=formula formulafile=allinone.frm > formulaname=MandelbrotMix4 function=recip passes=1 > center-mag=-1.51093310954631/+1.769058060551924/2.\ > 186424e+011/1/-82.5/-0.06180700158054 params=1/-1.\ > 414/0.1/-14.14/0/0 float=y maxiter=1000 inside=fmod > proximity=10 outside=tdis periodicity=10 > colors=000J4EH5CD68B848905B09E0DI0GM0JQ0NV0QX0kG05\ > j38g6Bd9DcDG`GI_JLXMNWP3Bzt0nuWJuz0fz8TvNEqd1kuMcd\ > fXPgVNhTNjRMkQMmPLnNLoMLmIMkENhCPg8Qd5Rc1Ta0TX3TR5\ > VL8WTI_WNaVPhJMc3GT1LW1QX1WY0_`0da0jc0ndDrWQuNcyGq\ > z8zz0jf6RIC90HW4aX8RXCHXG8XJ0XN0_Q0aT0dV0gX0hY0oH0\ > u00n00h00c00Y00T00N00M63LJ5LX9JjCJxEEuI9rL4oN0mR0j\ > V0gX0`VBVTLNQWHPfCNPm9QgGRcLTYRVVXWQaXLhYHn_DtaGqc\ > HofJmgLkfVddc_ckVauP`zJXvPTqVQkYMfcJ`gGWmDQqBTu9Wx\ > 6Xz5_z3az1cz0Qx0Dk00_00N03H0GB0V40g0G_M`RjuJz6_h4Q\ > q1Hy09z0Hr0Nd0WR0aE0j10q00q08q3Gq9NqGWqMcqTjq_k`fk\ > Mkk8qYLtLXv8jy0vz3ru9noGjjMfdTa__YVfVPmQLhRNdTP`TQ\ > XVRTWTQWVNQJLL9IH0LL4MP8PTCQXHT`LVcPWcMWdJWfGXfDXg\ > BXh8Xh5_d8a`BdXDgTGjPImLLoHNrDQu9Tx6VaNLHdDJhJLkQM\ > nXNqcPtjQvqRyxTzzXzy_ztazndzjgzdjz_mzVozQrzLuzGxzB\ > zz6zz1zz0zz0zz0zz4zz9zzEzzJzzPyzVxz_vzduyjtyorxuqx\ > zqxzoR6kP8hM8fJ8aH8_E8M3I } > >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================================== > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

1 0

FOTD 05-05-04 (The Total Distance [6])
by Jim Muth 05 May '04

05 May '04

FOTD -- May 05, 2004 (Rating 6) Fractal visionaries and enthusiasts: This will be a short discussion. I am falling behind in my work and must get caught up before I find myself in another morass. Yesterday's image was a meditation on the negative golden ratio; today's is a meditation on the negative square root of 2. The parent fractal is another grossly oversized thing with more places to investigate than could fit in an infinite universe. (oxymoron noted) Today's image was rendered with the outside set to 'tdis', which explains the name "The Total Distance". The inside was set to 'fmod' to fill in some holes. Since IMO the image is a bit above the uninflated FOTD average, I rated it at a 6. The render time of just over 6 minutes gives an overall value of 98. Rendering can be eliminated entirely by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A sunny but chilly day on Tuesday limited the cats' outdoor time to under two hours. But this was enough to keep their moods good. Today is starting sunny and warmer, but showers are possible later. We'll see how things go for the duo. For me, it looks like a normal day. Except for the left-over sawdust, that fallen limb has been disposed of. Until next FOTD, take care, and be at ease. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Total_Distance { ; time=0:06:04.00--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.51093310954631/+1.769058060551924/2.\ 186424e+011/1/-82.5/-0.06180700158054 params=1/-1.\ 414/0.1/-14.14/0/0 float=y maxiter=1000 inside=fmod proximity=10 outside=tdis periodicity=10 colors=000J4EH5CD68B848905B09E0DI0GM0JQ0NV0QX0kG05\ j38g6Bd9DcDG`GI_JLXMNWP3Bzt0nuWJuz0fz8TvNEqd1kuMcd\ fXPgVNhTNjRMkQMmPLnNLoMLmIMkENhCPg8Qd5Rc1Ta0TX3TR5\ VL8WTI_WNaVPhJMc3GT1LW1QX1WY0_`0da0jc0ndDrWQuNcyGq\ z8zz0jf6RIC90HW4aX8RXCHXG8XJ0XN0_Q0aT0dV0gX0hY0oH0\ u00n00h00c00Y00T00N00M63LJ5LX9JjCJxEEuI9rL4oN0mR0j\ V0gX0`VBVTLNQWHPfCNPm9QgGRcLTYRVVXWQaXLhYHn_DtaGqc\ HofJmgLkfVddc_ckVauP`zJXvPTqVQkYMfcJ`gGWmDQqBTu9Wx\ 6Xz5_z3az1cz0Qx0Dk00_00N03H0GB0V40g0G_M`RjuJz6_h4Q\ q1Hy09z0Hr0Nd0WR0aE0j10q00q08q3Gq9NqGWqMcqTjq_k`fk\ Mkk8qYLtLXv8jy0vz3ru9noGjjMfdTa__YVfVPmQLhRNdTP`TQ\ XVRTWTQWVNQJLL9IH0LL4MP8PTCQXHT`LVcPWcMWdJWfGXfDXg\ BXh8Xh5_d8a`BdXDgTGjPImLLoHNrDQu9Tx6VaNLHdDJhJLkQM\ nXNqcPtjQvqRyxTzzXzy_ztazndzjgzdjz_mzVozQrzLuzGxzB\ zz6zz1zz0zz0zz0zz4zz9zzEzzJzzPyzVxz_vzduyjtyorxuqx\ zqxzoR6kP8hM8fJ8aH8_E8M3I } 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==================================

1 0

Re: [Fractint] The "MandelbrotMix#"
by Jim Muth 05 May '04

05 May '04

At 12:29 AM 5/1/04 -0400, Hiram Berry wrote: <snipped> >After "Fractal Nonsense", which I think you also rated a 5, >I don't put much credance in your ratings Jim. That one, which >showed a morphologically sextic midget in the main filament of >a fractal with a quartic generator, showed something >fundamental about Mandeloid generation and thus ought to be >ranked somewhere near the top of the scale regardless of >whether your colorist's skills were in evidence that day or not. I think I had a whole series of images leading up to the spurious sextic midget, which should indicate that I noticed something mathematically unusual in it. My ratings are entirely subjective, and depend largely on my mood at the time I rate the images. Perhaps I should give my images two ratings -- one for artistic worth, the second for mathematical interest. >A while back you chided Sherlok Merfy for not initializing z on >a critical point in one of his fractals. The chiding was kind of hard to resist, especially in light of the cute spelling he came on with, and words and phrases such as 'SherLok', 'Merfy', 'private instigator', and 'brewhaha', etc. in his internet addresses. No harm was intended, and I doubt that SherLok was seriously offended. >That would seem to imply that you value the concept of >purposeful intent in fractal creation, rather than just >randomly trying a lot of parameter combinations in hope of >hitting something interesting. I aim for a blending of random discovery and purposeful intent. IMO, when fractals are over-planned, much of the surprise and therefore the fun is lost. >I suppose you wanted Sherlok to understand how to apply the >Fatou Theorem to generate a maximal set of fractal points. Not so. I have no idea what the Fatou Theorem is. The rest of the letter demands more careful consideration. It has some valuable ideas in it. Jim M.

2 1

FOTD 29-04-04 (Beyond the Limit [5])
by Jim Muth 05 May '04

05 May '04

FOTD -- April 29, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image has been named "Beyond the Limit". But don't succumb to skeptic's panic. We are not headed into the supernatural. Since fractals have no limit of their own, the limit mentioned in the name is the resolution limit of the math routine used by the program to generate the image. The diagonal smearing visible in the image is the first sign of resolution breakdown. I needed to include the mathtolerance entry in the parameter file to be sure that the image is drawn at the correct magnitude on all machines at all screen resolutions. When this is done, we find ourselves with a rather pleasant star-like image, which, if it were not afflicted with resolution breakdown, would rate a 7. As it is, I can rate the image no higher than a 5. The render time of 6 minutes makes the overall value an 82. Don't even think of checking the midget at the center of the image. Nothing but colored splotches are down there. The midget needs a few more magnitudes of resolution before it will reveal itself. The best way of viewing the image is to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and then step back a bit from the screen to where the impending breakdown is not visible. A sunny but chilly day here at Fractal Central on Wednesday was marginally satisfactory for the cat duo, who would have preferred a temperature of 70F 21C rather than the 59F 15C that actually prevailed. Today is starting equally sunny and notably warmer. The two ex-tomcats should be happy. For me it's just another routine day of too much work and too little play. But the work *will* be finished, and 24 hours from now the next FOTD fractal *will* appear. Until then, take care, and we don't even know what we don't know. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Beyond_the_Limit { ; time=0:06:07.62--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.429528921055553/+0.2562473412832469/\ 1.909924e+012 params=1/-1.5/0.01/-150/0/0 float=y maxiter=1200 inside=0 logmap=135 periodicity=10 mathtolerance=/1 colors=000N5CN8IMANMCVLFYLHdKJiKM\ qJOvJQzDSw7UvFZkMc`ThQ_zFzq5ki4ob4tW3xP3sRAnTHiVNe\ XU`Z_W`fSal`g`XUYTGVQ3ST9YWFbZKgaQldVqedczmRfzEzlJ\ hbNiTRiJVgKReLOcMLaMH_NEYOBXO8YPBYQEZRHZRK_SN_TQ`T\ T`UW`VZaVaaWdbXgbXjcYmcZpcZsWaqPdoIgmBil6OC9QEBSGE\ TIGVKIXLLYNN_PQaRSbTUdUXfWZgYai_ckaelbdjecigbgiafk\ `en_cpZbrZatXZrVWqTTpRQnPNmNKlLHkJEiHBhF8gD5fLLiS`\ kRbiRdhRefQgeQhcQjbQkaqhcskZunUwqPytKzwFozKdzPVzUU\ zWUzXUzYUzZUz`UzaUzbUzcUzeUzfUzgUzhUzjUzkUzlUzm`zr\ fzwmzhtzUzzFwzJtzNqzRozVlzZizbfzfdzjaznZzrWzvUzyWz\ vXztZzr_zpazmbzkcziezgfzehzbiz`kzZlzXmzVYz`Ize2zj6\ zf9zcDz`GzYKzVNzSRzPUzLYzI`zFdzCgz9kz6nz3qz0sz9uzH\ vzPxzXyzdyzVyzLyzCuzBqzBmzAjzAfz9bz9Zz8Wz8Sz7Oz7Lz\ 7Oz9RzBUzDWzFZzHazJczL`zOZzQWzSUzURzWPzYMz`KzbHzdF\ zfCzhAzj8zlAzfBzaCzXEzSFzNGzIHzDSzMazUZzTWzSTzSPzW\ MzZJzaGzdDzgAzj7zm4zp7zk9zgszzhzeZzLPz1Oz7 } 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==================================

2 1

FOTD 04-05-04 (Another Forest [6])
by Jim Muth 04 May '04

04 May '04

FOTD -- May 04, 2004 (Rating 6) Fractal visionaries and enthusiasts: In the two most recent FOTD discussions I wrote of making FOTD rating points by using unusual program features instead of skilled fractal hunting and coloring. Today's image emphasizes this dilemma, for in it I have used a bit of both. I have indeed used a bit of program trickery. The inside parts of fractals are 'really' flat black. In today's FOTD, I have departed from 'reality' by rendering the basically flat-black image using the 'bof61' feature, which colors the inside according to the number of the iteration that brings the points there closest to the origin. The fractal skill part lies in finding the scene in the first place. The parent fractal was created by combining Z^(-1.618) with 1/10 as much Z^(-16.18) and adding (1/C). This parent comes in two main parts, and consists of two oversized disconnec- ted areas of action, one north of the other. Both areas have open Mandeloid features with ample places to explore. I chose to explore some distance inland from the southeast shoreline of the indescribable Mandeloid lying in the northern half of the parent. I went rather deep before stumbling upon the scene illustrated in today's image. Once I found the scene, I evaporated it and applied the 'bof61' fill to what remained. Then I applied a bit of artistic skill when I colored the scene. The result appears as today's image, which, despite all the above talk, rates only a slightly-above-average 6. The overall value is 149. I named the picture "Another Forest", because it reminds me of a fantastic forest, and I have seen so many similar images that they are starting to become boring. But the image is still worth a look. It takes only 4 minutes to render, so boot up your version of Fractint and give the included parameter file a run, or hurry to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the completed image from there. A cold rain prevailed all day Monday here at Fractal Central, keeping the cat duo confined to their window shelf, where they spent the afternoon watching birds and squirrels. The tempera- ture of 48F 9C felt more like February than May. Today is starting sunny but quite chilly. The fractal cats will need to be brave if they hope to have any prolonged time outside. As for me, I'll finish the business work, then start disposing of that fallen fractal tree limb that is still half-blocking the fractal alley. When and if I complete these burdensome tasks, I'll visit Fractal Land. Until next FOTD, take care, and expect the unexpected. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Another_Forest { ; time=0:04:01.95--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.562994438322458/-1.573328025352637/1\ 331340/1/-157.5/2.17469432778338856e-006 params=1/-1.618/0.1/-16.18/0/1e+100 float=y maxiter=1000 inside=bof61 periodicity=10 colors=000A`vIozQnzYlzekzlizqlivoQzs6zv0xzCtz`qzzz\ `lz3`z9fzFlzLszQwzXzzbzzfzxnzwtzwzzvzzvzzwzzxzozze\ zzXG8O6Qi0hz6kxGnqQqi`tbkwVvzOzzIzxLzwOxvQwtSvsVsq\ Yqo`onb`qhOtlAvqMnhXf`f`TsTMzMFzG8zMCzSGzXLvbPqfTl\ lXhq`Z_e__i`W`SXfUX_S0X8C0AG0DJ0FM0IP0JS0MV0P`0Tc0\ Xh0YY0YV0YG0_8So0A_0FX0JT2OQ6SPCXMI_JMcIShFYlCbq9h\ t8nx5sz2xz0zz2wz2sz3nz3iz3ez5`z5Xz5Sz2cz0oz0zz0zz5\ zxFznPzc_zTiwJluOntQqqTspYvn`wnczlhzlkzjnzoqzsizvc\ zwYzzQzzLzzFzz9zz2zz0zz0zz0zz0zz0zz0zz5zw9zsDzoIzl\ OzhSzeXzb`xccvcetefqehnfilfkihnfhoeiqbis_ktYkvcolh\ scYXTXX_VXcSTbPQbOO`LL`IJ`GG_DD_AA_98Y66Y33Y20X00X\ 00X0`_0cY0fX0hV3kV5nT8oSAsQCvQFwPGzOJzMMzMOzLQzJSz\ JOzLJzMGzMCzO8zP5zP3zT3zX3w`3tc3qf3ok3ln3iq3hv3ex3\ cz6`w9_tCYqFXnIVkJTfMScPQ`SPYVOVXMSTPXQQ`PSeMViLXn\ IYsG_wJXxLVzOTzPQzSPzTOzXMzYJz`IzbGzeDzfCziAzk9zTF\ qCJ_DOXDSVDVS03D00D08S3Mf } 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==================================

1 0

FOTD 03-05-04 (Fractal Cheating [5])
by Jim Muth 03 May '04

03 May '04

FOTD -- May 03, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image is more of a demonstration of a Fractint program feature than a picture of a great fractal scene just discovered. I named the image "Fractal Cheating" because I used the 'decomp' option on yesterday's image to create it, which makes the image more of an intentional creation than a discovery. Yes, I cheated. But look at yesterday's FOTD, and you will see why I cheated. The standard rendering of today's scene makes a really nothing image. I humbly admitted my guilt by naming the image "Fractal Cheating". I also cheated with the formula I used. To create yesterday's version of the scene, I used the MandelbrotMix3a formula and entered the critical -8.888 by hand. For today's version, I turned to the MandelbrotMix4 formula, which calculated and entered the initial value of Z automatically. The benefit is a great increase in speed, though with an image as fast as today's, the difference is not very large. Most of my fractals are calculated by iterating a simple function of a complex number, producing another complex number, until either the number exceeds some pre-defined bailout value, or the maxiter is reached. The pixel corresponding to the starting point is then colored based on the result of that calculation. The decomp feature turns on another coloring method, in which the points are colored according to which section of the complex plane the final value lies in. The decomp parameter determines how many sections the complex plane is divided into for this purpose. In today's image, the plane is divided into the maximum 256 sections. I would have rated today's image higher than a 5, but the coloring is less than satisfactory, and I just can't shake the feeling that it is not a real fractal. Apparently, just as man has philosophically done with the sensory-created mental image of a physical universe, I have arbitrarily created a reality. I have decided that that the 'outside=iter' method produces the 'real' fractal, and all other rendering methods are mere distortions of the one ultimate fractal reality. But at least, I am still aware that I myself have created and decided what is fractal reality. The rating of 5 equals an overall value of 281 when the 1-3/4 minute render time is considered. The time required to download the image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is roughly the same. A warm sunny Sunday here at Fractal Central gave the dynamic duo ample time under the holly trees. When evening came, they were totally exhausted from doing nothing, and came inside for their evening meal without hesitation. In the late evening, a severe thunder-storm arose, which brought down a large limb from one of the fractal trees. But, other than the need to eventually remove the fallen limb, no harm was done, as it fell in the alley beside F.C. This morning is cloudy, chilly and damp, with occasional rain. What will the cats do to adapt? The most immediate task for me is to put the work that is now in front of me behind me. Then it's on to the fractals, and maybe that tree limb. Until next time, take care, and a fractal a day may keep the doctor away, but five hundred a day will bring the doctor running. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Cheating { ; time=0:01:46.83--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-22.97767772633961000/+0.06349061612053\ 014/3.426261e+008/1/-152.5/0.000251818031069418746 params=1/2/0.075/3/0/0 float=y maxiter=300 inside=0 logmap=34 decomp=256 periodicity=10 colors=000cmzzzVzzWzzWzyWzxXzwXzvXzuXztWysWxsVwrVv\ qVuqUtpUspUroTqnTpnTomSnmSmlSlkRkkRjjQijQhiQghPfhP\ egPdgOdfOceObeNbdNadNacM`bM`bL_aL_aLZ`KZ_KY_KYZJXZ\ JWYIWXGVXFVWEUVCUVCTUCTUBSTDSSDRSERRFQRGPQHPPIOPJO\ OKNOLNNMMMNMMOLLPLLPKKPKJPJJPIIPIIPHHPHGPGGPGFPFFP\ FEPEDPEDPDCPDCPCDPCEPCEPCFPCGPCGPCHPCIPCIPCJPBJPBK\ PBLPBLPBMPBNPBNNBOLBPJBPHAQFAQDARCASCASCATCAUEAUEA\ VEAWF9WF9XF9XF9YG9YG9ZG9ZG9_H9_H9`H8_G9aH9`H9aHAaH\ AaHAbHAbHBcHBcHBcHCdHCdICdICeIDeIDfIDfIDfIEgIEgIEg\ IFhIFhIFiJFiJGiJGjJGjJGjJHkJHkJHlJIlJIlJImKImKJnKJ\ nKJnKKoKKoKKoKKpKLpKLqKLqKLqLMrLMrLMrLNsLNsLNtLNtL\ OtLOuLOuLNvMOuLOtLOsLPsLPrLPqLPpLQpLQoLQnLRmLRmLRl\ LRkLSkLSjLSiLThLThLTgLTfLUeLUeLUdLVcLVcLVbLVaLW`LW\ `LW_LXZLXYLXYLXXLYWLYWLYVKZUKZTKZTKZSK_RK_QK_QK`PK\ `OK`NK`NKaMKaLKaLKbKKbJKbIKbIKcHKcGKcFKdFKdEKdDKdD\ KeCKeBKeAKfAKf9Kf8Kf7Kg7K } 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==================================

1 0

FOTD 01-05-04 (Burbling Burbles [6])
by Jim Muth 02 May '04

02 May '04

FOTD -- May 01, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's 6-rated image came about when I took Z^(-2.34), added 0.54 part of Z^(-4.32) to it, then added (1/C) to produce the typical shapeless, debris-filled parent fractal that results when two negative powers of Z are combined. The actual location of the image is near the southern perimeter of its parent, a short distance inland, not too far from a larger midget. The image reminds me of something like a pot of boiling corn starch, which inspired the not-too-classy and not-totally- gramatically-correct name "Burbling Burbles". Then, when I saw what I had done, I rated the whole thing at a 6, giving myself a one-point benefit of the doubt. The relatively harmless image was rendered with the outside set to 'tdis'. I did not try 'evaporating' it to see what this would produce. But one thing certain is that the short render time of 2-1/2 minutes on my 10-year-old P200 machine results in an overall value of 234, which takes us right back to the original formula. For convenience, the completed image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Conditions were near perfect here at Fractal Central on Friday. The cats thoroughly enjoyed the sunny skies, light winds, and temperature of 77F 25C. At one point a stray tomcat wandered into the yard. Tippy leaped to confront him, but after a few cat curse words, the other cat slinked off, and no blows were struck. The duo finished the afternoon peacefully. I have a bit of work to finish. Then I might tackle the fractal lawn, which has grown about 1/2 meter in the past week. When all this is finished, I will think of fractals. Until next FOTD, take care, and check out those ray-traced fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Burbling_Burbles { ; time=0:02:33.79--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.26548995960996870/-2.241402520338516\ 00/3738561/1/-137.5/1.59966557868040926e-007 params=1/-2.34/0.54/-4.32/0/0 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000VfRfz2fz5fz8fzBkr8pe6uT4yH2ZYF8nRIVPSBOc\ JTnRYyZbqYZjYVbYRWYNPYKQUIQRHRNFRKERHDRQKRZRRfYRod\ RwjMvhIufEueGlcHcbIWaJN`KE_L6ZYKajYdvjfsmgqogoqhms\ hjuihwifyjdzjernejpehuhezkdzmdzpczrdzpiwomumqrlspi\ tnftldrjaphZmfXkdUibSga_eRgaGlY6iV7cS8YP9SM9MJAGGB\ ADC4BC35C35M3TW3XeRcoXUTbY_hafnemtitymzqhwjdtc`qWX\ mPTjIPgKW`LbUMhNNoGOv9Pz2M_OJ8hLGcMOZNWUObQzj_xbZs\ VZnNZiFZd8ZCceIgbNj_TmXYpUcsRhvOmyLcxJVxHMxFDxD4xC\ 5pD6hE6`F7TG7LH8DI85JgO7bQCYRHTSLPUQKVUFWZBXbFZeI_\ hLakObnScqVetYfw`gzaYmaP`WUXQYTLaQFfM9jI4nFOlRgjbz\ hnsgfmg_fgT`fLUfEOf7KcIHaTE_bBYm8Ww9Xq9XlAYfAYaBZW\ BZRBZMIbKOfIUjG_nEfrClvArz8xz6vr9tfBrVEpJGo7Ie8RW9\ ZNAfDBn4Bv8OsC_qGloJxmUsccnUniKxdBuhFrkJpnNmqRjuVh\ xZezbczfiwMop2hlAahHVdOO`WHXbATi3PpAPiHPcOPYVPSaPM\ hPGoPAvP4rXLodalkqmzbhx`ct_ZqZVmXQjWLfVHcUVZHhV5bP\ CYJJDJvEKuFKtGLsHMrINqJNp } 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==================================

5 4

FOTD 02-05-04 (Fractal Patches [3])
by Jim Muth 02 May '04

02 May '04

FOTD -- May 02, 2004 (Rating 3) Fractal visionaries and enthusiasts: Today's image is a second thought. When I first stumbled upon it, I noticed its flatness. Flat images such as today's often do quite well with the alternate rendering options, so I tried some of them. The 'decomp' feature worked very well with the image, so I used it for the rendering. I named the result "Fractal Cheating", and decided that it would be the FOTD for today. I chose this name because the picture said more about the features of the program than it said about the scene I had discovered. Then I decided that the full worth of the 'decomp' feature would not be apparent unless the 'decomp' version could be compared to the drabness of the original 'outside=iter' version. Today's image is this 'iter' version. It rates only a 3, but the incred- ibly short render time of 40 seconds results in an unexpected and unjustified overall value of 449. The 'decomp' version of today's scene, which will rate notably higher, will appear as tomorrow's FOTD. Actually, all the 'outside' options do better than the standard 'iter' rendering of today's image, which is basically flat and featureless, but the scene renders so fast that the viewers can try these for themselves. I named the version of the scene that appears as today's image "Fractal Patches". That's all it is -- a few flat patches of color. The flatness is why the scene renders so fast. There is no fine detail to calculate. The route I took to today's image is rather interesting. Using the MandelbrotMix3a formula, I entered 1 and 2 as the p1 parameters, which drew the classic Mandelbrot set. Then I added 0.075 part of Z^3. This moved the M-set a bit to the left but had no other effect on the screen image. Next I entered -8.888... as the real(p5) parameter, which determines the initial point of Z, and just happens to be a critical point of the formula. The result was a blank screen. Never put off by blank screens, I did an outzoom and discovered that the action had moved far to the left. I zoomed in on the area of interest and found a new M-set. Except for the oddly- shaped iteration bands, this set looked normal, but on the X-axis some distance to the right of the new set, I spotted a tiny dot. This dot proved to be a tiny disconnected M-set with even smaller M-sets surrounding it like satellites around a planet. And I found that these satellites are in turn surroun- ded by satellites of their own. Today's image is that of a satellite of a satellite. Its surroundings are so flat because of its extreme isolation. The image may be seen by running the included parameter file or by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A pleasant spring afternoon here at Fractal Central on Saturday brought out the best in the dynamic fractal cats. Lots of sun and a temperature of 79F 26C were just what they needed for a comfortable three-hour lounge in the yard. But today things look ominous. It is starting cloudy with heavy rain forecast. Heavy rain does not stop the fractals however, so the next one will appear in 24 hours, give or take an hour or two. Until then, take care, and search for answers to the mysteries of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Patches { ; time=0:00:39.99--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident center-mag=-22.97767772633961000/+0.06349061612053\ 014/3.426261e+008/1/-152/0.00023170776981063651 params=1/2/0.075/3/0/0/0/0/-8.88888888889/0 float=y maxiter=300 inside=0 logmap=34 periodicity=10 colors=000bEKWILPNMIRNCVNQ_ZbdiohtPW2RU5TT8VSAWRDY\ QF_PI`OKWVSSa_OhgKooGuwO0MT2OX4Q`6Se8UiAWmCYqEZ0BJ\ LDKeFLzHMwFLuELrDLpCLmAKk9Kh8Kf7Kg7KcmzzzVzzWzzWzy\ WzxXzwXzvXzuXztWysWxsVwrVvqVuqUtpUspUroTqnTpnTomSn\ mSmlSlkRkkRjjQijQhiQghPfhPegPdgOdfOceObeNbdNadNacM\ `dM`eL_eL_fLZfKZgKYgKYhJXhJWiJWiIVjIVjIUkHUkHTlHTl\ GSmGSmFRnFRnFQoEPoEPpEOpDOqDNqDNrCMrCMsCLsBLtBKtAK\ uAJuAIv9Iv9Hw9Hw8Gx8Gx8Fy7Fy7Ez7Ez6Dz6Dz6Cz7Cz7Cz7\ Cz8Cz8Cz8Cz8Cz9Cz9Cz9Bz9BzABzABzABzBBzBBzBBzBBzCBz\ CAzCAzCAzDAzDAzDAzDAzEAzEAzEAzF9zF9zF9zF9zG9zG9zG9\ zG9zH9zH9zH8zG9zH9zH9zHAzHAzHAzHAzHBzHBzHBzHCzHCzI\ CzICzIDzIDzIDzIDzIEzIEzIEzIFzIFzIFzJFzJGzJGzJGzJGz\ JHzJHzJHzJIzJIzJIzKIzKJzKJzKJzKKzKKzKKzKKzKLzKLzKL\ zKLzLMzLMzLMzLNzLNzLNzLNzLOzLOzLOzLNzMOzLOzLOzLPzL\ PzLPzLPzLQzLQzLQzLRzLRzLRzLRzLSzLSzLSzLTzLTzLTzLTz\ LUzLUzLUzLVzLVzLwzHpzIizJ } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END 20.0 PAR-FORMULA FILE==================================

1 0

The "MandelbrotMix#" iterations, critical points and the Fatou Theorem, somewhat Re: [philofractal] FOTD 30-04-04 (Gossamer Glory [5])
by Hiram Berry 01 May '04

01 May '04

> "Jim Muth" <jamth(a)mindspring.com> previously opined: > > > Unable to find any really good or bad features in the image for > > today, I rated it at an average 5. > > After "Fractal Nonsense", which I think you also rated a 5, I don't put much > credance in your ratings Jim. That one, which showed a morphologically > sextic midget in the main filament of a fractal with a quartic generator, > showed something fundamental about Mandeloid generation and thus ought to be > ranked somewhere near the top of the scale regardless of whether your > colorist's skills were in evidence that day or not. > > > The parent fractal was created by combining portions of > > Z^(-1.95) and Z^(-5.91), then adding (1/C). > > Transforming the C part only in this kind of generator doesn't really > generate a new fractal; it stretches the domain (the complex plane) so you > get a distorted copy of what the fractal would look like if you used C > instead. I think 1/C should give you an eversion with reflection across the > real axis. I'm not sure whether this class of fractals should be called > mixes either. That would make me think that they had features similar to > the fractals generated from the monomials in the sum. "Fractal Nonsense" > showed that not to be always true. > > Also I believe you've used similar generating parameters for a series of > FOTDs. There are some details of this that bother me though. A while back > you chided Sherlok Merfy for not initializing z on a critical point in one > of his fractals. That would seem to imply that you value the concept of > purposeful intent in fractal creation, rather than just randomly trying a > lot of parameter combinations in hope of hitting something interesting. In > that instance I suppose you wanted Sherlok to understand how to apply the > Fatou Theorem to generate a maximal set of fractal points. Which is > commendable, and yet you've used the following deceptively simple formala > and its brethren: > > > frm:MandelbrotMix2 {; 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)+(p4)), > > k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): > > z=k*((a*(z^b))+(d*(z^f)))+c, > > |z| < l } > > many times. The initialization of z in the above appears to initialize z on > a particular critical point of the generator. But as I understand the Fatou > Theorem (please correct me if I'm wrong about this) it shows that every > point which converges using a particular polynomial generator (rationals > too?) for some initial z will converge for at least one z_init = a critical > point of the generating function. Emphatically not that it will converge for > any one of the critical points. So if you're trying to generate the full > fractal as above, there is a problem. You didn't test the other critical > points. In general, 0 will be one of them. The others will be the complex > roots of your first derivative equation (in your variable names) z^(f-b) > = -a*b*g*h . They do matter, as shown below. > Actually testing them all could be time consuming when f-b gets far away > from being an integer: today's FOTD has an exponent difference of 3.96 = > 99/25, so for n/(99/25) = integer the least value of n is 99 and it looks to > me like there are 100 critical points that need to be tested to get a > maximal set of inside points. Otherwise you get a lot of perturbed set > "eroded" boundaries. The fractals below illustrate the need to test all > critical points; I've only used integer valued exponents so far but I see no > reason it doesn't apply to fractional power generators too. > > Also, you greatly overspecify the number of parameters in the generating > formula. Notice that the expression > > z_1 = k*(a*z_0^b+d*z_0^f)+C can take a change of variable z = k1*w where k1 > = (k*a)^(1/(1-b)) to normalize it to > > w_1 = w_0^b + k2*w_0^f + C/k1, where k2 is the constant > k*d*(k*a)^((f-1)/(1-b)) > > Anyway, these fractals use a trick to render the different inside areas > different colors according to whether the point converges for the "critical > point of interest" or one of the other critical points but not the one of > interest. Right before bailing out, the value of z is reset to a value > that will be interpreted by the "inside=zmag" option as the desired color. > I've found that this works well for the inside for things like viewing the > intersection of two fractals to see if you can superimpose them. Does > anyone know if there is a comparable way to do this for outside points? > There isn't an "outside=zmag" option. > > In these fractals, the red regions converge for the "critical point of > interest" while the yellow and purple regions converge for other critical > points but not the one of interest. To make the formula work the exponents > have to be entered as a rational pair of integers, and the number of > critical points (as well as which one (an integer) is the c.p.o.i.) have to > be entered manually, though it ought to be possible to improve this > situation by having the formula calculate the number of cps. > > ==========PARS FOLLOW================ > AnOrder2sub2Mset { ; z->z^3+z^2+C, which has 2 critical points. Red areas > are > ; points which converge for one c.p. Yellow areas show > ; where the other c.p. converges but the former one > doesnt > ; Fractint Version 2003 Patchlevel 1 > reset=2003 type=formula formulafile=fatouthm.frm > formulaname=RatnlExpMandelO2 passes=1 > center-mag=-0.406646/1.0165e-005/1.041674/1/-90/3.88578058618804789e-016 > params=3/1/2/1/1/0/5/2/0/0 float=y inside=zmag periodicity=0; > colors=(a)2col_ins.map > colors=000zG0jz00ee<103>022022011<2>000000010<132>SwSSwSTxT<3>UzU000000 > } > > AnOrder2sub3_Mset { ; z->z^3+(0+1i)*z^5+C. Iterations starting from all 3 > ; critical points are necessary to generate the full > set. > ; Antisymmetry in the minibrots is interesting. > ; Fractint Version 2003 Patchlevel 1 > reset=2003 type=formula formulafile=fatouthm.frm > formulaname=RatnlExpMandelO2 passes=1 > center-mag=-1.905e-006/1.0165e-005/0.6666712 > params=3/1/5/1/0/1/10/3/0/0 float=y maxiter=1000 inside=zmag > periodicity=0; colors=(a)3col_ins.map > colors=000zG0jz0c0w0ee<102>022022011<2>000000010<132>SwSSwSTxT<3>UzU0000\ > 00 > } > > ===========PARS END==================== > ===========FRM FOLLOWS================ > RatnlExpMandelO2{ ; normalized order 2 M-set with rational real exponents > ; generator z -> z^A + k*z^B + C. p1=(A_num,A_denom) p_2=(B_num,B_denom) > ; p3=k(complex) p4=(bailout-4,# crit pts) p5=(crit pt of interest(int),0) > use > ; inside=zmag,periodity=off.Ins cols: 1=cpoi converged >1=sequential number > of > ; cp after cpoi which converged > IF(isinit==0) > ; 0 default proxies: > bailout = real(p4) + 4 > p1 = trunc(p1), p2 = trunc(p2) > IF(real(p1)==0), An = 3, ELSE, An = real(p1), ENDIF > IF(imag(p1)==0), Ad = 1, ELSE, Ad = imag(p1), ENDIF > IF(real(p2)==0), Bn = 2, ELSE, Bn = real(p2), ENDIF > IF(imag(p2)==0), Bd = 1, ELSE, Bd = imag(p2), ENDIF > ; end default proxies > k = p3, A = An / Ad, B = Bn / Bd, cps = imag(p4), cpoi = real(p5) > maxit = maxit > diff = A - B > angle = 2 * pi / diff ; angle to rotate critical points > rfactor = cos(angle) + flip(sin(angle)) ; rotate by complex mult > cpmod = ( -k*B / A ) ^ ( 1/diff ) ; real part only crit pt > isnotdiff = 0, execseq = 0 ; flags > IF(cpoi<0 || cpoi>=cps) > isnotdiff = 1 ; flag to not do difference map > execseq = 1 ; flag cp sequence 0 -> cpmod -> cpmod multiples > cpfirst = 0 > ELSEIF(cpoi == 0) > execseq = 1 > cpfirst = 0 > ELSE ; ordinary cp sequence cpoi -> 0 -> cpoi multiples > IF(cpoi == 1) > cpfirst = cpmod > ELSE > angle1 = angle * (cpoi - 1) > cpfirst = cpmod * ( cos(angle1) + flip(sin(angle1)) ) > ENDIF > ENDIF > isinit = 1 > ENDIF > zp = cpcurr = cpfirst ; z proxy--inside z is used for rendering > cpctr = 0, C = pixel, diverged = 0, iter = 1 > : > iter = iter + 1 > IF(diverged) ; then go to next critical point > cpctr = cpctr + 1 ; increment counter > IF( (execseq==1 && cpctr>1) || (execseq==0 && cpctr>2) ) > zp = cpcurr = cpcurr * rfactor > ELSEIF(execseq==1) > zp = cpcurr = cpmod > ELSEIF(cpctr==1) > zp = cpcurr = 0 > ELSE > zp = cpcurr = cpfirst * rfactor > ENDIF > ENDIF > IF(cpctr<cps) > zp = zp^A + k*zp^B + C > diverged = ( |zp| > bailout ) > ENDIF > z = zp ; for outside rendering > IF(diverged==0 && iter==maxit) ; inside point: set z for zmag rendering > ins_col = cpctr + 1 > z = sqrt( (ins_col*2-1) / maxit ) > ENDIF > cpctr<cps || diverged==0 > } > > ============FRM ENDS===================== > > Regards, > > Hiram > >

1 0

POV-Ray Fractal Raytracing Contest
by Paul N. Lee 30 Apr '04

30 Apr '04

Greetings, The following is a very interesting posting taken from the Usenet Newsgroups, and is well worth a visit to the specified site: _______________________________________________________________________ The final results of the POVRay Fractal Raytracing Contest have been announced, point your browsers towards the final presentation page. http://astronomy.swin.edu.au/~pbourke/povray/povfrac/final/ _______________________________________________________________________ Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

1 0

FOTD 30-04-04 (Gossamer Glory [5])
by Jim Muth 30 Apr '04

30 Apr '04

FOTD -- April 30, 2004 (Rating 5) Fractal visionaries and enthusiasts: There are some days when I just can't think of anything signifi- cant to mention about the day's fractal. Today is one of those days. My mind is a total blank. Normally my mind is just plain blank, but today the blank is total. Even the e-mail informing me that I have won the New Zealand Lottery had no effect. In fact, it actually caused me a bit of concern, since I cannot find the winning ticket, and I have forgotten where I purchased it. Oh well, at least I'll still be able to afford fractals. They are free. Unable to find any really good or bad features in the image for today, I rated it at an average 5. I don't recall why I chose the name "Gossamer Glory". It has a rather pleasant sound to it, though the image is not really all that delicate appearing. The parent fractal was created by combining portions of Z^(-1.95) and Z^(-5.91), then adding (1/C). The resulting fractal is an oversized thing consisting of the typical indescribable main bay filled with debris, with a much smaller satellite Mandeloid lying very near the eastern edge. Today's scene is located on a filament in the area between the satellite Mandeloid and the main debris-filled bay. The image contrasts broad flat areas with areas of intricate fractal detail, all of which surround a typical central midget. The render time of the included parameter file is a speedy 2 minutes. This bargain price raises the overall value of the image to 241. The image may also be seen by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant sunny day on Thursday, with a temperature of 77F 25C made the fractal cats very happy. They passed the after- noon under the holly trees, checking the little mounds that the cicadas are building up as they get ready to emerge. In the evening the duo came inside without urging and settled to sleep peacefully. I have about three hours work to finish before I return to fractal land to find the next FOTD, which will appear in 24 hours. Until then, take care, and see the light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Gossamer_Glory { ; time=0:01:10.42--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.69671384233176200/+0.032306360356109\ 19/1040471/1/-82.5/-1.65398982704401121e-009 params=1/-1.95/0.33/-5.91/0/0/0/0 float=y maxiter=1000 inside=0 logmap=37 periodicity=10 colors=000000000000000000000000VszmmzaTtdTvhTxkTzc\ SkURYURK_UMaWOcZPe`RgcSieUjhVljXnmYpo_rr`ttbuvcrud\ otdmsdjsdgrdeqdbpe_peYoeVneSmeQmeSnfTnfUnfVofXofYo\ gZpg_pgapgbqgcqhdqhfrhgrhhrhirhftjcuk`vlYxmVynSzoU\ wnWtmXqlZnk_kjahibehdbhf_ggXfiUejRdlOcmLboIapFalRW\ haQdmKaxEbvGbuHcsJcrKdpMdoNemPelQfkSfiTghVgfWheYhc\ Zib`iaahb`gb`gc`fc`fd`ed`ee`de`df`cf`cg`bg`bh`ah`a\ h`_ccYcfXciVclTcoScrQcuPcwNcrLcnJcjHceGcaEcYCcUAcP\ 8cL7cH5cC3c81d40f01h42i83jC3kF4mJ5mN5mQ6mU7mY7m`8m\ d9mh9mkAmoBmsBmvRhXec8ccBPcLBcVHcONcITcBZc5XcFWcOV\ cXUcfTcoScxQcqOckMceLc_JcUHcOFcIEcCGdDHeEIfEJgFKhF\ LiGMjGOkHPlIQmIRnJSoJTpKUqKXrV_sebtpduzavy_wyYxyWy\ yTzxRzxPzxNzxKzwIzwGzwEzwCzwPzqazknzezz_szalzbezcZ\ zdSzeQzdOzcMzbLzbJzaHz`Gz`Ez_CzZBzZ9zY7zX6zX5zZ5z`\ 5zb4zc4ze4zg4zh6ze8zcAzaBz_DzYFzVHzTIzRKzPMzNNzLQz\ JhzWdzcbzX`zR_zLYzEWz8Vz2 } frm:MandelbrotMix2 {; 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)+(p4)), 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==================================

1 0

Xfractint questions
by J Kotta 29 Apr '04

29 Apr '04

1. In the various file selection screens (e.g. loading par files), I can't get to other directories. There's no '..' like in DOS fractint, or any subdirectories. I could live with this except for... 2. How do you set default paths? I have a directory for pars, one for frms, etc. Xfractint seems to only look in the directory that I start it from. 3. This par was posted to the list about a month ago by SherLock Merfy; I finally tried to render it today. It starts out fine, but fractint eventually hangs and I have to kill it. Out_Of_Orbit {; Animation. Border tracing _treats_ periodicity, ; too. How would you check if the white line is dithered? ; Default map is too sticky in FRACTINT. reset=2003 type=mandel passes=b periodicity=-11 showorbit=yes center-mag=-0.765332/6.66134e-016/0.7772216/1.4732/90/3.88578058618804\ 789e-016 params=0/0 float=y maxiter=255 fillcolor=1 sound=beep colors=000<4>00000000zzz0000<4>000z000zzz0zzz00zzz0zyy00yyy0yxx00xxx0x\ ww00www0www00www0wvv00vvv0vuu00uuu0utt00ttt0tss00sss0sss00sss0srr00rrr\ 0rqq00qqq0qpp00ppp0poo00ooo0ooo00ooo0onn00nnn0nmm00mmm0mll00lll0lll00k\ kk0kkk00kkk0kjj00jjj0jii00iii0ihh00hhh0hhh00hhg0ggg00ggg0gff00fff0fee0\ 0eee0edd00ddd0ddd00ddc0ccc00ccc0cbb00bbb0baa00aaa0aaa00```0```00``_0__\ _00___0_ZZ00ZZZ0ZYY00YYY0YYY00XXX0XXX00XXX0XWW00WWW0WVV00VVV0VUU00UUU0\ UUU00TTT0TTT00TTT0TSS00SSS0SRR00RRR0RQQ00QQQ0QQQ00QQP0PPP00PPP0POO00OO\ O0ONN00NNN0NNN00MMM0MMM00MML0LLL00LLL0LKK00KKK0KJJ00JJJ0JJJ00III0III00\ IIH0HHH00HHH0HGG00GGG0GFF00FFF0FFF00EEE0EEE00EED0DDD00DDD0DCC00CCC0CCC\ 00BBB0BBB00BBA0AAA00AA909990099909880088808880077707770077606660066606\ 550055505440044404440033303330033202220022202110011101000 } Thanks, JK

2 1

Time and again
by darryl＠itworks.com 28 Apr '04

28 Apr '04

Jim Muth wrote: "There is something strange about time." Truer words are rarely written. This has long been one of the little idiosyncrasies that I use to describe The Human Condition ... we can easily conceive eternity in one direction only: forward. The human mind can grasp the concept of a line with no end, whether that line is time, space, or whatever. A line with no beginning is a different kettle o' fish. It's my contention that we cannot grok the concept. Oh, we can describe it, and tell ourselves that it exists, but in our minds, when we try to "see" it, our brains won't let us. It always starts somewhere, even if the starting point is in motion. The most common thing people do is to say that they are the same; I look forward and there is no end, I look back and there is no end. In that case the starting point is the point of view of the observer. Try as we might, we must, as humans, always start somewhere. We just don't end anywhere :)

1 0

FOTD 28-04-04 (Fractoid [6])
by Jim Muth 28 Apr '04

28 Apr '04

FOTD -- April 28, 2004 (Rating 6) Fractal visionaries and enthusiasts: I have before me the May '04 issue of 'Scientific American' magazine, which arrived in the mail yesterday. This magazine features articles of scientific interest that have been watered down and stripped of most mathematics so that they can be understood by the average educated person. The cover story is titled 'The Time Before Time', and proposes that time did not start with the so-called 'big bang', but might stretch backward forever into the past. If this is so, then time will never end. If an end to time were possible, it would already have happened, and we would not be here wondering about the start and end of time. There is something strange about time. In a way it is even more strange than space. To imagine a limit to time is as impossible as imagining it going on forever. I suspect that something is wrong with the questions we ask about time. Perhaps, instead of wondering whether time is limited or limitless, we should be wondering whether time is truly as objective as we assume. Our universe is four-dimensional. We know this. But why do we perceive one of the dimensions in such a different way? I have no answers, only ideas without proof, which some will agree with and others disagree with. But one thing certain is that the task of rendering of today's image has a very short extent in the space-time dimension -- 12-million miles to be almost exact. This distance seems long only because we compare it to our immediate surroundings. When compared to the size of our galaxy, 12-million miles is like an atom in a baseball. I could rate today's image no higher than a 6. It is more a demonstration of the outside=real option than a fractal discovery. The parent fractal is an indescribable thing created by combining Z^(-2) with Z^(-4) and adding (1/C). Today's image lies on a filament at the northwest edge of this parent. I named the image "Fractoid" a nonsense word that has a nice sound to it. perhaps the best feature of the image is its very short render time of one minute, which raises to overall value to a huge 566. This value will not be lost if the image is downloaded from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday was fair enough here at Fractal Central. The cats did not notice the blue skies and puffy white clouds, though they did enjoy the sun and temperature of 66F 19C. A rain squall arose in the evening, but by then the duo was safely indoors. Today is starting sunny but chilly. For me the day is starting with work to be done. Only then can I tackle the world of fractals. Until next time, take care, and never forget that FOTD accuracy is not guaranteed. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractoid { ; time=0:01:04.10--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.10780498607015700/+0.387334621764656\ 80/3984544/1/-145/5.90356517361084743e-006 params=1/-2/0.5/-4/0/0 float=y maxiter=300 inside=0 outside=real periodicity=10 colors=000UM8zQ9zUAzYCzaDzeEwaHuYKrUMpRPmNRkJUiGWk\ KZlN`nQboUdqXgr_isckufmvipxmryptzsvvpusmupkumhujfu\ fcucau`ZuYWtVUtRRtOPtLMtIKtFHtCFtFIpILlKOiNQePTaSW\ ZUYVX`R_cOafKdhGfkDin9kp6gm9dkB`hDYfFVcHRaKOZMKXOH\ UQESSHRVJQXLPZNO`QNcSMeULgWLiXPfYSdZVb_Z`_aY`dWahU\ bkSbmQVmLNmGGmB8m61m1KmDbmPtm_om`kn`gp`cr`ZtaVvaRx\ aNwaKwSIwIGw8EwACwBBwC9wD7wE6wF7wG7wH8wH8wI9wI9wJ9\ wKAwKAwLBwLBwMBwMEwJHwGJwILwKNwMPwORwQTwRVuTWsVYqX\ _oZan_coaepcgreisgjthkrglqgmofnnfolepkeqidrhdsfcte\ cucbvbbw`ax_ayY`yX`rZck`edbhYdjRelSfjSfhTgfTgdUgbU\ h`VhZViXWhVWgTXfRXePXdO_cVbc`dcfbcd`cbZc`Xc_VcYTcW\ ScVQcTOcRMcQKcOIcMHcLLcKOcJRcIVcIYcH`cGccFgcFjcEmc\ DpcDgcHZcKRcNIcR9bU1eX3eW5eW7eV9eVBeVDeUFeUGeUFdRE\ dPDdNDdKCcIBcGAcDAcB9b98b67b47b28d49e5Af6Bg8Bh9CiA\ DjBEkDFlEFmFGnHHoIIpJIqKJhOK`SLaWMb_NccOcgQceRcdTc\ bUc`_cJXcHVcFScCQcANc8Lc6 } 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==================================

