August 2003 - Fractint - mailman.xmission.com

FOTD 10-08-03 (A Fractal in Nirvana [7])
by Jim Muth 10 Aug '03

10 Aug '03

FOTD -- August 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: Years ago there was a small deli restaurant in the Fractal Central neighborhood, run by a Korean immigrant. The merchant has long since moved away, but I still remember the conversa- tions he and I used to have on slow days. He was a Buddhist who was eager to talk about religion, particu- larly his idea of Buddhism. He often told me that the goal of Buddhists is to escape the constant reincarnations on earth and enter Nirvana. He expressed amusement at the simplicity of our two main western beliefs -- that we go to heaven when we die, to be perfectly happy for all eternity, or that we simply cease to exist, eliminating the need to concern ourselves with the topic. When I asked him to describe the Nirvana that Buddhists believe in, he told me that it is hard to put into words, but that Nirvana is like a mixture of heaven and non-existence. We cease to exist when we enter Nirvana, which is the ultimate peace, yet somehow we can enjoy the ultimate peace of not existing. When I asked him what it is that does the enjoying, he simply shrugged and said that one must enter Nirvana before they can understand it. Nirvana is an oxymoron. Today's image is also an oxymoron. It consists of as much inside material as outside material, yet it is impossible to tell one from the other. I named it "A Fractal in Nirvana" when the etheric blues reminded me of the conversations about transcendental things that I once had at that small restaurant. The parent fractal is the same as the parent of yesterday's 'Wonderland' image, though instead of going to 'East valley' to explore, I went to one of the numerous tiny valleys on the west shore of the main bay. The 'inside' parts of the image have been made visible by the 'bof60' inside fill. This fill normally creates mostly bubbles, though the bubbles are not very apparent in today's image. The image is notably better that yesterday's hasty achievement, and IMO rates an honest 7. And the 9-minute render time allows ample time to ponder the mysteries of the beyond. Those more concerned with the here and the now may bypass the pondering by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain on Saturday amounted to only a few sprinkles here at Fractal Central, but even that was enough to wet the grass and dampen the spirits of the dynamic duo. Due to the high humid- ity, the temperature of 80F 27C felt more like 90F 32C. I have little hope for improvement, because today promises to be more of the same. For the cats, the day will be questionable. For me it's going to be a lazy day -- that is if I can get through it without finding any work that needs to be done. Until next FOTD, take care, and walk in the peace of eternal fractal oneness. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_In_Nirvana { ; time=0:09:09.69--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.55913935558906900/+0.103410051541293\ 70/709229.8/1/-170/-1.28612687166906881e-009 params=2/3/-2/0.05/0/0 float=y maxiter=1200 inside=bof60 periodicity=10 colors=000cCA_DAVFAQGBMHBHJBCKB8LBCNFFQIJUMMXPQXST\ _WWaZ_cabfe020ijkMrQOqUPoYRnaSmeUkiWjmXhqZgu_fxXXm\ VObSESQ5IR9KSDMTHNTLPUPRVTSVWUW_WXcXYgZYk`Zoa_sc_v\ dWscSpbPnbLkaHh`Ef`Ac_7a_8Z`8Xa8Ua8Sb8Pc8Nc8Kd8Ie8\ Fe8Df8Ag88gGLZNYRVjIavA621954C76FA8ICALECOHFRJHUMJ\ XOL_QNbTQeVShYUk_WmaYk_WjYUhWSgUQeSOdRMbPKaNJ`LHZJ\ AYIFWGKVEPTCUSAZR9cUFhXKmZPraUwd_wfdwiiwknweoz`jwW\ frQcmL_hG`cJafMchK`iJZjIXkHVlGTmFRmDOnCMoBKpAIq9Gr\ 8ErGLjOSbWZVceNklFzr7wq6tp6po6mn5im5el5bk4_k4Xj4Ti\ 3Oh3Ig3Ff2Ce29e2Dc5Gb8JaBM`EP_HTZKWYNZXQaVTdUWhTZk\ SanRdqQgtPjwOmpJbjESc9HY57Z6AZ7DZ8FZ9IZALZBNZCQZDS\ ZEVZFYZG_ZHbZHdUF`PDXKBUF9QA7M56J49N4CQ4FT4IW4LZ4O\ a4Rd4Tg8UeBVdFVcIWbMWaPX`TY_WYZ_ZYbZXf_Wi`Vm`UpaTs\ aSpYPnUMlRJiNHgKEeGBbC9`96Z53X21P95IF8BMB4SE9QCDPB\ IOAMN9QM8VL7ZK6cJ5gI4kH3pG2tF1xE0vI4tL7sOBqREoVHnY\ Ll`OkcRttimoegja`eZV`VKtM } 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 09-08-03 (Mandel Wonderland [5])
by Jim Muth 09 Aug '03

