April 2004 - Fractint - mailman.xmission.com

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==================================

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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==================================

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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==================================

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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==================================

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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==================================

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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==================================

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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==================================

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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==================================

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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==================================

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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==================================

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