1 0

Re: [Fractint] Monitor display question
by PCMASPEC＠cs.com 28 Apr '04

28 Apr '04

Paul, Thanks for your suggestions. I'll see what I can do with them. When I did a search for "Fractint" in CompuServe, I got a home page for Fractint that told me to download 20.0 as the newest version. I was pretty skeptical because I've had 20.0 since it was new. I downloaded my first Fractint well over ten years ago, but I have used it very little in recent years. I've had my XP machine for almost a year and hadn't discovered the problem until today. I appreciate the help. Dick Teeter

2 1

FOTD 27-04-04 (Iterative Hyperbolae [8])
by Jim Muth 27 Apr '04

27 Apr '04

FOTD -- April 27, 2004 (Rating 8) Fractal visionaries and enthusiasts: With today's image we return to the image quality that makes fractals worth the effort. The rating of an 8 is the highest in some time. Hopefully, this is a sign of things to come. To create the parent fractal, I mixed together Z^(-1.77) and Z^(-7.71), added (1/C) and let the mixture iterate for 1200 cycles. The resulting fractal is beyond description, an oversized thing consisting of numerous bays, valleys, long looping filaments, scattered bits and pieces, a curious almost- midget, as well as assorted other items of interest. The east side of the main bay is decorated with a prominent valley, which at first glance might be taken to be an East Valley. From the center of this valley extends a zig-zag filament strung with dewdrop-like nodes. Today's scene lies rather deep in one of these nodes. Surprisingly, the area has almost none of the typical 'East Valley' features. The standard equal-iteration-band rendering gives a good-enough image, but the evaporated version of the scene is better. It is this evaporated version that I used as today's FOTD. I made the totally-inside material visible by using the bof61 inside fill. Other fills might work equally well, but I have not yet tried any of them. When searching for a name, I noticed the hyperbolic elements and named the image "Iterative Hyperbolae". When figured into the 6-minute render time, the rating of an 8 gives an overall value of 135. What the overall value might be when the image is downloaded is up to the individual to decide. The download is available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Rain fell all day here at Fractal Central on Monday, while the temperature reached only 59F 15C. The cats did not approve and showed their disapproval by flipping into their sulking modes. A treat of tuna in the evening helped a bit, but a dish of fish cannot make up for a missed afternoon in the yard. Today looks somewhat better, so we'll see how it goes. For me it's a day of work before fun. Until next FOTD fractal, take care, and be at ease. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ IterativeHyperbole { ; time=0:05:55.50--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.40024400180910400/-0.000531620471100\ 73/3.385291e+010/1/15/0.000876059279207246078 params=1/-1.77/0.23/-7.71/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=0000V`0b_0jY0rW0mQ0iL7dGC_BIW5OS2qty`nfLjP`\ `YqTdzLmzGdzCYz7Pz3Hz0Az03zD2zY2yq2uiFq`QmTciLpfDz\ iKwkQqnYkqcfti`pfZmcYj`WgZVdWTbTS_QQYOP_WS`bTbiVcp\ WdwYfzZLg0Wj0dk0nn0xp0zq0zjTudutgwtixrkyrmzqnzqqzp\ rzptznpynmumjpmgkkdgkbbj_ZjYVzW`zVgrVnjVubVzWVzTSt\ QPfPMTMKGLH3GCIB7Z52n00zceC3OI0OF0OB0M80LD3LHADMGB\ QOAWV8_`5cg4ip3mw0rz0wz0zz0yu0ym0rf0uZ2rS2qK3mD3mC\ 7mBBnAFo8IpAMqFPsKTuPYwU`xZdycgzhkzmpzrtzrzzrzzrzz\ muzhrzcpzZmzUjzPgzKfyFcxH`xIZwLWuOTuPQtSOrTMrTItTF\ tTAtT5uT2uT0uP5qMDmKKiHSdD_`OYzPVzPTuPSpPQkPPfPO`P\ MYTOVWOSZPP`PMcPKtYbzdtzfpzgkzigzjdzk`zmYzmVgZ`PKg\ 75n00tSTjzzbzxWwqPrkKndDjZ7fT2gV0gW0iW0iY0jZ0jZ0k_\ 0k_0fT7bMDZGKTAQP3YL0cH0jO0dV0``2Yf4Tm8OtBKzFGzHCr\ Y7fk2Vz0Tt5SmFQfMP_WPVcMPVKLMIGDGC5F80PAD_BSjCftDu\ pFqmGmjHigHdcI``KYZLTWLQPOWKQ_DTd8Wi2Zn0`r0cwitCfq\ GdpKcnObmS80m50j35g0Dd0Lc } 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==================================

1 0

FOTD 26-04-04 (Sir Fractal [7])
by Jim Muth 27 Apr '04

27 Apr '04

FOTD -- April 26, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in an immense parent fractal that is too large to display in its entirety, and in fact might be infinite in its large as well as its small aspect. This huge parent was created by combining Z^(-1.25) with 0.24 as much Z^(-5.21) and adding (1/C). The location of today's scene at -11519.6 on the X-axis and -6756.86 on the Y-axis shows that we have wandered far from the familiar home grounds around the origin of the parent, into the dark mysterious outer reaches of Fractal Land, beyond which lies the unknown. Even way out here, we find the same scattering of midget copies of the Mandelbrot set. Apparently, Fractal Land is like the Physical Universe -- the general laws are the same in all its parts, no matter how distant those parts might be. This does not mean that the laws of Fractal Land are the same as the laws of the universe. There is no cosmic speed limit that corre- sponds to the velocity of light -- at least none that I am aware of. But there does appear to be something similar to gravity, which appears when two midgets approach to within a certain distance, and can be visibly seen stretching toward each other. Fractal Land is eternal. It does not change with time unless we ourselves make a series of separate images and join them into a single animation. But even here, it is we who have created the illusion of motion by joining in our minds a series of separate images into a single moving object. The situation is similar with the physical universe. We are told that there exists in physical reality a shortest possible length of time known as the Planck time, which is 10^-43 of a second. If this is true, then all the motion we think we see around us is an illusion of our own creation. Nothing is moving, we are merely observing a sequential series of eternally frozen three-dimensional universes and merging them in our minds into a single dynamic three-dimensional universe that changes in a time that we ourselves are creating. Our intellect has reached a stage where we are beginning to recognize the illusory nature of what we have long taken as the one external reality. Objective and subjective are no longer absolute. It appears that once we develop the long-sought-for 'theory of everything', the question will then become 'what is having the illusion?' And I would not be at all surprised if we were to discover that the universe, and ourselves as well, are merely intricately detailed fractals. Well, I appear to have gotten distracted from the business at hand, which is the FOTD. I have named the image "Sir Fractal" because in my opinion it has a certain solidness about it -- a nobility that would be expected of knights. I rated the image at a 7. This is an improvement over the recent images, which have not been the greatest. Combined with the render time of 6-1/2 minutes, the overall value rates a 107. Those who lack the time to render the image from the included parameter file may download the completed image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday remained cloudy and chilly here at Fractal Central, with a temperature that never rose above 64F 18C. Luckily the rain held off and the cats had a pleasant but slightly cool afternoon in the yard. But this morning is proving damp and foggy, with occasional light rain. It remains to be seen how the dynamic duo will react. What I'm going to do is the work that needs to be done. And when I finish, I'll take a trip to Fractal Land to worry about that great illusion. What I find there will appear as the next FOTD. So until tomorrow, take care, and see you soon. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sir_Fractal { ; time=0:06:32.66--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-11519.6/-6756.86/0.02217445/1/-12.5/\ 4.329384e-013 params=1/-1.25/0.24/-5.21/0/0 float=y maxiter=1200 inside=0 logmap=106 periodicity=0 colors=000ZZF__G``HaaIbbJccLddMeeNffOggPhhQiiSjjTk\ kUllVmmWnnXooVppUqqSqrRqsPqsOqsMqsLqsJqsIqsHqrFqrE\ qrCqrBqp9qn8ql6rj5rh3rf2rd1sb2t`2uZ3wX3xU4yP4zK4wF\ 3t93qA3nA3kB2hC2fC2cD2`E2YE1VF1SG1QG1NH1KI0HI0EJ0B\ K09K0EP7JUEOYLTbSXfZShUOjPKlKGmGKfJN`MQVPTPSWJVZDY\ a7``6d_6gZ5jY5mX5qW4tV4wV4zT6xS7vQ8tP9rNAqMBoLCmJD\ kIEjGFhFGfEHdCIcBJa9K_8LY7MX9NWANVBNUCNTEOSFORGOQH\ OPHSNHVLHYJH`HHcFHfDHiBHl9Ho7Hr5Hu3Hx2Ju3Ks4Lp5Mn6\ Ok7Pi7Qf8Rd9TaAU_BVXBWVCYSDZQE_NF`LFbIGcGHdDIeBJf9\ Je9Jd9Jc9Jb9J`9J_9JZAIYAIXAIVAIUAITAISAIRAIOFGLJFI\ NEGSDDWCA_A8d95h82l70p68pEGpMOpUWpabpidmgekeficgga\ _h`Sh_LiZDiY6iXBeUFbSK_QOXNTULXQJaNHeKEjHCnEArB8tX\ 6uV9vTCwRFxPIyNKzLNzJQzHTzFWzDYzB`z9cz7fz5hzUnzUoz\ UozUqzUszUuzWwzUxzWyzYzz_zzazzczzczzczzczzczzczzcz\ zczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } 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==================================

3 2

Monitor display question
by PCMASPEC＠cs.com 26 Apr '04

26 Apr '04

I don't know if this is the proper protocol to try to get an answer for a problem I'm having, but I'll send it and see what happens. I am trying to run FRACTINT 20.0 in a machine that has a Pentium 5 processor, 512M of memory and MicroSoft XP Pro as the operating system. My video chips are GeForce4 MX440, BIOS 4.17.00.28. Fractint works at 640x480x256, but when I try to choose 800x600x256, I get two clicks and a blank screen out of the monitor. ESC takes me back to the Fractint menu. 800x600 is my normal screen resolution for everything else under WinXP Pro. Can anyone tell what I need to do to get this to work? Thanks Richard M Teeter

3 2

FOTD 25-04-04 (Illusory Minibrot [5])
by Jim Muth 25 Apr '04

25 Apr '04

FOTD -- April 25, 2004 (Rating 5) Fractal visionaries and enthusiasts: All creation is an illusion. 'Reality' is a human invention. This is especially true with the visual semi-realities we know as fractals. Rational skeptics will disagree, irrational mystics will agree, but proof or disproof is part of the illusion, so none of this will mean a thing. The big question remains, 'what is the human mind?' Today's harmless image was created by combining various negative portions of Z^(-1.5) and Z^(-5.1), and adding (1/C). I named it "Illusory Minibrot" because the image, like all fractals and indeed all math, is an artifact of the way the human mind functions. Then I studied the image for a few minutes, and after deciding that it lacks something, I rated it at an average 5. I did not concern myself with what it is that the image lacks. When I considered the running time of 6-1/2 minutes, the overall value came in at a 76, which makes running the parameter file not a total waste. There's not much more to be said about today's FOTD other than the fastest way to see and hopefully enjoy it is to download the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Bright sun and mild temperatures gave the cats an enjoyable day in the yard on Saturday. Clouds and cooler temperatures will make today less enjoyable. The good news is that the next FOTD will appear right here in less than 24 hours. Until then, take care, and fractals hold the wisdom of the ages. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Illusory_Minibrot { ; time=0:06:33.81--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.13020483280054180/-2.013785067982037\ 00/1897110/1/-132.5/5.76382413255971393e-008 params=-1/-1.5/-0.29/-5.1/0/0 float=y maxiter=1200 inside=0 logmap=124 periodicity=10 colors=000MTMLVOKXPKYRJ_SIaUIcVHdXGfYGg_Fi`EjbEkcD\ leCmfCohBpiAqkArl9sn8uo8vq7wr6xt6yuCvvHsvMqvRnwXlw\ aiwfgxkdxpbxjhsknnmtiyzdwybux`swZqvYotWmrUkpSioRgm\ PelNfkMfiKfgIfeGggFghDgiBgkAhkCiiDhgEgeFedGdbHb`Ib\ ZJbXKcWLcUMdSOdQPePQeNRfLSfJTgHUgGVhEWhCXiAYi9ZiGV\ iNRiUNi`JigFinChoCgpCgpCfqCfrCerCesCdsCdtCcuCbuCbv\ CavCawC`xC`xC_yC_yCaqBbjBdcBeXBgQBhJBfHEdGHbFK`DNZ\ CQXBTVAWT8ZR7aP6dO5gN4hM4hL4hL3hK3hJ3hI3hI2hH2hG2i\ G1iF1iE1iD1iD0iC0iB0iB0iA4g97e8Bc7Ea7H_6LY5OW4SU3V\ S3YRCVWLT_UQdbOh`Qi_RiYTiXUiVVjUXjSYjRZjP`jOakMckL\ dkKekIgkHhlFilEklCllBnl9om8pm6rm5sm4tm8piClfFhcJd`\ M`YQXVTTRXPO_LLcHIfDFj9Cm59kAAjEAiIAgNAfRBeVBc_Bbc\ BagC_lCZpCYtCXxCWyBWzBXzBYzBZzB_zBbzBezBhzBkzBnzBq\ zBtzBwzBzzBzzBzzBzzBzzBzzBzzBzzBzzBzzCzzDzzDzzEzzF\ zzFzzGzzHzzHzzIzzJzzJzzKzzLzzLzzMzzMzzNzzOzzOzzPzz\ PzzQzzczzgzzczz_zzXzzTzzP } 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==================================

1 0

Oh No! Not again!
by Chris Curnow 25 Apr '04

25 Apr '04

Hi folks, You're going to kill me for this one! I've been going back through the posts to find the answer but I think it was all discussed about two years ago and those posts have gone! I've just been upgraded to Win XP. No Fractint! Please! Someone tell me how to create a boot disk for Dos from XP! If that's not do-able what must I do? I'm not, by any means, an operating system guru so, if you feel like replying, please aim at a twelve year old thicko! (I can tie my laces, look mum!) Chris

6 9

FOTD 24-04-04 (An Evaporated Scene [6])
by Jim Muth 24 Apr '04

24 Apr '04

FOTD -- April 24, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's image is another 'evaporated' one. It is basically one big black hole, nothing but the empty space left over when all the material in this particular universe has disintegrated. It could be the first signs of the cold death of ultimate entropy that the cosmologists now tell us will be the ultimate fate of the physical universe that we all know and some of us love so well. The expression being iterated combines Z^(-2.7) with Z^(-7.2) and adds (1/C) to create the parent fractal. This parent defies description, as do so many fractals. But it has one feature that I found a bit unusual -- a tiny area of chaos entirely enclosed in a negative-exponent shapeless blob. Within this chaos I found a midget. In the southern suburbs of this midget I found another midget. After trying several outside options, I evaporated the scene and rendered the remains with the bof61 option. The result is today's image, which I have rated at a 6. When the render time of 6-1/2 minutes is figured in, the overall value rates a 92. The name, "An Evaporated Scene", is a mere description. Things such as render times and overall values can be ignored by downloading the image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday's weather here at Fractal Central was mostly sunny with a temperature of 82F 28C. The thunder held off until evening, and by that time the dynamic cats were in for the day. The storm was minor, with light rain, light wind, and not even enough thunder to send the cats scampering for cover. Hopefully, today will be a repeat. It's once again the week-end -- time to try as hard as possible to have a relaxing time of it. Unfortunately, as soon as I find some spare time, I usually fill it with fractals, the next of which will appear in 24 hours. Until then, take care, and if I come back to earth, I want to do it as a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ AnEvaporated_Scene { ; time=0:06:32.94--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.53891493182580860/+0.706973166708245\ 30/8.457311e+010/1/70/-4.60000456888737252e-005 params=1/-2.7/0.375/-7.2/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000nBorAp_EhIIaRVQ_gFht4oi3_SCKALLFFMK9NO4o\ pHn`EmLCl5AdAAXEAPJAHNAARAJPHSNN`LUhJ_SdUCyOEnUFdZ\ GVcHLhMNjRPlVQm_SocTphVrlWsjHpi3mc5nY7nS9nMAnGCnAE\ n4FnDMbLTRIQPFOOCMMAJL7HJ4FI2DHEQPPaXUcVYdTafRegQi\ hOmjMqkKulJmgIfbHZYGSTFLOFQPKVQP_RTdSYiTanUfrVjrZm\ raprdrrgurjxrmzrnirnTloXfo``pcVpgQpjUIbYEQaBEWECRH\ AMK8HN6CN47T2200FL8RLGcGOfCVnEWnGXmIYmKZmM_lO`lQal\ SazwRUrJ0oCKUTNSNVVIaUDj`8faBtYD_cGWdITkLPfNMgPFbL\ 9YH3TD9ZGEdJJiM`oYrthrpjrmkrilrfmrbnr_orWprTqpVnnX\ klZhj_fhacfc`deYcfWSlZGra4wd4Uv6Vs8WpAXmCYjEZgF_d7\ fW0mN8fRG`VOUZWObcIfZBVU5KV6HW6FX6DY6BZ78_76`74`72\ cA8fDEiGKlJQoMWrPauSgwUlrPimKfhGdcBaZ6ZU2XV7_VCaWH\ cWLeVVVVdLVmBb`HjPNrCTz0Yv5ZsAZpF_lK_iP`fU`7GO9NLB\ TJDZGFeEHkBJq9OlCSgEWcH_ZJcULgQOkLQoHSgEU_BWS8YK5_\ C2`J6YQAWXETcIRjLPfJRbHSZFUVDVRBXN9YJ7_F6`W6Wk6S_5\ TP4UD3V23VGCYUL_gUafXVjCm } 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==================================

1 0

Re: [Fractint] Reading Digests
by nick.grasso＠hrads.com 23 Apr '04

23 Apr '04

Vortex Swirling <vortexswirling(a)bigfoot.com> wrote: >>>The question comes to mind, if this is the way I want it then why don't I just receive individual mails and place them in separate mailboxes. This could work but there are some drawbacks. First is that the increased individual items makes managing spam with MailWasher much more difficult. <<< I'm not familiar with MailWasher, but can't you just tell it to let through anything with [Fractint] in the header? You don't get spam that contains [Fractint] do you? Most all the mailing lists I belong to put their name in brackets like that. Nick

2 1

FOTD 23-04-04 (Star and a Half [5])
by Jim Muth 23 Apr '04

23 Apr '04

FOTD -- April 23, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's relatively harmless image takes us into the world created by combining portions of Z^(-1.8) and Z^(-8.1), then adding (1/C). To decide how much Z^(-8.1) to include, I simply divided 1.8 by 8.1. I doubt that this procedure has any special significance on the appearance of the resulting fractal, but doing it is kind of fun, and above all else, fractals should be fun. The image shows a midget (nothing unusual in that) located in a node on a zig-zag filament in a valley of the humdrum parent. I rendered the scene in the conventional manner (nothing unusual in that either) and named it "Star and a Half". I can give no good reason for the name other than it sounds poetic. Since everything about the image is normal and it takes 5-1/2 minutes to render, I rated it at a 5, which is as average as it is possible for a 'Fractal of the Day' to be. When the render time is taken into consideration, the overall value rates a 91. The task of copying this letter into the Fractint directory with a .par extension and running it as a parameter file may be avoided by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the GIF image from there. The rain held off Thursday, letting the cats have a pleasant afternoon in the yard. When the time arrived to come inside for dinner, they did so without complaint, settling to sleep only 5 minutes after eating. Today is starting sunny but oppressive -- the kind of day that produces thunder, which the cats do not enjoy. We will see how it goes. We also will see how the dynamic duo takes to the hordes of 17-year cicadas that are soon to make their appearance in the Fractal Central vicinity. Their holes are already starting to appear in the ground under the trees. These bugs come out by the millions every 17 years, doing little harm but making a terrible racket for a month or so. When they die, their dead bodies literally make eight-inch-deep cicada drifts in the gutters. When the cicadas last appeared in 1987, Squeaky and Little One, the predecessors of the present dynamic duo were overwhelmed. Things will be less overwhelming for me when the work is behind me, but to bring that about will require around 4 hours' effort. Until next time, take care, and fractals are clearly infinite, but unfortunately, people are not. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Star_and_a_Half { ; time=0:05:29.11--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.94988892809340500/-0.005789089823096\ 38/7552786/1/-92.5/-1.21952945740522178e-006 params=1/-1.8/0.22/-8.1/0/0 float=y maxiter=1200 inside=0 logmap=100 periodicity=10 colors=000XUCZXH`ZMaaQccVde_fhcgjhilmjoqlnvmoznqzn\ rzntznuznvznwzkxzhyzewzbwz_wzXwzUXTR`XOc`LfdJihNcj\ QYkd`tZYmTWaNUaISSCQP6EC1OD3RH5VK6XN8`RAbUBeXDg`Fj\ cGlfHmdInbJoaKo_LpZMqXNrWOrUPsTQtRQtQJqIDnA7l3Kn9X\ pFhrLjkOkdQlYSmSUnLXoEZzY`j1bp7_pDXoJVoPSnVPn`NmfK\ mgIhhJciK_jK5kc9leEkgIkiNkjRjlWjn_jpdirhismiuqhwvh\ yzhzvgxsfwpfvleuidtfdsccr_bqXbpUaoR`nN`mK_lHZkEZjJ\ afNdbRg_VjW_mScpPgsLkvImqJnlJpgJqcKsZKtUKvQLwLLyGL\ zCLyFKyHKyKKxMKxOKxRKxTKwVJwYJw_JvaJvdJvfJvhJsfOpe\ SmcWjc_gcddchaclZcpWctXcrXcpXcnXclXcjXchXcgYceYccY\ caYc_YcYYcWYcVicJdcM`cPWcRScUNcWJcZEcaAcc5cf1chWca\ Zc``c_bdYeeXgfWigVfhVciV`jVYkVVlVNmLFnB8o17p96qG6r\ O5sV5tb4ui4vp7woAxoDynGznJzmLzmOzlRzlUzkXzkZzjazjd\ zigzijzhlzhezd_z`UzXOzUIzQCzM6zJDzIJzIPzHVzH`zHbzS\ dzbfzmgzwVzqIzl5zgEzdMzbVz_bzYjzWdzX_zXVzXQzXLzXGz\ XBzX6zX1zX7zTCzQHzMNzJSzF } 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==================================

1 0

Re: Reading Digests
by gnome＠hawaii.rr.com 23 Apr '04

23 Apr '04

Better still, look for the "Fractint(a)mailman.xmission.com" in the FROM field, then all of us be freed from the wasteful practice of sticking the list name in the subject line. David gnome(a)hawaii.rr.com ----- Original Message ----- From: nick.grasso(a)hrads.com Date: Thursday, April 22, 2004 8:47 am Subject: Re: [Fractint] Reading Digests > > Vortex Swirling <vortexswirling(a)bigfoot.com> wrote: > > >>>The question comes to mind, if this is the way I want it then > why don't > I just receive individual mails and place them in separate > mailboxes. This > could work but there are some drawbacks. First is that the increased > individual items makes managing spam with MailWasher much more > difficult.<<< > > I'm not familiar with MailWasher, but can't you just tell it to > let through > anything with [Fractint] in the header? You don't get spam that > contains[Fractint] do you? Most all the mailing lists I belong to > put their name in > brackets like that. > > Nick > > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

2 1

Re: [Fractint] Reading Digests
by Vortex Swirling 23 Apr '04

23 Apr '04

Never mind. There is an option in Eudora Options/Attachments then check Receive MIME Digest as a Mailbox Attachment. After doing that the Fractint Digest comes with the index at the top and then a link to a .mbx file. Clicking on that link creates a virtual mailbox with all the individual subjects in it. This doesn't work with Yahoo Group Digests since they aren't in a MIME format. I don't know why the do this but I'm sure they aren't going to change it just for me. The question comes to mind, if this is the way I want it then why don't I just receive individual mails and place them in separate mailboxes. This could work but there are some drawbacks. First is that the increased individual items makes managing spam with MailWasher much more difficult. Secondly, if I get behind in my email, depending on what list it is I just delete the whole digest. (Never a Fractint one, though ;) Not even to mention the increased overhead. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.665 / Virus Database: 428 - Release Date: 4/21/2004

2 1

Murphy's Secret
by Private Instigator 23 Apr '04

23 Apr '04

On Thu, 22 Apr 2004, Paul N. Lee wrote: > I wrote: > > > > Paul N. Lee wrote: > > > > > > Both the spelling and the link are good. > > > And according to the access logs, several > > > different host addresses have been to the > > > page. What type of message are you getting?? > > > > I think you're trying to solve the wrong problem. > > > > Quite possible. There did not seem to be enough information from the > 'User' for me to determine specifics of what was really going on. I > assumed it was just an access problem to the webpage. The access problem has more to do with creatures of habit that like doing what works before they start experimenting and another element of psychology that makes people into great imitators that only get better when you challenje them. My own rule of thumb is that code doesn't belong in English text, and I'm not sure about Universal Resource Locators in e-mail (it would certainly be a refreshing change to see them omitted when. A rule for OKpists is similar in that numbers are spelt out, and I doubt that Googol ato1en squared twice is sufficiently distinct from a Universal Resource CONNECT 33600/ARQ/V34/LAPM/V42BIS IN APPEARANCES! (snip)...While I was waiting, I got a good idea on a thinly related topic. Cole's Law: Thinly sliced cabbage. If you ever get a refurbished or second-hand computer, then chances are you'll get some surprises in the configuration. I got that quotation from a program that I moved over a patch cable from my old computer (and I still haven't done that completely, because I didn't discover fmirror until _after_ I had done a lot of typing). Lewis' Law: No matter how long or hard you shop for an item, after you've bought it, it will be on sale somewhere cheaper. Dhu prohgram iz uv kohrs fild with sumthing akin to wut QOTD (Kwohtayshun uv dhu day) iz fild with, but speshalized, soh I wawnted tuu enshure dhat QOTD had ol dhu stuf frum "Murphy.exe". Within _dhat_ wuz an intenshunal ridl. I ran it with MURPHY /? and ol it tohld me wuz wut it just hapend tuu tel me for the first tuu weeks: "Nature sides with the hidden flaw". Dohn't ask me why, but I kut dhe swic kaarakter when I ran the prohgram again. Sumtiim layter, I manajed to piip dhee entire list of kwotayshunz, no formatting, intuu a fiil. So, why am I spoiling this? Simply, because I think that answering this riddle will be rare, this archive isn't on google (which is an economic riddle, due the sheer volume of storaje required to duplicate the internet), there's at least half a douze riddles in the basic operation of FRACTINT, and you can square that for the purposes and questions of direction in programming. The point is simply dhat I _prefer_ doing without swichez, whic mainly serv to let you name files in an obvious fashion when you should be avoiding that. As far as I can see, FRACTINT doesn't hav them. In jerman, someone avoided "doppeltgemopelt" or unnecessary redundancy. (I olsoh happen to hayt prohgrams that dohn't ask for parameterz when thay ar reekwired. It's just a link to a formatted payj. Noh reezon iz tuu skrimp on fiil-space wen it kumz tuu dhe dokyuumentashun in playn tekst).

1 0

re: Dynamic real, and static imaginary, eyc.
by Hugo 23 Apr '04

23 Apr '04

I think rudy rucker uses this in his cubic connectedness map cubic mandelbrot formula. It has six parameter spaces. -david ----- Original Message ----- From: <fractint-request(a)mailman.xmission.com> To: <fractint(a)mailman.xmission.com> Sent: Saturday, April 17, 2004 6:27 AM Subject: Fractint Digest, Vol 14, Issue 7 > Send Fractint mailing list submissions to > fractint(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > or, via email, send a message with subject or body 'help' to > fractint-request(a)mailman.xmission.com > > You can reach the person managing the list at > fractint-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Fractint digest..." > > > Today's Topics: > > 1. Re: FOTD 15-04-04 (Land of Fractals [5]) (SherLok Merfy) > 2. Re: FOTD 15-04-04 (Land of Fractals [5]) (James R. McKenzie) > 3. FOTD 16-04-04 (Image of Springtime [5]) (Jim Muth) > 4. nntp:/news.admin.net-abuse.sightings (SherLok Merfy) > 5. Re: FOTD 15-04-04 (Land of Fractals [5]) (Paul N. Lee) > 6. Re: FOTD 16-04-04 (Image of Springtime [5]) (Paul N. Lee) > 7. FOTD 17-04-04 (Polyester Minibrot [7]) (Jim Muth) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Thu, 15 Apr 2004 10:00:43 -0600 (MDT) > From: SherLok Merfy <brewhaha(a)freenet.edmonton.ab.ca> > Subject: Re: [Fractint] FOTD 15-04-04 (Land of Fractals [5]) > To: Fractint and General Fractals Discussion > <fractint(a)mailman.xmission.com> > Cc: philofractal(a)lists.fractalus.com > Message-ID: > <Pine.A41.3.95.1040415094447.29258D-100000(a)freenet.edmonton.ab.ca> > Content-Type: TEXT/PLAIN; charset=US-ASCII > > On Thu, 15 Apr 2004, Jim Muth wrote: > (...) > > frm:OblateMix2 {; Jim Muth > > z=real(pixel)+flip(real(p3)), > > c=fn1(flip(imag(pixel)))+imag(p3), > (...) > Dynamic real, and static imajinary -- then vice-versa. Nobody has > a monopoly on stuff that only they know how to work (or read, as the case > may be), but even if the formula doesn't spred, that's an interesting > idea. > > > > > ------------------------------ > > Message: 2 > Date: Thu, 15 Apr 2004 14:56:51 -0400 > From: "James R. McKenzie" <jimmckenzie(a)earthlink.net> > Subject: Re: [Fractint] FOTD 15-04-04 (Land of Fractals [5]) > To: "Fractint and General Fractals Discussion" > <fractint(a)mailman.xmission.com> > Message-ID: <000901c4231b$698d8cf0$09fb1743@yourxhtr8hvc4p> > Content-Type: text/plain; charset="iso-8859-1" > > This only rates a "5"? I wish I could run Fractint in XP (Been there tried > that, no go) so I could do a 3D transform of the image and see what comes up > or "out" as it were. 8-{> > > BTW if anyone does a 1280x1024 of this e-mail me, I'd like a copy. > ----- Original Message ----- > From: "Jim Muth" <jamth(a)mindspring.com> > To: <fractint(a)mailman.xmission.com> > Cc: <philofractal(a)lists.fractalus.com> > Sent: Thursday, April 15, 2004 10:52 AM > Subject: [Fractint] FOTD 15-04-04 (Land of Fractals [5]) > > > > > > FOTD -- April 15, 2004 (Rating 5) > > > > Fractal visionaries and enthusiasts: > > > > Today's image takes us into the fourth dimension. I have always > > been fascinated by the fourth dimension. I was not yet a > > teen-ager when, having just finished a book, (I think its name > > was "One, Two, Three, Infinity..."), I asked my father where the > > fourth dimension is, and, thinking of relativity, he told me > > that it is in the past and the future. This was not a very > > satisfactory answer. The past and future are time, not space. > > I wanted to know where the fourth dimension of space is. He > > then explained to me that as far as we know, there is no fourth > > spatial dimension, and even if there were, we would perceive it > > in three-dimensional terms. > > > > This is the problem. We are brain-washed to perceive our > > surroundings as a three-dimensional world. We have not been > > wired to perceive a four-dimensional space, and it is too late > > to change that. If we were suddenly dropped into a four- > > dimensional world, we would not see the fourth dimension. We > > would see a three-dimensional world that obeyed different rules. > > Solid objects would change shape as we watched; objects would > > appear and vanish. We would think the world had gone crazy. We > > would probably go crazy ourselves, (as some say I already have), > > but we would be no closer to visualizing the fourth dimension. > > > > Even now, we are able to fully visualize and understand the > > shadows that would be cast by four-dimensional objects onto the > > three-dimensional surface of our space. A 4-D hypersphere would > > cast a spherical shadow if the ray of light fell perpendicularly > > onto our space. If the light struck our space at an angle, we > > would see an oblate spheroid, the eccentricity of which would > > vary with the angle of the ray of light. But even though we > > understand all of this, we are still totally unable to visualize > > the hypersphere that would be casting the shadow. > > > > We can also know and fully visualize the three-dimensional > > slices of four-dimensional objects. The 4-D hypercube may be > > sliced to give many curious prisms, as well as a tetrahedron and > > an octahedron, and of course the expected cube. But even this > > is of no help in our quest to realize the fourth dimension. > > > > Our lack of visualizing ability is curious. We can program our > > computers to 'think' in four dimensions almost as easily as in > > three. We could even give them three-dimensional screens on > > which to better display the 4-D worlds they would have no > > trouble in manipulating. Of course, we would then be unable to > > view the 3-D screens in the proper manner, from outside our > > space. We would of necessity need to view the screens > > 'edge-on'. We appear to be forever doomed, trapped in a world > > of three dimensions, while able to know of the far greater > > vistas that would lie before us if only we could rewire our > > minds. > > > > Since our minds are not about to be rewired, it's best we turn > > to today's image. > > > > Today's image is a two-dimensional slice of a four-dimensional > > object. In this case, the object is the 4-D Julibrot created by > > iterating the formula (1/Z)-Z+C. I have sliced the Julibrot in > > what I call the Oblate direction, which is determined by the > > imaginary C and real Z axes. > > > > The picture has a certain surreal quality about it, which > > inspired the above outburst about higher dimensions. It could > > almost be something we might see if we were suddenly dropped > > into a four-dimensional space. This is why I named the picture > > "Land of Fractals". > > > > Since the image is such a departure from my usual fractal fare, > > I was not sure how to rate it. I finally decided on a rating of > > an average 5. The short render time of 2-1/2 minutes raises the > > overall value to a mighty 202. > > > > An alternate way of seeing the other-worldly scene is to > > download it from the FOTD web site at: > > > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > > > Light rain fell steadily all day Wednesday here at Fractal > > Central, keeping the fractal duo confined to the indoors. Even > > if it had not been raining, the temperature of 50F 10C would > > have been a bit chilly for their sensitive ears. Today is > > starting windy and chilly, but sunny. We'll see how the > > dynamic fractal cats take these conditions. > > > > For me it's work before play. The problem comes in separating > > the two. Until tomorrow's FOTD, take care, and most likely it's > > fractals all the way down. > > > > > > Jim Muth > > jamth(a)mindspring.com > > jimmuth(a)aol.com > > > > > > START 20.0 PAR-FORMULA FILE================================ > > > > Land_of_Fractals { ; time=0:02:28.69--SF5 on a P200 > > reset=2003 type=formula formulafile=allinone.frm > > formulaname=OblateMix2 function=ident passes=1 > > center-mag=-4.55271/3.10114/0.6584367/8.9718/-11.2\ > > 262659607652502/29.222244310548934 > > params=1/-1/-1/1/1/-0.2 float=y maxiter=1200 > > inside=255 logmap=yes periodicity=10 > > colors=000Di`Ei_FiZFhZGhYGhXHhWHhWHhWU_`fRfuHlsIkr\ > > JjpKjmLiUdkUckUbjUaiU`hU_gUZfUYeUXdUWcUWcUVbUVbUUa\ > > TUaST`QT`RS_PS_NRZMRZKQYJQYHPXGPXENWDLWBIVAGV8EU7C\ > > U8ET9MTANSBOSBPRCQRDRQETQFUPFWPGYOH_NIaMIcLJeKKgJL\ > > iIMkIMmINoIOqIPsINsHPtIQtIStITuJVuJWuJYvKZvK`vKawL\ > > cwLdwLfwLgxMixMjxMlyNmyNoyNpzOrzOszOtzOuvPusPupPum\ > > PvjPvgPvdPvaPubRtcTscVrdXqdZpe_oeanfcnfemgglgikhjj\ > > hliinhipgjrfhygjshlninhjpckrZltTmvOnxJozDpz8pz3lxE\ > > hrPdm_`gjYcvXbtXbsXbrXbqWbpWboWbnWbmVbkVbjVbiVbhUb\ > > gUbfUbeUbdUbcW`bY_bZZb`YbaWbcVbeUbfTbhRbiQbkPblObj\ > > NahNafM`dM`bL_`L_ZKZXKZVJYTJYRIXPIXNHWLHWJGVHGVFFU\ > > DFUBET9ET7DS5DS8GTBITELTGNTJQTMSTOVURXUU_UWaUZdUaf\ > > UgkVchU_fUXdTTbTQ`SMYSIWRFURBSQ2UJ8QQEMWKIbQEjPFhP\ > > GgPHfPIeOJdOKbOLaOL`NM_NNZNOYNPWNQVMRUMRTMSSMTQLUP\ > > LVOLWNLXMHUMLXLP_KTbJXeJ_gIcjHgmHkpGosFstCruFrvIrw\ > > LqxNqyQqzTqzWpzYpz`pzccwz } > > > > frm:OblateMix2 {; Jim Muth > > z=real(pixel)+flip(real(p3)), > > c=fn1(flip(imag(pixel)))+imag(p3), > > a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): > > z=(a*(z^b))+(d*(z^f))+c, > > |z| <= 100 } > > > > END 20.0 PAR-FORMULA FILE================================== > > > > > > _______________________________________________ > > Fractint mailing list > > Fractint(a)mailman.xmission.com > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > > > > > > ------------------------------ > > Message: 3 > Date: Fri, 16 Apr 2004 10:45:46 -0400 > From: Jim Muth <jamth(a)mindspring.com> > Subject: [Fractint] FOTD 16-04-04 (Image of Springtime [5]) > To: fractint(a)mailman.xmission.com > Message-ID: <1.5.4.16.20040416104907.0d67ef6e(a)pop.mindspring.com> > Content-Type: text/plain; charset="us-ascii" > > > FOTD -- April 16, 2004 (Rating 5) > > Fractal visionaries and enthusiasts: > > A longer version of today's discussion appears on the > philofractal list. > > Today's image, which combines various unlikely negative portions > of Z^(-1.4) and Z^(-14), has a certain feeling of springtime to > it. Since the season here in the Northern Hemisphere is in fact > spring, I named the picture "Image of Springtime". > > The shades of pink and white could be apple or cherry blossoms. > The greens could be the newly emerged leaves. The blues, of > course, are nothing but the blue of a clear springtime sky. > > It's a relatively harmless image, not stressful to look at, one > that I have rated a 5. The render time of under 4 minutes > raises the overall value to 135. The finished product is > available on the FOTD web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > Thursday was a good day here at Fractal Central. Warm sun, > cloudless skies, moderate winds and a temperature of 63F 17C > gave the dynamic duo a very pleasant afternoon in the yard. > When evening arrived, they came inside without urging. Today > promises to be even warmer. I expect another good day. > > The work is moderate today. Hopefully, the next fractal will > be of above moderate quality . Until next time, take care, > and the fractals never end. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Image_ofSpringtime { ; time=0:03:42.48--SF5 on a P200 > reset=2003 type=formula formulafile=allinone.frm > formulaname=mandelbrotmix4 function=recip passes=1 > center-mag=+1.46839349750336400/+0.281643707741821\ > 60/9.037591e+009/1/-19.9987125907157584/-0.0014716\ > 5417249400798 params=-4.5/-1.4/-0.9/-14/0/0 float=y > maxiter=550 inside=0 outside=tdis periodicity=10 > colors=000jKKhKKfKKdKKgMRkCTnBV1_X0ZZ0Z`0ZbLfhzvsz\ > vsyqoymlyiiyefy`byX_yTXyPUyLRwJTuIVsGXqFZoE_kCvnBl\ > i9hg8fe7hc5ja4l`3mb2Zc1Kd15c58c9BcDDcHGcLIcPLcTOcX\ > Qc`TcdVchYcl_dlXelUflSflPglNhlKplHwlFjlCjlAkmHlmNk\ > hPkcQkZSkUTkPVjKWjFYjAZj5`j1al4_m6Zo9YpBXrDWsGUuIT\ > vKSxNRyPQzRPvTQrVQoXRkZRh_RdaSacSYeTVgTRhTOjUKlUHn\ > VDpVAqVDpTFoRHnPJmNMlLOkKQjISiGVhEXgCZfA`e9XbHU_PR\ > XXOUdLRkPPhSNeVLbYJ_`HXdFUgDRjBOm9Lp7IqCIrGIrKIsOI\ > tSItWIu_IucInZHhUGbPFWKEQFDKBCQIIWPOaWUgb_miespjnn\ > jjmjeljajjXijThjX_d_R_cIUfBPaGSXLVTPXOU_JZbFbdNd`U\ > eXagThhPoiMlcGiYBfS6dM1YN6SOBMPGFQL9RQ3RUYh0kQMy8g\ > vCesGdpKbnNakR`hVZeZYcaXFS0wk5phDjeKdbRZ`YSYeMVlGS\ > sAQzBOwCMtDKrEIoFGlGEjHCgHAeEIhCQk9Yn7dpAcqCcrEcsH\ > btJbuLbuM_mNYfOW_PUTQRMRPFSN8TL1XL7`LCcLHWONPRTHUZ\ > SqcSqcJ`bOcbSeaWg`KMKKOMKQOMSQ0UN3WM6YK9_ICaHFcFIe\ > DLgCNiOOkXQm`RocNqf5si4ul } > > 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================================== > > > > > ------------------------------ > > Message: 4 > Date: Fri, 16 Apr 2004 10:01:45 -0600 (MDT) > From: SherLok Merfy <brewhaha(a)freenet.edmonton.ab.ca> > Subject: [Fractint] nntp:/news.admin.net-abuse.sightings > To: Fractint and General Fractals Discussion > <fractint(a)mailman.xmission.com> > Cc: philofractal(a)lists.fractalus.com > Message-ID: > <Pine.A41.3.95.1040416091435.45044C-100000(a)freenet.edmonton.ab.ca> > Content-Type: TEXT/PLAIN; charset=US-ASCII > > (...) > > Jim Muth wrote: > > > (248 junkers arrived since 11:30pm > > > last evening.) .........maybe I'll > (...) > On Sun, 11 Apr 2004, Paul N. Lee wrote of Earthlink's spam blocker: > > In that way you will never have to download the junk-email at all. > > You must know that the filters aren't that reliable. They begin > with a bunch of sites that are basically avowed spammers. My address is > about as old as Jim's, I post on USENET without a munged address, and yet > my spam load is about a fifth. > > The source of the difference is that my posts to nanas [NG > shorthand] are declining in favour of carefully looking at the headers for > the offender's site and notifying the postmaster at that site (forwarding > complete headers). (Some people would tell you that abuse@ that site is > the person to tell, but I don't think it makes a lot of difference). > > No better way is to get on the more important cut-lists, than > to let a spammer know that you report and that your reports get contracts > cancelled (especially if they're not alone). > > ...which reminds me of imagelinkusa.net They seem to hav a Master > Of Business Administration at their helpdesk, so I should check out the > Mail Abuse Prevention System to see if they're already listed, and if they > are then see if MY helpdesk has any idea how we might use the real-time > black-hole list. > > The discussion group in the hierarchy is > news:/news.admin.net-abuse.email > > I'm dead set against letting spammers chase ME around. If I get > tired of it, then I drop the internet connection (if not the computer) for > a while longer than usual, but the address won't change if I hav anything > to say about it, and all I hav to say about that is that hiding your > e-mail address doesn't work forever, and running (changing) it doesn't > work for long. > > > > > ------------------------------ > > Message: 5 > Date: Fri, 16 Apr 2004 12:03:52 -0500 > From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> > Subject: [Fractint] Re: FOTD 15-04-04 (Land of Fractals [5]) > To: fractint(a)mailman.xmission.com > Cc: philofractal(a)lists.fractalus.com > Message-ID: <408011F8.3C92(a)Worldnet.att.net> > Content-Type: text/plain; charset=us-ascii > > James R. McKenzie wrote: > > > > This only rates a "5"? > > I too feel that it should have been rated much higher. The unusual > images such as these are quite nice to see. > > > > > I wish I could run Fractint in XP (Been > > there tried that, no go) so I could do a > > 3D transform of the image and see what > > comes up or "out" as it were. 8-{> > > I have seen some Win-XP systems running FractInt produce an image on the > monitor that is basically a jumble of pixels. But after it has finished > rendering, if the "S" key is pressed to save the image to a directory > path, then viewing that image with some graphic editor shows it is not > the mess from the screen, and is the correctly formatted fractal > graphic. > > > > > BTW if anyone does a 1280x1024 of this > > e-mail me, I'd like a copy. > > Try running FractInt at that resolution, then save the image to disk > afterwards and see what you get. > > > Sincerely, > P.N.L. > ------------------------------------------------- > http://home.att.net/~Paul.N.Lee/PNL_Fractals.html > http://www.Nahee.com/Fractals/ > > > > ------------------------------ > > Message: 6 > Date: Fri, 16 Apr 2004 12:46:33 -0500 > From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> > Subject: Re: [Fractint] FOTD 16-04-04 (Image of Springtime [5]) > To: fractint(a)mailman.xmission.com > Message-ID: <40801BF9.1702(a)Worldnet.att.net> > Content-Type: text/plain; charset=us-ascii > > Jim Muth wrote: > > > > FOTD -- April 16, 2004 (Rating 5) > > > > A longer version of today's discussion > > appears on the philofractal list. > > > > And since I use the postings from the above discussion list for creating > Jim's FOTD webpages, then they are also available through the Internet: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > > Later, > P.N.L. > ------------------------------------------------- > http://home.att.net/~Paul.N.Lee/PNL_Fractals.html > http://www.Nahee.com/Fractals/ > > > > ------------------------------ > > Message: 7 > Date: Sat, 17 Apr 2004 09:27:02 -0400 > From: Jim Muth <jamth(a)mindspring.com> > Subject: [Fractint] FOTD 17-04-04 (Polyester Minibrot [7]) > To: fractint(a)mailman.xmission.com > Cc: philofractal(a)lists.fractalus.com > Message-ID: <1.5.4.16.20040417093023.2c0ff656(a)pop.mindspring.com> > Content-Type: text/plain; charset="us-ascii" > > > FOTD -- April 17, 2004 (Rating 7) > > Fractal visionaries and enthusiasts: > > Once again the time has come to enter Fractal Land, that strange > land that exists somewhere between the real world around us, > which might not be totally real, and the imaginary worlds within > us, which might not be totally unreal. > > The irregular real(p3) parameter of today's image shows that its > parent fractal was found by the Fractint 'evolver' feature. > Normally, I round off the odd numbers this feature produces, but > for some reason I skipped the rounding process when I started > working with today's parent. > > The parent fractal is a hugely bloated area of mostly disconnec- > ted rings. Today's scene is located near a larger midget that > lies in the interior of a ring in the distant north-northeast > suburbs of the parent. > > The unusual detail inside the midget itself is a sign that the > scene has been evaporated, and the ghost brought to life by the > bof61 inside fill. Fractals in which all the exponents of Z are > negative can be evaporated by raising the escape radius to a > full googol, which is the amount entered as the imag(p3) para- > meter of today's image. This trick usually traps every point. > > For reasons known only to myself and the 'intelligent designer', > (whatever you consider this to be), I named the image "Polyester > Minibrot". I might have done myself a favor when I rated it at > a 7, but the image is really rather pleasant to look at, and I > feel it earns its rating. The reasonably fast render time of > under 4 minutes gives an overall value of 184. > > The render time is fast, but the fastest way of all to enjoy the > image is to download it in finished form from the FOTD web site > at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > With a temperature of 67F 19C, gentle breezes, and warm sunshine > to keep them happy, the fractal cats put on their best moods > Friday. When the day was finished, they were so exhausted that > they forgot their customary evening treats, and went right to > sleep. Today is starting mostly sunny and warmer. I expect a > similar day. > > For me, most of the graphics work is caught up. If I can muster > the energy this afternoon, I'll give the grass the first > trimming of the season. If not, I'll do it tomorrow or Monday. > Until next time, take care, and don't get hot under the collar > when a cool fractal appears. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Polyester_Minibrot { ; time=0:03:48.11--SF5 on a P200 > reset=2003 type=formula formulafile=allinone.frm > formulaname=MandelbrotMix4 function=recip passes=1 > center-mag=+25.24771384422294000/+103.017140882474\ > 40000/4599911/1/-22.5/6.18164318095387744e-005 > params=2/-1.4/0.2/-8.6/-2.597094637897885/1e+100 > float=y maxiter=1200 inside=bof61 periodicity=10 > colors=00000U00o00u00x80zOAzdOzuazzozzzzzzzzzzzzzz\ > zzzzzzzzzzzzzzzzzzzzdz0Iz00u50UX02x00zo0Dz00zG0zg0\ > U0za0zg0zl0zu0rz0dz0Qz2Gz52zA0zD0zA0z80u50i20_05O0\ > AA0G00L00Q00X00a00g00l00g00a00X02U08O0AI0GD0LA0Q50\ > X00_00UD0NQ0LgGIoXDzhAsz5zz2zzzzxozodugQo_GiQ2KK00\ > Q0ou8_f0zD0zD2zDDzDLgDXODm520a00z00z20z80uD0rI0lL0\ > iQ0gX0aa0_g0Ul0Qo0Ou0Ux0_z0az0gz0iz0oz0rz0xz0zz0zz\ > 0zz0zz0zz0zz0zz0zz2zzAzzIzuQzi_z_gzOozDxz2zz0zx0zu\ > 0zr0zo0zl0zlIzlazluolzglzXlzOlzQozQozUozUozXrzXrz_\ > rz_rz_rzdxzizzlzzrzzuzzzzzzzzuzzlzzgzz_zzUzzGzz5zz\ > 0lz0Xa_dAzi5zl0zl0zo0zo0zr0zr0xu0uu0ox0lx0iz0gz0dz\ > 0iz0oz0rz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ > z0zz0zz0ro0da0UL2G822050080080000000000000A00O02a0\ > 8r0Dz0Iz0Oz0UiG_QadAxi0zo0zu0za0zI5x2Qi0lX0zI0z800\ > 00I0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Lu0Oo0Ql0Ug0Xa0__0a\ > U0dQ0gL0iG0lD0o80O0080008 } > > 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================================== > > > > > ------------------------------ > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > > End of Fractint Digest, Vol 14, Issue 7 > ***************************************