09 Aug '03

FOTD -- August 09, 2003 (Rating 5) Fractal visionaries and enthusiasts: This will be a short discussion because it's getting late and today's FOTD is far overdue. Today's pot-luck fractal, which was found in 10 minutes and rendered in 11, rates a 5. It is a scene in the East Valley area of the fractal that results when 2 parts of Z^0.05 are subtracted from two parts of Z^3. The parent fractal somewhat resembles the mouth of a crying clown turned on its side. I named the image "Mandel Wonderland", though it is a fairly routine, generic scene that might appear in almost any valley. The parent fractal almost certainly holds far more interesting scenes. I'll post one of these as tomorrow's FOTD. As always, the completed GIF image is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The numerous showers somehow all bypassed Fractal Central on Friday, and the temperature reached 86F 30C, giving the dynamic fractal cats several dry hours in the yard. Their moods were accordingly pleasant. The day ended with them sleeping peace- fully together in their favorite overstuffed chair. Today is overcast with heavy rain forecast, but the rain has so far failed to appear. The cats are currently romping in the yard. Hopefully, their good luck will continue for the rest of the day. We will know for sure in 18 hours, when the next FOTD appears. Until then, take care, and is the meaning of fractals the same as the meaning of life? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandel_Wonderland { ; time=0:11.41.14--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+2.19230087842847400/-0.000225004562220\ 96/1.734486e+011/1/-126.5/-0.00001734773581692533 params=2/3/-2/0.05/0/0 float=y maxiter=1300 inside=0 logmap=222 periodicity=10 colors=000GKPHJNIHLJGJKEHLDFMBDNABN99OFCPLEPRHQXJQ\ aMRgORmRSsTSxVRtWQqWQnWPkXOhXOdXNaXMZYMWYLTYLQYJW_\ Ia`HfbFlcEreDwf5xn4qi3ke2da2ZY1SU0MQ0GM9OKHWIQcHYk\ FesEatGZuHWuITvJQvKMwMJwNGxODxPAyQ7yR9xSAwTBvUDuVE\ tVFsWGrXIrYJqZKpZLo_Nn`OmaPlbQlbdLNaRK_XHYbEVhBTn8\ Rt5PuANuFLuKJuPHuUFuZDucBuhAumCoiEieFcbHZZITWKNSLI\ POLRROTURUWUWZXXa_Zca_fdaigbkjdnmeqpgsrhtmcuh_vcWv\ ZRwVNxQJxLEyGAzB6z72tA6oDAjGEeJI`MM_KP_JS_IV_HY_G`\ _FcZEfZDiZClZBoZArZ9tPRmFgf6x_9rZBlYDfXFaWHWVJQULL\ TMMRMMPMMONNMNNKNNJOOHOOFOOEPPCPPAPP9QQ7QQ5QQ4NRGL\ SRITbGTmMPrRMwTQtUTrVWpWZnWZnX_nX_otB1qE2nH3kJ4iM5\ fP6cR7`U8ZW9SbIMhQFoY9ueBtcDsbFr`Hq_JpYLoXNnVPnURm\ TTlRVkQXjOZiN`hLbgKdgJnYLwPNvMMvKLvHKvFJvDJpB5k9Al\ FFmLKnRPnXUobZphcpnhrnmqjrqgwqczq`zpXzpUzpQzqNzrKz\ sJztJzuJzvJzwIzxIzyIzzIzzHzzHzzHzzHzzGzzGzzGzzGzzP\ zzHzz9zz1zz3zz4zzPzzNzzMz } 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 for Aug 09 delayed
by Jim Muth 09 Aug '03

09 Aug '03

Fractal enthusiasts: Due to an unexpected rush job, the FOTD for Aug. 09 will be delayed several hours. -- Sorry! Jim M.