3 2

FOTD 22-04-04 (Rabbit Ears [6])
by Jim Muth 22 Apr '04

22 Apr '04

FOTD -- April 22, 2004 (Rating 6) Fractal visionaries and enthusiasts: To create the parent fractal of today's image, I took Z^(-1.6) and added 0.26 part of Z^(-6.1) to it before adding (1/C). The MandelbrotMix4 formula mixed these ingredients thoroughly. The 1200 iterations produced a fractal that retains many of the characteristics of the Z^(-1.6) and Z^(-6.1) Mandeloids, yet at the same time is something entirely new, with many features of the Z^2+C Mandelbrot set, such as bays, buds, valleys and midgets. Today's scene lies in one of the many valleys of this parent. The escape radius of the classic Z^2+C Mandelbrot set may be increased to as large a number as can be entered as a parameter, and the result will be nothing more than an outward shifting of the iteration bands. But when the escape radius of a fractal such as today's parent is increased, the image quickly falls apart. By the time the escape radius reaches one-googol, nothing is left but empty space. All the points have become trapped. I call this process 'evaporation'. Things are not lost however. All the points might be trapped, but they are still active, and the results of this activity can be made visible by rendering the image with the inside option set to something like 'bof61', which I believe colors the points according to which iteration takes them closest to the origin. All this stuff is relevant because the escape radius of today's image is indeed one-googol, and all the points have therefore been trapped. The original scene has evaporated. What we see on the screen are the things that the trapped points are doing in their confinement, made visible by the dynamic 'bof61' inside fill. What I see while staring at the image is a forest of rabbit ears. Maybe this means the residents of Fractal Land have over-the-air TV, but more likely it's just a coincidence. Whatever the reason, I named the image "Rabbit Ears", then rated it at a 6, which gives an overall value of a 66. Don't waste time investigating the detail inside the rabbit ears. This detail consists of moire patterns -- artificial patterns caused by limited screen resolution, which vanish faster than one can go after them. The only thing faster than a vanishing moire pattern is the download of today's pre-rendered GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> On Wednesday the temperature reached 73F 23C here at Fractal Central, while the sun shone frequently and the wind blew gently from the east. The cats enjoy such conditions, and made no exceptions on Wednesday, when they spent half of the morning and the entire afternoon lounging in the yard. Today is similar. The cats are already on their window shelves, gazing at the sun and planning a lazy afternoon. For me, it will be another in a seemingly endless string of days with work before play. The next fractal will hatch when the work is finished. Until next time, take care, and be back in 24 hours for the next fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Rabbit_Ears { ; time=0:09:08.16--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.20067893060894/+0.02108591826425907/\ 685450.6/1/-20/-1.18714037711242781e-007 params=1/-1.6/0.26/-6.1/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000ISTRYfXcrg_fpXUzTHzR2xXBnaKcgSTlZHpfIfnI\ XuINzIBz4zK8zXBrhEltHfzKevNenOefRcYTcPUcGWZOXWWYSa\ YOhZIo_EuaAza5zbDvcKkePZfWNf_8G8TOAUWBUaBWhDWnDWiI\ ZfObbTfYYiUbmRgockqpnrzqt0404PHBgZHxnTtlcpkmlhwhgz\ efxbep_chZb_XaSW_HGS70Ibz0hzBmzRhmYeZeaIlY0qXSgXnX\ z8zHiBSXW_IlhDmo8nv4oz0pz0pz0qz0rz0tx0tu0ur0vo2wm2\ wkEnhPegZXifSllNmqHoxBqz5rz0zzzzxwzpvzhuzZtzRrzHqz\ 7pz4mr2ii0f_0bX0aT0aP0_N0_I0ZE0ZL0OM0N52T58P5GL5LG\ 5SB5X7DZAKaBRcDWfGahHgkIigKo_frOzbRpNShYIahAUr0Ov7\ LzDIzIGzODzTAzPGzLLzHPzDUz8Zz4bz0gx0kkGlYXmKlnIhkI\ egHaeHYaGUZGRWGNTT_bcmlispmvrqwttxvzzzzzzzzzzzwzzu\ wzqvxotvlrtiqrgrveuxbvz_wzYxzUxxSxvOxtLxqIzoEzmBzk\ 8zh4zf0ze0wb0va0u_0rZ0qY0pX0nW0mU0lT0iS0hR0gP0fO0e\ N2eN8cLDcLIcKObKSbIXbI_aHeaHi_Gm_Gq_EvZEzZDzZDzHAx\ 08o4EmAKlGPkLUiSZgXcfahefmckpbokXteSxZNzTHzNBuULk_\ U_fbOmkBrr0xzzg7ze52E0BLE } 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==================================

1 0

Reading Digests
by Vortex Swirling 22 Apr '04

22 Apr '04

This is only a bit off topic since I receive the fractint list as a digest. Is there any sort of application that makes it easier to navigate the digest? --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.659 / Virus Database: 423 - Release Date: 4/15/2004

2 1

FOTD 20-04-04 (Gruesome-brot [3])
by Jim Muth 22 Apr '04

22 Apr '04

FOTD -- April 20, 2004 (Rating 3) Fractal visionaries and enthusiasts: Today's image takes us to the northeast shoreline of the main bay of the Mandelbrot set, where we examine the valley leading to the large period-4 bud there. This valley is centered at 0.25+0.5i, and the slope of the main bay at this point is 45 degrees, which makes it quite simple to examine the area from all kinds of strange four-dimensional directions. Today's view is halfway between the Parabolic and the Oblate directions. The tiny buds that line the edges of the valley do appear in the image, but they no longer appear as tiny empty circles. The circles have been stretched in one of their dimensions to infinity, and appear as parallel slits partially obscured by fractal debris. By changing the imag(p1) parameter, we can see many different views of the scene, all of which show the buds as slits. If imag(p1) is set at 180, the image is the same, but we are looking at it from the opposite direction. Some of these other views are quite interesting, though I had little time to investigate them. I might do so sometime in the future, but with today's image rating only a measly 3, I will be in no great rush. With a render time of almost 8 minutes, the image has an overall value of 39. I named the image "Gruesome-brot", not because it is horrifying to look at, but because it's not a very good example of fractal art. The completed GIF image is available on the FOTD web site at:. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It reached 91F 33C here at Fractal Central on Monday, a temperature that left the fractal cats with nothing to do but sleep. They passed the afternoon sleeping in the yard, dreaming whatever it is that cats dream. Their moods were good when the time came to come indoors, so I guess their day was satisfac- tory. Today is starting cooler, but still mild. We'll see how the duo takes things. I managed to trim half the grass yesterday. The second half will be finished sometime this afternoon. Until next FOTD, take care, and look for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Gruesome-brot { ; time=0:07:45.55--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 float=y center-mag=-2.2204e-016/-0.00217442/11.20316/0.2086 params=-45/0/2/0/0/0/0.25/0.5 maxiter=32000 inside=0 logmap=6 symmetry=yaxis periodicity=10 colors=000ZZh__i``jaakablbcmcdndeoefpfgqehqegpdfod\ encdlbckbbjaaha`g`_f_Zd_YcZXbZWaYV_XUZXTYWSWVRVVQU\ UPSUORTNQSMOSLNRKMRKLSLMTMMUNNUONVPOWQOXROXRPYSPZT\ Q_UQ_VR`WRaXRbYSbYScZTd_Te`TeaUfbUgcVhdVhdWieWjfWk\ gXkhXliYmjYlkamjYmfVmcSm_PmXMmQVmJbmCjc6rU7qK8pD9p\ DAoDBnDCnDDmDElDFlDGkDHkDIjDJiDKiDLhDMgDNgDOfDPeDQ\ eDRdDSdDTcDUbDVbDWaDX`DY`DZ_D_ZD`ZDaYDbYDcXDdWDeWD\ fVDgUDhUDiTBkUDjTFjTGjTIjTJjTLjTMiTOiTPiSRiSSiSUiS\ ViSXhSYhS_hS`hSbhRdhRehRggRhgRjgRkgRmgRngQpgQqfQsf\ QtfQvfQwfQyfQyhHzjQzlYznexmfvmfulgslgrkhpkhojimjil\ ijjijiijghkfhkdglcglafm`fmZenYenWdoVdoTdoScpQcpPbq\ NbqMarKarJ`sH`sF`wG`sH`pI`mJ`jK`gL`cMZ`NXYOVVOTUOR\ S4PB6NC7LD9JEAJFCKGDKGELHGLIHMJJMKKMLLNLNNMOONQOOR\ PPTPQUQQVQRXQSYRT_RU`SVaSVcTWdTXfU_hWbjYel_hnakpcn\ reotfoveowenxdnycozcqzbszbuzawz`yz`zz_zzZzzZzzYzzY\ zzXzzWzzWzzVzzUzzUzzTkzSz } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

6 7

FOTD 18-04-04 (Fractal Splendor [7])
by Jim Muth 22 Apr '04

22 Apr '04

FOTD -- April 18, 2004 (Rating 7) Fractal visionaries and enthusiasts: Take (1/Z), mix it with 1/2 as much Z^(-2), and add (1/C). What do you get? Why, a fractal of course -- an oversized fractal that is too large to fit on the default screen and needs to be shrunk by an outzoom before it becomes completely visible. This fractal has X-axis symmetry, but only because the exponents of Z are whole numbers. Changing (1/Z) to Z^(-1.1) or Z^(-2) to Z^(-2.1) gives a pair of entirely new fractals with no symmetry. This parent fractal is far richer in detail that the classic Mandelbrot set. The detail might not be any more varied, but it covers a far larger area. The fractal has an interesting area around +7 on the real axis, where two graceful arcs of delicate filaments come together. Today's scene is located in one of these arcs, very near the point where it touches the X-axis. I have colored the image to resemble something like a brilliant star blazing away in empty space, and named it "Fractal Splendor". I seem to remember a somewhat similar FOTD image from several years past, but if today's image is a near-repeat, I will consider it simply a variation on a splendid theme. I rated today's image at a 7, mostly because of the extra effort I put into the coloring. The render time of 11 minutes gives the image an overall value of 59. As always, the image may be seen most conveniently by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was as close to being a perfect day as we have come in quite a few months here at Fractal Central. Warm sun, light winds and a temperature of 84F 29C gave the fractal cats all they could ask for. If they had been 10 years younger, they would have romped all afternoon. But being 14-year-old cats, they slept in the shade of the holly trees most all afternoon, and romped, (if what they did can be called romping), only a few minutes. Today is starting just like yesterday. I assume the cats will have an equal day. As for me, I'll put off the grass trimming one more day, and take it easy. The work is light and I should have lots of time to get it done on Monday. The next FOTD will appear in 24 hours. Until then, take care, and try to prove that fractals are not real without defining reality. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Splendor { ; time=0:11:55.35--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+7.02311504952539200/+0.000296216423795\ 89/7.833267e+008/1/-142.5/0.00233171123971526173 params=1/-1/0.5/-2/0/0 float=y maxiter=2000 inside=0 logmap=248 periodicity=10 colors=0007LK7LK7LK7LK7LL7LL6LL6KM6KM6KM6KN6KN6KN6\ KN6JO6JO6JO6JP5JP5JP5JP5IQ5IQ5IQ5IR5IR5IR5HS5HS5HS\ 4HS4HT4HT4HT4GU4GU4GU4GU4GV4GV4GV4FW3FW3FW3FX3FX3F\ X3FX3EY3EY3EY3EZ3EZ3EZ3EZ4F_4G_5H`5I`6Ia6Ja7Kb7Lb8\ Lc8Mc9Nd9OdAOeAPeBQeBRfCSfCSgDTgDUhEVhEViFWiFXjGYj\ GYkHZkH_lI`lI`lIamJbmJcnKdnLeoMfoNgpOhpPiqQjqRkrSl\ rTmsUnsVosWptXqtYruZsu_tv`uvauwbvwcvxdwxewyfxygxzh\ yziyzjzzkzzlzzmzznzzmzzlzzkzzjzzizzhzzgyzfxzewzdvz\ cuzbuzatz`tz_szZszYrzXrzWqzVqzUpzTpzSpzRozQozPozOn\ zNnzMnzLmzKmzJmzIlzHlzGlzGkzGkzFjzFjzEjzEizEizDizD\ izChzChzChzBgzBgzBgzAgzAfz9fz9fz9ez8ez8ez7fz8ez8ez\ 8dz9dz9cz9cz9bzAbzAazAazB`zB`zB_zBZzCZzDZzEZzFZzG_\ zH`zIazJbzKczLczMdzNdzOdzPezQezRezSfzTfzUgzVgzWgzX\ hzYhzZhz_iz_iz_izZjzZjzZkzYkzYkzXlzXlzXlzWmzWmzVnz\ VnzVnzUozUozTozTpzTpzSpzSqzRqzRrzRrzQrzQszPszPszPt\ zOtzOuzNuzNuzNvzMvzMvzLwz } 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==================================

2 1

(marks.par) Mark'sMandel by the documentation.
by SherLok Merfy 22 Apr '04

22 Apr '04

MarksBug { ; Attempt at speeding up Mark's Mandel with flexibility. ; Methinks that the similarity between manzpower and ; Mark's Mandel is the error, but the hard-coded formula ; does seem to allow for larger exponents before it ; decays. Maybe it's z(n+1)=c^(ex-1)*z(n) +c z=fn1(pixel), c=fn2(pixel), a=c^real(P1)-1: z=a*sqr(z) +c, LastSqr<= imag(P1) } default { ; Not even close, but I'm pretty sure that ; is what the documentation says (without functions ; or the realization that part of the documentation's ; results are constant per iteration). reset=2003 type=formula formulafile=marks.par formulaname=MarksMandel function=ident/ident params=7/4 maxiter=255 inside=0 } MarksHand { ; This might be kinda nifty. reset=2003 type=formula formulafile=marks.par formulaname=marksmandel function=ident/ident center-mag=-3.486/3.66155/0.1051468/1.1186 params=7/4 float=y maxiter=255 inside=0 outside=atan invert=1.13584734211722/0.5/0.7 periodicity=0 colors=(a)altern.map } Heart { ; Some habits are hard to break. ; I would finish the set, but I've worked ; hard to establish this account, and something's ; very wrong with my ISP's response time. reset=2003 type=formula formulafile=marks.par formulaname=marksmandel function=conj/ident center-mag=0.22319/0/1.01533/1.1992/90/0 params=7/4 float=y maxiter=255 inside=0 outside=atan invert=0.5/0.25/0 colors=(a)altern.map }

1 0

FOTD 21-04-04 (Invasion of the Pods [4])
by Jim Muth 21 Apr '04

21 Apr '04

FOTD -- April 21, 2004 (Rating 4) Fractal visionaries and enthusiasts: I still have a fondness for those junky old sci-fi and monster movies that were made in the 1950's. Those movies were populated by an incredible variety of giant spiders, crabs, ants, mantises, living plants, and blobs of all consistency, not to mention the invading aliens from outer space. Except for the specialty networks, those movies are gone from TV now -- they have been replaced by computer effects, car chases and explosions -- but I still have hundreds of the junkers safely stored away in my vast collection of junky old movies. Whenever I find myself in the mood for some TV junk, I pop in a tape and sit down to see how long I can watch before falling asleep. I mention junky movies because today's image reminds me of one of my favorites -- "Invasion of the Body Snatchers" -- in which alien pods drop from space, hatch into duplicates, and take over our minds. I have named the image "Invasion of the Pods". When I studied the image, I found myself looking up into a clear blue sky at a shower of pods raining down to earth. I guess we will never know whether the invasion is successful, but with a rating of a mere 4, the image is only marginally successful. The parent fractal is basically a shapeless hole, created by combining portions of Z^(-1.2) and Z^(-2.1), which lies in a sea of sand, with a vast expanse of fat twisting filaments extending far to the south. I have found no signs of midgets in this parent fractal, but the sea of sand proved interesting enough to produce today's image. The invading pods may be seen by running the parameter file or by downloading the complete GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With lots of sun and a temperature of 77F 25C, Tuesday was another fine day here at Fractal Central. The cats must have thought so also, since they spent almost six hours in the yard, mostly sleeping. Today however is starting cloudy with showers in the area. It remains to be seen how the dynamic duo will make out. For me it's work, then play. Until next time, take care, and see you in 24 hours, when the next FOTD appears. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ InvasionOf_ThePods { ; time=0:03:11.53--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-7.81089/3.08437/31.9843 params=1/-1.2/\ 0.57/-2.1/0/0 float=y maxiter=1200 inside=0 logmap=yes periodicity=10 colors=000M`uKZuHXuFVuCTuARuCTpEUlGVhHWcJX_LYWM_RO\ `NQaJRbETcAVd6We2Zb3``3bZ3dX3fV3hS3jQ3lO4wn8xn8yn7\ zn7r`8vn8n_8rn8oZ8vm8l`8rg8hc8kf8ea8fb8aa8d_8YY8`W\ 8UUcSScQRcOPcNNcLLUJJUHHUUczUczUczUczUczUczUczUczU\ czUczUczUczUczUczUczUczUczUczUczUczUczUczUczUczUcz\ UczUczUczUczVczWczXczYczZcz_cz`czaczbczcczcczcczcc\ zcczcczcczcczcczcczcczcczcczcczcczbczacz`czZczYczX\ czWczVczTczSczRczQczPczNczMczLczKczJczHczGczFczEcz\ DczBczAcz9cz8cz7cz8cz9czAczAczBczCczDczDczEczFczGc\ zGczHczIczJczJczKczLczMczMczNczOczPczPczQczRczSczS\ czTczUczVczWczVczVczVczVczVczVczVczVczVczVczVczVcz\ VczUczUczUczUczUczUczUczUczUczUczUczUczUczTczTczTc\ zTczTczTczTczTczTczTczTczTczRczTczVczXczYcz_czaczc\ czdczfczhczgczhcziczjczkczlczmcznczoczpczqczrczscz\ tczuczvczvczucztcztczsczrczqczqczpczoczncznczkczhc\ zfczcczcczcczcczcczcczccz } 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==================================

1 0

sorry about the fat.
by David Lowenstein 21 Apr '04

21 Apr '04

I will trim my further messages. -david

1 0

FOTD 19-04-04 (The Wine-Dark Sea [5])
by Jim Muth 19 Apr '04

19 Apr '04

FOTD -- April 19, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's discussion will be very short -- reason: I can no longer put off the trimming of the fractal grass, and there is significant other work to be done as well. This means that the image will have to speak for itself. But careful listening will be needed to hear the words. Like most of the FOTD images, today's image has a midget at its center. The scene is located in an 'East Valley' type valley in the fractal that results when some Z^(-5.1) is subtracted from Z^(-1.5) and (1/C) is added. I named the image "The Wine-Dark Sea". The phrase is not original, but I forget in which piece of literature it appears. The rating of a 5 seems appropriate for an image that I needed to hurry along. When the 7-minute render time is taken into consideration, the overall value rates a 70. The finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature reached 87F 30.5C here at Fractal Central on Sunday, which was actually a bit too warm for the fractal cats, who did little more than lie motionlessly in the shade of the holly trees all afternoon. When evening arrived, they came indoors without hesitation to enjoy their meal. Today is starting even warmer. I expect a similar day. For me, the work is moderate, and the trimming of that grass is imminent. Until next FOTD, take care, and be lucky. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Wine-Dark_Sea { ; time=0:07:06.06--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+4.37697768075993700/-0.007125508732302\ 11/3.264379e+008/1/145/-0.000315981629220238314 params=1/-1.5/-0.294/-5.1/0/0 float=y maxiter=1200 inside=0 logmap=132 periodicity=10 colors=000RDIRFJTHLVJNXLPZNQ`PSbRUdTVfVXhaZje_lian\ mcppdqnfqkgqghrdir`jrYksUlsRmsNnsKooIikGcgEZcCT`AO\ X8IT6DP47M32Q83UD4YH5`M6dQ7hV8lZ9ocAsgBwlCzpCqiIhb\ N_WTRPYIIcABhDIbGPYJVTHYQF_ODaLBdJ9fG7hE5jCFiBOiBX\ hBehAngAwgAoa8hW6aQ4VL2YO3`Q3bT3eV3hX3j_4ma4pc4rf4\ uh4wj4vi8uhCtgGsfKreOqeRmbSj`TgZUdWV`UWYSXVQYSNZPL\ _LJ`IGaFEbCCc9Ad7QZ5dT3sN9tSEtWJt`OtdTuiYumburguvl\ uzivxgvvdvtbvr`wpYwnWwlTwjRxhPxfMxdKxbIx`KwaMwaNva\ PvaRvaSuaUuaVtaXtaZta_saasabsaamd`gf_biZXkYRmXMpWG\ rVBtYEq`GnbIkeLhgNfjPclS`oUYqWWmZViaUfdTbgT_jSWmRT\ oRSlQSiPSgPSdOSaNS_NSXMSULSSLSPKSNKURJVUIXYHY`G_dF\ `gEbkDcnCdqBbmE`iGZfJXbLVcOTdQReTPfVNgYLh_JibHjdFk\ fHldJmcLmbNmaPm_RmZTmYVmXXrWYlUZmT_mS`mQamPbmOYmx_\ msamncmiemdgo_iqVksQmuLowGnyLnzQnzVnzZnzcmzhmzlmzq\ mzvmzzoznqzcszTlzPfzM`zIUzFOzBIz8Cz5DzBDzGDzLDzQDz\ VDz_Gz`IzaKzaNzbQzFQzGRzH } 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==================================

1 0

FOTD 15-04-04 (Land of Fractals [5])
by Jim Muth 18 Apr '04

18 Apr '04

FOTD -- April 15, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image takes us into the fourth dimension. I have always been fascinated by the fourth dimension. I was not yet a teen-ager when, having just finished a book, (I think its name was "One, Two, Three, Infinity..."), I asked my father where the fourth dimension is, and, thinking of relativity, he told me that it is in the past and the future. This was not a very satisfactory answer. The past and future are time, not space. I wanted to know where the fourth dimension of space is. He then explained to me that as far as we know, there is no fourth spatial dimension, and even if there were, we would perceive it in three-dimensional terms. This is the problem. We are brain-washed to perceive our surroundings as a three-dimensional world. We have not been wired to perceive a four-dimensional space, and it is too late to change that. If we were suddenly dropped into a four- dimensional world, we would not see the fourth dimension. We would see a three-dimensional world that obeyed different rules. Solid objects would change shape as we watched; objects would appear and vanish. We would think the world had gone crazy. We would probably go crazy ourselves, (as some say I already have), but we would be no closer to visualizing the fourth dimension. Even now, we are able to fully visualize and understand the shadows that would be cast by four-dimensional objects onto the three-dimensional surface of our space. A 4-D hypersphere would cast a spherical shadow if the ray of light fell perpendicularly onto our space. If the light struck our space at an angle, we would see an oblate spheroid, the eccentricity of which would vary with the angle of the ray of light. But even though we understand all of this, we are still totally unable to visualize the hypersphere that would be casting the shadow. We can also know and fully visualize the three-dimensional slices of four-dimensional objects. The 4-D hypercube may be sliced to give many curious prisms, as well as a tetrahedron and an octahedron, and of course the expected cube. But even this is of no help in our quest to realize the fourth dimension. Our lack of visualizing ability is curious. We can program our computers to 'think' in four dimensions almost as easily as in three. We could even give them three-dimensional screens on which to better display the 4-D worlds they would have no trouble in manipulating. Of course, we would then be unable to view the 3-D screens in the proper manner, from outside our space. We would of necessity need to view the screens 'edge-on'. We appear to be forever doomed, trapped in a world of three dimensions, while able to know of the far greater vistas that would lie before us if only we could rewire our minds. Since our minds are not about to be rewired, it's best we turn to today's image. Today's image is a two-dimensional slice of a four-dimensional object. In this case, the object is the 4-D Julibrot created by iterating the formula (1/Z)-Z+C. I have sliced the Julibrot in what I call the Oblate direction, which is determined by the imaginary C and real Z axes. The picture has a certain surreal quality about it, which inspired the above outburst about higher dimensions. It could almost be something we might see if we were suddenly dropped into a four-dimensional space. This is why I named the picture "Land of Fractals". Since the image is such a departure from my usual fractal fare, I was not sure how to rate it. I finally decided on a rating of an average 5. The short render time of 2-1/2 minutes raises the overall value to a mighty 202. An alternate way of seeing the other-worldly scene is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Light rain fell steadily all day Wednesday here at Fractal Central, keeping the fractal duo confined to the indoors. Even if it had not been raining, the temperature of 50F 10C would have been a bit chilly for their sensitive ears. Today is starting windy and chilly, but sunny. We'll see how the dynamic fractal cats take these conditions. For me it's work before play. The problem comes in separating the two. Until tomorrow's FOTD, take care, and most likely it's fractals all the way down. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Land_of_Fractals { ; time=0:02:28.69--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=OblateMix2 function=ident passes=1 center-mag=-4.55271/3.10114/0.6584367/8.9718/-11.2\ 262659607652502/29.222244310548934 params=1/-1/-1/1/1/-0.2 float=y maxiter=1200 inside=255 logmap=yes periodicity=10 colors=000Di`Ei_FiZFhZGhYGhXHhWHhWHhWU_`fRfuHlsIkr\ JjpKjmLiUdkUckUbjUaiU`hU_gUZfUYeUXdUWcUWcUVbUVbUUa\ TUaST`QT`RS_PS_NRZMRZKQYJQYHPXGPXENWDLWBIVAGV8EU7C\ U8ET9MTANSBOSBPRCQRDRQETQFUPFWPGYOH_NIaMIcLJeKKgJL\ iIMkIMmINoIOqIPsINsHPtIQtIStITuJVuJWuJYvKZvK`vKawL\ cwLdwLfwLgxMixMjxMlyNmyNoyNpzOrzOszOtzOuvPusPupPum\ PvjPvgPvdPvaPubRtcTscVrdXqdZpe_oeanfcnfemgglgikhjj\ hliinhipgjrfhygjshlninhjpckrZltTmvOnxJozDpz8pz3lxE\ hrPdm_`gjYcvXbtXbsXbrXbqWbpWboWbnWbmVbkVbjVbiVbhUb\ gUbfUbeUbdUbcW`bY_bZZb`YbaWbcVbeUbfTbhRbiQbkPblObj\ NahNafM`dM`bL_`L_ZKZXKZVJYTJYRIXPIXNHWLHWJGVHGVFFU\ DFUBET9ET7DS5DS8GTBITELTGNTJQTMSTOVURXUU_UWaUZdUaf\ UgkVchU_fUXdTTbTQ`SMYSIWRFURBSQ2UJ8QQEMWKIbQEjPFhP\ GgPHfPIeOJdOKbOLaOL`NM_NNZNOYNPWNQVMRUMRTMSSMTQLUP\ LVOLWNLXMHUMLXLP_KTbJXeJ_gIcjHgmHkpGosFstCruFrvIrw\ LqxNqyQqzTqzWpzYpz`pzccwz } frm:OblateMix2 {; Jim Muth z=real(pixel)+flip(real(p3)), c=fn1(flip(imag(pixel)))+imag(p3), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^f))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE==================================

5 5

FOTD 17-04-04 (Polyester Minibrot [7])
by Jim Muth 17 Apr '04

17 Apr '04

FOTD -- April 17, 2004 (Rating 7) Fractal visionaries and enthusiasts: Once again the time has come to enter Fractal Land, that strange land that exists somewhere between the real world around us, which might not be totally real, and the imaginary worlds within us, which might not be totally unreal. The irregular real(p3) parameter of today's image shows that its parent fractal was found by the Fractint 'evolver' feature. Normally, I round off the odd numbers this feature produces, but for some reason I skipped the rounding process when I started working with today's parent. The parent fractal is a hugely bloated area of mostly disconnec- ted rings. Today's scene is located near a larger midget that lies in the interior of a ring in the distant north-northeast suburbs of the parent. The unusual detail inside the midget itself is a sign that the scene has been evaporated, and the ghost brought to life by the bof61 inside fill. Fractals in which all the exponents of Z are negative can be evaporated by raising the escape radius to a full googol, which is the amount entered as the imag(p3) para- meter of today's image. This trick usually traps every point. For reasons known only to myself and the 'intelligent designer', (whatever you consider this to be), I named the image "Polyester Minibrot". I might have done myself a favor when I rated it at a 7, but the image is really rather pleasant to look at, and I feel it earns its rating. The reasonably fast render time of under 4 minutes gives an overall value of 184. The render time is fast, but the fastest way of all to enjoy the image is to download it in finished form from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 67F 19C, gentle breezes, and warm sunshine to keep them happy, the fractal cats put on their best moods Friday. When the day was finished, they were so exhausted that they forgot their customary evening treats, and went right to sleep. Today is starting mostly sunny and warmer. I expect a similar day. For me, most of the graphics work is caught up. If I can muster the energy this afternoon, I'll give the grass the first trimming of the season. If not, I'll do it tomorrow or Monday. Until next time, take care, and don't get hot under the collar when a cool fractal appears. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Polyester_Minibrot { ; time=0:03:48.11--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+25.24771384422294000/+103.017140882474\ 40000/4599911/1/-22.5/6.18164318095387744e-005 params=2/-1.4/0.2/-8.6/-2.597094637897885/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=00000U00o00u00x80zOAzdOzuazzozzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzdz0Iz00u50UX02x00zo0Dz00zG0zg0\ U0za0zg0zl0zu0rz0dz0Qz2Gz52zA0zD0zA0z80u50i20_05O0\ AA0G00L00Q00X00a00g00l00g00a00X02U08O0AI0GD0LA0Q50\ X00_00UD0NQ0LgGIoXDzhAsz5zz2zzzzxozodugQo_GiQ2KK00\ Q0ou8_f0zD0zD2zDDzDLgDXODm520a00z00z20z80uD0rI0lL0\ iQ0gX0aa0_g0Ul0Qo0Ou0Ux0_z0az0gz0iz0oz0rz0xz0zz0zz\ 0zz0zz0zz0zz0zz0zz2zzAzzIzuQzi_z_gzOozDxz2zz0zx0zu\ 0zr0zo0zl0zlIzlazluolzglzXlzOlzQozQozUozUozXrzXrz_\ rz_rz_rzdxzizzlzzrzzuzzzzzzzzuzzlzzgzz_zzUzzGzz5zz\ 0lz0Xa_dAzi5zl0zl0zo0zo0zr0zr0xu0uu0ox0lx0iz0gz0dz\ 0iz0oz0rz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0ro0da0UL2G822050080080000000000000A00O02a0\ 8r0Dz0Iz0Oz0UiG_QadAxi0zo0zu0za0zI5x2Qi0lX0zI0z800\ 00I0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Gz0Lu0Oo0Ql0Ug0Xa0__0a\ U0dQ0gL0iG0lD0o80O0080008 } 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==================================

1 0

FOTD 16-04-04 (Image of Springtime [5])
by Jim Muth 16 Apr '04

16 Apr '04

FOTD -- April 16, 2004 (Rating 5) Fractal visionaries and enthusiasts: A longer version of today's discussion appears on the philofractal list. Today's image, which combines various unlikely negative portions of Z^(-1.4) and Z^(-14), has a certain feeling of springtime to it. Since the season here in the Northern Hemisphere is in fact spring, I named the picture "Image of Springtime". The shades of pink and white could be apple or cherry blossoms. The greens could be the newly emerged leaves. The blues, of course, are nothing but the blue of a clear springtime sky. It's a relatively harmless image, not stressful to look at, one that I have rated a 5. The render time of under 4 minutes raises the overall value to 135. The finished product is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday was a good day here at Fractal Central. Warm sun, cloudless skies, moderate winds and a temperature of 63F 17C gave the dynamic duo a very pleasant afternoon in the yard. When evening arrived, they came inside without urging. Today promises to be even warmer. I expect another good day. The work is moderate today. Hopefully, the next fractal will be of above moderate quality . Until next time, take care, and the fractals never end. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Image_ofSpringtime { ; time=0:03:42.48--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=+1.46839349750336400/+0.281643707741821\ 60/9.037591e+009/1/-19.9987125907157584/-0.0014716\ 5417249400798 params=-4.5/-1.4/-0.9/-14/0/0 float=y maxiter=550 inside=0 outside=tdis periodicity=10 colors=000jKKhKKfKKdKKgMRkCTnBV1_X0ZZ0Z`0ZbLfhzvsz\ vsyqoymlyiiyefy`byX_yTXyPUyLRwJTuIVsGXqFZoE_kCvnBl\ i9hg8fe7hc5ja4l`3mb2Zc1Kd15c58c9BcDDcHGcLIcPLcTOcX\ Qc`TcdVchYcl_dlXelUflSflPglNhlKplHwlFjlCjlAkmHlmNk\ hPkcQkZSkUTkPVjKWjFYjAZj5`j1al4_m6Zo9YpBXrDWsGUuIT\ vKSxNRyPQzRPvTQrVQoXRkZRh_RdaSacSYeTVgTRhTOjUKlUHn\ VDpVAqVDpTFoRHnPJmNMlLOkKQjISiGVhEXgCZfA`e9XbHU_PR\ XXOUdLRkPPhSNeVLbYJ_`HXdFUgDRjBOm9Lp7IqCIrGIrKIsOI\ tSItWIu_IucInZHhUGbPFWKEQFDKBCQIIWPOaWUgb_miespjnn\ jjmjeljajjXijThjX_d_R_cIUfBPaGSXLVTPXOU_JZbFbdNd`U\ eXagThhPoiMlcGiYBfS6dM1YN6SOBMPGFQL9RQ3RUYh0kQMy8g\ vCesGdpKbnNakR`hVZeZYcaXFS0wk5phDjeKdbRZ`YSYeMVlGS\ sAQzBOwCMtDKrEIoFGlGEjHCgHAeEIhCQk9Yn7dpAcqCcrEcsH\ btJbuLbuM_mNYfOW_PUTQRMRPFSN8TL1XL7`LCcLHWONPRTHUZ\ SqcSqcJ`bOcbSeaWg`KMKKOMKQOMSQ0UN3WM6YK9_ICaHFcFIe\ DLgCNiOOkXQm`RocNqf5si4ul } 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==================================

2 1

FOTD 11-04-04 (Transit [7])
by Jim Muth 16 Apr '04

16 Apr '04

FOTD -- April 11, 2004 (Rating 7) Fractal visionaries and enthusiasts: Those who react to the mention of spam with symptoms of high anxiety should skip to the second paragraph below. Today I think I set a new record in the number of junk e-mails I deleted. (248 junkers arrived since 11:30pm last evening.) The junk is easy to recognize, that is no problem, but the mere act of going down the list and deleting it is becoming a major task. Maybe I'll change my familiar 9-year-old e-mail addresses, or maybe I'll simply set up to reject every e-mail that arrives in 'html' format without checking. If I do this, those serious correspondents who post their e-mail in html format will be out of luck. If their e-mail program automatically formats their outgoing mail in html format, they will have to change it to plain text. If not, too bad. I will not receive their mail. But for today I am continuing to delete the junk by hand. I am also continuing to find ever more fractals with midgets at the center. Today's image mixes 1/100 part of Z^10 with one part of Z^1.5, and adds 1/C to produce an oversized parent fractal that needs an outzoom to shrink it small enough to fit on the screen. When this is done, a central Mandeloid appears, surrounded by satellite holes of every size and shape, some connected, some disconnected. One of the most prominent holes lies at the terminus of the main stem of the Mandeloid, which in this case leads off to the northeast. A small spiral appears where the stem joins the hole. Today's scene lies deep in this small spiral. When rendered in the conventional outside=iter inside=0 manner, today's scene, which consists of both inside and outside material, is pretty boring. Most of the other inside and outside options do little better. But when the inside is set to 'bof61' and the outside is set to 'fmod' with a proximity of 1, the scene really comes to life. My original name for the image was 'Night Crawlers', since something in it reminds me of searching for worms. But then I thought of a rare astronomical event soon to happen -- a transit of Venus -- and named the image "Transit". I have no reason for choosing the name other than I felt like it. It's not really a great image, but it is different enough from my normal style fractal to rate an above-average 7. And when the not-too-slow render time of 10 minutes is taken into account, the overall value reaches a 68. The value may be increased by downloading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Surprisingly, the rain held off and the clouds broke around noon on Saturday, leading to a mild afternoon, with sun and tempera- tures around 63F 17C. This is not as warm as the fractal cats would have preferred, but they made the best of things and had a pleasant two hours in the yard. This morning is Easter Sunday, but it is cloudy and cooler, with sprinkles of rain starting already. I fear the cats' good day will not be repeated. Most likely, I'll do little but take it easy for most of the day. Until next time, take care, and fractals also can rise from the dead. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Transit { ; time=0:10:17.16--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+5.76529353248651300/-1.537393722124820\ 00/9.426394e+007 params=1/1.5/0.01/10/0/0 float=y maxiter=1200 inside=bof61 proximity=1 outside=fmod periodicity=10 colors=000RfZSgPRfNQeMPdKOcINbHMaFL`EK_CF_5K`BPbGU\ gLWlSYkQZjO_jM`iLahJbhHdgGegEffCgeBhe9id7jd6ic9icB\ hbDhbFhaHgaJg`Lf`Nf_Pf_ReZTeZVdYXdYZdY`cXbcXdbWfbW\ hbVjaVlaUn`Up`Tr`Tt_Sv_SxZRzZRzZRzXQzWQzVQzUPzTPyS\ PxROwPOvOOuNNtMNsLNrKMqJMpHMoGLnFLmELlDKkCKjBKi9Jh\ 8Jg7Jf6Ie5Id4Ic3Ic6He9HfCGgEGhHFiKFjNEkPElSDmVDnYD\ o_CpbCqeBrhBsjAtmAup9vs9wu9xsCvqFupItnLsmOqkRpjUoh\ XngZmeakzzzzzryzmxzhwzerxdmvchsbcq_ZkXUeUP_RLWOSUL\ SRISOJTJJUKKVLKWNLXOLZPM`QMbSNdTNfUOhVOjWPlXPmYQpZ\ Qr_Rt`RvaSxbSzcTzdTzeUzfUzgVzhXxiVujTrkSolQllPhlNe\ mLbmK_mIYnFXmHXmIXmKXmLXmMWlOWlPWlQWlSWlTVkVVkWVkX\ VkZVk_WqXVk`UecT`gTVjSQnRKqRFtRFsRGqQGpQGnQHmQHkQI\ jPIhPIgPJePJdPhoPhoOhoOhoRhoRioRioRioRioRioRioRioR\ hoRgoReoRcoRboRaoR`oR_oRZoRYoRXoSWoSVoSUoTToTSoTRo\ TQoUPoUOoUNoUNoUNoUNoUNoUNoUNoUOoUQoUSoUUoUVoUXoTZ\ oO`oMboKcoMdoNeoOfoQgoRho } 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==================================

4 5

FOTD 14-04-04 (Inter-Dimensional [7])
by Jim Muth 15 Apr '04

15 Apr '04

FOTD -- April 14, 2004 (Rating 7) Fractal visionaries and enthusiasts: Fractals are said to be things with a fractional dimension. This concept is as hard to visualize as things with four dimensions, but I think I have a vague idea of fractional dimensions. The way I visualize an object or a space with, say, 2-1/2 dimensions is to picture something that extends indefinitely in two dimensions but has limited freedom to extend in the third dimension -- kind of like a lumpy plane. Of course, fractional dimensions are not supposed to be real things. Like the many interpretations of quantum mechanics, they are mathematical concepts which happen to work rather well. There is no uncertainty of the number of dimensions of today's image however. It most certainly has two dimensions. If it did not, it could not fill the monitor screen, and could not be printed on the surface of a sheet of paper. The scene is located in the fractal that results when 4.5 negative parts of Z^3 are combined with 3.375 negative parts of Z^4 and 1/C is added. This parent fractal consists of a main Mandeloid surrounded by numerous large holes, which act as the terminals of filaments. Today's image is located very near the point where a filament of a sub-bud of the main bud of the parent Mandeloid terminates in a hole. A good part of the image consists of empty holes, which have been brought to life by the 'bof61' inside fill. All this dimensional stuff inspired the name "Inter-Dimensional". I originally had rated the image at a 6, but then I happened to view it from across the room, and noticed that it looks as good at a distance as it does close-up. I raised the rating to a 7, which, when the render time of 7-1/2 minutes is considered, gives an overall value of 93. The most efficient way of viewing the image is to download it from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung tough all day Tuesday here at Fractal Central, while the rain fell in sudden short showers. Combined with a temperature of 48F 9C, these conditions proved too rigorous for the dynamic duo, who spent the afternoon on their shelf by the window, watching the birds and taking turns washing each other. In the evening, a generous treat of mackerel helped improve their moods. Today is starting like Tuesday did -- with clouds and light rain. I expect similar things from the duo. For me, it's work until it's finished. That should take around 5 hours, then it will be time for the daily trip to Fractaltown. In 24 hours, I'll report what I find there. Until then, take care, and who could possibly solve the mystery of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Inter-Dimensional { ; time=0:07:33.19--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.31630130595552000/+0.075484039727471\ 52/9.709767e+009/1/-17.5/-0.00200669961294230176 params=-4.5/3/-3.375/4/0/0 float=y maxiter=2000 inside=bof61 logmap=114 periodicity=10 colors=0000N_0PZ0RX0TV0VT0XR2_P4bN6eL8hJAkGEoAGs6J\ u0Nw0Pz0T60T60ZR0`M0eG0iPUmZ0shcvqmzqmzh0ziczA0zbU\ z60z6Kz60u60u80qG0oM0kT0g`0eh2bo4`u4Xd0zm0R80zz00z\ 00z00z06z0Ey0No0Vf0dX0kN0RXCRdPRj`PfdNdeNbgLZkJXmJ\ VoHRsGPuGNvEKzCIzCGzACz8Az88zGAzLCuRCmXEebEXgGPmGH\ sIAxI2qXGkkTeye`zsVzz0zm0zo4zoCuoHkoPdoXVobNoZKkVI\ iRGgNEeJAdG8bC6`86Z46V06T06R06P06N06L06J06H06T0Ad0\ Mo0Xz6hzuz0sy4swAssGsqLsoRqkXqjbqfeqdkqbqoZvoXzoTz\ oRzoPzgMz`KzVIzNGzHEzAAx48u06q06o06k06i06g0Cg0Ge0M\ e0Rd0Vd4`b6dbAjbEo`Hs`LyZPzZTzXXzXZzXPzeGzo6zx0zz2\ zz8zzEzzJuzPozVhz``zeTzkMzqGzv8zz6zz6zz6zz6zz6zz6z\ z6zz6zv6zu6zs6zo6zm6zk6zg6ze6zd6ze6zg6ziAziGzkMzmR\ zmVzo`xqfxqkxsqvuwvuzvszuqzsozqmzqkzokzmizmgzkezid\ zidzgbze`zeZzdXzbXzbbwZekXkZVoNTsCRuIJuNEvT6vZ0dh0\ Nq04z00z00z00z80yL0uX0qg0mu0jz0fz6bzGZzNXxXTseRmmN\ gvMbzIXzGRVjZLZgCPq2Gz06z } 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==================================

2 2

FOTD 13-04-04 (Numbers Playtown [6])
by Jim Muth 13 Apr '04

13 Apr '04

FOTD -- April 13, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's discussion will be brief, as I am having a printing problem with one of the non-fractal machines, which needs to be worked out. First, let me put to rest any rumors that I am quitting the FOTD. The FOTD will continue on a daily basis into the foreseeable future. I am not losing enthusiasm for fractals -- this happens only to mathematicians -- but my non-fractal work is picking up, and this may mean an occasional missed FOTD. When the FOTD does not appear on schedule, be patient. It will reappear in a day or so when the other work is caught up. Today's image is an 'evaporated' scene in the fractal that results when Z^(-2) is combined with 2/3 as much Z^(-3) and (1/C) is added. The resulting blank screen has been brought to life by rendering it with the inside option set to 'bof61'. The 'outside=summ', which appears in the parameter file is meaningless. There is no outside material remaining in the image. For some reason now forgotten I named the image "Numbers Playtown". I gave it a rating of 6. The render time of 11-3/4 minutes gives an overall value of 51. The value may be increased by letting Paul do the job of rendering the image, and downloading the finished product from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Rain and a temperature of 43F 6C kept the fractal cats indoors all day Monday. Their moods were surprisingly good however for such a bad day. Today is still cloudy, but the rain has stopped and it is not as cool. The cats should be in a somewhat better mood. As is always the case, my mood will improve when the equipment is working and the work is behind me. Until next fractal, take care, and there is a great mystery hidden in these fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Numbers_Playtown { ; time=0:11:46.40--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=t center-mag=+1.21706565054569500/+0.178731599667830\ 70/5.016175e+007/1/22.5/1.47126556840349032e-007 params=1/-2/0.67/-3/0/1e+100 float=y maxiter=1200 inside=bof61 outside=summ periodicity=10 colors=0000vL4vTAvbGviLvqRozXgzb_zeezgizkmzmqzqtzs\ vzvvzxvzzvzwwzzvzzvzzvzRvX0v00v40v60v80vA0vE2vG4vH\ 8vJCvLGvPHvRLvTPvVRvXZvZev`kv`svbzvdzvdxvXsvRmvLgv\ GbvAVo2Pi0Ja0EW08P02J0AR0GW0Lc0Ri0Xo0bv4ivAovEuvJz\ vPzvTzvZzvbzvgxvmovseoxXczLFNAF0HF0PH0MNUbeHiqRqvZ\ vvezvZzvTzoNzeHzYCzP4zF0zF0zF0zF0zF0zF0zF6zFEzFLuF\ VqFbmFiiFqeFxbFzXFzTFzPFzLNzGVzCaz8kz4sz0vz0vz0vz0\ vz0vu0vk0v`0vR0vG2v66v08v0Av08s06i04_02R00H00F00F0\ 0F00F00F80600HR0JN0Pb0Vm6_sCezHkzNqzg_VzL0vH0sF0oF\ 6kFCgFHbFNZFTVFZRFdNFiVFo`FseNvkVzqazvizznzzozztzz\ szzpzznzzpzzosxkkueds_XqWPoRHmLAkH2kF6gF8dFA`FEXFG\ VFHRFLPFNNFPLFTLFVJFXHF`GFbEFdEFeJJgPNgVRg`Vge_gkc\ gqggukgvmdxo`xqXzsTztRzvNzvJzvGzvEzvAzv6zv2zv0zv0z\ v0zv0kNzqTzvYzzazzgzzmzzszzvzzvzztzztzzszzszzquzoo\ zokzmezmbzkXziRziNzgHzgEze8zc2zc0za0zW0za0zg0zk0zq\ 4ztAzvGzvJ2vs0wb0vL0v40vE } 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==================================

1 0

FOTD 12-04-04 (Hidden Minibrot [5])
by Jim Muth 12 Apr '04

12 Apr '04

FOTD -- April 12, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today we have a fractal where anything goes. Don't bother looking for a theme -- there is none. The image jumbles together almost all the elements that appear in fractals, and comes up with a dish with a little bit of everything for everyone. Unfortunately, a little bit of everything equals a lot of nothing, and an image with a lot of nothing can hardly be considered above average. I rated the image at an average 5, which, due to the slow render time of 28 minutes, gives an overall value of only 17. The parent fractal was created by combining (1/Z) with 0.5 as much Z^(-2) and adding (1/C). I partially evaporated the fractal by raising the escape radius to 3600. Today's scene is located on a string of debris that runs down the shredded remains of a valley in the parent fractal. The image has a midget Mandelbrot set at the center, as do most of my FOTD images. But unlike most of the images, this midget is nearly impossible to find. It is so hard to pick out that I have named the image "Hidden Minibrot". Part of the difficulty in finding the midget is because it has almost none of the usual symmetry surrounding it. The fact that the image is a mixture of inside and outside material, with the inside colored by the 'bof61' option, adds to the difficulty. The difficulty is further increased because the midget is not in the 'normal' position, with the main stem pointing west. But the midget is there, and can be easily spotted if the image is re-rendered with the inside set to 'inside=0' and the imag(p3) parameter reset to -50. When this is done, much of the evaporated material re-condenses and the dead-black central midget becomes strikingly obvious. The 28 minutes required for the image to render may be avoided by downloading the finished product from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung thick all day Sunday here at Fractal Central, while the temperature hovered around 43F 6C and the rain fell lightly at intervals. All this unpleasantness kept the cat duo confined to the porch for the entire afternoon. The cats took the poor conditions better than expected. Most likely, they are getting used to indoor and porch life. Today is starting cloudy, cool and rainy. The cats' day will likely be no better. After a boring day of doing nothing but watching TV on Sunday, I will be a little busier today. The true fun will begin when the real work has been completed and I enter Fractal Land. Tomorrow at this time I will report on what I find there. Until then, take care, and be aware. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Hidden_Minibrot { ; time=0:28:05.15--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=+3.43578575292992600/+0.629786955360460\ 60/130.7805/1/160/-9.45222372594756166e-012 params=1/-1/0.5/-2/0/3500 maxiter=1200 inside=bof61 float=y outside=tdis periodicity=10 colors=000BJSBIPAHMAGJ9FG9ED8DA8C77B47B16D26E36G46\ H56I66K76L86N96OA5PB5RC5SD5UE5VF5WG5YH5ZI5_I6`J6`J\ 7aJ7aK8aM8bO9bP9bQAcRAcSBcTBdUCdVCeWDeXDeYEfZEf_Ff\ `FgaGgbGgcHhdHie3jfAkgHlh6miGljIkkKjlMimOhmQgmSfmU\ fmWjmYlm_mmanmcnmeomfplgpkhqjirijrhlsgmtfnteoudpvc\ qvbrwasx`xxctx`pvZltWirUepRaoPYmMVkKRiHNgFJfCGdACb\ 78`54Z21Y02X13W13V14U24T25S25R36Q37P37O38N48M49L49\ K5AJ5BI5BH6CG6CF6DE6DD7EC7FB7FA8G98G88H79H69I59I49\ J5AJ6AK7BK7BL8CL9CM9CMADNBDNBEOCEODFPDFPEFQFGQFGRG\ HRHHSHHSIITJITJJUKJULKVLKVMKWNLWNLXOMXPMTNEVOIXPMZ\ QQ`RUbRYdSafTehUijVmlUqkVpjVoiVniVnhVmgVlgVlfWkeWj\ dWidWicWhbWgbWgaXf`Xe_Xd_XdZXcYXbXYaYXbZWb_Vc`VcaU\ dbTdcSecPjdRgdSeeTceUafV_fWYgYVgZTh_Rh`PiaNibLjdIj\ eGkfEkgClhAli8pk2lj6hj9djC`jFXiITiLPiOLiRHhUDhX9h_\ 4id5hb6ha6h`7gZ7gY8gX8gW9eU9cTAaSB_RBYQCWPCUOBTNAS\ MARLAQKAPKAOKANKAMKALKAKK } 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==================================

3 2

FOTD 10-04-04 (A Trashy Fractal [5])
by Jim Muth 10 Apr '04

10 Apr '04

FOTD -- April 10, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's picture of a scene in the Z^2.05+C Mandeloid is simply trashy. It looks like a pile of trash, and I have named it "A Trashy Fractal". But it is trash with class that appears in the image. The parent fractal is a distorted Mandelbrot set, with a main bud that has split into two twin buds. The two branches of Seahorse Valley have spread quite far apart, and a third branch has appeared between the twin buds, while the north branch of the valley has broadened into an infinitely divided wedge. Today's scene lies in this broad north branch of what once was Seahorse Valley. Perhaps the most striking feature of the image is the absolute lack of any sense of order around the distorted midget near the center, with the surrounding features appearing unaffected by the presence of the midget. The left side of the image is of a far higher iteration count than the right side, where the most obvious fragments lie. Here again, the midget seems to have little effect on its surroundings. I have checked the smaller midget that lies a short distance north of the large midget, and found it less interesting. Many other even smaller midgets lie scattered about the scene however, and any one of these could be a real winner. Unfortu- nately, the number of midgets that lie hidden in the scene is infinite, and I do not have an eternity of time to check every one. Since the image is quite average, I rated it at an average 5. When the render time of just under 11 minutes is taken into consideration, the overall value jumps to a 46. When the rendering is avoided by viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> the overall value becomes trivial. Friday turned out to be a rather pleasant day here at Fractal Central. The warm sun and temperature of 65F 18C were just what the aging cats needed to keep them in a good mood. They spent several hours prowling in the yard and sleeping on the porch. This morning is starting cloudy, with rain due by evening. We'll see how it goes for the cats. For me, the work is still a little backed up, cutting into my fractal-searching time. But by this evening I hope to have it caught up. The next FOTD fractal will appear in 24 hours, so until then, take care, and don't be disappointed if every FOTD does not rate a 10. Remember that almost no FOTD's rate a 10. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Trashy_Fractal { ; time=0:10:51.25--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.60630187793427350/+0.506089672233819\ 30/475.1722 params=2.05/0/0/0 float=y maxiter=5000 inside=0 logmap=29 periodicity=10 colors=000eXAg_9ic8kg6mk5qp3on4nm5ml6lk6kj7ii8hh8g\ g9ffAeeBcdBbcCabD`aD_`EYZFXYGWXGVWHUVISUIRTJQSKPRL\ OQLMPMLONKNNJMOILPHKPINRIPTISUIUWIWXIZZJ`_JcaJebJg\ dJjfJlgKoiKqjKslKvmKxoKzpJxnJvlJujJshJrfJpdInbIm`I\ kZIjXIhVIgUHeSHcQHbOH`MH_KHYIGWGGVEGTCGSAGQ8GP7IO6\ JN6KN6LM6MM6NL6OL6PK6QK6RJ6SJ6TI6TF5UH6UI6VJ6VK7WL\ 7WM7WN7XO8XP8YQ8YR9ZS9ZT9ZU9_YD``G`cJafMaiPblSapTb\ oUboVbnWcnXcmYcmYclZdl_dk`dkadkaejbejceideiefhffhf\ fggfghggigfjgfjhekhelhdmhdnicoicoicpibqjbrjasjasj`\ tk`uk_vk_wk_wiYshWofUleShcQebOa`MZ_KVYISXGOfJFWFLM\ CZC9`26a37b48c59d5Ae6Bf7Cg7Dh8Ei9FjAGkAHlBImCJnCKo\ DLpEMqFNrFOsGPtHQuHRvISwJTxJUyKVzLWzMXzMYzNZzO_zO`\ zPazQbzRczRdzSezTfzTgzUhzVizWhzVizVizVizVizVizVizV\ jzVjzVjzVjzVjzVjzVjzVkzVkzVkzVkzVkzVkzVkzUlzUlzUlz\ UlzUlzUlzUlzUmzUmzUmzUmzUmzUmzUmzUnzUnzUnzUnzUnzUn\ zWpzVozUnzUnzTmzTmzSlzRlz } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 09-04-04 (Jet Blast [4])
by Jim Muth 09 Apr '04

09 Apr '04

FOTD -- April 09, 2004 (Rating 4) Fractal visionaries and enthusiasts: When you run today's parameter file, do not be concerned when the first line appears, then nothing more seems to happen. This is normal. I have used the passes=t option with today's image, and the bottom line, which draws next, is very slow and mostly black. After a minute or so, the image will continue developing normally. Today is the Good Friday semi-holiday here at Fractal Central, but from the amount of work lying before me, one would never guess it. Once again, I find myself giving short shrift to the fractal side of life. Today's image shows a lively little Mandelbrot midget located in the parent fractal that results when 1.8 parts of Z^(-1.2) are subtracted from Z^(-1.8) and (1/C) is added. I named the image "Jet Blast" because of the curious string of trapped points that appears to be blasting from the East Valley of the midget. A few other names came to mind, which are best left un-mentioned. In addition to our large midget, the scene is filled with other midgets, most of which lack the typical organized 2,4,8... pattern of elements surrounding them. When an area grows chaotic, the regular pattern breaks down. This is true even in the classic Mandelbrot set. Since I basically used the first object I found as today's FOTD, I could rate the image no higher than a 4. The slow render time of 32-1/2 minutes results in an overall value of 12. Those who think it worth the effort will run the parameter file included at the bottom of this letter. Others will save time by viewing the finished GIF image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cool temperatures in the low 50's (around 11C), thick clouds, chilly winds, and occasional sprinkles on Thursday kept the fractal cats confined to the porch, where they were somewhat sheltered from the unpleasant conditions. Tippy ventured down into the wet grass once or twice, but retreated to the porch when he felt the wetness. Thomas merely slept in his porch chair. The good news is that today is starting sunny. Perhaps the duo will have a good day. My day will be quite busy, especially for a day that is supposed to be a holiday. Until next FOTD, take care, and if the U.S.A. really does keep church and state separate, why are so many people on a holiday today? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jet-Blast { ; time=0:32:35.62--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=t center-mag=1.77561/4.48651/1.612403 params=1/-1.8/\ -1.8/-1.2/0/525 float=y maxiter=32767 inside=0 logmap=11 periodicity=10 colors=000UFMVGNWGPXHQYHSZIT_JU`JW`KW`KX_LX_LY_MY_\ NY_NZ_OZ_O__P__P_`Q``Q``Q``R``R``R``S`aS`aS`aS`aT`\ aT`aT`aU`aU`bU`bV`bV`bV`bV`bW`bW`bW`cXacXacXacYacY\ acYacYacZadZadZad_ad_ad_ad`ad`ad`ae`aeaaeaaeaaebae\ baebafc`ebadaac`bb_ba_b`Zc_YcZXcYWdXWdWVeVUeUTeUSf\ TSfSRfRQgQPgPOhOOhNNhMMiLLiKKiJKjIJjIIkHHkGGkFGlEF\ lDElCDmBCmACn9Bn9AnA9oB8oC8oDFnELmFMmGNmHOmIPmKQmM\ QmORmQSmSTmUUlWUkYVj_WiaXhcYgeYfgZgi_gk`gmagobgqbh\ schudhzehxfhyfizgizhiziizjizjmzjkzjizhgzgezedzcbza\ `z`ZzZYzXWzWUzUSzSQzQPzPNzNLzLJzJIzIGzIEzJCzKCyLBy\ MByNByOByPBxQBxRBxSAxTAxUAwVAwWAwXAwYAwZAv_9v`9va9\ vb9vc9ud9ue9uf8ug8uh8ti8tj8tk8tl8tm8sm7sm7sm7sm7sm\ 7rm7rm7rm6rm6rm6qm6qm6qm6qm6rm5qm6qm6qm6qm7qm7qm7q\ m8qm8qm8qm9qm9qm9qmAqmAqmAqmBqmBpmBpnCpoCppCpqDprD\ psDptEpuEpvEpwFpxFpyFpzGpzGpzGpzGozFozFozFnzFnzFnz\ FmzFmzFmzElzElzElzEkzEkzE } 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==================================

1 0

FOTD 08-04-04 (Test [NR])
by Jim Muth 08 Apr '04

08 Apr '04

FOTD -- April 08, 2004 (Rating NR) Fractal visionaries and enthusiasts: Watching the news this morning, I see that the president might be guilty of not having a proven fortune teller in his administration. And I am likewise guilty of not knowing in advance that I would lack the time to complete a FOTD fractal. But I do have a test fractal, and it is this test that I present as today's image. The image is a study in outside=fmod and inside=bof60. The formula is once again the MandelbrotMix5way, with the real(p5) parameter acting as the critical starting point of Z. Since the image was not completed, I have not rated it. The render time of 15 minutes can be bypassed by downloading the finished GIF image file from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature reached 75F 24C here at Fractal Central on Wednesday. At the same time the wind was light and the sun was bright -- conditions that make fractal cats happy. Their day was as pleasant as senior cats could hope for. Today is again starting mild, but it is cloudy, and rain is a possibility. Today promises to again be very busy. So I had best apply my energies to the task at hand. Until next FOTD, take care, and could fractals be the salvation of mankind? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Test { ; time=0:15:33.13--SF5 on a P200 reset=2003 type=formula formulafile=slices.frm formulaname=MandelbrotMix5way passes=1 center-mag=-0.76998805020114040/+0.001162931724501\ 04/3.493154e+011 params=0.2/4/1/3/1/2/1/-1/-1.2554\ 2034202/0 float=y maxiter=900 inside=bof60 proximity=0.9 outside=fmod periodicity=10 colors=000ePleOjdNidNgcMfcLdcLcbKabJ`bJZaIYaHWaHVb\ GUbGTcGScGRdGQdGPeGOeGNfGMfGLgGKgGJhGIhGHiGGiGFjGE\ jGDkGCkGBkGBbSMVbXMmgExrGvpHuoJsnKrmMplNokPmjQliRk\ hTigUhfWfeXedZcc_bb`aaa__bZZcYYdXXeVVfUUfTTgSShQQi\ PPjOOkNNkMMjOOiQPhSRhTSgVTfXVfYWe_XdaZdb_cdabfbbgc\ aie`kf`lg_niZpjZqkYqjXqiWqhVqhVqgUqfTqeSqeSqdRqcQq\ cPqbOqaOq`Nq`Mq_LqZLqZHL`PUcXafdiilqlsynsulsqjsnhs\ jfsgdscbs``sXZsUXsQVsNTsJRsGQqJPoLPnNPlPPkRPiTPgVP\ fXPdZPc`PabP_ePZgPXiPWkPUmPSoPRqPPsPOuPMwPLyPKxQJx\ RIwRHwSHvTGvTFuUEuVEtVDtWCtWBsXAsYArY9rZ8q_7q_7p`6\ pa5oa4ob4ob6lc8idAgdCdeDbeF_fHXgJVgLShMQhNSaOUWPVP\ QXJRYDQ`DPcEPfFOjGNmGNpHMsILvJLyJNwMOvOQuQRtSTsUUq\ WWpYXo_Ynb_md`kfbjhcijehlfgngfphgoignjgmkgmlglmgkn\ gjogjpgiqghrghqiiqjjpkkpllommoonoponqpmrqmsrluslvt\ kwukxvjywjzwgvqdrkbne_j_YgVVcPT_JQWDOT8PVBPXEQZGQ`\ JRbMRdOSfQShSTjUTlWTnYTp_ } frm:MandelbrotMix5way {; Jim Muth z=p5, c=pixel, a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 07-04-04 (Oscar [6])
by Jim Muth 07 Apr '04

07 Apr '04

FOTD -- April 07, 2004 (Rating 6) Fractal visionaries and enthusiasts: The work is quite heavy today, so the discussion will be short. With today's image we return again to the parent fractal of yesterday's image, where we search the north valley of the main- stem midget. This parent fractal is shaped like the Mandelbrot set, with the added attraction of an infinity of tiny cut-off dots that surround the set, each dot containing an even tinier M-set. Not surprisingly, the area of the parent fractal nearest to where the dots are located determines the nature of the midgets in the dots. Today's midget is located in a dot in the east branch of the north valley of the largest midget of the parent fractal. The midget displays the type of detail found in this area, though the cut-off nature of the dot in which it lies is very apparent. I named the picture "Oscar". It is as good a name as any. I rated the image at a 6, which joins with the render time of 12-1/2 minutes to give an overall value of 48. The rendering may be avoided by downloading the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With warm sun and a temperature of 59F 15C to enjoy, the fractal cats had a far better day Tuesday. Only a small bit of tuna was needed in the evening to keep their spirits up. Today is starting similarly; I expect the cats will have a similar day. For me, the work is still heavy. But with some concerted effort, it can be cleared away by late afternoon. Until next fractal, take care, and keep those fractals iterating. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Oscar { ; time=0:12:30.34--SF5 on a P200 reset=2003 type=formula formulafile=slices.frm formulaname=MandelbrotMix5way center-mag=+1.25187085006519900/+0.004851408472547\ 36/1.409139e+012/1/37.5/-0.00643738036985672807 params=0.2/4/1/3/1/2/1/1/-3.0679235938/0 float=y maxiter=1200 inside=0 logmap=215 periodicity=10 colors=000f0Ae0Ad0Ac0Ab0Aa0A`0A_0AZ0AY5AXAAWFAVKBU\ NCTPBSUAQZANc9Lh8Jm7Mr6Vw6ezBpzGzzLzmQzcVxU_uLZrLZ\ oLYlLYiLXfLXdLWaLWZLVWMVTNUQOUOPUSQVVRWUSXTTYTUZSV\ _SW`RXaRYbQZcQ_dP`ePafObgOchNdiNejQfkSglVhmUinSjoQ\ kpOloQkmShkUeiWcgUaeT_cSYaRW_QUYPSWNQUMOSLMQKKOJIM\ IGKHFKBEK6Cz7Zz8cw8hr9jq9rqAqlBqhCqcDp_EpVFpRGoMHo\ IIoDJo9KlBLiDLfFMdHNaJNZLOWNOUPRSNTRMVQLYOK_NJaMId\ KHfJGhIFkGEmFDoECrCBtBAvA9x98q8Ij7Sc7aX6kQ6tT7rV8q\ X9pZAnaBmcBleCjgDijEhlFfnGepGddJXUMQKKaAIm1HyDGoPG\ f`FXkFOjHNiJNhLNgMNfONfQMeSMdTMcVMbXMbYMaZK`_I_`GZ\ aEYbCXcAWd8Ve6Uf4Uf3SbBRZJPVROSYNUWMVULWSKYQJZOJ_N\ IaLHbJGcHFeFEfDEgCLiISjOZlUdm_bga`bcZXeXSgWMiUHkSB\ mQ6oP1qO6oNAnNElMIkMMiLQhLUfKYeKacJebJi`Im_IqYHuXH\ yWKvTMtRPqPRoNUmLWjJZhH`eFccDeaBf`Df`Eg`Fg`Gh_Hh_I\ h_Ji_Ki_LjZMjZNkZOkZPkZQjYSiYThYUhYVeZUb_U_`UXaUVa\ UXbTZbT`cTbcSdcSfdSkMTaPS } frm:MandelbrotMix5way {; Jim Muth z=p5, c=pixel, a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 06-04-04 (Spare Ribs [5])
by Jim Muth 06 Apr '04

06 Apr '04

FOTD -- April 06, 2004 (Rating 5) Fractal visionaries and enthusiasts: It has been rumored that I am a mathematician. I would like to take a moment to put such an unfounded rumor to rest. I am not now, nor have I ever been a mathematician. This fact can be easily demonstrated by engaging me in a discussion about math, which will clearly show my lack of knowledge. I am a graphic designer. I like pretty designs. I became fascinated with fractals because they make pretty designs. It has also been rumored that I am a troll. There is a bit more truth to this rumor. A troll enjoys stirring up an argument, and at times I have done just this. But we must never forget that a troll is ineffective if no one responds to his bait. Luckily, the members of the Fractint list have discipline enough to avoid getting into contrived arguments. And when I mention critical points, I mean numbers such as the -3.0679...., which I entered as the real(p5) parameter of today's fractal. This is a stationary point of the function being iterated -- 0.2z^4+z^3+z^2+z. I assume that points of inflection can also be critical points, but my limited mathema- tical knowledge prevents me from being sure. As for today's image, it reminds me of spare ribs, and that's what I named it. The rating is a 5, the overall value comes in at a 170. The finished product is available for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday was a sunny day here at Fractal Central, but the wind was high and the temperature was a low 39F 4C, giving the cats an unpleasant 1/2 hour in the yard. Their unhappiness was eased by a treat of tuna in the evening. Today is starting sunny with less wind and higher temperatures. I expect a far better day for the duo. For the rest of the day I'll be busy with real work. The fractals will have to wait until the other stuff is finished. But regardless, the next in the endless series of FOTD's will appear on schedule in 24 hours. Until then, take care, and don't be so knowledgeable that you take all the fun out of it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spare_Ribs { ; time=0:02:55.87--SF5 on a P200 reset=2003 type=formula formulafile=slices.frm formulaname=MandelbrotMix5way passes=1 center-mag=+1.14332713449146900/+0.001242158204517\ 41/1.490245e+008/1/11.5/4.34491689707550144e-006 params=0.2/4/1/3/1/2/1/1/-3.0679235938/0 float=y maxiter=300 inside=0 outside=tdis periodicity=10 colors=000kpbqsfjtadtYYtTStPLuLFuG8uC2u84mJ5eU6ZdP\ YRgXDyW0l`HmeFnjDooCptApy9qqCriEWZRtVJuNMvFOw7Rw0T\ vKavbivuqmnheg`YbTPULHND9H5DM5HQ5LU5OZ5Sb5Wf5Zj5Xe\ UV`rdbpmcnvdlrann_ojXqgVrcSt_QuXOvvYao`cibebegXgiR\ ikQhjQgiAXo7am4fk2ki4hd6h`7hX9hSAhOChKDhGLhDShB_h9\ fk7mq5el8ZhARiDKkFCmI5oKQqJjsIqubxwwtxlqyamzRjzHgz\ FezDbzB`z9Yz7Wz5Tz3Rz2RzmUznXzo_zpbzpezqhzrkzsnzsa\ zuPzwCzyHzpLzhPz_UzSYzJazBez3bzD_zNYzWVz_SzcPzgNzj\ KznHzrFzuEzqEznDzjDzgCzdCz`BzYBzVDzXEzZFz`HzbIzdJz\ eOzfSzgXzh`zidzjizkmzlqzlmzbjzUfzKczBZz8Vz6OzBIzFC\ zJEzPGzUIzZKzcMzhNzmXzoezqozsxzuozwgzx_zyVzqQzjLzb\ GzWFzYEz_DzaWzWnzQgzZ`zgUzpNzyOzvOztOzrPzpPznPzlPz\ jQzmQzoRzrRztMzrIzqDzo9znBzkCziDzfEzdFzaGz_IzXKzUL\ zRNzOPzLQzJszvlzlfzb`zUVzKPzAJz1azOszjrzaqzUpzLpzD\ kzEfzFazGXzHSzINzJIzKEzKNzPVzTbzXjz``zcSzfJzhAzk1z\ m5ze9zZDzSGzLFzLFzLYzVdzZ } frm:MandelbrotMix5way {; Jim Muth z=p5, c=pixel, a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE==================================

2 1

Tesseral Just For Show and other public misinformation.
by SherLok Merfy 06 Apr '04

06 Apr '04

Typo { ; z(n)=fn1(z(n+1))*fn2(z(n+1)) ; That might be more accurate than documentation ; that refers to neither zed nor the pixel. reset=2003 type=fn*fn function=ident/ident float=y bailout=4 inside=0 periodicity=0 } MegaCrab { ; If Tesseral were just for show, then the ; spines wouldn't be broken with solid guessing. ; 1:28.6/megapixel@350Mhz. colors=(a)preemoh.map ; z=(.72,.72)*z*z+(.72,.72)*z reset=2003 type=fn+fn function=sqr/ident passes=t center-mag=-0.5/0/0.2509/1.8129/-8/-7 params=0.72/0.72/0.72/0.72 float=y maxiter=255 bailout=4 inside=0 invert=0.77857365306758/-0.5/0 periodicity=0 colors=000z00zz00z00zV0zz0Wz00z<3>z0zz0Wz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz\ 00zV0zz0z<3>z0Lz0Bz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00z<3>e0zo0zz0zz0Wz00<\ 3>ze0zo0zz0<3>0z00zV0zz<3>0Lz0Bz00z<3>z0z<3>z0Lz0Bz00<3>zV0zb0zj0zr0zz\ 0<3>0z00zV0zz<3>00zV0zz0z<3>z00<7>z_0zc0zh0<3>zz0<3>0z0<3>0ze0zo0zz0Wz\ 00z<3>P0zV0z`0z<3>z0zz0Wz00<3>ze0zo0zz0<3>Lz0Bz00z0<3>0zz<3>0Lz0Bz00z<\ 3>e0zo0zz0zz0Wz00<3>zP0zV0z`0<3>zz0Wz00z0<3>0zz0Wz00z<5>V0z_0ze0z<3>z0\ z<5>z0Wz0Rz0L<3>z00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00zV0zz0z<3>z0az0Wz0Q<3>\ z00<3>zzz }

1 0

Re: FOTD 04-04-04 (Star of the Ages [7])
by Jim Muth 06 Apr '04

06 Apr '04

On Sun, 4 Apr 2004, I wrote: >> A formula as simple as Z^2+Z+C will merely >> shift the M-set around, while leaving it >> otherwise unchanged. SherLok Merfy replied: >That puts ears on your traditional snowman, >and his feet melt. <snipped> The ears and melting feet are what happens when Z is initialized to zero. To see the little fellow moved around while remaining otherwise unchanged, set the starting point of Z to -0.5 which is the critical point of the formula Z^2+Z. The MandelbrotMix4 formula automatically initializes Z to a critical point of the formula being calculated. Jim M.

2 1

Re: More Mandelbrot sets???
by Raymond Filiatreault 05 Apr '04

05 Apr '04

I did mention that the two formulas were FUNDAMENTALLY different. One uses the ACOS function of "z" while the other uses the ACOSH function of "z". With real numbers, the acos function could only take arguments which have an absolute value less than or equal to 1.0, and produce results between 0 and 2PI. Similarly with real numbers, the acosh function could only take arguments which are positive and greater than or equal to 1.0, and produce results between +INFINITY and -INFINITY. However, raising either of these functions of "z" (a complex number) to the 4th power and adding "c" have been producing the identical fractal, which also happens to be a quarter replica of the M-set. I wonder if some genius mathematician could make sense of this unexpected behaviour with complex numbers. I got the same results with Fractint using the following formula and testing with the acos and acosh functions: rayfil { c = z = pixel: z = fn1(z) z = z*z z = z*z + c |z| < 4 } Raymond _________________________________________________________________ Add photos to your messages with MSN Premium. Get 2 months FREE* http://join.msn.com/?pgmarket=en-ca&page=byoa/prem&xAPID=1994&DI=1034&SU=ht…

2 1

FOTD 05-04-04 (A Fool's Gold [6])
by Jim Muth 05 Apr '04

05 Apr '04

FOTD -- April 05, 2004 (Rating 6) Fractal visionaries and enthusiasts: I'm a bit busy today, so today's discussion will be short. The image is an evaporated scene in the fractal that results when 2 parts of Z^(-7.6) is combined with 4 parts of Z^(-1.4) before (1/C) is added. The scene has been evaporated by raising the escape radius so high that all the points are trapped. The trapped points have been brought to life by rendering them with the inside=bof61 option. I have added 1/C instead of C because fractals with negative exponents of Z are inside out, and 1/C turns fractals inside out again. The parent fractal is quite rich. I might do a bit more exploring in it before moving on. Because of its rich golden yellow, today's image has been named "A Fool's Gold". (That's what they called iron pyrite in the old west.) The rating of a 6 is raised to an overall value of 232 by the short render time of 2-1/2 minutes. As always, the finished GIF image has been posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> High winds, clouds and a temperature of 43F 6C kept the cats indoors on Sunday. Cheered by an extra dollop of tuna, they took their confinement stoically. Today is starting sunny, but the wind is still high. We'll see how things go for the dynamic duo. For me, it's back to work. When the work is finished, the fractal fun will begin. How can I keep up my enthusiasm for fractals? I don't know. But one thing for near certain is that the next FOTD fractal will appear in 24 hours. Until then, take care, but when you do so, don't make life boring. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Fools_Gold { ; time=0:02:35.60--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.85808245798638/+1.665377798426092/\ 1.383526e+011/1/-77.5/4.76209247881331788e-005 params=4/-1.4/2/-7.6/0/1e+100 float=y maxiter=350 inside=bof61 logmap=38 periodicity=10 colors=000PHKPIKSJPVHUYGW_EabDbeBcgAdjJYmRSp_LsgFv\ p8xx2tZ1pA0mB3kC6iC8fDBdDEbEG_EJYFMWFOTGRRGUPHWMHZ\ KIaIIcHKdGMeFOhEQmDSrCUwBWzNYzR_zUazRdzzgzTjzXmzaU\ zeJXjHTnGQsEMwDJqIPkMVeR`_VfU_lOmzIwzHwzHwzHwzHwzH\ nhHoezpbKn`NlZQjXThVWfTZdRabPd`NfZLeXOdWRdVUcUXbTZ\ bSaaRd`Qg`PibSfdUcfW`hZYj`VkbSrdPygMziJzkGzmDzjCzg\ CzdCzaCzZCzWCzTCzQCzNCzKCyHCwECuBCr8Cp5Co2CcCKdLSe\ U_fVagVbhVciWejWfkWglWimXjnXkoXmpXnqYorYqsYrtYsu3y\ v7uwAqxEmyHizLezOazRbzTbzVczXczZczadzcdzedzgeziezl\ fznfzpfzrgztgzvgzoizhkzbmzWozPqzJrzNqzQpzTozWnzZnz\ bmzelzhkzkjznjzlizjhzhhzggzegzcfzaez`ezZdzXdzVczUc\ zXJzTIzQHzMGzJFzFEzCDz9DzHAzP8zX6zd4z`5zY5zV5zR5zO\ 6zL6zH6zE6zB7z77z47z17z4Bz7EzAIzDLzGOzJSzMVzPZzSaz\ VdzYhz`kzbnz`lzZjzYhzWfzVdzTbzR`zQZzOXzNVzLTzJRzIP\ zGNzFLzHRzJXzLbzNhzPnzRtzSzzXtz`ozdjzidzm_zqVzuQzi\ VzZZzNczCgzDhzEizFjzFkzGl } 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==================================

1 0

Re: [Fractint] Re: More Mandelbrot sets???
by Russell Walsmith 05 Apr '04

05 Apr '04

Opps, belay that last message... z = z^m z = z^n + c is same as z = z^(m*n) + c come to think of it... --------- Original Message --------- DATE: Mon, 05 Apr 2004 04:04:45 From: "Raymond Filiatreault" <rayfil(a)hotmail.com> To: fractint(a)mailman.xmission.com Cc: >I did mention that the two formulas were FUNDAMENTALLY different. One uses >the ACOS function of "z" while the other uses the ACOSH function of "z". > >With real numbers, the acos function could only take arguments which have an >absolute value less than or equal to 1.0, and produce results between 0 and >2PI. Similarly with real numbers, the acosh function could only take >arguments which are positive and greater than or equal to 1.0, and produce >results between +INFINITY and -INFINITY. > >However, raising either of these functions of "z" (a complex number) to the >4th power and adding "c" have been producing the identical fractal, which >also happens to be a quarter replica of the M-set. I wonder if some genius >mathematician could make sense of this unexpected behaviour with complex >numbers. > >I got the same results with Fractint using the following formula and testing >with the acos and acosh functions: > >rayfil { > c = z = pixel: > z = fn1(z) > z = z*z > z = z*z + c > |z| < 4 >} > >Raymond > >_________________________________________________________________ >Add photos to your messages with MSN Premium. Get 2 months FREE* >http://join.msn.com/?pgmarket=en-ca&page=byoa/prem&xAPID=1994&DI=1034&SU=ht… > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

1 0

Re: [Fractint] Re: More Mandelbrot sets???
by Russell Walsmith 05 Apr '04

05 Apr '04

Well, if I understand what you're asking, I've noticed in similar investigations that z = z*z z = z*z + c is equivalent to z = z^4 + c. In general, as becomes obvious when you look at it for awhile, z = z^m z = z^n + c is equivalent to z = z^(n+m) + c. Ciao, Russell --------- Original Message --------- DATE: Mon, 05 Apr 2004 04:04:45 From: "Raymond Filiatreault" <rayfil(a)hotmail.com> To: fractint(a)mailman.xmission.com Cc: >I did mention that the two formulas were FUNDAMENTALLY different. One uses >the ACOS function of "z" while the other uses the ACOSH function of "z". > >With real numbers, the acos function could only take arguments which have an >absolute value less than or equal to 1.0, and produce results between 0 and >2PI. Similarly with real numbers, the acosh function could only take >arguments which are positive and greater than or equal to 1.0, and produce >results between +INFINITY and -INFINITY. > >However, raising either of these functions of "z" (a complex number) to the >4th power and adding "c" have been producing the identical fractal, which >also happens to be a quarter replica of the M-set. I wonder if some genius >mathematician could make sense of this unexpected behaviour with complex >numbers. > >I got the same results with Fractint using the following formula and testing >with the acos and acosh functions: > >rayfil { > c = z = pixel: > z = fn1(z) > z = z*z > z = z*z + c > |z| < 4 >} > >Raymond > >_________________________________________________________________ >Add photos to your messages with MSN Premium. Get 2 months FREE* >http://join.msn.com/?pgmarket=en-ca&page=byoa/prem&xAPID=1994&DI=1034&SU=ht… > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >

1 0

Default of fliprnot reflects what can happen to a name.
by SherLok Merfy 04 Apr '04

04 Apr '04

fliprnot { ; function=zero/ident/recip . Radical orbits. z=fn1(pixel), c=fn2(pixel): z = sqr(z) +c c = fn3(c) LastSqr <=real(P1) } Default { ; As good as any reason to start zed at zero. ; It might be interesting to hear this with ; orbits connected as in mandelcloud. reset=2003 type=formula formulafile=fliprnot.par formulaname=fliprnot function=zero/ident/recip passes=t params=4/0 fillcolor=255 inside=255 cyclerange=1/247 symmetry=xaxis periodicity=-3 showorbit=yes }

1 1

FOTD 04-04-04 (Star of the Ages [7])
by Jim Muth 04 Apr '04

04 Apr '04

FOTD -- April 04, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to the land created when 0.2 parts of Z^3 are subtracted from Z^2, where we further study the possibili- ties of the 'fmod' option. We also make use of the 'bof61' inside coloring option, which is effective because a good part of the image consists of areas of trapped 'inside' points. Yes, I do feel a bit guilty about the departure from fractal reality that took place when I decided to use these two options rather than outside=iter, inside=0, but the image is not bad, in fact it rates a 7, and is worth its moment in the sun as FOTD for April 4. I saw a letter on the fractint list recently wondering whether formulas other than Z^2+C will produce undistorted Mandelbrot sets. I would say the answer is yes. I have been producing them for years with the MandelbrotMix series of formulae. A formula as simple as Z^2+Z+C will merely shift the M-set around, while leaving it otherwise unchanged. Curiously, when Z is added to any power of Z other than 2, an entirely new fractal will result. See what happens when the formula Z^(2.5)+Z+C is calculated. And the formula Z^2+2Z+C has no effect whatsoever, producing a Mandelbrot set that is both undistorted and in its proper position as well. When searching for a name for today's image, I was struck by the eight-pointed star, and thought of the name "Star of the Ages". The name has a kind of religious sound to it, but no connection to religion was intended. When combined with the render time of over 5 minutes, today's image has an overall value of 131. For convenience, the completed GIF image will soon be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Though the weather was improved here at Fractal central on Saturday, it was still too wet and chilly (50F 10C) for the cats to remain in the yard longer than 30 minutes. They spent the remaining 23-1/2 hours sleeping. The problem this morning is more rain, colder temperatures, and high winds, so I doubt that the day will be any better. For me, it might be an afternoon of 'antiquing' as the fractal lady calls examining the junk that others have thrown away. When the crisis has passed, I'll return to fractal land. Until tomorrow, take care, and I have yet to see a discarded fractal in one of those antique shops. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Star_of_the_Ages { ; time=0:05:19.73--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.89130860945648100/+0.000079946227141\ 96/1464693/1/15/-1.43131317909e-008 params=1/2/-0.\ 2/3/0/0 float=y maxiter=1500 inside=bof61 proximity=0.3 outside=fmod periodicity=10 colors=050BLrBLrBLrBLrBLrBLqBLqBLqBLqBLoALnALnALnA\ LnALnALmALmALmALmALmALm8Lk8Lk8Lk8Lk8Lk8Lj8Lj8Lj8Lj\ 8Lj6Li6Li6Li6Li6Li6Lg6Lg6Lg6Lg6Lg3Kf4Lg4Lg6Lg6Lg6L\ g8Lg8Lg8LgALgALgALaBLgBLgDLgDLgDLgFLgFLgFLhGLhGLhG\ LhILhILhILhJLhJLhLLhLLhLLhMLhMLhMNhONhONhONhPNhPNh\ RNhRNhRNhSNhSNiSNiUNiUNiUNiVNiVNiVNjWNjWNjYNjYNjYN\ jZNjZNjZNj`Nj`Nj`NjaNjaNjaIjaKiaLgaLfaNeZNcYOZWQTV\ QNSOGRNGPLHMKIOIJOGKOFLPDMPBNP9OP9PR9QR9RR9SR9TSDU\ SGVSIWSKXUKYUKZUK_VK`VKaVLbVLcWMdWNeWOfWPgYQhYRiYS\ jYSkZTlZTmZTn`To`Tp`Tq`TraUsaTtaTuaTvcTwcTxcTxcTxd\ UxdUxdVxcWydWydXydXzfYzfYzfZzgZzh_zi`zj`zkazlazmby\ nbyocypcxqdxrdxsewtewufwvfvwgvxhvziozkrzluznuzouzq\ uzruztuzuuzsuzsuzquzquznuznszlqzkozhmxhjwgivgftees\ ebrdapcZoaXnaUl`Rk`Qj_Nh_MgYJfXHdWEcWEcVDcVDdVDdWD\ dXDfXBfZBg_Bh`BibBibBjcAkeAkfAmhAnhAniApk8rl8sm8um\ 8vo8wp8IKkGKjGKjFKjDKjDKj } 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==================================

2 1

FOTD 03-04-04 (A New Land [7])
by Jim Muth 03 Apr '04

03 Apr '04

FOTD -- April 03, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to the same area of the same fractal that yesterday's image was found in. A different, larger, midget lies at the center of the screen in today's image, though the underlying character is the same as yesterday's. The big change is that today's image has been rendered with the 'fmod' option, while yesterday's was rendered using the standard 'iter'. As is typical of images rendered with the 'fmod' option, today's image consists of overlapping bubbles. Extra interest is added because of the discontinuities, which cause some of the bubbles to be broken. I particularly enjoy the tiny, apparently disconnected pieces floating around in the scene. These are common in 'fmod' images. When I create a fractal using something other than the traditional 'equal-iteration-band' method, I sometimes feel I am cheating. The real fractal, the theme if you will, is what appears when the image is colored according to how many iterations it takes any particular point to pass beyond the escape radius. All other fractals are variations of the real thing. But sometimes variations can be quite interesting, and today's image is a very interesting version of a fractal that otherwise would be almost a repeat of yesterday's. The colors have turned out unusually smoothly for a GIF fractal image, in fact, the individual color bands are so subdued as to be almost invisible. (I said 'almost' invisible for the benefit of the extra-observant fractalists, who will still see the bands.) Since today's image is a near-repeat of yesterday's, I rated it at a similar 7. The faster render time of 3-3/4 minutes gives an overall value of 185. I named it "A New Land" for no particular reason. The completed GIF image, along with this letter, has been posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The steady rain continued all day Friday here at Fractal Central, while the temperature hovered around 43F 6C. These were rather unpleasant conditions for enjoying the outdoors. The cat duo remained sullen most of the day, though their bad moods were not very noticeable, considering that they now spend around 22 hours every day sleeping anyway. A treat of salmon in the evening cheered them somewhat. Today is again starting cloudy, but it is not raining. We'll see how the day goes. It should be a rather good day for me. There are only a few minor bits of work to get into shape before the fractal fun begins. Until tomorrow's FOTD, take care, and report any sightings of alien fractals to your local fractal police. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_New_Land { ; time=0:03:45.80--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.7\ 7212345977/-0.10483788219/10845.41/1/-22.5/6.03545\ 893818058232e-011 params=1.55/0/0/0 float=y maxiter=3600 inside=0 outside=fmod periodicity=10 colors=000DkEDkEClEBlEBmFAmF9nF8nF8oF7oF6pF6pF7oG7\ nG7mG8lG8kG8jG9iG9hH9gHAgHAfHAeHBdHBcHBbHCaIC`IC_I\ D_IDZIDYIEXIEWIEVJFUJFTJFSJGSJGRJGQJHPKHOKHNKIMKIL\ KIKKJKKJJKJILKHLKGLKFLLELLDLLCL3A7CBELCLUDSbEZkFes\ FlpHjmIhkJfhKdeMccNa`O_ZPYWQXTSVRTTOURMVPJXOGYMEZK\ B_I7ZE8_G9`H9`IAaKAaLBbMBbNCcPCdQDdRDeSEeUEfVFfXFg\ YGhZGh_Hi`HibIjcIjeJkeJlgKlhKmiLmkLnlMnmMonNpoNpqO\ qrOqsPruPrvQswRrzQsxQrxQqxQqxQpwQowPnwPnwPmvPlvPkv\ PkvPjuOiuOhuOhuOgtOftOetOetNdsNcsNbsNbsNarN`rN_rM_\ rMZqMYqMXqMXqMWpMVpLUpLUpLToLSoLRoLRoKQnKPnKOnKOnK\ NmKMmKLmJLmJKlJJlJIlJIlJHkJGkIFkIFkIEjIDjICjICjIBi\ HAiH9iH9iH8hH7iH6gI5hH6hH6gH6gH6gH6fH6fH7eH7eH7dH7\ dG7cG7cG7bG8bG8aG8aG8`G8`G8_G8_F9ZF9ZF9YF9YF9XF9XF\ 9WFAWFAVFAVEAUEAUEATEATEBSEBSEBREBREBQEBQEBQFCRGDS\ HESHFTIGTJHUKIUKJVLKVMLWNMWNMXONXPOYQPYQQZRRZSS_ST\ `TU`UVaVWaWXbXYcYZdZ_e_`f } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

formulafile=cards.par
by SherLok Merfy 02 Apr '04

02 Apr '04

(That's not actually necessary, unless you want to see what comes without parameters, but renaming the file is, because no root seems to be on this Lynx-fronted UNIX-compatible terminal system of late.) Your rights to this work do not exclude commercial development, and you are welcome to make recognizable changes to the tune, the colour maps or the methods of imaje composition in order to call it yours. Failing such uses that I would consider fair, and recovering your costs of production means that you owe me. The contents of this message are otherwise meant for intact distribution. Other rights or obligations may follow from laws or institutional guidelines respecting attribution or netiquette in your society. A private instigator transmitted this message. Square { ; Stripped formula for diamond. params=1/0/2/0/ident ; Display=function first. Public domain. z=z-z, c=fn1(pixel), delta=P1: z=(z+delta)*(z-delta)*(z+flip(delta))*(z-flip(delta))/c |z| <= real(P2) } PixelPower { ; Formula for club. Public domain. z=fn1(pixel), s=P2+fn2(pixel), if(P3==(0,0)) P3=sqrt(0,2) endif: z = z^s +P1, |z| <=real(P3) } Heartx { ; Stript version of hearty. params=1/0/4/0/ident ; Public domain. s=z=fn1(real(-1/pixel) +flip(imag(-.5/pixel))): z=s*(z-P2)*(P2-z) |z| <= real(P1) } Rock { ; Formula for Diamond. z=z-z, c=fn1(pixel), iter=-1: iter=iter+1, if(iter>-1 && iter< 14 ) note= 11 elseif(iter> 13 && iter< 36 ) note= 13 elseif(iter> 35 && iter< 42 ) note= 17 elseif(iter> 41 && iter< 52 ) note= 19 elseif(iter> 51 && iter< 66 ) note= 16 elseif(iter> 65 && iter< 80 ) note= 23 elseif(iter> 79 && iter< 102 ) note= 31 elseif(iter> 101 && iter< 108 ) note= 29 elseif(iter> 107 && iter< 118 ) note= 23 elseif(iter> 117 && iter< 132 ) note= 31 elseif(iter> 131 && iter< 146 ) note= 11 elseif(iter> 145 && iter< 168 ) note= 10 elseif(iter> 167 && iter< 174 ) note= 13 elseif(iter> 173 && iter< 184 ) note= 17 elseif(iter> 183 && iter< 198 ) note= 13 elseif(iter> 197 && iter< 212 ) note= 29 elseif(iter> 211 && iter< 234 ) note= 51 elseif(iter> 233 && iter< 240 ) note= 59 elseif(iter> 239 && iter< 254 ) note= 44 elseif(iter>= 254 ) iter=-1 endif, note=note* 19 / 460 z=(z+note)*(z-note)*(z+flip(note))*(z-flip(note))/c |z| <= real(P1) } Hearty { ; Might be worth compiling as overlay. s=z=fn1(real(-1/pixel) +flip(imag(-.5/pixel))), iter=-1: iter=iter+1, if(iter>-1 && iter< 7 ) note= 11 elseif(iter> 6 && iter< 18 ) note= 13 elseif(iter> 17 && iter< 21 ) note= 17 elseif(iter> 20 && iter< 26 ) note= 19 elseif(iter> 25 && iter< 33 ) note= 16 elseif(iter> 32 && iter< 40 ) note= 23 elseif(iter> 39 && iter< 51 ) note= 31 elseif(iter> 50 && iter< 54 ) note= 29 elseif(iter> 53 && iter< 59 ) note= 23 elseif(iter> 58 && iter< 66 ) note= 31 elseif(iter> 65 && iter< 73 ) note= 11 elseif(iter> 72 && iter< 84 ) note= 10 elseif(iter> 83 && iter< 87 ) note= 13 elseif(iter> 86 && iter< 92 ) note= 17 elseif(iter> 91 && iter< 99 ) note= 13 elseif(iter> 98 && iter< 106 ) note= 29 elseif(iter> 105 && iter< 117 ) note= 51 elseif(iter> 116 && iter< 120 ) note= 59 elseif(iter> 119 && iter< 127 ) note= 44 elseif(iter>= 127 ) iter = -1 endif, note=flip(note* 19 / 460 ) z=s*(z-note)*(note-z) |z| <= real(P1) } Tool { z = z-z, iter=-1, c=fn2(fn1(pixel)): iter=iter+1, if(iter>-1 && iter< 3 ) note= 47 elseif(iter> 2 && iter< 5 ) note= 23 elseif(iter> 4 && iter< 16 ) note= 37 elseif(iter> 15 && iter< 21 ) note= 29 elseif(iter> 20 && iter< 24 ) note= 31 elseif(iter> 23 && iter< 26 ) note= 29 elseif(iter> 25 && iter< 37 ) note= 31 elseif(iter> 36 && iter< 42 ) note= 23 elseif(iter> 41 && iter< 45 ) note= 31 elseif(iter> 44 && iter< 47 ) note= 29 elseif(iter> 46 && iter< 58 ) note= 41 elseif(iter> 57 && iter< 63 ) note= 47 elseif(iter> 62 && iter< 66 ) note= 43 elseif(iter> 65 && iter< 68 ) note= 47 elseif(iter> 67 && iter< 79 ) note= 23 elseif(iter> 78 && iter< 84 ) note= 31 elseif(iter>= 84 ) iter=-1 endif, z = z^(note/ 33.875) +c z = z*z z = z*z +c |z| <= imag(P1) } DiamondH { ; ~14s/megapixel. Use the absolute negative of ; this to mask off the border of DiamondV. reset=2003 type=formula formulafile=cards.par formulaname=rock function=ident center-mag=0/0/0.0583274/1.3374 params=16/0 float=y maxiter=255 invert=1.32/0/0 symmetry=xyaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5 colors=zzz000<4>000zV0<3>zzz<3>0Wz0z00zz00zz0z00z<3>mmzzzzzzuppzzzkeez\ zz`WWzzzRLLzzzGBBzzz000zpzA<3>Bzo0zz00zz00BAzzBCMKzzMPYVzzY`hdzzhmtnzz\ tz000uzu000<4>000<3>0009z900z0zzzz0hzhzzzz000z0z666z6zCCCzCzIIIzIzOOPz\ PzUzVzVz__`z`zeegzgzkkmzmzqq000000zzz<4>zIzz9zz0z000<26>000<4>000z8000\ 0<69>000<4>0000wzzV000zzz0z0z0z0z000wzzV000zzz0z0z0z0z000wzzV000zzz0z0\ z0z0z000wzzV000zzz0z0z0z0z000wzzV000zzz0z0z0z0z000wzzV000zzz0z0z0z0z00\ 0z0 video=SF5 savename=diamondh } DiamondV { ; Use this after above modification to drop ; luminance of DiamondH. Raise luminance through ; negative of this. ~35s/megapixel@350Mhz ; Map Needed for other parameters. reset=2003 type=formula formulafile=cards.par formulaname=rock function=ident center-mag=0/0/0.0583274/1.3374 params=16/0 float=y maxiter=255 outside=atan invert=1.32/0/0 symmetry=xyaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5 colors=(a)grayhack.map } DiamondS { ; fmod view for mask on negation, maybe. ; ~30s/megapixel. reset=2003 type=formula formulafile=cards.par formulaname=rock function=ident center-mag=0/0/0.0583274/1.3374 params=16/0 float=y maxiter=255 inside=0 proximity=1 outside=fmod logmap=old invert=1.32/0/0 symmetry=xyaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5 colors=000<151>wwwxxxxxx<3>zzz000<95>000 } ClubsH { ; Sorting off. Start with DiamondH. ; ~1m/megapixel. reset=2003 type=formula formulafile=cards.par formulaname=pixelpower function=sin/sqrt center-mag=1.42995/0/0.1520244/1.4243/90/3.88578058618804789e-016 params=0/0/0/0/0/0 float=y maxiter=1024 inside=0 invert=1.45742001678948/1.33/0 symmetry=xaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5 colors=000z00z10z40z70zB0zG0zK0<3>zf0zl0zs0zz0zz0<9>Oz0Kz0Gz0<3>0z0<9>\ 0zb0zf0zj<3>0zz<9>0Oz0Kz0Gz<3>00z<191>z0z } ClubsV { ; ~1.5m/megapixel @ 350Mhz. reset=2003 type=formula formulafile=cards.par formulaname=pixelpower function=sin/sqrt center-mag=1.42995/0/0.1520244/1.4243/90/3.88578058618804789e-016 params=0/0/0/0/0/0 float=y maxiter=1024 inside=0 outside=atan invert=1.45742001678948/1.33/0 symmetry=xaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5 colors=(a)grayhack.map } heartH { ; Chrominance: Alter through masks. ; ~2m/megapixel@350Mhz. reset=2003 type=formula formulafile=cards.par formulaname=hearty function=atanh center-mag=0/-1.1811/0.347/1.18 params=37/0 float=y maxiter=255 inside=0 symmetry=yaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5; colors=(a)preemoh.map colors=zzzz00zz00z00zV0zz0Wz00z<3>z0zz0Wz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz\ 00zV0zz0z<3>z0Lz0Bz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00z<3>e0zo0zz0zz0Wz00<\ 3>ze0zo0zz0<3>0z00zV0zz<3>0Lz0Bz00z<3>z0z<3>z0Lz0Bz00<3>zV0zb0zj0zr0zz\ 0<3>0z00zV0zz<3>00zV0zz0z<3>z00<7>z_0zc0zh0<3>zz0<3>0z0<3>0ze0zo0zz0Wz\ 00z<3>P0zV0z`0z<3>z0zz0Wz00<3>ze0zo0zz0<3>Lz0Bz00z0<3>0zz<3>0Lz0Bz00z<\ 3>e0zo0zz0zz0Wz00<3>zP0zV0z`0<3>zz0Wz00z0<3>0zz0Wz00z<5>V0z_0ze0z<3>z0\ z<5>z0Wz0Rz0L<3>z00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00zV0zz0z<3>z0az0Wz0Q<3>\ z00<3>zzz } heartV { ; Drop luminance through this "graymask". ; ~3.5m/megapixel@350Mhz. reset=2003 type=formula formulafile=cards.par formulaname=hearty function=atanh center-mag=0/-1.1811/0.347/1.18 params=37/0 float=y maxiter=255 inside=0 outside=atan symmetry=yaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5; colors=(a)grayhack.map } heartS { ; Mask on negation. Last. Raise contrast. ; ~3.5m/megapixel@350Mhz. reset=2003 type=formula formulafile=cards.par formulaname=hearty function=atanh center-mag=0/-1.1811/0.347/1.18 params=37/0 float=y maxiter=255 inside=0 proximity=1 outside=fmod symmetry=yaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5; colors=(a)grayhack.map } Spades_Crude { ; If I do say so, myself. 8-) ; 23.62s/megapixel@350Mhz. reset=2003 type=manzpower center-mag=-0.9616/0/1/1.19/-90/3.88578058618804789e-016 params=0/0/4/0 float=y maxiter=255 inside=0 proximity=4 outside=fmod invert=0.47/-0.47/0 symmetry=xaxis colors=(a)grayhack.map } Spades { ; 4by5 is 2400*1575 for 8"*5.25" @ 300dpi. ; Same colours as HeartH with first colour black. ; ~50s/megapixel@350Mhz. reset=2003 type=formula formulafile=cards.par formulaname=tool function=flip/recip center-mag=0/0.541224/0.1891708/1.97 params=2/4 float=y maxiter=255 inside=0 symmetry=yaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5 viewwindows=0/0/no/600/315 colors=(a)preemoh.map } SpadesVV { ; Disk-video modes only work with passes=1. ; grayhack.map=-altern.map with first colour set to black. ; ~1m/megapixel@350Mhz. I deleted my true graymaps, ; because it's usually an error for me to use them, ; and they're easy to jenerate, approximately. reset=2003 type=formula formulafile=cards.par formulaname=tool function=flip/recip center-mag=0/0.541224/0.1891708/1.97 params=2/4 float=y maxiter=255 inside=0 outside=atan symmetry=yaxis periodicity=0 viewwindows=0/0/no/600/315 video=SF5 viewwindows=0/0/no/600/315; colors=(a)grayhack.map }