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Nautibroids
by Russell Walsmith 08 Aug '03

08 Aug '03

I still can hardly believe that I'm seeing this stuff... here are more fibrot/nautibroid images: -------------------------startparfile----------------------------- The_Jungle { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=Fibrot1 passes=3 center-mag=1.32611/-0.0253659/7.041667 params=0/2/1/0 float=y maxiter=300 colors=000ruonsjQdrLdtblU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6\ ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5z\ P5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4\ H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1o\ r2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>F\ cgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8X\ a<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3\ >hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0zj0000zr1\ zz1zzC<2>zzzvxu } --------------------------endparfile------------------------------ The Jungle reuses the Lee Skinner map I borrowed earlier. Great map Lee, but I'll be glad when I"ve got a grip on the pallet tools... is there a tutorial for that anywhere? La Concha uses a throughly generalized formula, the MandelbroidG. The frm3 option was intended to toggle from 'ident' to 'abs' so to view the 'naked' fractal (i.e., absent the field lines), but of course it turns out to offer a bit more than that... Let p4=2; then p1=p2=p3=1 and fm1=fm2=fm3=ident generates the Mset. -------------------------startparfile----------------------------- La_Concha { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=NautibroidG function=conj/cabs/ident passes=3 center-mag=-0.843279/0.34679/0.51358 params=5/1/3/1/-1/0/2.618/0 float=y maxiter=300 outside=imag colors=653xwulHICXNwuIDCTjCRATl653xwulHICXNwuIDCTjCRATlccc<238>c\ cc } --------------------------endparfile------------------------------ It still blows my socks off to realize that just a few tweaks ago La_Concha was the Mandelbrot set!!! Finally, there's the device of putting d=pixel^2 into the M-set iteration loop like so: z=z^2 + c + p1*d. This induces the Mset's shy twin to fly in from infinity. It works in the MetaNaut formula as well: -------------------------startparfile----------------------------- Hummingbrot { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=metanaut passes=1 center-mag=-2.77783/-1.41777/0.1529238 params=4/1/0.707/0.707/2/0 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } --------------------------endparfile------------------------------ -------------------------startfrmfile----------------------------- frm:Fibrot1 { z = 0, c = pixel, j=0, k=1: a = p2*j + p1*k j = k k = a z = z^k + c z < 1000 } frm:NautibroidG { z = 0, c = pixel, k=p4, j=p3: j=p3*j k=p1*fn1(k)*j z = z^k + c j=p3*j k=p2*fn2(k)*j z = z^k + c fn3(z) < 1000 } frm:MetaNaut { z = 0, c = pixel, d = pixel^2, k=p3: k=p1*k z = z^k + c + p2*d z < 1000 } fn3(z) < 1000 } ---------------------------endfrmfile-----------------------------

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FOTD 08-08-03 (No Luck Today [4])
by Jim Muth 08 Aug '03