2 2

FOTD 02-04-04 (Helios [7])
by Jim Muth 02 Apr '04

02 Apr '04

FOTD -- April 02, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a view of a sub-midget that lies in the 'East Valley' area of a larger midget situated near the main bay of the Z^(1.55)+C Mandeloid. I put the words east valley in quotes because the valley might or might not be an actual East Valley. I consider it an east valley because it appears to be connected to the main body of the parent fractal by a broken series of elements. The thing that appears in today's image is a close-up of the center of one of these disconnected elements. When I saw the completed image, I was immediately reminded of a strange alien sun bursting through storm clouds. The name "Helios" quickly came to mind. I rated the image at a 7 because it is rather striking when viewed for the first time. When the render time of 9-1/3 minutes is figured in, the overall value rates a 75. To see the alien sun, run the included parameter file, or let Paul do the work, and download the image from his FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The rain fell steadily all day Thursday here at Fractal Central, with a temperature than never made it above 46F 8C. The dynamic fractal cats were most dis-satisfied with the conditions, and let their frustration be known by getting into a fight. The fight started when Thomas tried to take the spot on the couch that Tippy had already settled in. Thomas received a scratched head; Tippy got a nick on his ear. When they made up, I treated them to some tuna, and they ended the day peacefully. Today is starting cloudy and quite cool, with occasional light rain showers. Hopefully, the duo will get through the day without fighting. My work is reasonably light, but even this small amount of work will never be finished unless it is started. Until next fractal, take care, and watch out for alien fractals invading from outer space. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Helios { ; time=0:09:18.09--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.7\ 9192732503137/-0.10521279334263/1625891/1/-82.5/-1\ .3239373070073e-009 params=1.55/0/0/0 float=y maxiter=2500 inside=0 logmap=263 periodicity=10 colors=000O0AO0AP0AP0AQ0AQ0AR0AR0AS2AS4AT6AT8AUAAU\ AAVAAVAAWAAX8AY6AZ4A_2A`0Ab0Ad0Af0Ah0Aj0Az0zzbevzG\ rzJpzLlzNjuPgoTeiVcdX_ZZYTbUNdSHeQCg_HeiNdpRbzXbz`\ `zeZziZneeFbmH`oJZoJXoLVoLToMToORqOPqQNqQLqSJqSJqc\ PdlTTvXHzbPzgXzXXzNX5PzMHzjCzz4zz0zz0zz0zz0zz0zz0z\ z0zv0zr0zl0zg0zc0zg0zj0zn0ur0ov0iz2dz6ZzATzENzHHzL\ CzP6zT0zX0z`0zd0ze0zg0zk0zm0zo0zs0zu0zv0zz0zz0zz0z\ z0zz0zz0zz0zz0xz0tz0rv0ns0jo2ik4ee6ab8YZ8WVASRCONE\ MJESRHWXLabNegRimTnsXrxZvzbzzdzzgzzipzzjzzezz_uzUq\ zQmzLgzFdz9`z5Vz5Rz5Nz5Hz5Ez5Az58zQ8zn8zz8xz8vz6uz\ 4sz2sz0qz0qz0oz0mz0mz0kv0gz0sz0i_0eY0dY2bY6ZWCXYGV\ SJTMNPHRNBXL5`H5eG5uE5uC5sH5qN5qR5eX5eb5de5dk5bq5`\ u5`z5Zz5Zz5Xz5XzM0xzkLzT8tzPWze9zuFzsJzsOzsSzqWzqa\ zqezojzonzorzmxzmzzmzzkzzkzzkxzTgzASz0az0jz0tz0zz2\ zz4zz6zz8zzGWzLQzELz6Hz0Bz05z05z05z05z05z27zC7zJ9z\ R9z`_zb_zeaziazmazqOz0Mz4 } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 01-04-04 (Historical Midget [7])
by Jim Muth 01 Apr '04

01 Apr '04

FOTD -- April 01, 2004 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image reminds me of an extinct prehistoric creature crawling on the floor of some ancient sea. On the surface, the image shows no signs that it might hold minibrots, but in the world of fractals, things often are not as they first appear. Look closely at the northeast extremity of yesterday's image, and two tiny tails will be found that appear different from the rest of the figure. Such 'different' areas are places where the more interesting and unusual midgets are most likely to be found. When one of the 'tails' is enlarged to fill the screen, places with two-way symmetry that lie in it become visible. Two-way symmetry often means that a midget is lurking invisibly at the center of symmetry. Today's scene lies in one of the tiny tails of yesterday's image. The overall character of the feature that appeared in yester- day's image is quite well reflected in the pattern surrounding the midget at the center of today's image. The eight straight bars immediately surrounding the midget are filled with far more detail than is visible in today's view. They are well worth a closer look, if over two hours is not too long a time to wait for that closer image to finish. I named today's image "Historical Midget" because it is located in a larger image named "Pre-Historical". I rated the image at a 7. The frustratingly slow render time holds the overall value to a similar 7. This slow render time may be avoided however by downloading the completed GIF image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I sent the image to Paul separately, so it should be posted as soon as this letter appears on the site. Heavy clouds, cool temperatures and light rain kept the dynamic duo indoors most all day Wednesday. They checked the outdoors once during the afternoon, but the rain wet their whiskers and the temperature of 48F 9C chilled their ears, and they were back inside in less than 5 minutes. A treat of tuna was definitely needed to restore their spirits. Today is starting with heavier rain; I assume the duo will have another frustrating day. For me it's work then play. Until tomorrow's FOTD, take care, and once you catch that runaway fractal, what will you do with it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Historical_Midget { ; time=1:37:32.90--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-5.05379463172109000/-0.034860595256326\ 77/1.699752e+010/1/30/0.000271903463149959779 params=1.03/1.6/0.0001/100/0.1/0 float=y maxiter=12000 inside=0 logmap=2026 periodicity=10 colors=000IILJKNKMPLOQMQVNS_OUdPWiQYnR_sS`wTaxUbyV\ czWdzXezSfzNgzIhzEjzGgzIewJbrL_mNWkOTiQRgSNeTJcVGa\ XD_YAYXBWWCUVDSVDQUEOTFMSGKSGIUFGWEEXGC_IAaKAcMBdO\ DfQEhSGkUIoWJrYLu_NxaOzcQzeRzdQzcQxbPu_PrWOpUOmVNk\ ZNjcMigMhkLhoLflJdiIbgH`dFZaEX_DVXBTUASS9M_6Gf3Am0\ Ck3Ei5Fg8HeAIcDKaFL_INYKOWNQUPRSSTQUUOXWMZXK`YJbZJ\ dZJe_Jg`Ih`IjaIkaImbHncHpcHqdHsdHtbLu`OuZRvXVvWYvU\ `wSdwQgxPjxNnxLqyJtyIwy6ivA`cDSLFUMHWMJYNLZNM`NObO\ QcOSeOUgPViPXjPZlQ`nQaoQcjNefKgbIiZFkVDmRAoN7qJ5sF\ 2tB0uHBvMLvRWwWew`oXQnURkSRiPSgNSdKSbIT`FTYDUWAUU8\ UR5VP3VN1VL6YOA_RFaTJcWNfYSh`Wjb_lednhhqjlsmquozzz\ zzzoswenzdkvchrbfobckaah`Zd_W`_UYZRUYPRXMNXJJWHGVE\ CVC9TGBRKCQODOSENWFL_GJcIIgJGkKmoLmsMmwNmuLmtKmsJm\ uImwHmxGfz_MzKNzKOzKPzKNzMLzPJzRIzTGzVEzXCz_Aza8zc\ 6ze5zgAzhFzhJzhOziTziXziazjfzjjzjizghzegzcfzaezZdz\ XczVczTbzQazO`zM_zKZzHYzF } 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==================================

1 0

FOTD 31-03-04 (Pre-History [6])
by Jim Muth 31 Mar '04

31 Mar '04

FOTD -- March 31, 2004 (Rating 6) Fractal visionaries and enthusiasts: For today's FOTD I depart from my usual unending stream of midgets and present one of the many other objects that exist in the world of fractals. The object I chose resembles something that might be found crawling along the floor of some pre-historic sea. It might be a trilobite, it might be something entirely unknown, but whatever it is, it has been extinct for many millions of years. I named the picture "Pre-History" in recognition of something that came and went so long ago. Today's image is part of the fractal that results when the Z of yesterday's formula is changed to Z^(1.6), and the other parameters are kept the same. At first glance it appears as though no midgets lie hidden in its depths, but the midgets are there, and one of them will appear as tomorrow's FOTD. The rating of 6 combines with the render time of 34 minutes to give an overall value of 18. The rendering may be avoided by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Unusually chilly temperatures and heavy clouds here at Fractal Central on Tuesday limited the fractal cats' outdoor time to less than 1/2 hour. Considering that the temperature never rose above 45F 7C, their moods were quite good. Today is starting similarly unpleasant. I expect a similar reaction from the duo. It's now time to put the day's tasks behind me, so until next time, take care, and which way did that fractal go? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Pre-History { ; time=0:33:58.94--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-5.05380875308290200/-0.034858178076994\ 84/76981.01/1/30/-8.37821326205023809e-010 params=1.03/1.6/0.0001/100/0.1/0 float=y maxiter=18000 inside=255 logmap=676 periodicity=10 colors=000ONpNNpMNqLNqLNqJRpHVoFZnFamKelPikUljZpic\ thhwhmtehqbcn_ZkYUhVPeSKbQF_NAXK8UH9RF9OCAL9AJ7BMC\ BOHCRLCTQDWVDYZD_cEbhEdlFgqFivFjzGjwHivHhuIgsIfqJe\ pJdnKdlKckLbiLagM`fM_dNZbNYaOY_OXYPWXPVVQUTQTSRSQR\ SPPTROTTNTUMTWLTYJTZIT`HTaGTcFTeETfCThBTiATk9Tm8Tn\ 7Tp5Tq4Ts3Tu2Tv1Tx0TyAUwJUuSUs`VqiVorVmiWe`WZSXSJX\ LBXEBWNBVWBVdBUmBUvD7AC68B66G75L84P94UA3YB3bC2fD2k\ E1oE1kH4gK6dN8`PAYSCUVERYGN_IKbKGeMDgO9xOEuVJs`Npf\ SnmXks`iy_do__fZVXZQOZLFWIJTGMRDQOBTL8XJ6_G3cE1fK4\ gP6hV9i_BjeEkjGlpJmuLmqNjmPhiRfeTcaUaYW_UYXQ_VN`TL\ YSKVRJTQHQPGOOFLNDIMCGLBDK9BJ88I76HADGCKFFREHYDKdC\ MkBPrARx9SvEStJSsOSqTSoXSnaSlfSjkSioMdgG__BWT5RL0N\ E1PG2RI3TK4VM5XNGUTRSZ`QdkOjuMptOjtPetQ`uRbvScw8ex\ UfyVhzWizXkzYlzZnz_oz`pzalzbhzcdzd`zeXzfTzgPzhLziH\ zjDzk9zl6zmPznfzoxzpvzquzrtzssztrzuqzvpzwozxmzylzz\ kzzjzzizzhzzmzznzznzzozzo } 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==================================

1 0

FOTD 30-03-04 (Congregation [7])
by Jim Muth 30 Mar '04

30 Mar '04

FOTD -- March 30, 2004 (Rating 8) Fractal visionaries and enthusiasts: To create the parent fractal of today's image, I took Z and added to it a very insignificant 0.0001 part of Z^100. When the tiny bit of Z^100 turned out to be not so insignificant, I added 0.03 parts more Z to the mixture on a whim. To complete the mixture, I multiplied the entire thing by 1.1 by setting real(p3) to 0.1. (I could have done the same thing by changing real(p1) to 1.133, real(p2) to 0.00011, while leaving real(p3) at zero.) I then began my exploration. With these parameters, all the action lies beyond the west border of the default screen, but can easily be found with one outzoom. I'll not try to describe what lies there, but it does have a tiny East Valley populated by elephants that remind me of the 'Flattop' character of the Dick Tracy comic strip. Today's scene lies on the southern shore of that valley, in the trunk of one of the flat-topped elephants. There are so many interesting things in today's image that, when I studied it, searching for a name, it reminded me of a congrega- tion of fractal features. I named the image "Congregation" accordingly. The rating of an 8 might be a bit overblown, but, with its plethora of detail, the image is definitely above average. The overall value is held down to a 26 by the 1/2-hour render time, but the image is still worth the time spent. And as always, those who would rather not spend time rendering images may see the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With more sun than expected and a temperature of 48F 9C, Monday turned out to be a better day than had been forecast by the experts. The fractal cats, who don't listen to weather reports, were never concerned, and had a quite pleasant afternoon in the yard. Thomas even worked up enough energy to bat around a few dried-out magnolia leaves. In the evening, the duo retired without asking for tuna. Today is starting cloudy and cold. We'll see what happens with the duo. For me, it appears today will be un-notable. But I'll try to find a fractal worthy of at least some note. My success (or lack thereof) will appear in tomorrow's FOTD. Until then, take care, and don't go along with the non-fractal crowd. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Congregation { ; time=0:30:23.81--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-7.39578216954515400/-0.236832685099223\ 50/2.07789e+008/1/97.5001386452413072/-0.000193294\ 786338664426 params=1.03/1/0.0001/100/0.1/0 float=y maxiter=9000 inside=0 logmap=572 periodicity=10 colors=0004M24N23P23Q22R22S21T21U20V20W25Y8A_DFaIK\ cNOeTTgYYibbkgfmlhonipojqqlrrmssntupuvqvxrwysxzqly\ paxoRwnGvmJsmMpmOmmRjlTglWelYbl`_kcXkeUkhSkjPjmMjo\ JjrGjtEZmLOgRCaY1Wc3Xe4Yf5Zg6_i7`j8ak9bmBcnCdoDeqE\ frFgsGhuHivIjwJgsJepJbmJ`jJZgJWdJUaKRYKPVKNSKKPKIM\ KFJKDGKBDJFHJILJMPJPTJTXJW`I_cIbgIfkIioImsIpwIszPn\ vWjrbfnibjpZgodbniYmoTmtPluSkvUkwWjxYiy_izafnVdbOb\ RH`FAUQJN`SGk`AvhGsbMpYSmTYjNcfIicDo`8la7i`6f`6c_5\ `_5Y_4Va4Sc3Re3Ug4Xi4_k4bm4eo4hq5ks5nu5qw5ty5wzNzz\ dzzuzzzzzzzzzzzzwvutrmomeehYWcQWeIWgASi7Ut7Zw7cu8h\ t9msArrBzqCzpDroEmmFclGUkHKjI9iJ8zK8gL7eQ7cV6aZ6_c\ 5Yh5Wl4Uq4Tu6Xq7_n8bj9egBhcCk`DnXEqUFtRTbbeLnr4yp9\ snEnlJikOdiS_gXVfaQdfLbkGaoBmm_xkxslwnmvimvdnu_otV\ otQpsLpsKqmJqhIrcHrZGsUFsPEtKDtFCuACu5Gv6Kw7Ox8Sy9\ Vz9ZzAbzBfzCizCmzDqzEuzFxzFuzDszCqzBozAmz9kz8hz7fz\ 6dz5bz4`z3Zz2Xz16z25z25z2 } 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==================================

1 0

viewwindows=0/0/no/1024/1024 and batch mode.
by SherLok Merfy 30 Mar '04

30 Mar '04

That the above command works fine is a highlight for what Mister Osuch might want to leave alone in the code. The bug he might want to feed or cultivate in the code won't be very friendly if he tries to fix what works (which is always multiples of i, but that bug works fine). Finagle's Third Law: In any collection of data, the figure most obviously correct, beyond all need of checking, is the mistake. No mathematic reason is to prefer a power of two over the metric definition of _megapixel_ other than matters of convenience and maximal use of the screen. It's also slightly conservativ to accomodate the time for saving it. It's easy to work out that 512 by 512 is a quarter of that. I seem to hav learned too late that I prefer batch mode, but maybe that's because I would hav had to use my brain to come up with 600*525 as an even division of 2400*1575 (that's about the maximum that PSP will handle in truecolor (and this is not for lack of either RAM or virtual memory), so I want to check out The Gimp for Win32s). As to how I might encode the method, I'm not sure it's worth doing. In particular, if a specified dimension is larger than the screen and prime, then I am inevitably left with a window that is a remainder of dividing the specified dimension by the screen's maximum. The relevant calculations would be like y_multiples_output=width/800 . For the size of the bottom screen, I would take the remainder. For the size of the bottom screen in cartesian coordinates I would re-do the calculation, but y_multiples_input would be a float. In case you're missing my point, there should only be two output numbers from the viewwindows screen, and if you feel like trying to kill two birds with one of those stones in the soup, then you could connect that form to the batch creation code. If you felt adventurous, then you could re-write the batch-job creation code to write self-contained batch jobs, where the parameter files and formulas were embedded in a long echo to the console. (Heh. Heh. I should ensure that I can do this by hand, because I recently discovered that copying a concatenation of files to the console won't pipe through more under DOS. I *knew* that a purpose was for ^z in the middle of an ASCII file, but I doubt that I can echo a very long line through the pipe without an extra tool. Perhaps I can do the embedding with a dependency on the filename and formulas that read as comments to batch language). I would do it myself, but what I'm doing works, and English is much more fun than FORTRAN (although I am curious about what sqrt(0,2) is when, to the literal eye, this involves a division by zero), and I still feel like I'm leaving too many things hanging to be picking up a compiler that's probably more powerful than the Borland one that I seem to hav lost (and that probably won't compile for Linux without a major upgrade). _______ No faster way is to get things done than to always giv jobs to the person who looks too busy to handle them. They'll burn out, but it's better to burn out than fade away. Rise up...gather round... --Def Leppard

1 0

Last call message
by Jim Muth 30 Mar '04

30 Mar '04

>Return-Path: <gumbycat(a)allisonart.com> >Reply-To: "gumbycat" <gumbycat(a)allisonart.com> >From: "gumbycat" <gumbycat(a)allisonart.com> >To: <jamth(a)mindspring.com> >References: <1.5.4.16.20040328093309.299fb970(a)pop.mindspring.com> >Subject: Last call message >Date: Mon, 29 Mar 2004 13:11:44 -0500 >X-MSMail-Priority: Normal >X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1165 > >Hi, Jim! > >I still can't post to Fractint - still not sure why. Would you please post >this for me? Thanks, Jim! > >Linda > >***************************** > >This is the last open call for you to submit your fractal artwork for >consideration for inclusion in the Fractal Universe ® Calendar 2006. > >All the information you will need is detailed on the following website: >http://www.fractalforum.com > >Please make your submissions and any additional enquires you may have via >the contact form on the above website. > >This message has been posted to some of the fractal art newsgroups, mailing >lists, and forums. If you think it may be of interest to others please feel >free to forward it, as it is written here, to other 'net sites where fractal >artists meet to share and discuss fractals. > >Thanks and good luck! > >Linda Allison and Tina Oloyede > > >

1 0

FOTD 29-03-04 (The Infinite Mosaic [7])
by Jim Muth 29 Mar '04

29 Mar '04

FOTD -- March 29, 2004 (Rating 7) Fractal visionaries and enthusiasts: To produce today's fractal, I mixed together portions of Z^4 and Z^5 before adding C, and cooked them slowly over a low flame. The resulting dish took almost 1-1/2 hours to finish, but it was worth the wait. I named the finished product "The Infinite Mosaic". With its unusually intense colors, the image does have a kind of mosaic feel about it. And most fractals certainly are infinite. So the name seems justified. The render time is a puzzle. It is hard to say why an image with such routine parameters should take so long to calculate. >From its appearance, I would expect it to finish in something like 10 minutes. I can blame no one who decides to save an hour or so by downloading the completed image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I sent the image file to Paul separately, so it should be posted by the time you read this letter. The extraordinarily brilliant colors raise the rating from a 6 to a 7. But the unusually slow render time lowers the overall value to a humble 8.2. It's still an interesting image however, with its tight mosaic-like spirals and tiny midget hiding almost invisibly at the center. The clouds moved in on Sunday here at F.C., then they moved out, leaving warm sunshine and a temperature of 63F 17C, which was enough to keep the fractal cats happy. The weather experts' forecast for today is again cloudy, but I see lots of sun and blue sky out there. I expect the cats will find this acceptable. For me, the work is in the modicum range, which I should finish in plenty time to find the next FOTD fractal. Until tomorrow, take care, and become one with the fractal universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ TheInfinite_Mosaic { ; time=1:25:01.15--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+2.06994532777612900/+0.379001200947109\ 80/2.290883e+011/1/85.0010974549234959/-0.00072585\ 6327050203309 params=-0.15/4/0.045/5/0/0 float=y maxiter=14400 inside=0 periodicity=10 colors=000zztzzzzzzzzzzzzzzzzzbt_Cr70tA0wA0zC0zC0z\ F0z20zF0zS0ze0zr0wz2mzCbzKSzVKzbNz_NzXzzXzzVNzSNzS\ NzQNzQNzNNzKNzKNzINzINzFNzCNzCNwANr7No7Nm4Ng4Ne2Nb\ 0NX0NV0NS0KQ0KQ0KQ0IQ0IQ0IQ0FQ0FQ2FQ2CQ2CQ2CQ2AQ2A\ Q2AQ27Q47Q47Q44Q44Q44Q42Q42Q42Q70Q70Q70Q70Q70Q70Q7\ 0A20Q7XeCzrFoj7_b0KX02Q00I00C00F00F00I00I00I00K00K\ 40KA0NF0NK0NQ0QV2Q_4Qe7SjASoCStCVzFVzIVzKXzNXzQZzS\ _zV_zV_zQazNezKezIgzCgzAjt7jo4mg0m_0oS0oK0rC0t00r7\ 0rF0qN0pV0ob0oj0or0mw0mz0mz0mz0jz0jz0jz0ez0Zx0Yl0W\ j0Tl0Qm0Hp0Op2Nv4Kw7Ix7FyAAzC7wF4tI2oK0mN0gQ0eS0_V\ 0XZ0S`0Qb0Xe0bj0gm4mrArtFwzKzzQzzVzz_zzkzzozztzzwz\ zzzzzzzzzzuzzpzzizzbzzXzzSzwNztKzoFzjAzg4zb0zX0zV0\ zQ0zI0zN0zS0zV0w_2tb7ogFmjKgoSet__weXzmSzrQzzKzzJz\ zIzzKzwKztNzrNzoQzmQzjQzeSzbSz_VzXVzVVzSXzQXzK_zI_\ zF_zCbwAbw7ew4ew2ez0gz0gz0ez0bw0_t0Xo0Vj4Szo0zo0zr\ 0zt4ztCXwIezNmzVrz_zzgzzm } 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==================================

1 0

FOTD 28-03-04 (Back to Normal [7])
by Jim Muth 28 Mar '04

28 Mar '04

FOTD -- March 28, 2004 (Rating 7) Fractal visionaries and enthusiasts: A wise old man once said that order lies hidden in even the most chaotic disorder, and it is up to the individual seeker to find it. Today we dive through the confusion of the past several days and find the orderly fractal world we know and love so well. There at the center of the image, lies a familiar quadratic midget, surrounded by the pattern quadratic midgets are supposed to be surrounded with. The scene of today's image lies on one of the spiral filaments surrounding yesterday's sixth-order pseudo-midget. The sixth- order stuff as well as the cubic stuff in yesterday's image was all a sham. Those holes were no more sixth-order and cubic midgets than I am. They were simply some of those randomly shaped holes that appear so often in fractals created by combining several powers of Z. But it was a rather convincing illusion, and well worth the trip. Today's image rates a 7 and has an absolute value of 79. I named it "Back to Normal" because it reveals fractal meaning even where none was immediately apparent. Does this hidden meaning have anything to do with everyday life? probably not, but I would not be quite so quick to call the universe a random accident without a purpose other than what mankind gives it. The meaning of life will likely remain forever a mystery, but it is no mystery that the fastest and easiest way to see today's image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the completed GIF image file from there. Despite clouds and early morning rain, Saturday turned out reasonably pleasant here at Fractal Central. The dynamic duo of fractal cats agreed, and then spent several hours in the yard, enjoying the temperature of 68F 20C and watching birds. This morning is starting cooler, with clouds moving in again. We'll see how well the cats adjust. I have little to do for the rest of the day but read, watch TV, and search for fractals. If I want to finish these tasks, I had best get started. Until next FOTD, take care, and may the power of fractals be with you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Back_to_Normal { ; time=0:08:54.86--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.52008286818602610/+0.000772311970516\ 58/3.828469e+010/1/-148.5/0.00431551213243278053 params=1/3/0.3553/4/0/0 float=y maxiter=1300 inside=0 periodicity=10 colors=000T_eTWbTR_SNXSIURERR9OR5LP4KO3KN3KM2KK1JJ\ 1JI0JH0JI5dJAzNExQHvTLuWOsZRraVpdYogamjdlmgjpkisng\ vqflpacoXVnTMzODvJ4sF5nE5lE6jD6hD7fC7dC8bC8`B9ZB9X\ AAVAAVAAV8DY9G_AJbAMcBOdCRfCUgDXiDZjEakFdmFgnGioGj\ pFkqFkrElrElsEmtDnuDnuCovCowCpxBqxBqyArzArzAmwDhtF\ drH_oKVmMRjOMhRHeTDcVNhXXmZfr`pwbntdlrekpfinghlhfi\ iegjcekacl`amZZnYXoWVpVTqTRrSPsLRtFSt8Uu2Vu4Uv6Tv7\ Tv9SvBRvCRvEQvGPvHPvJOvKOvJNwIMwHMwGLxFLxEKxDJyCJy\ BIyBIyDMzFQzHUzJYzK`zJ_wIZuHZrGYpFXmEXkDWiCVfBVdAU\ a9T_9TYGN7FQCESHDUMCWRBYVA__9ad8ci7emAekDeiGegIeeL\ edOebRe`TeZWeXZeWaeUceSfeQieOkeNgcJdaG`_CYZ9XY8XY7\ RK6RK6QK5QK4PK3PK3LKBMqIIzQEwXMrZUm`ahbicdqZfvVgtT\ `qRVmPPjNIfLCcJ6gH0jHAnHKrHUuH_rFbmDbhBabPaZS``T`d\ V_lW_sYOx`Dzc2wb3sa4q_5mZ6hX7`W8WV9STAOSBJQCFPDBOD\ EQEGREJSFLUFOVGQXGTZHV_HX`I_aIacJceJehKhkKinLjpLmp\ Tfo`bth_xpXtmVpkTliUhkUdh } 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==================================

1 0

an application for Sierpinsky triangles :-)
by Michael Weitzel 28 Mar '04

28 Mar '04

Hi, I am working with binary "don't care"-expressions/-numbers. For example, the expression "11xx0" represents a sum of binary coordinates: 11xx0 = 11000 + 11010 + 11100 + 11110 "x" means "don't care if 0 or 1". for all expressions of length 3 ... a Sierpinsky triangle appears xxx = 000 + 001 + 010 + 011 + 100 + 101 + 110 + 111 xx1 = 001 + 011 + 101 + 111 x1x = 010 + 011 + 110 + 111 x11 = 011 + 111 1xx = 100 + 101 + 110 + 111 1x1 = 101 + 111 11x = 110 + 111 111 = 111 now, one reformulate this as a matrix multiplication with a coefficient matrix: |xxx| | 1 1 1 1 1 1 1 1 | |000| |xx1| | 0 1 0 1 0 1 0 1 | |001| |x1x| | 0 0 1 1 0 0 1 1 | |010| |x11| | 0 0 0 1 0 0 0 1 | |011| |1xx| = | 0 0 0 0 1 1 1 1 | * |100| |1x1| | 0 0 0 0 0 1 0 1 | |101| |11x| | 0 0 0 0 0 0 1 1 | |110| |111| | 0 0 0 0 0 0 0 1 | |111| The matrix can (as you probably know) be evaluating the recurrence: | M1(t) M1(t) | | M0(t) M0(t) | M1(t+1) = | | with M0(t+1) = | | | M0(t) M1(t) | | M0(t) M0(t) | for don't-care-expressions of length n this matrix consumes O(2^n*2^n) = O(4^n) units of memory. This memory can be saved if the matrix elements can be queried on the fly without constructing the matrix. So my idea ... * the don't-care expressions of length n xx...x to 11...1 are numbered with i=0,...,2^n-1 * the binary coordinates of length n 00...0 to 11...1 are numbered with j=0,...,2^n-1 to see, if a binary coordinate has to be added to the don't-care sum one has to compare both digit by digit: [1] if don't-care's digit is "x" the binary digit is allowed to have a '0' or '1' [2] if don't-care's digit is "1" the binary digit must be also "1" [3] if checks [1] and [2] pass for all digits of the binary coordinate, is must be added to the don't-care sum. checks [1] and [2] can be summarized in a truth table: dc bc | pass? dc = don't care, bc = binary coord. ------+------ x 0 | 1 (yes) x 1 | 1 (yes) 1 0 | 0 (no) 1 1 | 1 (yes) this means, checks [1] and [2] pass iff dc='x' or dc='1' and bc='1' (short: ~dc|dc&bc). The checks can also be applied to the indices i and j themselves if one thinks 'x' for the '0'-bits in i. The checks can be serialized if one uses C's binary operators: (~i|i&j). If the result consists of n '1'-bits, the matrix contains a '1' in element (i,j); a '0' otherwise. Because it's easier to check whether a number's value is zero and the boolean expression ~(~i|i&j) can be simplified to i&~j: M(i,j) == 1 <=> i&~j == 0 A small C-program that prints the Sierpinsky triangle: #include <stdio.h> int main() { int i,j; for (i=0; i<32; i++) { for (j=0; j<32; j++) putchar((i&~j)?' ':'#'); putchar('\n'); } return 0; } The triangle flips, if you play with the negation symbol "~" before i and j. I had the suspicion I wasn't the first who discovered this ... and indeed I found the formula in a book [[1]] on fractals - discovered by "E.E. Bloch" (1810-1893) - but without mentioning the justification/proof. So if you knew this formula and didn't know why this works ... ;-) [[1]] Peitgen, JÃŒrgens, Saupe: Bausteine des Chaos - Fraktale -- Michael Weitzel ... all work and no play makes Jack a dull boy ...

1 1

FOTD 27-03-04 (Fractal Nonsense [5])
by Jim Muth 27 Mar '04

27 Mar '04

FOTD -- March 27, 2004 (Rating 5) Fractal visionaries and enthusiasts: No, there is no mistake. That actually is a Mandeloid midget of the 6th order displayed in today's image. And the generating formula combines nothing other than Z^3 and Z^4. If this isn't nonsense, I have never seen it. Actually, the nonsense is deeper than what is immediately apparent. Check that large midget toward the northeast corner of the screen, and you will find that it most definitely is of the cubic variety. To make matters even sillier, the midgets located in the nodes of the filaments radiating from the large midget have no established shape whatever. They appear to be randomly shaped. But there is hope. Throughout the image, the deeper we search, the closer the midgets come to the expected quadratic shape, until finally, at a magnitude of around 0.000000001, order is restored and the world has once again become one we feel comfortable in. I'll leave it to the math geniuses to figure exactly what is going on in today's image. If it were explained, I probably would not understand it anyway. So for now, I'll simply call the apparent higher-order midgets in today's image 'pseudo- midgets' and let it go at that. It is this kind of unexpected stuff that keeps my fascination with fractals as strong as it was on the day I discovered them, which as I recall was in 1985. It is the same kind of unexpected stuff that makes modern physics almost as fascinating to me. We live in an intuitive world of sequential time, and three- dimensional space filled with objects. We feel comfortable in our well-ordered world. But the gurus of science tell us that this familiar comfort is built on a foundation of sub-atomic things (if they are things) that exist in a world totally beyond our comprehension. We fill our physics books with pages of abstruse mathematics and announce that we understand it all. But do we? It sometimes seems to me as if the whole sub-atomic world with its carefully contrived math is a human invention. If this is so, then maybe the comfortable 'intuitive' world around us is also a human invention. But we'll not start down that road at this time. Once this journey is begun, there is no turning back, and there are an infinity of fractals right here yet to find. I named today's image "Fractal Nonsense" and rated it at an average 5. When adjusted for the render time of 32 seconds, the overall value comes in at a whopping 918. It will take about as long to prepare this letter to be run as a parameter file as it will to download the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A summer-like day here at Fractal Central on Friday, with warm sun and a temperature of 75F 24C, brought out what little kitten was left in the fractal cats. They actually romped in the yard, chasing each other about like they did so long ago when they were real kittens. When the end of the day came, they were exhausted and ready to settle down for a long rest. This morning is cloudy and light rain is falling. The cats will not have a repeat day. My task now is to do as little work as possible for the rest of the day. This will leave as much time as possible for a trip to fractal land. Unfortunately, with the warm weather comes yard work, so I might not find as much time for fractals as I would like. In any case, the next fractal will appear in 24 hours at this same spot. Until then, take care, and be sensible with nonsense. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Nonsense { ; time=0:00:32.68--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=-0.52300582159624930/0/276.6252 params=1/3/0.3553/4/0/0 float=y maxiter=1000 inside=0 logmap=14 symmetry=xaxis periodicity=10 colors=000SRhNWm_Zek`ZwbSveQvgOvjMvlKiXLYIMM3MEJP6\ YRCYWHY_KKHDID7G91F6AEAIDDQCHZBKfAOn9Rv8UnDVgHV`LV\ UPVNUWGYW9aW2eWBc_KacHRoEHzDJtCKnBMhANb9PX9QSBVWD_\ ZFdbHieJniLslPnkTjkXfj`ajdYihUikQikEPk35QCL5L`GmoN\ lqTlrZksdktOUyJxXKvWLuWMtVNsVOrVT0zX2y`4yd6xg8xkAw\ oCwsEvvFvmNweVxXbxPjyGrz8zzBttDnoFmjHmeOmNKmTHmYEm\ cBmh`mkPmDOmOOgZNiiNksLmuJonIqgHs`GuUFwNEyHCzOAzV9\ z`LzXWzTgzPrzLpzGnzBmz7gzQazhXzzZz1XzPVzkNzWFzHDzG\ CzGBzG5zkvzHszLqzPozTmzXkz`izdgzhaziWzjQzkKzlEzm8z\ m7zj7zg6zd6za5zZ5zX8zVAzTCzREzPGzNIzLKzJrzPNz4TzBZ\ zHczNdzOdzPezQezRezSfzTfzUfzVezVezUdzUczTbzTazSazS\ `zR_zQZzQZzPYzPXzOWzOVzNVzNUzMTzMSzLSzLRzKQzKPzJPz\ JOzIOzIOzIgzYizXkzWCzOLzTTzY`zbizgqzlyzqqznjzkbzhW\ zeOzbHz_AzYNza_zelziyzlxzixzgxzexzcxzaxzZxzXxzVwzT\ wzRwzOwzMwzKwzIwzGwzEszDozClzChzBdzBazAYzAUz9Rz8Nz\ 8Jz7Gz7Cz69z6czUfzSazYXzb } 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==================================

1 0

%$&* view-window
by SherLok Merfy 26 Mar '04

26 Mar '04

Does anybody else write these parameters directly? I was using Version 19.6 to write my parameter files, and I still do for multi-image batch renderings. 19.6 does the other rendering methods in disk-video, but it doesn't go up to 2400*1575 or yield maximal colours with outside=atan like more recent releases. So...I set the view parameters in 19.6 along with the batch parameters, then I move the parameter file and batch files to my new release's directory and change the reset value -- for outside=atan. For this kind of stuff, I usually use SF5 ,VESA Standard interface ,4f02, 100, 0, 0, 28, 640, 400,256,OK: Andy Fu - Chips&Tech mode, because it's close to 600*315 which equals 2400*1575 as a 4 by 5 batch file and the autodetect modes don't work for me any more. Maybe someone should check into external helpfile formats or aggregation with Lynx (the obvious format being HTML), because I got this from a 590+K documentation file that's probably a major reason why I can't shell out of FRACTINT to edit formulas and parameters anymore -- not without a mode change and Norton Editor 4.2, anyway: (...) Patch 10 Took out a sanity check in the VESA detection routines that certain graphics cards don't pass, but work fine anyway. This is probably the first version that would make a mess at the top of the screen on my Mach 64 with the autodetect modes, which I don't use in V.2003. Perhaps the result of the test should be displayed before you ask someone to ignore it. In my case, I uncommented the modes I wanted in FRACTINT.CFG and put them in place of the messy autodetect modes. I hope that's the only reason why FRACTINT doesn't like the defaults (F4) I get from the view-window form. (...) Added inside=fmod and inside=atan. The inside=atan option should only be used with periodicity=0. Now you tell me. I'm not sure why, though. Negative periodicities are better than inside=period when you get to set the threshold, too. As far as OUTside=atan, I wonder why it seems to require 255 iterations to get that many colours. (...) During an image save to disk, the 's' key is now ignored. While you're at it, you could ignore the mouse. And...it's hard to avoid noticing that the status screen is more informative than the disk-video screen -- which is where I learned that batch-mode doesn't want you doing anything but watching.

1 0

Re: Quadratic midget? Is this one?
by Jim Muth 26 Mar '04

26 Mar '04

On Fri., March 26, 2004 Hiram Berry wrote: >Okay, Jim. But what does the "quadratic" part of "quadratic >midget" mean? By a quadratic midget, I mean any midget shaped like a miniature classic Mandelbrot set, which is created by the quadratic formula Z^2+C. In quadratic midgets the surrounding elements split in two as they approach the midget. When I mention cubic midgets, I refer to midgets with two main lobes, shaped like the Z^3+C Mandeloid. In these midgets, the elements triple in number at every split. The midget drawn by your parameter file is of the sixth order, (Is this order called hexic?), with five main lobes and elements that split into six smaller versions at every split. Jim M.

1 0

FOTD 26-03-04 (What is it? [4])
by Jim Muth 26 Mar '04

26 Mar '04

FOTD -- March 26, 2004 (Rating 4) Fractal visionaries and enthusiasts: In today's image, things get stranger yet. Now, the midget itself has been infected by whatever is happening in this part of the fractal world. What we have in the image is a quadratic midget that has begun to morph into a midget of the sixth order. The five lobes of sixth-order midgets are already taking shape. The smaller satellite midgets however still retain the familiar Mandelbrot outline. Check the westernmost extremity of the large midget, on the X-axis where the stem branches out. You will find a perfect Mandelbrot bud there. Then check the smaller outlying midgets. Some of these are irregular holes with a decidedly non-critical appearance, but others are perfect mini-Mandelbrot sets. Finally, notice the 6,36,216... series of elements leading to the central midget -- a sure sign of an emerging sixth-order midget. What's happening here is crazy enough, but we have not yet seen the worst of it. Stay tuned over the next few days for even stranger fractal wonders. Since today's image has only limited artistic worth, I have rated it at a 4, which is a little below average, but not low enough to make the 1-1/4 minute render time too much to ask. Thanks to the short render time, the overall value registers an impressive 323. Perhaps the fastest way to see the image is to download it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Fine early spring weather on Thursday made the fractal cats happy. The warm sun and temperature of 68F 20C was just what the duo was waiting for. They spent the entire afternoon in the yard, doing what old-age cats do best -- sleeping. When they came inside, the treat of tuna completed their day. This morning is starting even warmer. Another good day seems to be coming. I have several hours work to accomplish, then it's back to the fractal screen. Until next FOTD, take care, and who knows what is possible in the world of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ What_is_it { ; time=0:01:14.37--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.509759593836255/0/351.2859/1/180 params=1/3/0.355/4/0/0 float=y maxiter=900 inside=0 logmap=15 symmetry=xaxis periodicity=10 colors=000LB9L96L84OC6RF7UI9XLA_OBbRDeUEhYFk`HncIq\ fJtiLwlMzoNymKylIykGyjEyiCwgFvfIudLtcOsaQr`TqZWpYZ\ oWanVclYdj_dhadfcddedbgdaid_ldYndWpdUrdStdQvdPxdOw\ cNvcMubLubKtbJsaIraHr`Gq`Fr`Es_Dt_CuZBvZAwZAxbAyfA\ ziAzmAzqAzuAzxlztgzpczlbziczcdzYezSfzNgzQhzSizVjzX\ kz_lzamzdnzfozipzkqznrzpszltziuzfvzcwz`xzYyzUzz2zz\ FzzRzzbzzczzdzzezzfzzgzzhzzizzjzzkzzlzzmzzmzzlzziz\ zfzzczz`zzXzzUzzRzzOzzLzzIzzFzzCzz9zzAzzBzzBzzCzzC\ zzDzzEzzEzzFzzFzzGzzHzzHzzIzzIzzNzzSzzXzzazzVzzOzz\ HzzPzzWzzbzzjzzqzzxzzuzzrzzozzlzzjzzgzzdzzazzZzzXz\ zUzzRzzOzzMzzOzzPzzQzzRzzPzzNzzLzzJzzHzzFzzEzzCzzB\ zzAzz9zz7zz6zz5zz4zz3zz6zz8zzAzzCzzFzzHzzJzzLzzNzz\ QzzTzzWzzZzzazzczzfzzizzlzzozzqzzdzzSzzFzz3zz6zz8z\ zBzzDzzFzzIzzKzzMzzPzzRzzTzzXzz_zzbzzezzhzzkzzhzze\ zzbzz`zzVzzQzzUzzXzz_zzczzfzzizzmzzpzzszzozzkzzgzz\ dzz`zzXzzOzzLzzJzzGzzEzzB } 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==================================

1 0

FOTD 25-03-04 (Somber Snowflake [6])
by Jim Muth 26 Mar '04

26 Mar '04

FOTD -- March 25, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal pictures a quadratic midget. There is nothing unusual in having a quadratic midget at the center of the screen. Most of my images have them. But this midget is strange indeed. By their nature, quadratic midgets are surrounded by symmetrically spaced elements that continually split in two as they approach the midget. The first indicator of a midget is the presence of two symmetrical elements that split into four similar but smaller elements. This splitting continues in the series 2,4,8,16,32... as the elements approach the midget. We now can see what is wrong with today's midget, which I have named "Somber Snowflake". I gave the image this name because the pattern surrounding the midget is shaped quite like a dark snowflake with a green aura. But snowflakes have six sides, and the number 6 is not part of the 2,4,8,16... series. Something has gone wrong. Some other series has infected the quadratic series, and this infection will become only worse as the exploration of the Z^3+x(Z^4) fractals continues in the days to come. Though it is on the dreary side, today's image rates a 6, which is just a little above average. The render time is a speedy 2-1/2 minutes, which results in an overall value of 233. The pre-rendered GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With sun and a temperature of 61F 16C, Wednesday was a rather pleasant day here at Fractal Central. Thomas, the oversized orange, spent several hours in the yard. Tippy, the lean wiry tabby, passed the day sleeping on his window shelf. Since 14-year-old cats do little but sleep, it was hard to tell if Tippy did not feel good. In the evening all appeared well when the tuna treat vanished as it should. This morning is starting with clearing skies and warmer temperatures. I expect a good day for the duo. As for me, being not quite as old on the human scale as the cats are on the cat scale, I still enjoy an occasional bit of the unusual, but it appears it will be another in a seemingly unending stream of normal days, with the exception of a new fractal at the end. Until tomorrow, take care, and fractals are never boring. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Somber_Snowflake { ; time=0:02:34.39--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.54195976260355410/+0.002250716455883\ 61/127978.5/1/-52/1.42828571886299827e-009 params=1/3/0.357/4/0/0 float=y maxiter=1000 inside=0 logmap=37 periodicity=10 colors=000NMfONgPOhQPiRQjSRkTSlSTmRUnRVmQWlPYkP_j`\ kf_mcZr`YvXWyUUzRTyOQtQNoSLjTIeVG`WCXT9TR6PP3LN0IL\ SXIrjFg_GYPHOEIE3JD9ICEHBJHBPGAUG9ZF9cFH`COZAVX7aU\ 5hS2oQ0lV6iZCfbIcfOajUenVjqXnuZrx_pubnrdlofjlhhijf\ fldcnb`p`Yr_UoZRmYNjXKhWHfVDcUAaU7_W9`YAa_BbaCcbDd\ dEefFfhHgjIhkJimKjoLkqMlsNmtOnpMhmKbjIYgHSdFMaDHZB\ BWA6YD5ZF5_H5`J5aM4cO4dQ4eS4fV3gX3iZ3j`3kc2le2mg2n\ i2jk9fmFboMZqSVsZRudX2hR3fM3eG3dB3cJA_QHXXOTdVQkaM\ rhJynGvqNttTrwZpudamfOcgQcbRcZScVTcRRcQQePPgOOiOMk\ NLmMKoLJqLcsJYuLSvNMwPHxREyRBzR8zR5zRlzujzmizfhz_f\ zTezMdzFcz8azD_zIYzMWzRUzWSz_Yzebzkgzqlzwszvyzvwzk\ uzaszSrzIjzUczegzfjzgmzgpzhszhgziWzjKzjUzkczlmzmvz\ mpzfkz`fzUazOXzHSzBNz5IzQEzjDzjDzjDzjDzjDzjIziNzgS\ zfXzeazdazeazfazgazgazhaziazjazjazkazlazl`zp_zsZzv\ YzyXztXzoXzkXzfXzaXzYXzTXzOXzKVzIUzHTzGSzFQzDPzCOz\ BNzALz8Kz7Jz6Iz5Hz4Iz9JzD } 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==================================

2 1

FOTD 24-03-04 (X-Y Mandel Fractal [5])
by Jim Muth 24 Mar '04

24 Mar '04

FOTD -- March 24, 2004 (Rating 5) Fractal visionaries and enthusiasts: In today's image things start to go wrong. The midget at the center is clearly of the quadratic variety, as are almost all midgets in fractals created by the MandelbrotMix* series of formulae. But the expected 2-4-8-16... series of elements leading toward the midget is not as well defined as it might be. The confusion is just starting to appear, but it is there, and from here on, the confusion will only increase. The parent fractal of today's image is virtually the same as the parent of yesterday's image -- a seemingly harmless mixture of Z^3 and Z^4 that would be expected to do little but create a routine combination fractal. In the world of fractals however, surprises are common, which is why I find fractals so fascina- ting. The surprises coming in the next few days are some of the greatest I have yet stumbled upon. I have named today's image "X-Y Mandel Fractal". Something about the image reminds me of pictures I have seen of the X and Y chromosomes that determine an individual's sex. I believe all individuals start as women, but half are mutated into men by an X-Y chromosome. If this is true, then half the population of earth consists of alien mutants bent on death and destruction. After watching the news, I guess it's true! Before getting sidetracked into politics, an ever-present danger, I must get back on the fractal track and admit that I could rate today's image no higher than an average 5. When the render time of 4 minutes is taken into consideration, the overall value jumps to 118. The best value of all is to download the GIF image file from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A warmer temperature of 48F 9C, lots of sun, and lighter winds gave the fractal cats a pleasant afternoon in the yard here at Fractal Central on Tuesday. Today is starting still warmer, but with clouds moving in, the duo might not be as happy. For me, it looks like another routine day of getting the work finished, then exploring in Fractal Land. So until next time, take care, and good fractals make unhappy cows give more milk. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ X-Y_Mandel_Fractal { ; time=0:04:13.92--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.52128983921205970/+0.000169467990356\ 02/988403.5/1/90/3.88578058618804789e-016 params=1/3/0.3555/4/0/0 float=y maxiter=1200 inside=0 logmap=78 periodicity=10 colors=000AGQAHR9IS9JT8KU8LV8LW7MX7MY6NZgzzTzxRzvV\ vsZrpbntfjwifzdZu_RqVJmz_KzUKzBKxI2uHCsGLpFVnEclI_\ jMWhQTfTPdzMbuIapFdkKffPicUk`YnYbpVgrSkqPhqSfqWcp_\ arcZvgXzkVg1ElHBqW9zj7zhBzfEzdHwbKt`OqZRnXUkWXhTZe\ Q`bNa_KcXHdUEfRBgOKjLSlI_noVopRpqNqrIrsEstAtu6trBn\ pFhnKblOXjTRhXMoi`lgWjeShdOfbKdaGbcCad9`e6_f3Zg0px\ _lx`hwadwb_wcWvdSveOvfhVdjSkkQqjR_jRJZOLNLMMQOMVQL\ _RLdTLiVKnWKsYKxZaHHWJKRKNMLQGNTBOW6PZCSbIUfNWjTYn\ Z_rcaveXtfSshOriJpkEolAneBmZBlSCkLCjEDi8DiGEhNFgVF\ faGeiHdpHcfQWYZOOgGFo8JkFNgMQdSU`ZYXe`UkZKlXAlW0lS\ 1mP2nM3oI4pF5qC5r9Jn6Xj4igHccUY`fSYsMVtQZtTatXdt_g\ i_j_`mQapGbsFcrEdqDepCfpBgoAhnAinOjZ`kJml4jm9hnEfo\ IcpNaqS_rWWsQTtKPuDMv7Jw1DxB8yK3zT9zXFz`LzdRzhXzlb\ zphztmzwjzrgzndzjaze_zaXzYUzTRzPPzLLzQIzVEzZBzc8zg\ 9zh9zhAziAziAzjBzjBzkCzkCzlCzlDzmDzmEznEznEznDzlDz\ jDzhCzfCzdCzbBz`BzZBzXAzV } 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==================================

1 0

FOTD 23-03-04 (Another New World [7])
by Jim Muth 23 Mar '04

23 Mar '04

FOTD -- March 23, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image is the first glimpse into a new fractal world. This is why I named it "Another New World". New fractal worlds are no big deal. They can be created at will. But the world introduced by today's image is rather unusual, as the next several FOTD's will illustrate. On the surface, the image appears to be a routine quadratic midget in the fractal that is created when 0.355 parts of Z^4 are added to Z^3 before C is added. And this is indeed what it is. But in its heart lies a deep secret, which I will reveal in stages over the days to come. For now, enjoy today's image, which is already good enough to rate an above-average 7. The overall value is brought down to 25.5 by the render time of 27 minutes, but this value can be increased by avoiding the rendering entirely, which can be done by downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 37F 3C and brisk winds, Monday was far too harsh for the delicate paws of the fractal cats. They did manage an hour or so on the porch, but the clouds that kept obscuring the warm sun gave them no end of annoyance. Luckily, cats have short memories, and by the time they had finished their evening tuna, they had nearly forgotten their bad day. Today is sunny and warmer, and the wind has died. The duo is already thinking of going out. And I'm thinking of finishing the work that must be done so I can get to the fractals that are fun but not absolutely necessary to survival. Until the next wonderful image appears 24 hours from now, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Another_New_World { ; time=0:27:25.89--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.52321930545120110/-0.002589589762561\ 87/2.048744e+010/1/-54.9998285074083242/4.87322811\ 3853878e-005 params=1/3/0.355/4/0/0 float=y maxiter=10000 inside=0 periodicity=10 colors=000z06u39m8EeDKYGPPLU9ozCozCozCozCozCozCozC\ ozEozEozEoxEouElrEipEgmHdjHagHZeHWbHT_HRY00z00z00x\ 00p03j9Dbz0zj0z0J00L00L04L09O9EOMz0zz0xz0xz0uz0uz0\ uz0rz0rz0pz0pz0pz0mz3mz3jz5ju8jr8gpBgmBegDeeDebGb_\ GbYJ_SJ_PL_MLYKOY0oE0gK4aPCTU0iz0gu0dr0am0Zj0Xg4Tb\ CR_1Lz4Oz4Oz4Oz4Oz4Oz6Oz6Oz6Oz6Oz6Oz9Oz9Oz9Oz9Oz9O\ zCOzCOxCOuCOrPJrPGpPGjSGeSDbSDYSBUUBPzoMzoPxoUroYm\ g_gZbbTgYLjSDmP8pKJjERe9Z_4iU0oP0oK0oH0oK0oK0oK0oM\ 0oM0oM0oM0oP0oP0oP0oS0oSPoEMo1CoE1oP0o_0dm0Rx0Dz00\ z03z03z03z05z05z05z08z08z08z0Bz0Bz0Bx0Du4LU0Du0Dr0\ Dr0Gp0Gm0Gm0Jj1Jg4Jg6Le9Le9LbCO_EO_HOYz00z00z00z00\ z00z00z00z00z00z00z00z00z00z00x30u50r51m84j86gB9eD\ CbDE_GHUGKSJMPLPMLSKOUzo0zo0zo0zo0xo0uo0uo0ro0po0m\ o0jo0go0gl0ei1bg4_g6Yd9UaCUZESXKPXMMTPKRSHOU0op0om\ 0om0om0oj1oj1oj1og4og4og6oe6oe6oe9ob9sbCobCk_Cf_Ea\ _EXYHTYHRYz00zm0zg0zb0zX1 } 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==================================

1 0

FOTD 22-03-04 (First Fractal Flight [8])
by Jim Muth 22 Mar '04

22 Mar '04

FOTD -- March 22, 2004 (Rating 8) Fractal visionaries and enthusiasts: Today's image is still another view of the Julia rectangle in the Z^2.003 Julibrot. I should not call it a rectangle today however, for today's orientation has been rotated 0.63 degree, which is just far enough from the Julia direction that the rectangle has been stretched into a near perfect square. But the square is only a small part of today's image, which resembles some fantastic bird in flight. Having been shrunk to near insignificance, the square lies where the wings are attached to the body of the big bird. This resemblance of the entire image to a bird in flight inspired the name "First Fractal Flight". I rated the image, perhaps a bit over-enthusiastically, at an exceptional 8. When the render time of 13 minutes is figured in, its overall value rates a 60. This value may be increased by saving the time that would otherwise be spent rendering the image. And this may be done by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cold winds, only occasional sun, and a temperature of 41F 5C limited the cats' outdoor time to less than an hour on Sunday, but a generous treat of tuna in the evening kept their moods from becoming too sullen. This morning it is still windy and the temperature is down to 28F -2C. It looks like another less- than-ideal day for the fractal duo. I have near the normal amount of work to finish before retiring to fractal land. Today, I will bid a temporary 'good-bye' to the rectangle, and set out for unexplored territory. What I find there will appear as tomorrow's FOTD. Until then, take care, and float like a fractal, whatever that means. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ FirstFractalFlight { ; time=0:13:21.14--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.000138176/-0.00692793/21.92537/1/-40\ /-5.05012698326368081e-014 params=90/90/89.27/90/\ -1.7435/0/0.00019/0.07388/2.003/0 float=y maxiter=60000 inside=0 logmap=29 periodicity=10 colors=000RASSATTAUUAVVAWWAXXAYYAZZA__A``AaaAbbAcc\ AddAeeAffAggAhhAiiAjjAkkAllAmmAnnAooAppAqqArrAssAt\ tAuv9vtCurEuqGtoJtnLslNskPriSrhUqfWqeZpc`pbbo`do_g\ nYinXkmVnmUplSrlPumRtlTskVrjWqjYpi_ohanhbmgdlfflfh\ keijdkidmhcogbpfbreatd`ud`sc_qc_oc_nc_lbZjbZibZgbZ\ ebZcaYbaY`aYZaYYaYW`XU`XS`XR`XP`XN_WM_WK_WI_WH_WIY\ UJXTKWSKVQLUPMTONSMNRLOQKPOIQNHQMGRLESKDTJCTIAUH9V\ G8TC8VF7XH7ZJ6_M6aO5cQ5dT4fV4hX3jZ3ka2mc2oe1ph1rj0\ tl0qn0kf7gZEiRLkJRmLSoNUqPVsRXuTYwVZyX`zZaz`czbdzd\ fzfgzhhzjjzlkznmzpnzrpztqzvrzrszoszlsziszeszbsz_sz\ XszUszUszUszUszUszUszUszUszUszUszUrzWqzYqz_pzapzco\ zeozgnzinzkmzmlzolzqkzskzujzwjzyizzizzhzzhzzhzzgzz\ gzzgzzfzzfzzfzzezzezzezzdzzdzzdzzczzczzczzazz`zz_z\ zZzzYzzXzzWzzVzzTzzSzzRzzQzzPzzOzzNzzMzzKzzJzzIzzH\ zzGzzFzzEzzDzzEzzEzzFzzFzzFzzGzzGzzHzzHzzHzzIzzIzz\ IzzJzzJzzKzzKzzKzzLzzLzzN } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 21-03-04 (Correct version -- A Space Oddball [5])
by Jim Muth 21 Mar '04

21 Mar '04

FOTD -- March 21, 2004 (Rating 5) Fractal visionaries and enthusiasts: For today's adventure in fractal land we return to that rectangle in the Julia set of the Z^(2.003) Julibrot. But we do one thing very different. Instead of viewing it in the Julia direction, we turn our viewpoint 90 degrees and view it in the Oblate direction, which is determined by the real(Z) and imag(C) axes. Surprisingly, the rectangle is still a rectangle, though it is now quite squashed, and its top and bottom edges are no longer sharply defined, but have become fuzzy. When viewed from this direction, the scene has origin symmetry, the lateral elements being transformed into graceful swirls. With few more good features to tell of, the image could be rated no higher than a 5, which, with a 21-minute render time, equals an overall value of 24. Perhaps remembering that great film of 35 or so years ago, which was set in a future that is now 3 years in the past, I named the image "A Space Oddball". And I wonder why none of the things foreseen in that film have come true. I guess it's a plot of the evil space aliens to keep us helpless in preparation for the coming takeover and enslavememt. :-) The enlightened will avoid the aliens and save 20 minutes by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Those who enjoy watching their fractals come to life will run the included parameter file. The first day of spring turned out to be very pleasant here at Fractal Central on Saturday. The fractal cats took full advantage of the sun and temperature of 59F 15C by spending most of the afternoon in the yard, checking the spring bulbs that are already showing. At sunset, they came inside for their evening treat without urging. Today is starting mostly sunny and mild, but it is quite windy, and the duo dislikes wind, which conceals the sound of danger. It remains to be seen what kind of day they will have. Regardless of the cats' day, my day will be pleasant, and the fractals will all be above average. Until next time, take care, and hang on to your fractals. Once you lose them, they are gone forever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Space_Oddball { ; time=0:20:55.04--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0/3303.206/0.0232/0/-77.7313946499058\ 517 params=0/0/90/0/-1.7435/0/0.00019/0.07388/\ 2.003/0 float=y maxiter=60000 bailout=9 inside=0 logmap=66 periodicity=10 colors=0008355450532654765877999AAABBCCDEDEFEFHFHI\ GIKHJMGLNFMPENREPSDQUCRVBSXBUZAV_9Wa8Yc8Zd7_f6ag5b\ i5ck4el3fn2gp2iq1js0kt0ls3is6gr9drCbqF`qIYpLWpOToR\ RoTPnUOmVOlVOkWOjWOiXNhYNgYNfZNeZNd_Nc_Mb`MaaM`aM_\ bMZbLYcLXcLWdLVeLUgLTiKSkKRmKUoK_qKatJcuJexJhyJhzJ\ hzKhxJevKbsLZsLUoMPnMKkNFiOFgOEePEePDdQDcRCcRCbSBb\ SBaTB`UA`UA_V9_V9ZW8YX8YX7XY7XY6WZ6V_5V_5U`4U`4Ta4\ Ta5Wc5Ye6_f6bh7di7fk8il8kn9mo9pqArrAtt8wvAvuBvtCvs\ DvrEvqFvpGvoHvnIvnJvmKvlLvkMvjNviOvhPvgQwfRwfSwdTw\ bTwaUw_UwYVwXVwVWwTWwSXwQYwOYwNZwLZwJ_xI_xG`xE`xDa\ xBaxAbxBcxCdxDexEexEfxFgxGhxHixIixIjyJkyKlyLmyMnyN\ oyOpyPqyQryRsyStyTuyUvyVwyVxyWyyXzzXzzYzzYzzZzz_zz\ `zzazzbzzczzdzzdzzezzfzzgzzhzzizzjzzjzzkzzlzzmzznz\ zozzpzzpzznzzlzzkzzizzhzzfzzezzczzFzzEzzEzzDzzCzzC\ zzBzzBzzAzzAzz9zz8zz8zz7zz7zz6zz5zz5zz4zz4zz3zz2zz\ 3zz3zz3zz3zz4zz4zz4zz4zz5 } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 21-03-04 (A Space Oddball [5])
by Jim Muth 21 Mar '04

21 Mar '04

FOTD -- March 21, 2004 (Rating 5) Fractal visionaries and enthusiasts: For today's adventure in fractal land we return to that rectangle in the Julia set of the Z^(2.003) Julibrot. But we do one thing very different. Instead of viewing it in the Julia direction, we turn our viewpoint 90 degrees and view it in the Oblate direction, which is determined by the real(Z) and imag(C) axes. Surprisingly, the rectangle is still a rectangle, though it is now quite squashed, and its top and bottom edges are no longer sharply defined, but have become fuzzy. When viewed from this direction, the scene has origin symmetry, the lateral elements being transformed into graceful swirls. With few more good features to tell of, the image could be rated no higher than a 5, which, with a 21-minute render time, equals an overall value of 24. Perhaps remembering that great film of 35 or so years ago, which was set in a future that is now 3 years in the past, I named the image "A Space Oddball". And I wonder why none of the things foreseen in that film have come true. I guess it's a plot of the evil space aliens to keep us helpless in preparation for the coming takeover and enslavememt. :-) The enlightened will avoid the aliens and save 20 minutes by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Those who enjoy watching their fractals come to life will run the included parameter file. The first day of spring turned out to be very pleasant here at Fractal Central on Saturday. The fractal cats took full advantage of the sun and temperature of 59F 15C by spending most of the afternoon in the yard, checking the spring bulbs that are already showing. At sunset, they came inside for their evening treat without urging. Today is starting mostly sunny and mild, but it is quite windy, and the duo dislikes wind, which conceals the sound of danger. It remains to be seen what kind of day they will have. Regardless of the cats' day, my day will be pleasant, and the fractals will all be above average. Until next time, take care, and hang on to your fractals. Once you lose them, they are gone forever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Space_Oddball { ; time=0:20:55.04--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0/3303.206/0.0232/0/-77.7313946499058\ 517 params=0/0/90/0/-1.7435/0/0.00019/0.07388/\ 2.003/0 float=y maxiter=60000 bailout=9 inside=0 logmap=66 periodicity=10 colors=0008355450532654765877999AAABBCCDEDEFEFHFHI\ GIKHJMGLNFMPENREPSDQUCRVBSXBUZAV_9Wa8Yc8Zd7_f6ag5b\ i5ck4el3fn2gp2iq1js0kt0ls3is6gr9drCbqF`qIYpLWpOToR\ RoTPnUOmVOlVOkWOjWOiXNhYNgYNfZNeZNd_Nc_Mb`MaaM`aM_\ bMZbLYcLXcLWdLVeLUgLTiKSkKRmKUoK_qKatJcuJexJhyJhzJ\ hzKhxJevKbsLZsLUoMPnMKkNFiOFgOEePEePDdQDcRCcRCbSBb\ SBaTB`UA`UA_V9_V9ZW8YX8YX7XY7XY6WZ6V_5V_5U`4U`4Ta4\ Ta5Wc5Ye6_f6bh7di7fk8il8kn9mo9pqArrAtt8wvAvuBvtCvs\ DvrEvqFvpGvoHvnIvnJvmKvlLvkMvjNviOvhPvgQwfRwfSwdTw\ bTwaUw_UwYVwXVwVWwTWwSXwQYwOYwNZwLZwJ_xI_xG`xE`xDa\ xBaxAbxBcxCdxDexEexEfxFgxGhxHixIixIjyJkyKlyLmyMnyN\ oyOpyPqyQryRsyStyTuyUvyVwyVxyWyyXzzXzzYzzYzzZzz_zz\ `zzazzbzzczzdzzdzzezzfzzgzzhzzizzjzzjzzkzzlzzmzznz\ zozzpzzpzznzzlzzkzzizzhzzfzzezzczzFzzEzzEzzDzzCzzC\ zzBzzBzzAzzAzz9zz8zz8zz7zz7zz6zz5zz5zz4zz4zz3zz2zz\ 3zz3zz3zz3zz4zz4zz4zz4zz5 } SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

1 0

The Pseudo-Dragon Spacefilling Tree...
by Tony (Anthony) Hanmer 20 Mar '04

20 Mar '04

Here is an old L-system find of mine, which I have recently explored further. It started out as a speedup to one of my favourite discoveries, a curve which could be adjusted from being a spacefilling 1:sqrt2 rectangle to the TwinDragon, which is 2 Dragon Curves laid end to end. Then I discovered that this curve could also be transformed into Levy's Curve; and recently found its Dragon Curve version as well. This led me to a curve which seems to be halfway between the DC and TD! Other variations are possible: indeed, if one translates the curve into d version from f version, its Angles can be incremented to arbitrarily fine differences, making animations between the various curves possible. (This is the case with many L-systems...) Below, included with the curve, are many of the variations I have found. Paste the whole thing into a text editor, and call it pdsft.l Keep this file open, and Alt-Tab into Fractint. Here you can try all of the variations one at a time, by jumping back into the file in the text editor and removing the preceeding; semicolon from the string you wish to try, saving the file, and jumping back into Fractint. I have left it with the variation which is a half-DC, half-TD mix as default. One question: given 8 positions for an angle change, such as + or - (before and after each of f, x, f and x), and 8 possible changes of angle for Angle 8 (0, +, ++, +++, |, +++++, ++++++, -), what is the total number of permutations? (Some of these permutations will lead to a flat line or other redundant variations.) Tony Hanmer Tbilisi, Republic of Georgia (adh5306l {; Anthony Hanmer 7/3/2004 Angle 8 ; pdsft (Pseudo-Dragon SpaceFilling Tree) speedup, various variants Axiom x ; Choose any string by removing its preceeding ;semicolon ; (All possibilities: 1f1, 1x1, 1f1, 1x1 and ; 0, +, ++, +++, |, +++++, ++++++, -: = ...?) ;x=d[@iq2\90x]\180d[@iq2\90x]; rectangular sft ;x=f[@iq2++x]|f[@iq2++x]; rectangular sft ;x=f[@iq2+x]|f[@iq2+x]; TD ;f=f+@iq2f|f+++@q2; TD 4026, multiple-layer redundant (mlr) (needs Axiom f) ;f=f+++@iq2f|f+@q2; TD 4027 mlr (needs Axiom f) ;x=d[@iq2\45x]\180d[@iq2/45x]; DC 5306m ;x=f[@iq2+x]|f[@iq2-x]; DC 5306n; 1-string all-f DC eludes me so far! ;x=f[@iq2+x]f|[@iq2-x]; Fat DC, 13/3/2004 ;x=f[@iq2+x]|f[@iq2x-]; Halfway between DC & TD, 13/3/204 ;x=f[@iq2+x]f|[@iq2x-]; Halfway between DC & TD, 13/3/204 ;x=f[@iq2+x]-f[@iq2x]; Levy's Curve, 13/3/204 ;x=f[@iq2++x]|f[@iq2x]; Partway between DC & sft?, 13/3/2004 ;x=f[@iq2++x]|f[@iq2+x]; Partway between DC & sft?, 13/3/2004 ;x=f[@iq2++x]|f[@iq2-x]; Partway between DC & sft?, 13/3/2004 ;x=f[@iq2+x]f[@iq2+x]; TD tree ;x=f[@iq2+x]f[@iq2-x]; Levy's Curve, 12/3/2004 x=f[@iq2+x]|f[@iq2x]; *Halfway BETWEEN* DC & TD! - 8/3/2004 ;x=d[@iq2\45x]\180d[@iq2x]; *BETWEEN* DC & TD!, d-version - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2/15x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2/30x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2/40x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2\15x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2\30x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\45x]\180d[@iq2\40x]; *BETWEEN* DC & TD!, Angle 8 - 9/3/2004 ;x=d[@iq2\30x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\60x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\15x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\75x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=d[@iq2\90x]\180d[@iq2x]; Just playing - 9/3/2004 ;x=f[@iq2+x]|f[@iq2+!+x]; Just playing - 9/3/2004 ;x=f[@iq2-!x]|f[@iq2++!x]; Just playing - 9/3/2004 ;x=f[@iq2-x]|!f[@iq2+!x]; TD - 9/3/2004 ;x=f[@iq2|!x]-!f[@iq2+!x]; sft - 9/3/2004 ;x=f[@iq2-!+!x]+f[@iq2+!x]; Just playing - 9/3/2004 ;x=f[@iq2-!+!x]|!f[@iq2+!x]; Just playing - 9/3/2004 ;x=f[@iq2-!--x]|!f[@iq2+!x]; Rt Triangle - 9/3/2004 ;x=f[@iq2---x]|!f[@iq2+!x]; Rt Triangle - 9/3/2004 ;x=f[@iq2---x]+++f[@iq2+!x]; Just playing - 9/3/2004 ;x=f[@iq2---x]+++f[@iq2|x]; Nice new DC - 9/3/2004 ;x=f[@iq2+x]-f[@iq2+x]; playing, 12/3/2004 ;x=f[@iq2x]f[@iq2-x]; playing, 12/3/2004 } _________________________________________________________________ MSN 8 helps eliminate e-mail viruses. Get 2 months FREE*. http://join.msn.com/?page=features/virus

1 0

FOTD 20-03-04 (Discombobulated [5])
by Jim Muth 20 Mar '04

20 Mar '04

FOTD -- March 20, 2004 (Rating 5) Fractal visionaries and enthusiasts: In today's image we once again visit the Z^(2.003)+C Mandeloid, and examine the area just east of the East Valley of the large midget on the negative X-axis. The large midget cannot be said to lie on the main stem. There is no main stem in this Mandeloid. The stem has broken into fractal dust, and as for the large midget -- it has been distorted into a monstrous thing that must be seen to be believed. When I say that today's scene is located just east of this monstrous midget's East Valley area, I am not actually speaking correctly. The midget has no East Valley. What once was East Valley has broadened into an area that can better be described as East Plateau. The top of this plateau consists of newly created features that do not exist in the traditional Mandelbrot set. There are newly created bays and valleys here, with sub- features unlike any found in the M-set. The strange Julia rectangle lies in this area, along with the figures of overweight people raising their arms in praise of something. And of course there are midgets. Today's image illustrates one of the smaller midgets in the area. Its dis- organization is typical of the entire area, and has inspired the name "Discombobulated". To add to the interest I rendered the image with the outside set to 'tdis'. It seems to have worked too well. The disorganiza- tion actually goes a bit too far, spoiling the overall artistic worth and cutting the rating to a merely average 5. The rather slow render time of over 1/2 hour further cuts the overall value to a lowly but not disgraceful 15. For tomorrow's FOTD I might remain in the same area or I might move on. It all depends on my mood when fractal time arrives this evening. Meanwhile, up to 1/2 hour of precious time may be saved by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the completed GIF image from there, thereby avoiding the rendering entirely. The weather slowly improved through the day Friday here at Fractal Central, until at 3pm, with full sunlight, the tempera- ture reached a high of 48F 9C. The fractal cats must have approved, for they went outside just after 2pm and did not return indoors until 5pm. At one time I saw Tippy perched several feet up one of the holly trees, but he climbed down without incident. Today is starting sunny, and it is due to be warmer. This bodes well for the fractal duo. As for me, I've got a bit of work to finish, and then who knows . . . anything could happen. Until next FOTD, take care, and wait with bated breath . . . you might catch a great fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Discombobulated { ; time=0:33:28.30--SF5 on a P200 reset=2003 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-1.74350051908036900/+0.000000081693461\ 53/1.972472e+011/1/-20/-4.43607331641199254e-005 params=2.003/0/0/0/0/0 float=y maxiter=18000 inside=0 outside=tdis periodicity=10 colors=000NfYKi_IkaGmcEoeGkcIgaKd_M`YOYWQUURRTTNRV\ JPXGNZCL`9Jb5Hc2Gb4Ia5Ka7M`8O`AP_BRZDTZEVYGXYHYWOX\ VUXT`WSfWQcYO`_MZ`KWbJUcHReFOfDMhBJiAHk8El6Bn49o26\ q14r28l2Bf2E`2IW2LQ2OK2RF3UE4WE5YE6`E7bE7dE8gE9iEA\ kEBnECpECrEDnGEjIFfKGbLHZNIVPJRRKNSLJUMFWMCXQITUNQ\ YTNaYKebHihEmmBpr8grEZrJQrPEIO9DK48G97JE7LJ7OO7QT7\ SY7Vb7Xg7_l7aq7cp9RpBFpC3oE5nG7mH9lJBkKCjMEjNGiPIh\ QJgSLfTNeVPeWQbbY_hdXolVusSklQaeOTZMJSKAMDGL6MK0SK\ 9UNIWPRYRZZUg`WpbYxc_u_asXcqUeoRgmOikLkzZzgFoxCqc9\ re8nf8kg7gi7dj6ak6Ym5Vn5Ro4Oq4Lr3Hs3Eu2Av27w24r65m\ A6iD7dBE`AKW9RS8XO6cJ5iF4pB3vHFjNQ_T`OZkDdv2cr7cnB\ bkFbgJadNa`S`XW`U__Qc_NgbPddQbfS_hTYjUVlWTnXQpYOnb\ SlfVjjZhoafseewhhubjzYmqTopNzzItlDvz8plFkmLenS`nYV\ odQpjLppIqjGqdEqZBqT9qN7qH5qB6mF7jJ8gN8dR9zVAZZBWb\ BTfEJNDFNCCNIJKOQITWGZbDchBio9nu7tfUcTpmWnrZlw`kwc\ ivfguhftkdtnbspars_RbTPdW } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

1 0

Here are a few pearls stitched onto some lace.
by Hal Lane 20 Mar '04

20 Mar '04

Here are a few pearls stitched onto some lace. This region is a zoom out near Jim Muth's 19-3-04 FoTD - Semaphore; One color map location was set to black to get a dark background. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START 20.0 PAR-FORMULA FILE================================ Lace_and_pearls { ; Hal Lane 3-19-04 ; CPU=P400 1024x768 t=0:01:45 ; Near Jim Muth's Semaphore ; 19-3-04 FoTD reset=2003 type=formula formulafile=pastengo.par formulaname=slicejulibrot4 passes=1 center-mag=0.00245812/-0.147774/7.843562 params=89.63/90.33/89.72/90.31999999999999/-1.7435/4\ e-005/0.00019/0.07388/2.003/0 float=y maxiter=6000 bailout=9 inside=fmod proximity=0.02 logmap=50 periodicity=10 sound=off colors=000000NKL<2>QKJRKMSKO<3>WNYXN_YObZPd<3>_Sm<3>\ NcsJfuGivDlxAny<7>TuzVvzXvz<2>cyzeyzgxy<3>lvwmuvnuv<\ 3>sst<4>xG7<3>PFZGFdII_KczLPPWTJ<3>dKOfIPhGRjESlCT5M\ O<8>c`QfaQjcQ<3>yiQ<3>ocKmaJk`H<3>bVC<6>nIBoGBqEB<3>\ w7B<3>SXYKbbLd`<5>QoTRqRRsQ<3>UzL<3>OnMNkMLhM<3>GYMh\ rBdlE`gHmbK<3>mHWmCZm7a<5>mDfmEgmFg<3>mJj<2>mWI<3>mT\ WnSZpSb<3>uPovPruLhtIZuFQvCGw97x8Cy8H<3>z6ZzDVzKR<2>\ z`Gz`CzdjzZazTU<3>zSfzSizTe<3>zWUzXRzXNz`8zYK<3>z`8z\ UF<3>z_7zKYzLv<5>zTYzUTzVP<3>z_9zCOzLHzTBzAS<3>zKJzN\ HzPF<3>zZ7zvn<5>zcBzJj } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END 20.0 PAR-FORMULA FILE================================== --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.634 / Virus Database: 406 - Release Date: 3/18/04

1 0

FOTD 19-03-04 (Semaphore [6])
by Jim Muth 19 Mar '04

19 Mar '04

FOTD -- March 19, 2004 (Rating 6) Fractal visionaries and enthusiasts: There is a very unusual rectangle in the Z^(2.003)+C Julibrot. It is located in the Julia set with a C-value of -1.7435 at Z-coordinates of 0.00019,0.07388 and a magnitude of around 75. I have several times mentioned this nearly-perfect rectangle in my FOTD discussions, and since the two most recent FOTD's took me to the general area, I decided to take a peek at the rectan- gle while I was there. The rectangle is quite critical. If imag(C) is changed even 0.0001 from zero, the near-perfection is lost. In today's image, the value is changed only 0.00004 and already strange things are happening. I aided the strange happenings by rotating the view less than one degree from the exact Julia orientation. As a result of my tweaking, the once near-perfect rectangle has been changed into what can be best described as a semaphore flag. (What ever happened to the days when they actually communicated with those things?) The lower right half of the rectangle is filled with reddish high-iteration outside stuff, while the upper left half is composed of trapped inside points given life by the 'fmod' inside fill. Several other inside fills would have worked nearly as well. The "SliceJulibrot4" formula that generates today's image is a generalization of the "SliceJulibrot2" formula to any power of Z. It is a new formula, which I have not previously posted. I named the image "Semaphore" and rated it at a 6. When the render time of 7 minutes is considered, the overall value equals an 82. Rendering may be avoided entirely by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday was not too cold and not too cloudy. It was also not windy, and as a result, the fractal cats had almost two hours of quality time in the yard. When they came in, they settled down without demanding their usual treat of tuna. Rain fell during the night, but it has already moved off. If the clouds move out, the cats will have a fair chance at another good day. The work that I must finish is about average. It's 10:30am and time to get started, so until next FOTD, take care, and be lively. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Semaphore { ; time=0:07:16.94--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/77.51938 params=89.63/90.33/89.72/9\ 0.32/-1.7435/4e-005/0.00019/0.07388/2.003/0 float=y maxiter=6000 bailout=9 inside=fmod proximity=0.02 logmap=50 periodicity=10 colors=000MKMNKLOKKPKJQKJRKMSKOTKRULTVMVWNYXN_YObZ\ Pd_Qf_Ri_Sk_SmWVoTYpQ`rNcsJfuGivDlxAnyDozFpzHqzKrz\ MrzOszQtzTuzVvzXvz_wzaxzcyzeyzgxyhwxiwxkvwlvwmuvnu\ vptuqturstssttkjuc`vWRwOHxG7oFEfFLYFSPFZGFdII_KczL\ PPWTJYRK`PLbNNdKOfIPhGRjESlCT5MO9OPDQPHRPLTPOUPSWP\ WYP_ZQc`QfaQjcQneQrfQvhQyiQvgOtfNrdLocKmaJk`HhZGfY\ EdWDbVCdTBfRBgPBiNBkLBlJBnIBoGBqEBsCBtABv8Bw7BoEHg\ KN_RSSXYKbbLd`Mf_NhYOjXOlWPnUQoTRqRRsQSuPTwNUyMUzL\ SwMRtMPqMOnMNkMLhMKeMIbMH_MGYMhrBdlE`gHmbKmXNmSQmN\ TmHWmCZm7am8bm9cmAdmBdmCemDfmEgmFgmGhmHimIjmJjmO`m\ SRmWImVMmUPmUTmTWnSZpSbqRerQhtQluPovPruLhtIZuFQvCG\ w97x8Cy8Hz7Lz7Qz6Vz6ZzDVzKRzPNzVJz`Gz`CzdjzZazTUzS\ YzS`zSczSfzSizTezUbzV_zVXzWUzXRzXNz`8zYKzZHzZEz_Bz\ `8zUFzWDzXBzZ9z_7zKYzLvzNqzOmzPizQezSazTYzUTzVPzXL\ zYHzZDz_9zCOzLHzTBzASzDPzFNzILzKJzNHzPFzSDzUBzX9zZ\ 7zvnzrgzo`zlVziOzfIzcBzJj } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

1 0

roarbit.par ... puzzles?
by SherLok Merfy 19 Mar '04

19 Mar '04

I know better than to bother with subjects where my address is repeated. But someone sent me something that said "you" in the subject and referred to puzzles. I deleted it, and this is perhaps part of the reason why mailing lists typically repeat their _own_ name. It's rare for a subject to require that word. They are usually not sentences, though, so it was a mistake. Out_Of_Orbit { ; Animation. Border tracing _treats_ periodicity, ; too. How would you check if the white line is dithered? ; Default map is too sticky in FRACTINT. reset=2003 type=mandel passes=b periodicity=-11 showorbit=yes center-mag=-0.765332/6.66134e-016/0.7772216/1.4732/90/3.88578058618804\ 789e-016 params=0/0 float=y maxiter=255 fillcolor=1 sound=beep colors=000<4>00000000zzz0000<4>000z000zzz0zzz00zzz0zyy00yyy0yxx00xxx0x\ ww00www0www00www0wvv00vvv0vuu00uuu0utt00ttt0tss00sss0sss00sss0srr00rrr\ 0rqq00qqq0qpp00ppp0poo00ooo0ooo00ooo0onn00nnn0nmm00mmm0mll00lll0lll00k\ kk0kkk00kkk0kjj00jjj0jii00iii0ihh00hhh0hhh00hhg0ggg00ggg0gff00fff0fee0\ 0eee0edd00ddd0ddd00ddc0ccc00ccc0cbb00bbb0baa00aaa0aaa00```0```00``_0__\ _00___0_ZZ00ZZZ0ZYY00YYY0YYY00XXX0XXX00XXX0XWW00WWW0WVV00VVV0VUU00UUU0\ UUU00TTT0TTT00TTT0TSS00SSS0SRR00RRR0RQQ00QQQ0QQQ00QQP0PPP00PPP0POO00OO\ O0ONN00NNN0NNN00MMM0MMM00MML0LLL00LLL0LKK00KKK0KJJ00JJJ0JJJ00III0III00\ IIH0HHH00HHH0HGG00GGG0GFF00FFF0FFF00EEE0EEE00EED0DDD00DDD0DCC00CCC0CCC\ 00BBB0BBB00BBA0AAA00AA909990099909880088808880077707770077606660066606\ 550055505440044404440033303330033202220022202110011101000 } Default { ; I wouldn't jeneralize the formula, because ; it illustrates significance of sign. ; Try other methods of rendering. ; Try different periodicity thresholds. reset=2003 type=formula formulafile=roarbit.par formulaname=club_lambda function=zero/ident passes=t center-mag=-0.274835/8.88178e-016/0.7025121/1.214/90/0 params=3/0 float=y maxiter=255 fillcolor=1 periodicity=-1 sound=beep showorbit=yes; colors=(a)orbit.map colors=000<4>00000000zzz0000<4>000z000zzz0zzz00zzz0zyy00yyy0yxx00xxx0x\ ww00www0www00www0wvv00vvv0vuu00uuu0utt00ttt0tss00sss0sss00sss0srr00rrr\ 0rqq00qqq0qpp00ppp0poo00ooo0ooo00ooo0onn00nnn0nmm00mmm0mll00lll0lll00k\ kk0kkk00kkk0kjj00jjj0jii00iii0ihh00hhh0hhh00hhg0ggg00ggg0gff00fff0fee0\ 0eee0edd00ddd0ddd00ddc0ccc00ccc0cbb00bbb0baa00aaa0aaa00```0```00``_0__\ _00___0_ZZ00ZZZ0ZYY00YYY0YYY00XXX0XXX00XXX0XWW00WWW0WVV00VVV0VUU00UUU0\ UUU00TTT0TTT00TTT0TSS00SSS0SRR00RRR0RQQ00QQQ0QQQ00QQP0PPP00PPP0POO00OO\ O0ONN00NNN0NNN00MMM0MMM00MML0LLL00LLL0LKK00KKK0KJJ00JJJ0JJJ00III0III00\ IIH0HHH00HHH0HGG00GGG0GFF00FFF0FFF00EEE0EEE00EED0DDD00DDD0DCC00CCC0CCC\ 00BBB0BBB00BBA0AAA00AA909990099909880088808880077707770077606660066606\ 550055505440044404440033303330033202220022202110011101000 } Club_Lambda { ;Try inversion. Simplified since last post of it. z=fn1(pixel), c=fn2(pixel): z = z*z -conj(z) +c |z| <= real(P1) }

3 3

FOTD 18-03-04 (Rising Alleluias [7])
by Jim Muth 18 Mar '04

18 Mar '04

FOTD -- March 18, 2004 (Rating 7) Fractal visionaries and enthusiasts: After I found the twin midgets in yesterday's image, I did a bit more exploring in the same area and turned up the scene that appears in today's image. I named the picture "Rising Alleluias" because of the eight elements surrounding the central midget, which appear, at least to me, like overweight people raising their arms in praise. I cannot say what the people are praising. It could be the immense and unlimited worlds of fractals, or the equally great physical universe, or perhaps the religious figure of their choice. It could even be science, which developed the machines that first revealed the worlds of fractals, and which some consider to be almost a religion. More thoughts along this line are included in the version of the FOTD that appears on the philofractal list. I rated today's image, which renders in under 7 minutes, at a 7, which gives an overall value of 104. The rendering stage can be eliminated by letting Paul do the rendering and downloading the finished image from his FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday remained cloudy and chilly here at Fractal Central. The temperature of 39F 4C was a bit too chilly for the cats' ears, and they spent the day wishing. In the evening a treat of tuna eased their frustration. My frustration will ease when the work I have scheduled for today is finished, and that will happen about 4 hours after I start. Then I'll take a trip to one of the infinite worlds of fractals. In 24 hours I'll return with whatever I find there. Until then, take care, and prepare for the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rising_Alleluias { ; time=0:06:43.98--SF5 on a P200 reset=2003 type=manzpower passes=1 center-mag=-1.7\ 43238677909744/+0.00011432724916339/1.458905e+008/\ 1/177.5/-2.35020439424138416e-005 params=0/0/2.003\ /0 float=y maxiter=2000 inside=0 logmap=194 colors=000MDLNEMOHNPGNQHORIPSJRTKRVLSXMSZNSbOUdPWg\ QWjRVmRSoRQsSOvSLxSJzSGwWKtZOrbQodUmgWjj_hmbeoecsh\ `vkZxnczshzwkzzmzznzzozzpyzqzzrzzszztzzuzzvzzwzzxz\ zrzzmzzVzzbtziozqmzxczzVzwPzoJzgCz_6rR0hK0ZH0UG6UF\ CUAZUFdPKcKPhGUnHZuJcyKEdSLU_SJh_7oY5iW2cU0YS0RQ0L\ P0FR0CS4BVAAWF8YL7_Q6`W5b`2dg1ek0gr0iw0jz0kz0mz0nx\ 5ns8ooEqjJqeMrbRsYWsS_tOdvKivFmwArw6voJwhVx`gyUszO\ zzRxwUssWnoZik`chcZdgU`iPYkJUnEQq8Ms4Jv0FcZULzgKzh\ KzhKxhKvhKsiKqiKniKkiKijKgjKdjKbjK_jLYhLVgLSdLRcLP\ bMM_MLZMJWMGVMFUg6Wz0Yz8`zHdzQgz_jzhmzqqzyszttvotq\ jtmgthbtcYvZSvVPvQKvLFvHBvJEwJGwJJwJLwJOwJQxKSzKZz\ KczKgzKizKkzKnxPmrSkmWjh_icch_hgVkeQodLscGtbCt`Es_\ ErZEqYEoWEnVEmUEkUEjUFiUFhUFgUFeUFdUFcUFdUFeUEgUEh\ UEiUEjUCkUCmVCnWCoYBqZBr_Bs`Btb7vc5wd2xe0ye0ze0ze0\ ze6zeBzeHzeOzeSzeGze5ze6ze6ze7ze7ze8ze8zeAzeAzeBze\ BzeCzeCzeEzeEzeEzeMzeRzeY } END PARAMETER FILE=========================================

1 0

FOTD 17-03-04 (The Twinship of Twins [4])
by Jim Muth 17 Mar '04

17 Mar '04

FOTD -- March 17, 2004 (Rating 4) Fractal visionaries and enthusiasts: The day started with a bang here at Fractal Central, when I opened my e-mail box and discovered that I had just won 3 million-dollar lotteries that I have no memory of entering. Talk about good luck -- it doesn't get any better than this. Now I'll be able to give up working and devote all my time to finding more fractals. ;-) Now on to today's fractal. I recently was asked if such a thing as twin fractals exists. I'm not sure about twin fractals, but twin midgets certainly do exist. A pair of them is illustrated in today's image. The twin midgets are located in the Z^(2.003)+C Mandeloid. This Mandeloid is part of the Julibrot that holds the near-perfect rectangle that I occasionally distort and use as a FOTD image. The parent Mandeloid is almost indistinguishable from the classic Mandelbrot set, the major difference being found in the area of the main stem, which has split into fractal dust. Today's image is located in this dust. Though the midgets in the image are close together, their basins of attraction do not interfere with each other. A major discon- tinuity that lies between them isolates them. Sometimes, the basins of closely-spaced midgets do overlap, and sometimes the midgets themselves merge, but in these cases, it is always corresponding parts of both midgets that come together. Two main stems can merge, or two East Valleys, but never an East Valley and a main stem. The two large twin midgets in today's image lie in a field of smaller midgets, some of which are quite attractive, surrounded by networks of fractal railroad tracks. The Julia sets of this area can also be unusually attractive, but that's another story. I named today's picture "The Twinship of Twins". The name doesn't make too much sense, but it has a nice sound to it. The rating of 4 is just a bit below average. Combined with the render time of near 4-1/2 minutes, this gives an overall value of 90. The rendering may be avoided entirely by downloading the finished image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A steady windy rain that fell all day Tuesday here at Fractal Central, and a temperature that never rose above 34F 1C, kept the fractal cats solidly confined to their indoor shelves by the windows. Their moods were not as bad as might be expected however. Most likely, as they gazed out at the miserable weather, they were thankful that they were not one of the homeless cats who have no place to go on such miserable days. In the evening I gave them a small treat of tuna as a reward for their good behavior. Today is starting cloudy and cold, but it is dry. We shall see how the day goes. For me it's just another day with work to be done and fractals to find. The next fractal will appear here in 24 hours. Check then for something you have never seen before. Until 24 hours have passed, take care, and almost all FOTD fractals are things that have never been seen before. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Twinship_of_Twins { ; time=0:04:25.18--SF5 on a P200 reset=2003 type=manzpower passes=1 center-mag=-1.51984679271885400/+0.011001816585014\ 69/5927.148/1/-100.000000000060254/3.5317263002987\ 4313e-011 params=0/0/2.003/0 float=y maxiter=3200 bailout=9 inside=0 logmap=40 periodicity=10 colors=000K8qJ9nJ9kI9iI9fI9dH9aH9ZG9XG9UG9SF9PF9ME\ 9KE9HE9FD9CD99C97C94C92BB5BC7BDABECBGEBHHBIJBJMBKO\ BMQBNTAOVAPYAR_ASaATdAUfAViAXkAYmAZpA_r8axA`tB_pC_\ lDZhEZdFY`GYXHXUIXQJWMKWILVEMVANU6OU3TXAYZGa`NfbTk\ d_ofethlxjrwipvhnuhlugktgisfgsffredqebqdapd_ocYobX\ nbVmaTmaSl`Qk`Ok_Nj_LiZJiZIh`NhaRfWSeQTdKUcEVb8Wa3\ Wb5Rb6Nc7Ic9EdA9dB5fF4gI4iM4jP4lT4mW4nZ4pb4qe4si4t\ l4vp4ws4xv4NadQceSdeVffXgf_ifajgdlgfmgiohkphnrhpsi\ suitwluviuuguueutcvsavs_vrYvqWwqUwpSwoQwoOxnMxmKxm\ IxlGxlEujHriKphNmgPkfSheVfdXcc_`bbZadW`gU_jRZlPYoM\ XrKWtJXqIYnHYkGZhF_eE_bD`_CaXBaUAbR9cO8cMBbLEbLHcL\ JdLMeKPfKRgKUhKXiK_jJakJdlJgmJinJhoIhpIhqHhrHhsGht\ GhuFhvFiwEjxEkyDlzDmzCnzCozBpzBqzArzAsz9tz9uz8vz8w\ z7xz7yzAzzDzzGzzJzzLzzOzzRzzUzzWzzZzzazzdzzkzzfzzb\ zzZzz_zzVzzRzzNzzJzzFzzGzzHzzOzzNzzMzzMzzLzzKzzJzz\ JzzIzzHzzHzzOzzUzz_zzezzk } END PARAMETER FILE=========================================