08 Aug '03

FOTD -- August 08, 2003 (Rating 4) Fractal visionaries and enthusiasts: Sometimes fractal luck, like any other luck, can turn bad. This happened to me during my fractal explorations on Thursday evening, when I was tracking today's scene. Today's scene is a slow one, and I had already been on its track for over an hour when I started calculating the final frame, fully expecting to find a midget at the center. But I had been fooled. Today's image is not one of a midget, it is another of those 'dry lakes' that from a distance look like the basin surrounding a midget but up close prove to be nothing more than an area of symmetry. Normally, I discard such failures, but I had put so much time and effort into today's image that I decided to declare it the FOTD for 8-8-03 despite the lack of a midget. (Also, even without the standard midget, it is an interesting scene.) Actually, I never had a chance of finding a midget even if one were at the center of the basin. The image as it appears is of such a great magnitude that it is already showing signs of resolution breakdown. If a midget were at the center, I would never be able to reach it. This excessive magnitude is the reason I included the 'mathtolerance' entry in the parameter file. I named the final result "No Luck Today" and rated it at a below- average 4. The unusually slow render time of almost an hour is admittedly excessive for such a mediocre image. I advise letting Paul and Scott render the image, and then picking it up from one of their FOTD web sites. The URL of Paul's site is: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's site is: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The clouds and occasional light rain prevailed all day Thursday here at Fractal Central. The temperature of 79F 26C was comfortable enough, but the wet grass kept the fractal cats confined to within a few feet of the porch. When they came indoors, their moods were so sour that a squabble broke out and a few punches were thrown before a treat of tuna eased their frustration. Today is forecast to be another showery day. Hopefully, the duo will weather any rain better than they did yesterday. I'm going to spend the day finishing the modicum of work still waiting to be done, and then I'll search for a better fractal. Until tomorrow, when that better fractal will appear as the FOTD, take care, and don't get run down by a DUI fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ No_Luck_Today { ; time=0:55:52.48--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.628689612431902/+0.00008782771078793\ /2.832453e+013/1/90/3.88578058618804789e-016 params=2/0.05/2/3/0/0 float=y maxiter=12000 periodicity=10 mathtolerance=/1 colors=000nTqpTqqXnq_lqbjqehncekaci_afYZcXXaVVZTSW\ RQUPOROLOMJMKHJIEGGCDE9EFAFGAFGAGHAHHAHIAIJAIJAJKA\ KKBKLBLMBMMBMNBNNBNOBOOBPPBPQBQQCRRCRRCSSCSTCTTCUU\ CUUCVVCVVCUWDTXESXFRYFQZGPZHO_HN_IM`JLaJKaKJbLNfKJ\ bLG_MDXNAUO7RPDUUJWYPZaU`f_cjeenomwjgrfbnaYiYTeTO`\ PJXKESG9OC4KE6LF8LG9LHBMIDMJEMKGNLINMJNNLOOMOPOOQQ\ PRRPSTPUVQVWQWYQX_RY`RZbR_cS`eSagSbhTcjTdlTemUfoUg\ pUkr_otesvkwxqqvpktoero_pnUnnOlmEjtJkmOkgTlaYlVamP\ fmJknCpn6tn0pi3me6i`9fXCcSF_OIXJLUFNVHMWILWJKXKJXL\ IYMHYNGZOF`ODZPEYPEXQEWQEVREURETRESSERSEQTEPTEOTEN\ UEMUELVEKVEIVFHWFGWFFXFEXFDXFCYFBYFAZF9ZF8ZF7_F6_F\ 5`F4`F1cC3`F5YH7VJ9TLBQNDNPFLSHIUJFWLDYNA_P7aQ5cT4\ dV4dX3eZ3ea2fc2fe2fg1gj1gl0hn0hp0ho1in1in1im1jl1jl\ 1jk1kj1kj1ki1kh2lh2lg2lf2mf2me2me2md2nc2nc2nb3oa3o\ a3o`3o_3p_3pZ3pY3qY3qX3qY2rX3qX4pW4oW5nW5mV6lV6kU7\ jU7iU8hT9gT9fTAehTqjTqlTq } 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 07-08-03 (Mantis Cases [7])
by Jim Muth 07 Aug '03