1 0

FOTD 16-03-04 (Paddles [6])
by Jim Muth 16 Mar '04

16 Mar '04

FOTD -- March 16, 2004 (Rating 6) Fractal visionaries and enthusiasts: In a recent FOTD I wrote that almost all midgets in fractals created by the MandelbrotMix* series of formulas (formulae for the over-educated) are variations of the quadratic Mandelbrot set. Note that word 'almost'. Today's image shows a midget that most definitely is not quadratic, but cubic. And to top off the strangeness, the midget does not appear to be fully defined, almost as though it were cut in a non-critical plane. The pattern around the midget is perfectly defined however. This appearance of an imperfect cubic midget is far from the strangest scene I have stumbled upon in my adventures in fractal land. I have actually found perfect cubic midgets side-by-side in the same frame with midgets of the 6th order. A FOTD that appeared several years ago illustrates the scene. At the moment, the particular image is lost, but I would like to find it for further investigation. For some reason, the real(p2) parameter of today's image, which determines the amount of Z^5 to be subtracted from Z^3, is extremely critical, as it is in all fractals that I have so far found which contain higher-order midgets. I named the image "Paddles". The three prominent arms remind me of the paddle blades of an old-fashioned windmill. (Old-fash- ioned always seems to be more picturesque.) I rated the image at a 6, which is above average, but not outstanding. When the image's short render time is considered, its overall value comes in at a hefty 357. In a recent letter to the fractint list it was asked what I mean by a plane oriented halfway between the Mandelbrot and Julia orientations in the Z^2+C Julibrot. I am really not sure. The more I think about it, the less certain I become as to what I mean. I'll have more to say about this in the next FOTD that uses the Julibrot formula. I also recently was asked whether there is such a thing as twin fractals. I am not sure what the writer means by twin fractals, but there certainly are twin midgets. A pair of them will appear as tomorrow's FOTD. Though today's image is a fast one, the minor annoyance of running the included parameter file can be eliminated by downloading the completed image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal cats, Thomas the lazy oversized orange and Tippy the thin wiry tabby, had one of their best days ever on Monday. It was one of those days when everything that could go right in the world of cats did go right. The weather was sunny, with a temp- erature of 63F 17C, but the big excitement came when a squirrel came too near Tippy, who appeared to be asleep. Tippy suddenly lunged and for a moment got his jaws on the squirrel's tail. Luckily for both the squirrel and Tippy, the squirrel pulled free and scampered up a holly tree, where he scolded loudly before going back to his hole. Thomas actually became alert during the scuffle. When they came indoors, I treated them to chicken, which they enjoy even more than tuna. But today is starting cold and rainy, and the two fractal cats are already turning sulky. We'll see how it goes. For me, it looks to be an average day. And if all goes well, the fractal I find will be above average. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Paddles { ; time=0:01:40.79--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.4615028914331138/0/9778.83/1/-90/3.8\ 857805861880479e-016 params=1/3/-0.21/5/0/0 float=y maxiter=2000 inside=0 logmap=25 periodicity=10 colors=000h0hh0hh0hh5hhAhhFhhKhhPggUffZeecddhc`k4V\ f9PbDJYIESMTLLZCKYHPYLTYPXXU`XYdXahWglWlpWqtYqrZrq\ _qoaznbulcpkdpj16l28m3An4Co5Ep5Gp6Iq7Kr8Ms9Ot9QtAS\ uBUvCWwCYwGTrKOnOJjREfV9bZ4Za0VZ5SWAPTFNQKKNPIKUFH\ YDFRNEKXCDeB6oA0xH6vNCtUIr_OpfUnl_lsejyjhvgiseiqci\ n`ilZiiXigViiWjjWjkWjlXkmXkoXkpYlqYlrYlsZmuZmvZmw_\ nx_ny_nz_nuakqbimcfiedefbag_YhYUjWQkTMlRImPEZRBKT8\ 6VAARBENCIJELGFPCGT8HW5G_4Fb4Ee3Dh3Cl2Bo2Ar19u1Ct2\ Fs3Ir4Lr5Oq6Rp7Uo8Wo8VmAVlCVlDVmFVnGUoIUpJUqLUrNUs\ OTtQTuRTvTTwUTxWTyXdzdpzlkzmgznczo_zpWzqSzrOzsKztG\ zuOzdWzOcz7bzAbzDbzGazJazMazP`zS`zU`zX_z__zb_zeZzh\ ZzkZzmPz5Pz7Pz9PzBPzDPzEPzGPzIPzKPzMPzNPzPPzRPzTPz\ VPzWSzXUzYXzZZz_az`cz``zZYzYVzWSzVPzUMzSJzRGzQWzaj\ zmhzhgzdez`dzWczSazO`zJZzFYzBXz7Uz6Sz5Pz5Nz4Lz4Iz3\ Gz3Ez2Bz29z17z17z17z17z16z16z16z16z16z16z16z15z0Zz\ hbzkeznizqlztpzwszzrzyqzx } 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==================================

2 1

Tracing Negativ Periodicity
by SherLok Merfy 16 Mar '04

16 Mar '04

If you're like me, then you hit 't' at the spash screen of FRACTINT instead of believing in default fractals or complaining about maps that disappear whenever you switch fractal types. It's worth noting that it's FRACTINT that defines negative periodicity, and it means "show your work". A picture is worth a hundred lies, so I'll mention that before I start: Methods { ; A look at the internals of tesseral, border ; tracing, and diffusion at the inversion of where x=1/3. reset=2003 type=mandel passes=t center-mag=-0.533722/6.10623e-016/0.9699869/1.5686/-90/-1.233735336114\ 70521e-014 params=0/0 float=y maxiter=255 fillcolor=2 inside=255 invert=0.47/-0.33333333333333333/0 periodicity=-2 colors=0zzzzz00zz0zz0Wz00zV0zz0<3>0z00zV0zz<3>00zV0zz0z<3>z00<3>ze0zo0\ zz0Wz00z0<3>0ze0zo0zz<3>00zV0zz0z<3>z00<3>ze0zo0zz0<3>Lz0Bz00z00zV0zz<\ 3>0Lz0Bz00z<3>z0zz0Wz00<3>ze0zo0zz0<3>0z0<3>0ze0zo0zz<3>0Wz0Oz0Gz08z00\ z<3>z0zz0Wz00<3>zz0Wz00z0<3>0zz<7>0Rz0Nz0Iz<3>00z<3>z0z<3>z0Lz0Bz00zV0\ zz0<3>az0Wz0Qz0<3>0z00zV0zz<3>0Lz0Bz00z<3>e0zo0zz0z<3>z00<3>ze0zo0zz0<\ 3>Lz0Bz00z00zV0zz<3>0az0Wz0Qz<3>00zV0zz0z<3>z00zV0zz0<5>Wz0Rz0Lz0<3>0z\ 0<5>0zV0z_0ze<3>0zz<3>00zV0zz0z<3>z00<3>ze0zo0zz0Wz00z0<3>0zP0zV0z`<3>\ 0zz<3>000 } Bogus, my cat, was last seen evading American Foreign Policy on a rocket destined to annoy Marvin The Martian. I had a joke about "advanced connect the dots" in high school that I thot was funny, so little did I know that the mathematic art form could safely be called "Advanced Paint By Number" to piss off the blondes who thot they knew all about that. In the above "methods", you would see three critical rejions; White On Blue: First Escapees. Black On Blue: Rejion of unlikelyhoods. Yellow On Blue: Rejion of dispute. [Negativ periodicity is required to make border tracing work in this example, so if you zoom or pan this fractal to where border tracing yields what could be mistaken for a dubl fawlt, then try a more pessimistic number.] The rejion of dispute is the only part that rendering this fractal with passes=diffusion will highlight. Border tracing will highlight all of the mandeloids (physically on the outside, while mathematically on the inside of an inversion), while tesseral makes for a clear-cut reminder that this is art in the midst of analytic minds -- where geers and artsies work together with bounded chaos. This rejion is yellow on blue. If a bug is here, then it looks kinda cool, so maybe THIS should be the default parameters, no matter what you think of periodicity checking. Perhaps periodicity should be moved to the X-screen, while one of the doo-dads like biomorph or decomp (that don't seem to apply to orbital fractals, either) can move to Y. Synchronous Orbits? That's so close to the bleeding edge that it doesn't work with inversions. Now, as an excercise for the reader, which means I'm too lazy to answer the question myself: Why does border tracing require colour number zero?

1 0

for jim muth
by David Lowenstein 15 Mar '04

15 Mar '04

since I am a twin of my brother hugo, are there such thing as twin fractals? -david

1 0

FOTD 15-03-04 (Eggplant on your Face [5])
by Jim Muth 15 Mar '04

15 Mar '04

FOTD -- March 15, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's brief diversion takes us to the fractal created when the negative square root of 2 is combined with 1/4 part of 1/100th of the negative sign of the beast. With all this negativity going for it, the resulting fractal must be beastly indeed. If not beastly, the image is certainly mystical. Stretching to infinity as it does, the square root of two is as close to eternity as one could come while still on earth. And as for that mystical 666 beast, the less said about him the better. The name I gave the image is "Eggplant on your Face", which has nothing at all to do with the appearance of the image. I think I was listening to my standard morning fare of talk radio when the totally irrelevant phrase came to me. And since I can't seem to concentrate on the fractal of the day, it might be time to say I rated it at a 5, with a value of 53, and end the discussion, which seems to be going nowhere anyway. As always, the pre-rendered image is available for viewing and download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung around most all day Sunday here at Fractal Central, but the temperature reached 50F 10C, which was mild enough to let the cats to enjoy their needed time outdoors. They ended the day happy. Today is starting even warmer, and the sun is bright. It looks like another good day. For me, it will not be a good day until the work is finished. And that time is yet several hours off. Until next FOTD, take care, and one of these days I might actually learn enough math to claim to be a mathematician. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ EggplantOnYourFace { ; time=0:09:24.64--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.80348715162360600/-0.266042032269169\ 20/8.291078e+008/1/-17.5/7.15007914269885636e-005 params=1/-1.414213562373/0.25/-6.66/0/0 float=y maxiter=1200 inside=0 logmap=167 periodicity=10 colors=000zXLxVLy0LvSLt0LqRLl0Pi0Se8VbEXaL__QaXWeY\ `fVei_jlaoofspiysmzupzxszztzxtzwuzuuztwzswzqxzpxzo\ zzmzzlzzkzzizzhzzfzzezzczzazz`zz`zvPzrAzn0wm2pm9im\ FcjH_gIVeIQcKL`LHZLAWN5UNA`YHShKkpIioHgoFdoFdoCaoA\ ZoAXm9Wm7Um7Sm5Qm2Om1Mm1Ll0Jl0Hl0Fl0El0Cl0Alxdzqgz\ lixfjt`mqVnmmoimqemsamtYmvUmxQmtPmsNmrLmqKAoIFnHKm\ FNkFSjCViA_g9ae7fd5ic2la2kZ5iX7iW9hUAfSCfRFeQHeOIc\ MKaLLaJN`HN_FP_EQYCSYAUX8VV5XV4YU2_S0`S0aQ0cQ0cX0a\ a5`hC_mH_sMYxRXzWXz`VzdUzgUzZXzR_qJ`h8cY0fP0ham0_n\ 0Xo0Uq0Qs0Nt0Kv0Hx0Cy09z05z11z10z10z20z20z20z90zF0\ zI0zN1zQ2zV5z_9zaAyfCyiFxmIvqKttLsxNszQvxSxuVzsXzp\ _zm`zkczhezefzaYzQQqCHg07X09Z09Z09Z09Z5A`9A`FA`IA`\ NC`QCaVCaYCaaFafFaiFcmFcpHctHcwHczHdzIdzIdzIdzIdzP\ izVmz_ozeszivzozztzwxztzzqzzozzqzzszztzzuzzwzzxzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzLzzLzzL } 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==================================

1 0

[Fractint] Hearts finalist. heartsf.par = whole message with snipped rambling.
by SherLok Merfy 15 Mar '04

15 Mar '04

I don't use "frm:formula_name", because that means you can't also run FRACTINT with "formulafile=heartsf.par" and expect to see your formulas. FRACTINT will let you try to run parameter specs. as formulas from such merged files, though. If you missed my QBASIC for blowing music _into_ Fractint, then you can reverse the enjineering with this formula, otherwise more QBASIC might come later with the other three formulas that I will use. My tuning is simple: whole numbered multiples of a source frequency. It doesn't matter what the source frequency is unless you want an orchestra to accompany the computer, because it's ratios that matter to the ear. My tune has literally changed. This one works quite nicely, but that's challenging, because it makes for a look very different from the basis equation: heartx, and I want more unity or commonality among the images than that. I wonder if PDF is sent to PostScript printers without rendition, because writing this stuff in PostScript and converting to PDF might let me compress my output (for cards) to what fits on a floppy (or takes less time to download than to render). If rendition of PDF is done on the host of the printer, then there's no problem, but if it's sent to the printer, then the FRACTALS must be very fast or they'll make it time out. It's tempting to explicitly copyright this work, even if it takes an hour and a half plus some editing on a box older than five years. It falls under collective works, but this doesn't: http://ecn.ab.ca/~brewhaha/img/hearts.jpg , so fair use rules apply, whatever that means with MicroSoft source code running around making a mess of everything else that doesn't work. _______ heartsH { ; Chrominance: Alter through mask of HeartsV as ; grayscale. reset=2003 type=formula formulafile=heartsf.par formulaname=hearty passes=d center-mag=0.00844324/-1.37358/0.3241387/1.2195 params=2/0 float=y maxiter=255 inside=0 colors=000z00zz00z00zV0zz0Wz00z<3>z0zz0Wz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz\ 00zV0zz0z<3>z0Lz0Bz00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00z<3>e0zo0zz0zz0Wz00<\ 3>ze0zo0zz0<3>0z00zV0zz<3>0Lz0Bz00z<3>z0z<3>z0Lz0Bz00<3>zV0zb0zj0zr0zz\ 0<3>0z00zV0zz<3>00zV0zz0z<3>z00<7>z_0zc0zh0<3>zz0<3>0z0<3>0ze0zo0zz0Wz\ 00z<3>P0zV0z`0z<3>z0zz0Wz00<3>ze0zo0zz0<3>Lz0Bz00z0<3>0zz<3>0Lz0Bz00z<\ 3>e0zo0zz0zz0Wz00<3>zP0zV0z`0<3>zz0Wz00z0<3>0zz0Wz00z<5>V0z_0ze0z<3>z0\ z<5>z0Wz0Rz0L<3>z00<3>zz0Wz00z0<3>0zz<3>0Lz0Bz00zV0zz0z<3>z0az0Wz0Q<3>\ z00<3>zzz } heartsV { ; Drop luminance through this "graymask" after raising 50%. reset=2003 type=formula formulafile=hearty.par formulaname=hearty passes=d center-mag=0.00844324/-1.37358/0.3241387/1.2195 params=2/0 float=y maxiter=255 inside=0 outside=atan; colors=(a)rainboh.map colors=000z50z70zB0<3>zJ0zL0zM0zN0zP0zR0<5>z_0z`0za0zb0zd0<14>zu0zv0zw\ 0zx0zy0<14>lz0kz0jz0<5>bz0az0`z0<4>Tz0Sz0Rz0Pz0Nz0Mz0Lz0Iz0Hz0Ez0Dz0Bz\ 0<2>0z00z30z70zB0zD0zH0zJ0zK0zL0zN<3>0zS0zT0zV0zX<4>0zc0zd0zf<14>0zu0z\ v0zw0zx0zy<8>0rz0qz0oz<4>0jz0iz0hz<8>0Xz0Vz0Tz<3>0Pz0Nz0Lz0Jz0Hz0Gz0Dz\ 0Bz<2>00z30z70zB0zD0zF0zG0z<4>P0zQ0zS0zT0zV0z<2>_0z`0za0zb0zc0z<3>h0zi\ 0zk0z<9>u0zv0zw0zx0zy0z<13>z0mz0lz0k<3>z0fz0dz0cz0az0`<4>z0Vz0Tz0S<3>z\ 0Lz0Jz0Hz0Gz0D<3>z04 } heartsS { ; Mask for stripes of fading. Maybe needs work. ; Perhaps wood grain, like on my skull. reset=2003 type=formula formulafile=hearty.par formulaname=hearty passes=d center-mag=0.00844324/-1.37358/0.3241387/1.2195 params=2/0 float=y maxiter=255 inside=0 proximity=1 outside=fmod colors=000zzz000zzz000000zzz000000000zzz000<3>000zzz000<5>000zzz000<4>\ 000<4>000zzz000<4>000<4>000zzz000<6>000<4>000zzz000<10>000<4>000zzz000\ <12>000<4>000zzz000<16>000<4>000zzz000<22>000<4>000zzz000<24>000<4>000\ zzz000<30>000<4>000zzz000<29>000 } Hearty { ; Formula. Needs arrays for speed. Cropped as above, ; about 30min. on 350MhzPII @ 1280x1024, ; more for atan and fmod. s=z=atanh(real(-1/pixel) +flip(imag(-.5/pixel))), iter=0, t=|P1|, mean= 24.15789473684211: imod=(iter/ 127 -trunc(iter/ 127 ))* 127 , ; imod=remainder(num_notes/iter) iter=iter+1, if(imod>-1 && imod< 8 ) note= 11 elseif(imod> 6 && imod< 19 ) note= 13 elseif(imod> 17 && imod< 22 ) note= 17 elseif(imod> 20 && imod< 27 ) note= 19 elseif(imod> 25 && imod< 34 ) note= 16 elseif(imod> 32 && imod< 41 ) note= 23 elseif(imod> 39 && imod< 52 ) note= 31 elseif(imod> 50 && imod< 55 ) note= 29 elseif(imod> 53 && imod< 60 ) note= 23 elseif(imod> 58 && imod< 67 ) note= 31 elseif(imod> 65 && imod< 74 ) note= 11 elseif(imod> 72 && imod< 85 ) note= 9 elseif(imod> 83 && imod< 88 ) note= 13 elseif(imod> 86 && imod< 93 ) note= 17 elseif(imod> 91 && imod< 100 ) note= 13 elseif(imod> 98 && imod< 107 ) note= 29 elseif(imod> 105 && imod< 118 ) note= 51 elseif(imod> 116 && imod< 121 ) note= 59 elseif(imod> 119 && imod< 128 ) note= 44 endif, z=s*(z-flip(note/mean))*(flip(note/mean)-z) |z| <= t } Heartx { ; Formula. The core of hearty. s=z=atanh(real(-1/pixel) +flip(imag(-.5/pixel))), iter=0, t=|P1|,: z=s*(z-(0,1))*((0,1)-z) |z| <= t }

2 2

September That Never Ended On The Buglist
by SherLok Merfy 15 Mar '04

15 Mar '04

<a href="http://www.google.com/search?hl=en&as_qdr=all&q=VESA+video+card+driver&btnG…" >If you were searching for a driver, and you found FRACTINT, instead, then this link might help.</a> You might not need a Terminate and Stay Resident DOS program like HDILOAD to enjoy the higher resolution modes of your video card and monitor. VESA might be on the card, unless it's "Designed For Windows", and even in the extreme of those cases, it's possible to save images from FRACTINT at higher resolutions than any monitor known to be in production, as well as splice a lot of smaller parts of an image into one very large fractal poster. You'd think I was getting paid for this. In a way, I am. FRACTINT is the best way to disconnect from that mess we call English Spelling on the Internet without ignoring your computer or turning off your girlfriend. And it would be even if it didn't let you render formulas that hav absolutely no practical meaning in the real world, but to which your friends say: "That Looks Cool...What is it?". But, let me remind you that <a href="http://www.drivers.com/"> these people supply drivers.</a> We don't. Not unless we own the hardware, the documentation, a month of Sundays, and stock in the manufacturer.

1 0

FOTD 14-03-04 (The Great Mystery [not rated])
by Jim Muth 14 Mar '04

14 Mar '04

FOTD -- March 14, 2004 (Rating none) Fractal visionaries and enthusiasts: Anyone looking at today's image would recognize it at once. They would know that it is a picture of the Mandelbrot set. And they would be wrong. One might examine the image as carefully as possible, and they would find no evidence that it is not the Mandelbrot set. But it is still not the set. The Mandelbrot set is the slice that cuts a two-dimensional hole through the center of the Z^2+C Julibrot in the plane of the two C-axes. There is only one such slice, therefore there can be only one Mandelbrot set. But what then is today's image, in which the formula Z^2+C is iterated? It is a slice of the Julibrot cut in an oblique direction halfway between the Mandelbrot and Julia orientations. Since a double rotation is needed to turn from the Mandelbrot to the Julia orientation, there are many slices oriented in the half- way position. Today's slice is only one of them. It can be easily demonstrated that today's image is not the familiar M-set by changing the starting point of C. Instead of merely shifting the image around on the screen, changing initial C in today's image actually changes the shape of the fractal as the image shifts. Changing initial Z also shifts the image and changes the fractal's shape. Discovering this second Mandelbrot set, which I call the shadow set, was perhaps the greatest surprise of my entire fractal career. It has linear dimensions 1.4142 times that of the familiar M-set and an area double that of the familiar set. An entirely new set of coordinates is needed to find the familiar objects. In the shadow set, East Valley terminates at 0.35355 on the X-axis, while the largest midget is centered at -2.47485. This shadow set has the curious property that the C and Z coordinates of every point are of equal value. The set also is curious because of the fact that some points as far from the origin as 2.8284 are trapped. This means that the trapped points of the Julibrot are not contained within a hypersphere of radius 2. I think a radius of 2.8284 might do the job, but I am not sure. And yes, it is possible to get a marginally greater resolution of a Mandelbrot object by examining the shadow set, though the screen coordinates of the object being sought must be multiplied by a factor of 1.4142 before the search begins. I have never stopped to figure in how many ways a plane may be oriented halfway between the Julia and Mandelbrot directions. I could probably make quite a project of finding all of them. And I also have doubts that the present SliceJulibrot2 formula can draw them all. But it's something to think about. I did not rate today's image, since its interest is almost totally mathematical. The render time of under three seconds makes up for the lack of artistic merit. The name "The Great Mystery" fairly describes the very simple image of today's FOTD. As always, the completed GIF file is available for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday was sunny but breezy and chilly here at Fractal Central. With the sun now rising well above the holly trees during the middle of the day, the fractal cats did manage over 1/2 hour in the yard, but finally, the temperature of 43F 6C chilled their ears beyond endurance, and they came inside to enjoy their tuna. Today is starting with less wind and higher temperatures, but the clouds are moving in. The cats have yet to express their opinion of the conditions. As for me, I'm going to take it easy for the rest of the day. I might even get dragged to one of the countless local antique emporiums to look at the stuff that others have thrown away. One thing certain, (unless the world ends), is that the next FOTD will appear in 24 hours. Until then, take care, and believe it or not, here in Maryland they are talking of taxing our potato chips. They call it a 'snack tax'. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Great_Mystery { ; time=0:00:02.97--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=-0.7071/0/\ 0.612855 params=45/0/45/0/0/0/0/0 float=y maxiter=255 passes=b inside=255 logmap=yes symmetry=xaxis periodicity=10 colors=000JC0ME0PG0SI1VK2YM3`O4cQ5fS6iU7lWEgYL__SS\ aZKceCekJgnQiqXktbmwempgmijmblmWnmQnmQmmQmmRmmRmmR\ lmRlmRlmSkmSkmSkmTjmUjmVjmWimXimYimZim_hm`hmahmbhm\ cgmdgmegmffmgfmhfmiemjemkemldmmdmodmqcmscmucmwcmyb\ mzbmzbmzamzamzamz`mz`mz`mz_mz_mz_mzZmzZmzZmzZmzYmz\ YnzYozXpzXqzXrzWszWtzWuzVvzVwzVxz3yz6zz9zzBzzEzzGz\ zJzzLzzOzzQzzTzz_zzZzzZzzZzzZzzZzzZzzZzzZzzZzzZzzY\ zzYzzYzzYzzYzzYzzYzzYzzYzzYzzYzzXzzXzzXzzXzzXzzXzz\ XzzXzzXzzXzzXzzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzWzzVz\ zVzzVzzVzzVzzVzzVzzVzzVzzVzzEzzJzzNzzRzzbzzazzazza\ zzazzazzazzazzazz`zz`zz`zz`zz`zz`zz`zz`zz_zz_zz_zz\ _zz_zz_zz_zz_zzZzzZzzZzzZzzZzzZzzZzzZzzYzzYzzYzzYz\ zYzzYzzYzzYzzXzzXzzXzzXzzXzzXzzXzzXzzWzzWzzWzzWzzW\ zzWzzWzzWzzVzzVzzVzzVzzVzzVzzVzzVzzozznzznzznzzmzz\ mzzmzzlzzlzzlzzlzzkzzkzzkzzjzzjzzjzzjzzizzizzizzXz\ zYzzZzz_zz`zzazzbzzczz000 } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================

2 1

Re: Kathy
by JackOTradez 13 Mar '04

13 Mar '04

Kathy, It seems like you trying to run fractint from windows shell. This usually works, but sometimes (as you see) there can be problems. It is best to run in native DOS. As your system boots up, hit F8 key. This will give you a menu. Choose "command prompt only". This will boot you into Dos 7.0. Run fractint there. When you are done, just type "win" and hit ENTER key and you will be in windows. You should also know how to use DOS, like navigating to directories, using DOS commands, and the EDIT program. If you use fractint a lot (like I do) you can configure your win98se system to boot to DOS every time without need F8 key. I can tell you details how to do this if interested. Too much to spell out all here. JoTz ----- Original Message ----- From: <fractint-request(a)mailman.xmission.com> To: <fractint(a)mailman.xmission.com> Sent: Wednesday, February 11, 2004 10:06 AM Subject: Fractint Digest, Vol 12, Issue 6 > Send Fractint mailing list submissions to > fractint(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > or, via email, send a message with subject or body 'help' to > fractint-request(a)mailman.xmission.com > > You can reach the person managing the list at > fractint-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Fractint digest..." > > > Today's Topics: > >    1. Problems running Fractint (Kathy Roth) >    2. Re: Problems running Fractint (Paul N. Lee) >    3. FOTD  08-02-04  (Jungle Lushness [6]) (Jim Muth) >    4. Fractint version 20.3 patch 1 (Jonathan Osuch) >    5. FOTD  09-02-04  (Apples and Oranges [7]) (Jim Muth) >    6. FOTD  10-02-04  (Order from Chaos [5]) (Jim Muth) >    7. FOTD  11-02-04  (Watchtower [8]) (Jim Muth) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sat, 07 Feb 2004 21:31:29 -0800 > From: Kathy Roth <kroth(a)well.com> > Subject: [Fractint] Problems running Fractint > To: Fractint and General Fractals Discussion > <fractint(a)mailman.xmission.com> > Message-ID: <4025C9B1.8000109(a)well.com> > Content-Type: text/plain; charset=ISO-8859-1; format=flowed > > Hi > I recently had some work done > on my computer and am unable to run > Fractint now- I have a very knowledgeable > computer consultant but he is not particulary > familiar with Fractint so I was wondering > if i can get some input from the list. > here are the details- >     Since about 1999 I have  had a Pentium > 500 running Windows '98 which was > put together by the consultant.  It has > a Matrox something or other card that was > chosen for Fractint and I have been > very happy with this system.  I use Netscape > rather than Microsoft Explorer and it was > version 4 something, have recently been > unable to access  some web sites because > of the old version of Netscape.  I use a modem. > This did not bother me much because > we have a fast connection at work and > if I needed to find something I could do it at > work.  I did want to be able to > listen to streaming audio and download > MP3's which I was not able to do but > other than that was happy.  I would not > have changed anything except there > started to be a smell and I > thought the fan had broken- it > was intermittent, turned out to > be the power cord burning and it was > replaced.  Meanwhile, they upgraded > Netscape and installed some virus > software and other stuff and now > I cannot run Fractint.  I had version 18.6 > in a file with about 2000 formulas, gifs, > unrelated stuff.  It would draw the default > mandelbrot and then the computer > would freeze, Ctrl-alt- delete would not > work and it needed to be unplugged. > I downloaded the newest version of > Fractint into a separate file and it > worked once but could not access the > other files.  I backed up those files > onto a CD (and as i came back into > the room where the computer was > not in its usual place, tripped over > the open CD drawer and broke it.) > Then I decided to download the new > Fractint into the old file, thinking > the program was corrupted in some way. > It did not work and froze the computer. > Then I tried the other version in the new > file and it also does not work reliably > but sometimes works- it seems to > depend somewhat on what video > mode I choose but mostly freezes the > computer.  I suspect something in the > new software is interfering- is this likely?- > I'll list the new software below. > While the computer was being fixed I > had  decided  to get a new laptop > to take to work and to connect to > the T1 line and to do new > stuff on, and to keep this computer > to run Fractint and some older DOS > programs etc., so I would be happy > to go back to the old situation > if I knew what the problem was. > (BTW I selected a beautiful light > IBM think pad, their customer > service and technical support has > been superb, they answer the phone > in 90 sec and know who you are, > unfortunately the laptop died midway > through set-up and they are > replacing it no questions asked, > so you can imagine I'm > a little frustrated.) > > Here's a list of the new software: > Netscape 7.1 > real Player latest free version > WinAmp > Ad-aware6.0 > Norton antivirus 2003 > Live!ware > new Windows Media Player > > Anyone have any ideas??? > Thanks so much- > Kathy Roth > > > > >  > > > > > > > ------------------------------ > > Message: 2 > Date: Sat, 07 Feb 2004 23:55:53 -0600 > From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> > Subject: Re: [Fractint] Problems running Fractint > To: fractint(a)mailman.xmission.com > Message-ID: <4025CF69.5BC0(a)Worldnet.att.net> > Content-Type: text/plain; charset=us-ascii > > Kathy Roth wrote: > > > > I recently had some work done on my > > computer and am unable to run Fractint > > now-     ........ > > ....so you can imagine I'm a little > > frustrated. > > > > Anyone have any ideas??? > > Personally, I would say as soon as you get your laptop back, and it is > in good working condition, just back up the files you want to keep and > then reformat the whole drive and reload Win-98 as if it were a new > system. > > Sometimes starting from scratch is much better, and you only have to > install those few programs you actually will need.  This will leave you > with a much cleaner system than one that has had several programs and > applications installed and removed over the years. > > Sincerely, > P.N.L. > ------------------------------------------------- > http://home.att.net/~Paul.N.Lee/PNL_Fractals.html > http://www.Nahee.com/Fractals/ > > > ------------------------------ > > Message: 3 > Date: Sun, 08 Feb 2004 09:55:09 -0500 > From: Jim Muth <jamth(a)mindspring.com> > Subject: [Fractint] FOTD  08-02-04  (Jungle Lushness [6]) > To: fractint(a)mailman.xmission.com > Cc: philofractal(a)lists.fractalus.com > Message-ID: <1.5.4.16.20040208095739.0d6f4c84(a)pop.mindspring.com> > Content-Type: text/plain; charset="us-ascii" > > > FOTD -- February 08, 2004 (Rating 6) > > Fractal visionaries and enthusiasts: > > I named today's image "Jungle Lushness".  Perhaps I should have > named it something like "Too Lush".  The image has almost too > much richness.  No jungle on earth was ever as lush as the scene > in the image, not even in the deepest depths of the Amazon rain > forest. > > This over-abundance of detail and color has cost the image one > full rating point.  After careful consideration, I could give > the image a rating no higher than a 6, which is still somewhat > above average, but falls short of the 7 that I first considered. > > The parent fractal was created by combining 1 negative part of > Z^(-1.1) with 0.1 negative part of Z^(-11) and adding (1/C).  > This parent is several orders too large to fit on the default > screen, but a single outzoom reveals the most interesting parts. > The interesting part of the parent consists of an oversized > banana-shaped hole with a Mandelbrot set lying at its southwest > extremity.  The banana-shaped hole splits the East Valley of the > M-set as it joins with the set.  Today's scene is located on the > shoreline of the hole, near the point where it joins the M-set. > > The traditional equal-iteration-band method of rendering today's > scene produces a very interesting image -- almost good enough to > be a FOTD.  The evaporated version, which appears as today's > FOTD, is improved just enough to be the version I chose. > > As an 'evaporated' image, today's scene consists entirely of > trapped inside points made visible by the 'bof61' inside fill.  > This fill traces quite faithfully the foundation features of the > 'real' image that has been evaporated, but adds bells and > whistles that the real image never had. > > Sometimes a humdrum scene can be improved by evaporating it, > sometimes not.  The only way to find out is to go ahead and > evaporate an image and see what can be done with the ghostly > remains.  There are also 'half-evaporated' and 'extra-condensed' > versions of images created by negative exponents of Z, but I > have yet to do much investigating in these areas. > > The render time of today's image is 13-3/4 minutes.  Combined > with the rating of a 6, its overall value is 44 -- a value that > is not too bad.  The image may be seen quicker by downloading it > from Paul's web site at: > >        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > Saturday turned into a quite pleasant day here at Fractal > Central, when sun and an unexpectedly warm temperature of 43F 6C > prevailed most of the afternoon.  The cats enjoyed the few spots > where the sun is now shining above the holly trees in the early > afternoon, and ignored the remaining ice.  But this morning > things are again frozen solid.  It once again feels like winter. > I doubt that the duo will have a second good day. > > My day will probably be average . . . most days are . . . that > is unless something unexpectedly good or bad happens.  Since > nothing like this is likely to occur, the day will probably pass > with nothing more notable taking place than the appearance of > the next FOTD fractal image.  When that happens, we will have > found tomorrow's FOTD.  Until then, take care, and does the > brain create the mind, or does the mind create the brain . . . > or is it all just one big fractal? > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Jungle_Lushness    { ; time=0:13:47.67--SF5 on a P200 >   reset=2003 type=formula formulafile=allinone.frm >   formulaname=MandelbrotMix4 function=recip passes=1 >   center-mag=-1.38105363973058900/-5.353386666406572\ >   00/1.344518e+009/1/-137.5/0.000903528871152227409 >   params=-1/-1.1/-0.1/-11/0/1e+100 float=y >   maxiter=2000 inside=bof61 periodicity=10 >   colors=000ePadQ`dSZcTXcVVbWUbYSaZQa`O`aN`cL_dJ_eIm\ >   ulnqmnnnojnogopdop`pqYpqVqrRrrOrsLssHstEttBtmHfAMT\ >   EKSHIRKGQNEQQCPTAOW8NZ6Na4Md2Lg0LXHNMYPBmQEiTHeVKb\ >   XMZ_PWaSScUOfXLh_HjaEl_JnZNpYSrXWtW_vUdwThySlyRqyQ\ >   uyPyyOvyOtyOrwOptOnqOlnOjkNghNeeNcbNa_N_XNYUNWRNUO\ >   LSPJRPHPPGOQEMQCLQBKQ8KN6KKEEIM8GT3FS6HS8JRALRCMRE\ >   OQGQQIRPKTPMVPOWRLaSJfTHkVFpWDuXByY9yWAyUBySCyQDyO\ >   ExMFvKGuIGtGHrEIqCJoAKn8Lm6Mk4Nj2NivEfuHhuJjtLltNn\ >   tPpsRrsUtrWvrYxr_yqayqcyqeyr`ysXutSouOjvJdwF_xBVxH\ >   _xNdxThyZmydryjwypyimuVjpGgk1df8_eFVeMQdTLd_GcfBcG\ >   DyHLyITyI_yJgyJnyOosSokXod`oXeoQioImoBijJeeQb`XZWc\ >   WRjTQgQPeNOcLNaIM_FLYCKWAJU7IS4HQ2HOKRUa`Zrjcogfle\ >   hickfamc_p`YrYVuVTwSRyPPyMNyJLyOQyTVyZ_ycdyhiyV_jb\ >   bhZabflnkomekb_gSUdIQ`HMXHITGEPGDOKDONDNRDNUCMYCM`\ >   CMdCLgCLkBKnBKrBJuBJyBJyDLsEMkFNcGPWHQOIRGJUKaCTbE\ >   WcFYdG_eHafIcgJegKgfMeeNc } > > 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================================== > > > > ------------------------------ > > Message: 4 > Date: Sun, 8 Feb 2004 17:25:05 -0600 > From: Jonathan Osuch <osuchj(a)avalon.net> > Subject: [Fractint] Fractint version 20.3 patch 1 > To: Fractint and General Fractals Discussion > <fractint(a)mailman.xmission.com> > Message-ID: <200402081725.05278.osuchj(a)avalon.net> > Content-Type: text/plain;  charset="us-ascii" > > Fractint and Xfractint version 20.1 patch 1 is now available on the > developer's web site. > > What's new: > > Fixed the float bailout for the lambdafn fractal type when the EXP function > is used so the float and integer images match. >   > Jan Andres contributed Xfractint fixes that allow compiling with newer > versions of gcc because varargs.h is no longer supported.  Enabled the > use of the long double type on Solaris.  Moved the getwd() macro definition > in prompts1.c after the #include lines, to avoid the mess that happens when > the prototype for getwd() is included but it's already defined as a macro. > Added some Solaris-specific comments to the Makefile. > > Fixed the sound in Xfractint so the beep turns off now. > > Changed lsys.c to use inline1 instead of the reserved word inline. > > Jonathan > > > > ------------------------------ > > Message: 5 > Date: Mon, 09 Feb 2004 10:11:57 -0500 > From: Jim Muth <jamth(a)mindspring.com> > Subject: [Fractint] FOTD  09-02-04  (Apples and Oranges [7]) > To: fractint(a)mailman.xmission.com > Cc: philofractal(a)lists.fractalus.com > Message-ID: <1.5.4.16.20040209101426.0da7473e(a)pop.mindspring.com> > Content-Type: text/plain; charset="us-ascii" > > > FOTD -- February 09, 2004 (Rating 7) > > Fractal visionaries and enthusiasts: > > Today's image takes us once again to that ultimate fractal > reality, the Mandelbrot set, for a brief stay in one of the more > remote valleys.  I call the M-set the ultimate fractal reality > with some misgivings.  I am not certain that such a thing as > fractal reality exists.  As far as that goes, I am not even > certain that such a thing as physical reality exists.  (I am > reasonably certain that I exist however.)  But if anything like > ultimate fractal reality does exist, the Mandelbrot set comes as > close to filling that definition as we have yet come. > > The scene of today's action lies in a spiral deep in the outer > side of the right branch of the valley leading to the large > period-4 bud on the northeast shoreline of the main bay of the > Mandelbrot set.  The features that appear in the image are > familiar to those with experience exploring the M-set.  This > familiarity cost the image one full rating point.  But to make > up for the familiarity, the coloring is somewhat unexpected, and > this originality added one full point to the rating.  As a > result, we have an image with a rating of a 7 and, due to the > short render time, an overall value of 321. > > I named the image "Apples and Oranges".  The tiny orange spots > remind me of oranges.  The apples were added just to make a more > interesting name. > > There are two ways of viewing the image: first, by running the > included parameter file; second, by downloading the completed > GIF image from: > >        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > It remained sunny but breezy and quite cold here at Fractal > Central on Sunday.  The temperature never rose above freezing, > which kept Tippy the tabby indoors.  Thomas, the rusty, ventured > out onto the remaining ice for a few minutes before deciding > that comfort was the better part of valor, and hastily retreat- > ing back inside.  They both ended the day with a treat of left- > over salmon.  Today is starting milder.  Hopefully, it will > be better for the duo. > > For me, it looks like today might be a bit on the busy side.  > But unless an avalanche of unexpected work arrives, I'll find > time to dredge up another fractal worthy of FOTD status.  Until > tomorrow, when that next fractal will appear, take care, and see > you then. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Apples_and_Oranges  { ; time=0:02:10.88--SF5 on a P200 >   reset=2003 type=mandel passes=1 center-mag=+0.25604\ >   36923746491/+0.4940656109920195/3.6466e+007/1/177.5\ >   /1.38515831929475475e-008 params=0/0 float=y >   maxiter=15000 inside=0 logmap=1560 periodicity=10 >   colors=000D7WD5YC3ZC2_B4ZB5YB6XB7XB8WA9VAAUABUACTA\ >   DSAER9FR9GQ9HP9IO9JO9KN8LM8ML8NL8OK8PJ8QI7SI7TH7UG\ >   7VF7WF7XE6YD6ZC6_C6`B6aA6b95c95d85e75f65g65h54i44j\ >   34k34l24m14n16m37l48l59k6Bk7Cj9DjAEiBGiCHhDIhFJgGL\ >   gHMfINeJOeLQdMRdNScOTcPVbRWbSXaTYaU_`V``Xa_YbZZdZ_\ >   eY`fYbgXciXdjWekWflVhnVioUjpUkqTlrTmqSjpRhpQfoPdnO\ >   bnN`mMZmLWlKUkJSkIQjIOjHMiGKhFIhEFgDDgCBfB9eA7e95d\ >   83d81eA3eB4fD6fE7fF8gHAgIBgJDhLEhMFiOHiPIiQKjSLjTM\ >   jUOkWPkXRlZSl_Tl`VmbWmcYmdZnf_ngaoibojdokepmfunhzo\ >   izqkzrlztmzuozvpyxrxyswztvyuuzvtzwszxszyszzszzszzs\ >   zzszzswwsvwsvwsvwsvwquupttossnsrmrplqokqnjpmiolhoj\ >   gnifmhelgdlfckdbjcajb`ia_h_ZhZYgYXfXWeWVeUUdTTcSSc\ >   RRbQQaOPaNO`MN_LM_KNZKOYKPYKQXKRWKSWKTVKTVKUUKVTKW\ >   TKXSKYSKZRK_QKaQKcPKeOKgOKiNKkNKlMKmLKnLKoKKpKKqMK\ >   rOKsQKtSKuUKvWLwYLx_MyaMzcMzcNzcNzcOzcOzcOzcPzcPzc\ >   QzcQzcQzcRzcRzcRzcSzcSzcT } > > END 20.0 PAR-FORMULA FILE================================== > > > > ------------------------------ > > Message: 6 > Date: Tue, 10 Feb 2004 10:41:00 -0500 > From: Jim Muth <jamth(a)mindspring.com> > Subject: [Fractint] FOTD  10-02-04  (Order from Chaos [5]) > To: fractint(a)mailman.xmission.com > Cc: philofractal(a)lists.fractalus.com > Message-ID: <1.5.4.16.20040210104331.2aa7fa40(a)pop.mindspring.com> > Content-Type: text/plain; charset="us-ascii" > > > FOTD -- February 10, 2004 (Rating 5) > > Fractal visionaries and enthusiasts: > > With today's image we tunnel quite deep into the Mandelbrot set. > At the end of our trip we find ourselves in a remote valley just > off the northwest shoreline of the main bud of the large midget > on the negative X-axis.  This area consists of areas of wild > chaos interspersed with relatively orderly and almost straight > filaments.  The nature of the general area, with its mixture of > order and chaos, is reflected quite well in today's image, which > I have named "Order from Chaos". > > The magnitude of the image is really in the range of arbitrary > precision math, but I have forced the program to use the conven- > tional math routine by including the 'mathtolerance=/1' entry in > the parameter file.  In such a chaotic image, the resulting > breakdown in resolution is barely noticeable, and the time saved > is a sizable part of a day. > > One result of forcing the use of conventional math is the > unwanted stretching and skewing, which is reported on the 'tab' > screen of the image.  This distortion is barely noticeable, but > those who wish to render the image marginally more accurately > may be re-enable arbitrary precision math by striking the 'g' > key and entering the command 'mathtolerance=/0'. > > The 'logmap' method of coloring does not work with today's > image.  The 'tdis' option runs very slowly.  The other outside > coloring options either create too much chaos or run far too > slowly.  The best method I found of coloring today's image is > also the simplest -- outside=iter logmap=0. > > When the time came to rate the image, I was undecided whether to > consider the overworked nature of the M-set.  Is today's image > really that unusual?  After almost 20 years of exploration, is > there anything truly new to be found in the M-set within the > range of conventional math?  One would think so.  At the magni- > tude of today's image, the entire M-set would be about as large > as the solar system.  And except for the X-axis symmetry, no two > spots of the M-set are identical.  But the differences are often > infinitesimal, and for all practical purposes, the major varia- > tions have long since been found.  Considering all this, I rated > today's image at an above-average 6, which, with the render time > of just under 5 minutes, gives an overall value of 125.  I must > get a machine fast enough to make arbitrary precision math prac- > tical.  Way down deep is where the undiscovered M-set goodies > lie. > > To see the image, run the included parameter file and sit back > to watch the fun, or go to Paul's FOTD web site at: > >        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > and download the image from there. > > The clouds moved in quickly here at Fractal Central on Monday, > but the temperature reached 46F 8C, which was mild enough for > the fractal cats to enjoy a full 90 minutes in the yard.  They > must have enjoyed their outing.  When the day ended, they were > content to settle down without a special treat. > > Today brings both work and fractals for me.  The work I will > finish; the fractals will never be finished.  I shall return in > 24 hours with more goodies, some concrete, some abstract.  Until > then, take care, and the search for truth is all too often > hindered by the difficulty in recognizing and accepting it. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START 20.0 PAR-FORMULA FILE================================ > > Order_from_Chaos   { ; time=0:04:50.28--SF5 on a P200 >   reset=2003 type=mandel passes=1 bailout=9 >   center-mag=-1.77551631029264878/0.0045532172225712\ >   74/3.305215e+013/1.0404/13.9106570650115682/-0.977\ >   835246052904727 params=0/0 float=y maxiter=80000 >   inside=0 periodicity=10 mathtolerance=/1 >   colors=000_hnaiocjpekqflrdiocgmcekccicagc_ecYccWcc\ >   UccSccQccOccMccKccIcdGcdEcdCceAce8ce6cf4cf2cf0cg6c\ >   gCcgIchKchKchKciKcjKckKclKcmKcnHcoCco7cpAcpDcqGcrI\ >   csLctOcuRcvQewPgxOiyNkzMmzNnzOpzPrzQryRovPosOmpMhm\ >   LckKZiIUgHPeFKcEFaDA_BAZAAY8AX7AW6AV4AU3AT2AS4AR6A\ >   Q7AP9AOBANCAMEALGAKHAJJAILAJMAKNALOAMPANQAORAPSAQT\ >   BRUCSVDTWEUXFVYGWZHX_IY`IZaJ_bK`cLadMbeNceOcgPchQc\ >   iRajS_kTYlTWmUUnUSmUQlUOjUMhUKgUNeSPcQRbQU`SWZUYYW\ >   `WZbU`dTbgRdiPfkOhhNgfNfcNeaNd_McXMbVMaSM`QL_OLZLL\ >   YJLXHLWJNVKOULPUMQTNRTOTSPUSRVRSWQTXQUZPV_PW`OXaOZ\ >   bN_dM`eMafLbgLchKdiKbgLaeL`cL_aLZ_LYYMXWMWUMVSMUQM\ >   SPNRNNQLNPJNOHNNFOMDOLBOK9OJ7OI6OK5MM5LO5KQ5IR5HT5\ >   GV5EX5DZ5C_5BXCEUJHRQJOXMLcOIjRGpTKlVNhXQdZT``XXb_\ >   TdbPfeLhhIjaMfWPbQTZJWWD_S7bO1eL7gMChNIiNNjOSkOYmP\ >   bnQhoQmpRrqRnmPjjNfgLbdJZaHWZFSVDOSBKP9GM7EYbGZcI_\ >   dK`eMafObhQciSdjUekWflYgm } > > END 20.0 PAR-FORMULA FILE================================== > > > > ------------------------------ > > Message: 7 > Date: Wed, 11 Feb 2004 10:06:23 -0500 > From: Jim Muth <jamth(a)mindspring.com> > Subject: [Fractint] FOTD  11-02-04  (Watchtower [8]) > To: fractint(a)mailman.xmission.com > Cc: philofractal(a)lists.fractalus.com > Message-ID: <1.5.4.16.20040211100854.0d77289a(a)pop.mindspring.com> > Content-Type: text/plain; charset="us-ascii" > > > FOTD -- February 11, 2004 (Rating 8) > > Fractal visionaries and enthusiasts: > > In yesterday's FOTD we tried to show what happens in filaments > along the shorelines of midgets that lie on the negative X-axis > of the Mandelbrot set.  This first attempt was only moderately > successful. > > Today we make the second attempt -- one that is somewhat more > successful.  We jump to a midget on the X-axis a short distance > beyond the largest midget, and examine the filaments near its > shoreline.  The filaments here are covered with tiny nodes which > remind me of long fences with watchtowers positioned every > kilometer or so.  These fractal watchtowers are islands of chaos > with smaller midgets at the center.  Today's image illustrates > one of these watchtowers -- an island of chaos sitting in a > prairie of order. > > I named the image "Watchtower" and rated it at an 8.  The rating > might be a bit excessive, but I do rather enjoy the image.  When > combined with the render time of 44 seconds, the image has an > overall value of 1067.  (I really must bring some consistency to > the way I determine the overall value.) > > The image may be seen by running the attached parameter file and > enjoying the lightning-fast rendering show, or by taking a trip > to Paul's FOTD web site at: > >        <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > and downloading the completed GIF image from there. > > Tuesday turned out to be the best day in over a month here at > Fractal Central.  The temperature of 52F 11C, gentle breezes, > and warm sun, gave the cat duo all they could ask for.  They > explored the yard from noon until sunset, somehow managing to > stay out of trouble for over 5 hours.  Today is starting colder, > but not extremely so.  It remains to be seen what the cats will > make of the day. > > I'm going to make another work day of it.  About 4 hours of work > waits in the rack beside the desk, and the only way to move it > to the finished rack is to get started.  So until next FOTD, > take care, and how many fractals could fit on the head of a pin? > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START PARAMETER FILE======================================= > > Watchtower         { ; time=0:00:43.45--SF5 on a P200 >   reset=2003 type=mandel passes=1 mathtolerance=/1 >   center-mag=-1.86119088257009000/+0.000407298011668\ >   70/2.823726e+012/1/-7.27769909978726215/0.00000603\ >   84787128533 params=0/0 float=y maxiter=7500 >   bailout=9 inside=0 symmetry=none periodicity=10 >   colors=000NleRuhVzkTzlRxmQunOroMopLlpJiqIgrGdsEatD\ >   ZtBWu9Tv8Qw6Nx5LxJT_W_CUZGTZJRZMQZPOZSNYWLYZKYaIYd\ >   HYgFXdEXbDW_CWYBWVAVT9VQ8VO7UL6UJ5UH5UI5TJ5TJ7JY7J\ >   Y7JY7JY7KY7KY7KY7KY7KY6LX6LX6LX6LX6MX6MX6MX6MX6NX6\ >   NX6NX6NX6NXyHvwIuvItuIttIssIsrIrqIroIqnJqmJplJpkJo\ >   jJoiJngJnfJmeKldKlcKkbKkaKj_KjZKiYKiXLhWLhVLgULgSL\ >   fRLfQLePLeOMdNMcMMcKMbAEAAEAAEAAEAAEBAECAEDAEEAEFA\ >   EGAEHAEIAEJAEKAELCEMFENIEPLGROIURKWUM_WOcZNicMnhLr\ >   mOwrRywUzzWwwbrrgmmjhmmcmoZmqUmsUnuWowYqyZsz`uzawz\ >   buvbrqbmlchgcc`cZYcUVdPTeNRfRPgWNh_LicJjgHklFlpDmt\ >   Bnx9nvHdtPVsXMqdCpl3kk6fj9aiCYhFTgHOfKKeNFdQAcT6cV\ >   7bW7aX8`X8_Y9ZZ9YZAX_AX`BW`BVaCUbCTbDScDRdDRdFVgGY\ >   iHakIdmJhoKkqLgmMcjN_gOWdPSaQOZRKWSGTTCQU8NU5KSISR\ >   U_PfgOrnNsoNspNsqNsrMssMstMttMtuLtvLtwLtxLtyLtyNnv\ >   OitPdrQZpRUnSPkTJiUEgV9eW4c87mEEmKLmQSmWZmadmYajV_\ >   hRXfOVdLSaHQ_ENYBLWFV_Jcb } > > END PARAMETER FILE========================================= > > > > ------------------------------ > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > > End of Fractint Digest, Vol 12, Issue 6 > ***************************************

3 3

how about a girl mascot for fractint?
by David Lowenstein 13 Mar '04

13 Mar '04

I like to call her "Julie Brot!" What do you think? -david

1 0

FOTD 13-03-04 (Merely a Scene [5])
by Jim Muth 13 Mar '04

13 Mar '04

FOTD -- March 13, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image is an error. When setting the parameters, I inadvertently forgot to reset the formula function to 'floor'. The results of the mistake were not all bad however. Like the 'Tim's error' formula in Fractint, the mixed-up formula produced quite an interesting image. So that this mix-up does not happen again, I will rewrite the MandelbrotBC1 formula, rename it MandelbrotBC2, and change the variable parameter to a fixed one. But the image that was produced in error will keep its honored position as FOTD for March 13. The parent fractal consists of a large irregular bay with several tiny bays along its smooth eastern shore. The western shore of the bay consists of what I call wetland -- a large area of near total chaos. But as today's image, which is a scene in this wetland, shows, near total chaos does not equal uselessness. I have given the image the simple name "Merely a Scene". That's what it is. There is no sign of my ever-present midgets, though some rudimentary ones do exist is other parts of the parent fractal. The image consists of a single shaft jutting down from the top of the frame and meeting a fragment of a second shaft near the bottom of the frame. The distant background is filled with similar shafts. The main shaft has an unusually vivid three-dimensional appearance, an effect that is not always easy to achieve with colors alone. I gave the image a rating of a 5. The lack of a midget dropped the rating as much as two points. Another bad feature is the slowness of the image, which takes over one hour to render on my machine. When the rating and render time are combined, the over- all value comes in at a lowly 7.2. The hour wait for the image to render can be avoided by down- loading the completed GIF file from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The image is slow, so before visiting the site, give Paul a chance to render and post it. Too much wind and too low a temperature kept the fractal cats confined indoors on Friday, but today is starting with much less wind. Hopefully, the temperature will rise to a level that is acceptable to the cat duo. If not, it's back to the tuna. As for me, I've got a bit of work to finish, and then it's all fun and games. Until next time, take care, and if you don't take care, watch out. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Merely_a_Scene { ; time=1:09:15.00--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=+0.67813638334978250/+0.185081778774343\ 90/1.597705e+007/1/-40/1.216475693094354e-008 params=1.2/0/0/0 float=y maxiter=10000 inside=255 logmap=874 periodicity=10 colors=000aUY_TWYSUVRSSQQPOONNMKLKHJIEIGCGE9FC6DAA\ 494C97FB9HDBJEELGGNIIPJLRLNTMPVORXQUZRW`TYbV`dWbfY\ dhZfj`hlbjnclpenrgpthrvjtwkvxmwyoxzqyzszzuzzwzzyzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzfHFfIFeJGeKHdLHdMIcNJcOKbPKbQLaRM\ aSM`TN`UO`UOZVNYVNXWMVWMUXLTXLRXLQYKPYKNZJMZJLZJJ_\ II_IH`HF`HE`HDaGBaGAbF9bF6YJ7`H8bF9eDAgCBjACl8Fz9D\ n7Cc6CT2BT5AT89TA9TD8TG7TI7TL6TN5TQ5TT4TV3TY3T`2Tb\ 1Te1Tg9WaGZX_VQYURWTSUTTSSUQRVOQWMPXKPYIOZGM_EK`CI\ aAHb8Fc6Dd4Be18g29e3Ac3Cb4E`4G_5IY6JX6LV7NU7QS8TR8\ WP9YOAUMA_LBdJBiIClGCnFIeHNXJSOLXFNY4Fa6Pe8Yj9eiAf\ hBghCggDhgEifFi`GheHjdIkdJlcKlcLmbMmbNnaOo`Po`Qp_R\ p_SqZTrZUrYVsSYuVXtYWs`VubUweTyhSzkRzmQzpPzsOzuNzv\ RzvUzvUzwUzwUzwUzwUzxUzxUzxUzyUzxUzwUzvUzuUzuUztUz\ sUzrUzrUzqUzpVzoTznQznNzmLzlIzkFzj9zkDzkHzlLzlOzlS\ zmWzm_zsfzpdzmbzjazh_zeZz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(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|<a } END 20.0 PAR-FORMULA FILE==================================

1 0

sorry
by David Lowenstein 12 Mar '04

12 Mar '04

thank you, noel giffin.

1 0

FOTD 12-03-04 (The African Veldt [6])
by Jim Muth 12 Mar '04

12 Mar '04

FOTD -- March 12, 2004 (Rating 6) Fractal visionaries and enthusiasts: There once was a time when I wandered freely through Fractal Land, roaming wherever my day's journey took me to study the surroundings. I was not on a search for any particular quarry. I photographed whatever was surrounding me in the place where I stopped for the day. Then something happened. I became fasci- nated with the so-called 'midgets' that I occasionally stumbled upon. I began seeking midgets, ignoring the sometimes spectacu- lar scenery that I passed by in my search. Midgets in fractals are higher-dimensional analogs of the maxi- mum or minimum stationary points so often found when the graphs of functions are plotted. And just as all stationary points have a similar parabolic shape, so do all midgets have a similar shape. With only a few hard-to-find exceptions, this shape is that of the classic Mandelbrot set. The familiar shape is some- times distorted beyond recognition, but even when unrecognizable the shape is there, and could be undistorted back into the M-set. It is hard to say why I became so fascinated with midgets, but this kind of thing seems to happen with fractals. Many become fascinated with spirals. When I come upon spirals, which I do many times in my search for midgets, I usually pass them by. They all look the same to me. It is curious that the same bore- dom has never arisen as I discover ever more of the super infi- nity of similarly shaped midgets that are out there, waiting to be found. Maybe I should devote a month or two to fractals without mid- gets. The discontinuity patterns in low-order fractional-power fractals can be quite interesting, and certainly deserve more exploration. The odd slices of the Z^2+C Julibrot can also be interesting. It is really surprising what Seahorse Valley looks like when viewed from some of the unfamiliar angles and double angles of four-dimensional space. Yes, I think I'll soon take a break from the endless stream of midgets, and have some fun with the other things found in the world of fractals. But that break from midgets does not appear in today's image, which is another adventure into the parent fractal of the two most recent FOTD's. I named the image "The African Veldt". I can give no reason for the name other than I think it sounds ex- citing. I also might have been thinking of an old story by Ray Bradbury named "The Veldt", which as I recall is about a house with animated walls that depict an African grassland scene. I rated today's image at a 6. Combined with the render time of 4 minutes, this gives an overall value of 142. The render time can be changed to a faster download time by visiting Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished GIF image has been or soon will be posted. Thursday was quite a pleasant day here at Fractal Central. The warm sun, light winds and temperature of 56F 13C made conditions near ideal for an afternoon in the yard. The cats took advan- tage of the opportunity. This morning is starting sunny, but it is colder, and the wind is high. We'll see what the cats think of this. I'll think more of fractal things once I get the work behind me. Until the next FOTD appears, take care, and see you in the land of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_African_Veldt { ; time=0:04:14.47--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.31518718326216360/+5.515004364619150\ 00/2.11448e+007/1/-17.5/3.45976670992897972e-008 params=0.55/-1.1/0.11/-3.1/0/0 float=y maxiter=600 inside=0 logmap=78 periodicity=10 colors=00000K00I01G05E08C0CA0F80J50M05T0FZ0Rc6ahDm\ mMxrTzx_zqTzjOueJsZDpR6lM1jF0gA0fH0gM6eT8bZAZeKXjU\ VmZVoXTqTTtRRvORxMJt_Cqm5mzzxczrqzozfRz53zACzDJrJQ\ eMXRQcDTJTX0hf1lq5oz6rzAvzCxz8mz6cz3Vz1Kx0At01r08q\ 0Fo1Mo3Tm5_l6fj8mj8rZMhMZ_AjQ0vH0oQ0jX0ee0_l0Vt0Qz\ 6JxVDvr8rz3qahc0zQ5zRDtRKfTTTT_HTROaJTjC_q3ez0lz0q\ z0lz0fq0ae0XV0RJ0M60H00D00Q00a00m10z80zD0zJFzTflcm\ aQtRCzH0rK8lMHeQQZR_RVhKXqJceHhTHoHFt5Fz06zfXhQvQ8\ z80cxrXxmOxhHxc8zX1zR0zM0zH0zC1z88z5Fz1Mz0Tz0_z0fz\ 0Mt03_D6OKe_TTeTJjV6oV0tX0xX0me0el5XrCOzHFzMQzR_zX\ hxarvfzrlzqHXe00T50HM05a0Dq0Mz0Vz0cz3az6azA_zD_xHZ\ tKZqMZmHTjDQf8Me5Ja0FZ0CX08j05v01z00z00h_05z03z01z\ 00z00t00o00h00c0ex5zzFozXJmm0Zz0Kz06t00o3DT6V80T00\ T00T0RxzMxzJytFzmAzf6z_3zVAzQFzMKzHQzDXzAaz5fz1lz0\ qz0vz0zz0zz0zz0zz0zz0zz0zz0zz6zzMzz_zzmzzjzzfzzecz\ FDz0Az06z03z00z30z6ozeezl } 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==================================

1 0

THANKS NOEL GIFFIN
by David Lowenstein 12 Mar '04

12 Mar '04

so the rudy set is a new fractal type. -david

3 2

FOTD 11-03-04 (Shark Teeth [9])
by Jim Muth 11 Mar '04

11 Mar '04

FOTD -- March 11, 2004 (Rating 9) Fractal visionaries and enthusiasts: The FOTD's that rate a 9 are few indeed, but today's image rises, perhaps with a little exaggeration, into that lofty range. The parent fractal that has been the source of the two most recent FOTD images is the source of today's image also. But instead of being located in the vicinity of the two large Mandeloids, today's image is located in a smaller area of chaos on a filament some distance south of them. The theme of filaments strung with areas of chaos prevails throughout the parent fractal, particularly so in the area where today's image is found. The decorated filaments make fine images when rendered in the traditional manner, but for today's image I wanted something different. I tried various outside rendering options, some of which worked fairly well, some of which were total failures. Then I evaporated the image by raising its escape radius to one-googol, and rendered the resulting blank screen of totally inside points with the 'bof61' option. The result was spectac- ular indeed. A little bit of color tweaking produced today's image, which, at least in my opinion, is the best in quite a while. I named it "Shark Teeth". The image does rather resemble strings of shark teeth, with a lovely pink flower at the center. The rating of 9 and the render time of 7 minutes combine for an overall value of 124. As always, the minor task of rendering the image from the included parameter file may be avoided by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A Wednesday morning snow shower here at Fractal Central failed to whiten the ground, but was enough to keep the fractal cats confined to the indoors for the day. The temperature reached a high of 45F 7C, which changed the snow to rain before it ended. Today is starting much improved. The cats will be happy. As is usually the case with me, I have official business to put behind me before settling down to search for the next fractal. The chance that my search will be successful is 100 percent. So until 24 hours from now, take care, and some but not all frac- tals deserve rave reviews. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Shark_Teeth { ; time=0:07:13.63--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-9.50479709963300900/-4.541802019973394\ 00/5.042148e+008/1/2.5/-0.0059717742853601305 params=0.55/-1.1/0.11/-3.1/0/1e+100 float=y maxiter=1000 inside=bof61 periodicity=10 colors=0000_73WD9SJFPPLLS9Ph0Sz0Wz0Uz0Uz0Uz0Uz0Sv1\ Sr3Sn5Sm7Qh9QeBQaDQYFPUHPQJPNLPLFWS9aY3hc0nh0tn0np\ 3hr7ctB_vFUxJPzPLzSFzW9z_5zc0zf0zj0zc0zW0zQ0zJ0zB0\ z50z70z90v90rB0nD0jD3fF9cHDaHHYJNULQQLUNN_JPcFPfDJ\ hBDj97m71n50p3j1Fh5Fh7Fh9FhBFfDFfFFfJFfLFeNFePFeQF\ eSFaQHYPHWNHSLHQJHNHJLFJHDJDBJB9J77L55L13L01L00L00\ N00N00N00N00N00P00P00P00P00L00P00Q00U00W00Y00a00c0\ 0f00h00j00n00p00t00v00x10v90tH5rPDrWLpaUnhamphmxpj\ zxhzzhzzhzzzzxzzvzzrzznzzmzzhwzerzcmz_hzWhyUhwQhvN\ huLhtHhsDhrBhq7hp3ho1hn0hm0hzFhzKfzPezUczZazc_zcYx\ cYvcWvcUtcSrcQpcPpZNnUNmPLjKJjFHhAFf0De0Be05e0BS3H\ HHN3SQ0eW0pa0re0tf0mf0ef0_f0Sf0Lh0Dh07h00h00h00r00\ h00a00U00P00L00H00D03F05H09J0BL0FN0HN0LP1NQ7QSDSUJ\ WWNYWPWYPW_QW_QWaSUcSUcUUeUUeWSfWShWShYSjYSj_Qm_Qn\ aQnaQpcPrcPrePtePtePvfNxfNxhNzhNzjLzjLzmLzmLzpHzmL\ zjPzhSzeWzc_zacz0a00a10_5 } 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==================================

1 0

Diffusion-Only -- or you'll miss it.
by SherLok Merfy 11 Mar '04

11 Mar '04

RainBrot { ; Make passes=1 or g to skip the last 256 iterations. ; Tesseral agrees with passes=d on where fractal ends. ; 16.75s on a 350Mhz PII @800x600. RainBoh.map ; My monitor doesn't click on mode changes at this res. reset=2003 type=mandel passes=d center-mag=-1.26297/0.0125867/1.258975/1.0274/-90/3.88578058618804789e\ -016 float=y maxiter=512 inside=0 invert=0.000546391309332721/-1.4/0 colors=000z50z70zB0<3>zJ0zL0zM0zN0zP0zR0<5>z_0z`0za0zb0zd0<14>zu0zv0zw\ 0zx0zy0<14>lz0kz0jz0<5>bz0az0`z0<4>Tz0Sz0Rz0Pz0Nz0Mz0Lz0Iz0Hz0Ez0Dz0Bz\ 0<2>0z00z30z70zB0zD0zH0zJ0zK0zL0zN<3>0zS0zT0zV0zX<4>0zc0zd0zf<14>0zu0z\ v0zw0zx0zy<8>0rz0qz0oz<4>0jz0iz0hz<8>0Xz0Vz0Tz<3>0Pz0Nz0Lz0Jz0Hz0Gz0Dz\ 0Bz<2>00z30z70zB0zD0zF0zG0z<4>P0zQ0zS0zT0zV0z<2>_0z`0za0zb0zc0z<3>h0zi\ 0zk0z<9>u0zv0zw0zx0zy0z<13>z0mz0lz0k<3>z0fz0dz0cz0az0`<4>z0Vz0Tz0S<3>z\ 0Lz0Jz0Hz0Gz0D<3>z04 }

1 1

Orbit Fractals with an Arbitrary Formula
by Hiram Berry 11 Mar '04

11 Mar '04

Is it possible to get fractint to plot these and if so how? Fractint seems to have specialized orbit types like the Henon attractor, but I want to specify the formula. IOW the "formula" type iterates over the screen pixels in an orderly gridlike fashion, but I want to go from pixel to pixel by iterating Pixel_new = F (Pixel_old) and mark the pixel each time. I found this process that seems to generate continuous(with sufficient iteration) fractal curves that look like wads of string with knots in random places (with greater iteration count, the large-scale length of the curve grows, but less than proportional to the number of iterations, and backfilling occurs at the same time at seemingly random locations so the curve is probably dense): x(n) = summation[m=1 to n]( sin(f(n)) * n^-a) y(n) = summation[m=1 to n]( cos(f(n)) *n^-a) where a is a constant between 0 and 1. One f that gives a fractal curve (briefly described above) is sqr, while f=log gives a smooth spiral. I'd like to plot these with fractint which has deep zooming capabilities, instead of the program I used which does not, and which failed at around 40000 iterated points. I know about the orbit screen in fractint, but it seems to me that if I use that with a "formula" type it will run the hundreds of thousands of iterations for every single pixel of the screen until the maximum iteration count is hit. That would take much too long. Is there some arcane .par magic to get fractint to display an orbit generated from only one point instead of the main screen? Hiram Berry

7 8

FOTD 28-02-04 (Cellular Patterns [6])
by Jim Muth 11 Mar '04

11 Mar '04

FOTD -- February 28, 2004 (Rating 6) Fractal visionaries and enthusiasts: For some reason, today's image reminds me of the cells of a cellular telephone network. I named it "Cellular Patterns". It is actually a scene in the fractal that results when portions of Z^(-1.74) and Z^(-7.4) are combined, and (1/C) is added. Speaking of cell phones, they appear to be taking over the world. A simple 25-mile trip will reveal the network antennas everywhere -- many on their own cell-phone towers, or electric transmission towers, but also lurking in the least likely places such as on the roofs of schools and other buildings, hidden in church bell towers, perched on advertising billboards, water tanks, even on abandoned grain elevators. It appears to be only a matter of time before we will have cell-phone antennas on every light pole, on every telephone and utility pole in every neighborhood. We are living in an ever-increasing ocean of electromagnetic radiation. We can't escape it. We know that the natural electric energy in the human body helps control tissue growth. Tests have already demonstrated that the radiation from a hand- held cell phone causes measurable brain damage in laboratory animals, and does so at levels in the range of those now in use. Can anyone imagine permitting a substance to be added to food intended for human consumption if that substance has been demonstrated to cause brain damage in laboratory animals? If this were done, the outcry would be overwhelming. But where is the outcry about cell-phone radiation. All we hear are hints of concern and not very convincing assurances that all is well. I wonder whether cell phones will be the asbestos and cigarettes of the future, and the telephone companies will have a reputa- tion like the giant tobacco corporations have today. Or perhaps we will need to shield our homes in faraday cages to escape the sea of deadly radiation. . . . Hmmmm . . . look at the outburst that a simple fractal just caused. Today's image rates a nominal 6 and has an overall value of 84. It was rendered with the outside set to the 'tdis' option, which stands for 'total distance' -- the total distance the points travel before escaping beyond the escape radius. The scene is nearly as interesting when rendered with the traditional equal- iteration-band method. I chose the 'tdis' method by the flip of a coin. The render time of 7 minutes may be bypassed by downloading the finished image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 48F 9C, Friday was pleasant enough here at Fractal Central. At least the cats must have thought so. They spent over three hours on the porch, enjoying the sun, which is just now making it over the holly trees in the afternoons. My day was acceptable, and the fractal I found was acceptable. This is just about all one could ask for. Hopefully, today will be a repeat, and the fractal will be even better. Until next time, take care, and we survived for thousands of years without carrying telephones everywhere we go. Why has it now become almost impossible to go about our everyday lives without one? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cellular_Patterns { ; time=0:07:09.25--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.88786870396801200/-0.000456232474488\ 38/6.944164e+011/1/-10.0008080291402823/0.00695999\ 736778776107 params=1/-1.74/0.4/-7.4/0/0 float=y maxiter=1200 inside=0 outside=tdis periodicity=10 colors=000pHEhRN``WTjdLtmMqjMohMlfMjdNhbNe`NcZNaXM\ cTLdPLeLKfIJgEJhAIi6Ij3PhHWgVafhYikVlnRoqOrtKuwHwz\ FuxDtvCstArr8qp7pn5ol4nj7ikAelCamFYmHUnKQoMMoNQjOT\ fOXaP_YPcTQfPQiL3gfKXX_MORBmL9nF8o97p46p6Dq8JqAPrC\ VrE`sGfsIlsHooGrkFugFwcJwbNwbQwbUwbYwb`wbdwbgwbhqc\ hiciadiVdjNejFej8eNJELKKJKQHKWFKaDKgBKm9Ks7KyBMoEN\ fIOXLPOOQFQUBSX8U_5heDvjLlmMcoNUrOLtPHuNDvL9wKDrOG\ mRJiUMdXQ__TWbWReZNhCkDGmPKo_OqjSsuNdWTcZZcadbcjbf\ paiuakpfikjgfneascXwaSw_NwZTwaZwddwgjwjpwm`5tljpjc\ riWsgPueIvdBw`FlXJaTMSYNQaNOeOMiOKmPIqPGuQEyQDjOAW\ N8HN63N44Q94TE4WI4ZN4aS4dWAfUGhTLiRRkQWlPTmQRrRPwS\ NzTLNUJLUIN_HOeGPkKQpPXjUbdZhZcoThuNmwHqwFuwDwwBzw\ 9zw7zw5zw3zw2zl9zaGzRMmGTh5ZcI`_UaWfbSrcjwrbwsWrtP\ muJitDes7ar1Yr2Wq2Vq3Tq3Sq3Rp4Pp4Op4Np9GqEAq6t2AjL\ E`bE`bF_bF_bFZaFZaFYaFYaFX`FX`FX`FW`FW_FV_FV_FU_FU\ _FTZFTZFSZFSZFRYFRYFQYy74 } 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==================================

5 5

Ternary Julibrot (or other process phase space) Slicing
by Hiram Berry 11 Mar '04

11 Mar '04

The technique that Jim has been using to generate FOTDs over the past ~3 weeks isn't limited to just the Julibrot space. It seems to be a general technique of looking at phase spaces for parameterized processes. In this particular case, Jim has made the observation that the M-sets, perturbed M-sets and quadratic Julia sets are all products of the same process, ie. z->z^2+C, which has two complex variables. Thus the process can be parameterized on 2 complex variables (the beginning value of z, z0, and C), each of which he splits into 2 real variables to get a four dimensional R-space. Defining planes by an anchor point and a pair of angles, and a viewing direction by another pair of angles, he generates the planar cut through the space to be viewed. I guess I stated the very obvious here, but that procedure leads naturally to a way to generalize the slicing to spaces defined by other processes. IOW, generally one has a process z->F[K1,K2,K3,...](z) parameterized by the K, one constructs the space K1xK2x..., then defines a linear slice through it which can be viewed on the screen. The means of definition of the sliceshould be in such a way that it's easy to understand variations in the K and do manipulations to get different views. So, when David brought up the cubic Mandelbrot sets, which have a third parameter, it occurred to me that we could do slicing in their Julibrot-equivalent spaces, ie. an R2 slice in an R6 space, if you are comfortable with splitting a complex dimension into two real parts. I am not comfortable with that approach, preferring to work natively in the complex dimensions and mapping the slice to R2 only in order to view it on my computer screen. Probably the two approaches are equivalent, but I'm not positive the views generated are the same. In any event, one can generate such slices for _any_ process with 3 process constants, which for wont of a better term I'm calling "ternary slicing" for the obvious reason. Now, I haven't worked these up into a .frm yet for the Rudy sets, cubic Mandelbrot sets, whatever you want to call them. I'm sure I will in the next few days, but in the meantime I noticed that the power-Msets make another natural extension of the Jbrot process, ie. z -> z^a + c, gives a phase space in C3 of {z0,a,c}. The Julibrot becomes a special case of the plane through the Ternary Julibrot space that is defined by a=2+0i constant, and arbitrary Julibrot slices are defined by lines on that plane. I'm sure everyone gets the idea. But the nice thing is that plane is parallel to ones containing the quartic Julibrot, etc., which can be generated by changing a single value in the parameters on the fractint z-screen. And, of course exploring the perpindicular and oblique slices through this extended space by varying other, angle parameters. Some results are not what one would expect; I have only looked at a few views, but here is a view I would never have thought was inherent in a M-set-like space. This was generated with the first .frm I tried, which inputs angles in complex format and so is not really user friendly at entering the viewing angle, and possibly my entering what should have been "pi/2" as "1.57" may have contributed to the strangeness, but... /************FRM BEGIN***********************/ TernaryJulibrotSlc { ; C1 linear slice of a C3 parameter phase space ; slices the power Julibrot (the quadratic Julibrot is the subset ; with a=(2,0) ). ; The phase space is of {z0,a,C} in the process z->z^a+C ; p1,p2,p3 are complex coords of an anchor point in the space ; p4,p5 are the complex latitude,longitude direction of the line ; emanating from the anchor point. IF (scrnpix==(0,0)) ; once per screen initialization hack ismand = true lim = 100 ; don't know what this should be-- may depend on "a" ;lat = (real(p4)*pi/180, tan(imag(p4)*pi/360)*pi/2) ;long = (real(p5)*pi/180, tan(imag(p5)*pi/360)*pi/2) lat=p4 ; temporary patch -- conversion from (deg,deg) to complex long=p5 ; angle failed to parse so enter angles in raw form Muz= cos(lat) * cos(long) ; meaning of lat and long accid. transposed Mua= sin(lat) * cos(long) ; but retained because used in Xtampak series Muc= sin(long) ; slice's polar coord unit direction in C3 space ENDIF k = pixel ; pixel position is the parameter of variation z=p1+k*Muz, a=p2+k*Mua, c=p3+k*Muc ; find pos in (z0,a,c) space : z = z ^ a + c |z| <= lim } /**************FRM END***********************/ /**************PAR BEGIN**********************/ ThePalaceAtXtampak { ; This was supposed to be a mundane slice of the ; ternary phase space cubic julibrot. It doesn't ; look anything like the typical Mandelbrot features. ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=ternaryjulibrotslc ismand=y passes=1 center-mag=-2.02478/-0.0573754/0.5629118/0.3572/90/1.31075705844807544e-\ 014 params=0/0/2/0/0/0/1.57/0/0/0 float=y maxiter=200 inside=zmag logmap=yes colors=000h`z0e0<3>eL0eeeLLL<4>ssLzzLzzz000555<3>HHHKKKOOO<3>ccchhhmmmss\ sU0cxzw<3>xjUxfNxbFxi8wU0<4>ZfQUiV0e0Koe<3>0zz<2>0Gz<3>rVzzVzzVrzVjB`0zV\ V<3>zzV<3>VzV<3>VzzVrzVjzLW0hhz<3>zhz<3>zhh<3>zzhvzhqzhWQ0hzh<2>hzvm00xi\ 8hqzhlz00S<3>S0SS0LS0EeL0000S70<2>SS0<3>0S0<3>0SS0LS0ESeee000IES<2>SES<3\ >SEE<3>SSEPSELSELLL000ESI<2>ESS<2>EHSKKS<2>QKSSKSSKQSKOSSL000SMKSOKSQKSS\ K<2>MSKKSKKSMKSOKSQKSSKQSKOSZZL000<8>PPCRRDUUF<3>eeL000<8>TTCWWDZZF<3>ll\ L000<8>XXC``DddF<3>ssL000<8>``CeeDiiF<3>zzL000<6>XXXaaafff<3>zzz000zzz } /*******************PAR END**********************/ Now, I did cobble together one possible mapping between complex angles and what Jim calls double angles in the R4 space, based only on the observation that the transcendental functions repeat every 2*pi the real direction, but not in the imaginary direction, and applied it to this more user friendly version of the .frm that takes ordinary degree measured angles as input for the directions (maps the imaginary part of the angle with tan() so that 90 deg -> pi/2*i and 180 deg -> inf * i). Here is it: /***********************FRM BEGIN******************/ TernaryJulibrotSl2 { ; C1 linear slice of a C3 parameter phase space ; slices the power Julibrot (the quadratic Julibrot is the subset ; with a=(2,0) ) in 6 dimensions with a 2 dimensional slice ; The phase space is of {z0,a,C} in the process z->z^a+C ; p1,p2,p3 are complex coords of an anchor point in the space ; p4,p5 are the complex latitude,longitude direction of the line ; emanating from the anchor point. They are input in user friendly ; (degree,degree) form instead of complex angular form. ; To start with the classic M-set initialize p2=(2,0);p4=(90,0);rest 0. IF (scrnpix==(0,0)) ; once per screen initialization hack ismand = true lim = 100 ; ? lat = real(p4)*pi/180+flip(tan(imag(p4)*pi/360)*pi/2) long = real(p5)*pi/180+flip(tan(imag(p5)*pi/360)*pi/2) ;lat=p4 ; temporary patch if ;long=p5 ; angle fails to parse then enter in complex angular form Muz= cos(long) * cos(lat) Mua= sin(long) * cos(lat) Muc= sin(lat) ; slice's polar coord unit direction in C3 space ENDIF k = pixel ; pixel position is the parameter of variation z=p1+k*Muz, a=p2+k*Mua, c=p3+k*Muc ; find pos in (z0,a,c) space : z = z ^ a + c |z| <= lim } /**********************FRM END**************************/ And here is a nice view of the quintic Mandelbrot that serves as a quick rendering entry point for z-screening your way through the TJ space: /************************PAR BEGIN**************************/ JovianCrown { ; Jumping-off place to explore the ternary Julibrot ; z->z^a+c. p1..p3={z0,a,c};p4,p5={lat,long}each(deg,deg) ; This is the power a=5 M-like ((lat,long)=((90,0),(0,0))) ; Fractint Version 2003 Patchlevel 1 ; Fractint Version 2003 Patchlevel 1 reset=2003 type=formula formulafile=exprmntl.frm formulaname=TernaryJulibrotSl2 ismand=y passes=1 center-mag=-8.88178e-016/6.10623e-016/1.041667 params=0/0/5/0/0/0/90/0/0/0 float=y maxiter=200 inside=zmag logmap=yes cyclerange=2/10 colors=000m00eee0000000L00e0<3>eL0SSLllLssLzzLzzz000555<3>HHHKKKOOO<3>cc\ chhhmmmsssU0cxzw<3>xjUxfNxbFxi8wU0<4>ZfQUiV0e0Koe<3>0zz<2>0Gz<3>rVzzVzzV\ rzVjB`0zVV<3>zzV<3>VzV<3>VzzVrzVjzLW0hhz<3>zhz<3>zhh<3>zzhvzhqzhWQ0hzh<2\ >hzvm00xi8hqzhlz00S<3>S0SS0LS0EeL0000S70<2>SS0<3>0S0<3>0SS0LS0ESeee000IE\ S<2>SES<3>SEE<3>SSEPSELSELLL000ESI<2>ESS<2>EHSKKS<2>QKSSKSSKQSKOSSL000SM\ KSOKSQKSSK<2>MSKKSKKSMKSOKSQKSSKQSKOSZZL000<4>EE7HH8JJ9MMBPPC<3>__IbbKee\ L000<4>GG7JJ8NN9QQBTTC<3>eeIiiKllL000<4>II7MM8QQ9TTBXXC<3>llIooKssL000<4\ >LL7PP8TT9XXB``C<3>rrIvvKzzL000<3>JJJOOOSSS<6>zzz000zzz } /************************PAR END*****************************/ Hopefully this is interesting to someone, -- Hiram Berry

2 2

Once per image calculations in formula functions
by Hiram Berry 10 Mar '04

10 Mar '04

Somewhere in the fractint documentation I came across explanation to the effect that calculations done in fractint fell into one of three categories, once per image, once per pixel, and every iteration. I assume an example of the first is assignment of p# values on the z-screen, stuff before the ':' encompasses the second, and stuff after the ':' is the third category. But what about expressions that will be constant over an entire image, but need to be specified in the body of the formula before the ':' ? Is there a way to explicitly tell the parser to do that so that it doesn't redo the unnecessary calculations every pixel? I think it is too much to ask to expect the parser to make this optimization implicitly, and my benchmarking indicates that such optimization is not done. Maybe I missed something in the documentation for using the formula editor on this count, but if so then so did others; I notice that Jim M's formula for slicing Julibrots in R4 space, "SliceJulibrot2.frm" could very profitably take advantage of once per image evaluation. In it he converts input angles from a user friendly degree form into the machine friendly radian form, and generates some expression coefficients from the sines and cosines of those angle which are constant over the duration of the image. Once-per-image evaluation of those terms would let that .frm run much faster, yet I noticed that the very accomplished and knowledgeable Jim does not do anything to explicitly force such an evaluation scheme for those terms, which leads me to suspect that there isn't a "nice" syntactic mechanism for doing so. And yet I do recall the categorization somewhere in the documentation that implied it was possible to do once per image calculations. So if anyone knows _how_ to do this "the right way", please reply. I raise the question of syntactic orthodoxy only because I did find a hack, which follows, that seems to accomplish it. It really doesn't feel right though. The hack is to put the once per image initialization code inside an IF..ENDIF block that (hopefully) executes only on the first pixel of the image. It worked when I applied the technique to "SliceJulibrot2.frm", speeding up the rendering of an "easy" image severalfold. However, the code just doesn't feel right. It relies on an assumption that the drawing technique will render pixel (0,0) first, which I tried to ensure by setting the PASSES=1 option, but I really don't think that can be assumed. So I really hope someone will tell us the orthodox way to accomplish once per image initialization. In the meantime, Jim's original .frm was: SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } , while my hack to speed it up (which it does substantially in most cases tried) with o.p.i.i. is: SliceJulibrot2a {; SliceJulibrot2 with per screen initialization IF (scrnpix==(0,0)) a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), term1=cg*cd, term2=ca*sb*sg*cd+ca*cb*sd, term3=cg*sd, term4=ca*cb*cd-ca*sb*sg*sd, term5=ca*sb*cg ENDIF pix=pixel, u=real(pix), v=imag(pix), p=u*term1-v*term2, q=u*term3+v*term4, r=u*sg+v*term5, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } Again, the drawing method should be set to single pass, but if anyone has a better solution or can shed more light on this problem, PLEASE reply. Sincerely, Hiram Berry

3 4

fixed formula file
by David Lowenstein 10 Mar '04

10 Mar '04

since the fractals had the wrong names, I renamed them. -david

2 1

Colors of Posted Pars
by Lee H. Skinner 10 Mar '04

10 Mar '04

I also need to note that Hiram did attach sloshdun.map to his message, but the list moderated has specifically said not to post any attachments to the list. The Fractint recordcolors=Y command easily gets around this restriction. Lee

4 5

Colors of Posted Pars
by Lee H. Skinner 10 Mar '04

10 Mar '04

SherLok Merfy and Hiram Berry have recently posted some pars. Unfortunately I (and presumably others on this list) cannot generate them as posted because the pars contain reference to non-standard map names. Whereas chroma.map is included in the Fractint distribution files, kayos.map and sloshdun.map are not. Anybody can name a color map, but others will not have access to the map file. The way to get around this is to put recordcolors=Y into your sstools.ini file, so that the colors will get recorded into the par entry submitted for posting. I would be grateful if SherLok and Hiram would repost their pars with the colors. Otherwise, I can generate the pars as already posted with default.map, but I'm sure they won't look as well as the images on the machines of the original artists! Thanks. Lee

4 9

FOTD 10-03-04 (Entropy [7])
by Jim Muth 10 Mar '04

10 Mar '04

FOTD -- March 10, 2004 (Rating 7) Fractal visionaries and enthusiasts: To find today's image I returned to the same parent fractal that held yesterday's scene, and investigated the large eastern Mandeloid. Instead of the East Valley area, I checked the tip of the negative, or in this case, the main positive stem. In contrast to the main stem of the classic Mandelbrot set, the stem of the Mandeloid in today's fractal winds into a loose spiral as it nears its end. This spiral nature is reflected in the pattern surrounding today's midget. I named the image "Entropy", which is a word that refers to the amount of disorder in a closed system. Disorder refers to the amount of energy unavailable for useful work. Unless outside energy is introduced, entropy always increases and the system reaches a state of luke-warm death. In some fractals, the disorder seems infinite, in others there is nothing but order. Some day soon I might wax philosophic about this, but today is not the day. Today's image is in a state of partial entropy, a fact that inspired the name. The rating of a 7, combined with the render time of just under 14 minutes, gives an overall value of an even 50. The curious will run the parameter, the wise will download the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday passed chilly and cloudy here at Fractal Central. The temperature of 45F 7C was a bit too cold for the cats, who ventured outdoors only long enough to smell a few bushes. When they sulked back inside, a generous treat of tuna eased their troubles. In my case, it will take a bit smaller pile of work waiting to be done to ease my troubles. The work will be finished however, and the next fractal will appear on schedule in 24 hours. Until then, take care, and keep iterating. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Entropy { ; time=0:13:54.76--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+4.77816002409709700/+1.319995900632449\ 00/1.15829e+011/1/-25/0.0294780650801364785 params=0.55/-1.1/0.11/-3.1/0/0 float=y maxiter=1500 inside=0 logmap=288 periodicity=10 colors=000M0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM0SM\ 0SM0SM0SN0SN0SN0SO0SO0SO1SP2SP3SP4SQ5SQ6SR7SR8SS9S\ SASSBRTCQTDPUEOUFNVGMVHLWJKXIJZIH`IGbIFgHElHDrHCwU\ CzUCwHBrIBmJBiJBgKBfLAdLAbMA`NAZNAYO9WP9UP9SQ9QR9P\ R9TUAWWAZYAb`AebAhdBkfBoiBrkBumByr7xoBwmEvkIuiLtgP\ seSrcWqaZp_boYenWimUllSpqUxnSukQshPpeNnbMk_KiXJfUH\ dRGaOE_LDYPGZSJ_WM_ZP`bS`eVaiYal`bocbggd`kfTogMsiE\ wk7zlChfGR`K9VLBYLC`MDcMEeNFhNGkOHnPEsOIpNLmMOjLRg\ KVdJYaI`ZHcWFhTGfUGdUHbUHaUH_UIYUIXVJVVJTVJSVKQVKO\ VKNVHKTFHRCDP9AN77MC9KGAILBGPDEUECYFBWLEURHSXKQbNO\ hQMnTGxTKsWOoZSj`Wfc_bebYhfUjjQmnLorHruDttFssGrsHq\ rJqrKpqLovHuqMolRjgWdb`_YeUVmOUjPTgPSdPRaQSZQUWQWT\ QYRR_OR`LRaIRbFSdCSf9Sh7SjQGjQLjQQjQVjQ_jQdjQijQnj\ QsiTzjQxkNwlMumLtmKrnLqoMopNnpOmqPnrQosRptSquTrvUs\ wVtxWuyXvzYwzZxz_yz`zzazzbzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } 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==================================

1 0

[Fractint] so noel giffin, the rudy sets and your sets belong to the same family
by David Lowenstein 10 Mar '04

10 Mar '04

so what will it be called? -david

2 1

FOTD 09-03-04 (Jeweled Minibrot [7])
by Jim Muth 09 Mar '04

09 Mar '04

FOTD -- March 09, 2004 (Rating 7) Fractal visionaries and enthusiasts: After a three-day delay, today's image takes us into the oversized fractal that results when unlikely portions of Z^(-1.1) and Z^(-3.1) are combined and (1/C) is added. The parent fractal is an oversized thing, too large for the most interesting part to fit on the default screen. But one outzoom reveals two Mandeloids, sitting butt to butt, with their East Valleys connected by a most extraordinary filament. I have not yet examined the filament, which I suspect has the same appearance regardless of how deep one looks into it. What I did examine was the southern shoreline of the East Valley of the western Mandeloid. A short distance inland I found a network of lacy filaments, spotted with midgets resembling jewels on a string. The midgets are surrounded by the basic 'East Valley' patterns, but these 'brain-like' patterns are surrounded in turn by most interesting networks of filaments, a good example of which is illustrated in today's image. Extending southwest-northeast from the central midget is a lovely network of jeweled filaments like the filament network on which today's image lies. Extending northwest-southeast from the midget are filaments like those that connect the two large Mandeloids in the parent fractal. Most likely, in their depths, these filaments simply go on and on forever. I named the image "Jeweled Minibrot", which fairly well describes it. The unlucky-appearing render time of 13 minutes, 13.13 seconds is one of those unlikely statistical coincidences that happen now and then. But the image itself is worth a moderately high 7, and those who spend 13 minutes watching it slowly appear on their screens will be lucky indeed. They will be lucky because most machines now in use are faster than my old P200 unit, and will render the image in far less time. When the render time is considered, the overall value is 53. Those who download the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will save the most time, but miss some of the fun. The greatest weather excitement since the last FOTD came on Saturday afternoon, when an unexpected severe squall struck the harbor and flipped over a water taxi. Sunday was bright and chilly. Monday was cold and blustery, with occasional flurries of snow. The fractal cats did not appreciate the Monday condi- tions at all, and showed their disapproval by returning inside only a few minutes after going out. Today is starting in a similar manner. We'll see what the cats think of this. For me, the greatest amusement so far today came when I opened my e-mail box and found a spam letter with a subject line telling me that the sender had gotten my password and credit- card information. Imagine that -- an honest thief who warns me of his theft and gives me a chance to cancel the card before he uses it. I wonder what was for sale on the web site the letter directed me to. The graphic-design work is still heavy, but under control. The next FOTD will appear in 24 hours. Until then, take care, and be alert for runaway fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jeweled_Minibrot { ; time=0:13:13.13--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-6.56488536701683900/+0.815957995544778\ 90/8.81e+005/1/45/-2.44425623421862248e-008 params=0.55/-1.1/0.11/-3.1/0/0 float=y maxiter=3200 inside=0 logmap=279 periodicity=10 colors=000DGMDGNEHOFHPGIQGIRHJSHJTIKUIKVJLWJLXKMYK\ MZLN_LN_MO_MO`NPaNPbOQcOQdPRePRfQSgQShPTiOTjNUkNUl\ MWmMYnL_oKapPcqTerXgs`itdkuhmvlmwpmxtmyumzvmzwmzwm\ zwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzw\ mzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmz\ wmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwmzwm\ zwmzwmzwmzwmzwmzwmzwmzwmzwnzwozwozwnzwmzwlzwlzwkzw\ jzwizwizwhzwhzwhzwizwjzwkzwlwymtxmqwmnwmkvmhvmcrmZ\ rmUomPokKmmHmhFhfChdAeb7ce4cf2fh0ij0ml0po0sn0vr0sp\ 0pp0nn0km4ik8fiDdgHafL_dPXbTVaXT_VSZTRYRPXQOWONVML\ UKKTJJSHHRFGQDFPCIQBLRBOSBRTBUUBXVB_WBbWBeXBhYBkZB\ n_Bq`BtaBwbBybBq_GjXKcUOWRSPOWIL_BIcLRNU_7XX5_V3aX\ 1cY0d_0f`0ha0ic0kd0mf0ng0ph0rj0sk0um0wn0xo0wn0vo0u\ p0tq0sr0rs0qt2pu4ov7nw9mxClyEkzG4zF6zE8zEAzEBzEDzE\ FzEGzEIzDKzDMzDNzDPzDRzDSzDQzAOz8Mz5Kz3Iz1Gz0Ez0Cz\ 0Hz2Mz9RzHlzGzzZkzTYzNKzH } 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==================================

1 0

[Fractint] the cubic mandelbrot cubic connectedness map has views in six planes of wxyz space
by David Lowenstein 08 Mar '04

08 Mar '04

they are, wx, xy, yz, wz, wy, and xz. in terms of rudy rucker's abuv they are ab, bu, uv, av, au and bv. -david http://www.mathcs.sjsu.edu/faculty/rucker/cubic_mandel.htm 3D cross sections are wxy, xyz, wyz, wxz. --------------------------------------------------------------------------------

1 0