07 Aug '03

FOTD -- August 07, 2003 (Rating 7) Fractal visionaries and enthusiasts: Is nothing sacred? When I opened my e-mail box this morning, I found two letters from the Fractint programmers list. This is unusual, since normally, the list is considered active if it has one letter per month. But I was soon disappointed. The subject of the first letter was 'hey wgtjvjh...' This letter contained total gibberish and was likely posted only to determine if it would actually be sent out to list members. The second letter, which was sent from the same address a short time later, directed the reader to a web site selling 4-percent mortgages. I didn't bother visiting the web site. I'm sure the 'list member' who sent the spam will soon be deleted from the list. Today's unusually brilliant image rates a 7, but most of the rating is due to program features, not to an exceptional scene that I discovered and rendered. The feature that made the image is the 'fmod' inside fill option of Fractint, which was used to render the 'inside' parts of the image. This option produces an effect of overlapping bubbles. A good part of today's scene consists of trapped 'inside' points, and it is these areas that create the frothy, bubbly effect. The frothy areas of the image remind me of the egg case of a praying mantis, which is the reason for the name "Mantis Cases". The parent fractal, which was created by subtracting Z^(0.2) from 2 parts of Z^3, is so convoluted that it is impossible to describe. But it does have a 'Mandelbrot Molecule', or midget, at its northern extremity. The 'East Valley' of this midget is split into two parts. Today's scene is located in a spiral on the shoreline of the western branch of the split. Those who suspect that the colors of today's image are not quite natural are correct. I gave the original bland color palette a huge boost in contrast in a separate graphics program. This is no cause for concern, because when I run Fractint images through a separate program, I always make sure the changes can be encoded accurately into a parameter file. Running today's attached parameter file will take 10 minutes and will reproduce the enhanced image as it appears on my screen. Not all fractalists enjoy sitting back and watching images slowly appear on their screens. Those who desire instant fractal satisfaction can find it on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday was fair enough here at Fractal Central, with lots of sun and a temperature of 81F 27C. The problem was that a brief but heavy shower passed over at 1pm and again made things too wet in the holly thicket for the intrepid duo. They spent the afternoon on the porch, their moods questionable. Today is starting cloudy and threatening to bring more showers, so the moods of the duo have yet to be determined. I've got a bit of work to do and some fractals to find. Until the next FOTD appears, take care, and retain your enthusiasm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mantis_Cases { ; time=0:10:55.81--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.45558038289711040/+0.654666421634426\ 80/7.187779e+009/1/32.5/-7.89103793002315923e-006 params=-1/0.2/2/3/0/0 float=y maxiter=1200 inside=fmod proximity=0.1375 periodicity=10 colors=0000Rr0Nr0Kr3HrUKz6Hr0HH0H00000H00D00D00D0A\ DARDRkAhzAyzAzzAzzAzz6zz3zz0zz0zz0zz0zz0zz0zz0zz0u\ z0rz0kz0hz0dy0Yu0Ur0Nn0Kk0Dh0Ak000000K00kH0za0zu0z\ z0zz0zu0zn0zh0zR0zAHz0Yz0nz0zz0zz0zz0zz0zz0zz6zzRz\ zkzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzyzzuzz\ rzzkzzhzydzyazyYzyYzyUzuUzuRzuRzuNzrNzrKzrz0zKzraz\ dnzRzzDzh0zK0z00z00z00z00z00z00z00z00z30z60zA0zD0z\ K0zN0zR0zY0za0yd0uh0na0kY0hR0dN0aK0YD0UA0R66N0DK0N\ H0UD0aA0k60r30y00z00z00z00z00z00z00z03z0Az0Dz0Kz0N\ z0Uz0Yz0az0hz0kz0rz0uz0uz0yz0zz0zz0zz3zzAzzDzzHzzK\ zzNzzRzzYzzazzdzzhzzkyznvzrrzrnzugzu_yuVnyTdyURz0H\ v06s00m03d06U0DH0H63K0DR0RU0dY0nd0zh0zk0zy00aDKKAA\ U00X00_00b00e00h00k00m03o03r06t0Pv3Uw0Zx0cy0hz0myR\ rzzzkzynzuryruzzzzzzzzzzzzyzzxzzwzzuzzszzqzzozzmzz\ kzzizzgzzezzczzazz_zzXzzUzzDzz0zz0zz0zz0zu0zn0yr0u\ r0rr0nr0kr0hr0dr0ar0Yr0Ur } 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 05-08-03 (Fractal Wilderness [5])
by Jim Muth 06 Aug '03

06 Aug '03

FOTD -- August 05, 2003 (Rating 5) Fractal visionaries and enthusiasts: Sometimes I like to ponder questions that would never be considered by a sensible person. Of course, this is no handicap, because I have never claimed to be, nor do I make an effort to be, a completely sensible person. (I find such individuals a bit boring.) And even if I tried my best to be sensible, we would need total agreement on what constitutes sensible thought. (For example, is it sensible to believe in precognition when one has personally and unambiguously experienced it?) My current ponderings are somewhat more sensible than experiencing the future before it happens. I am pondering the Mandelbrot set. Is the set an objective thing, a subjective thing, or something in between, as ghosts are supposed to be? Would the Mandelbrot set exist if the universe were empty of intelligent life? And as far as that goes, did it exist before the 20th century? The answers, if such things as answers exist, depend on abstractions such as the much-debated nature of reality. We could state that the M-set (or at least the potential for the M-set) always existed, but the set itself was not discovered (or was it created?) until the latter part of the 20th century. We can also debate whether today's image is a real fractal, since it has no dividing line that separates trapped points from points that tend to infinity. In fact, it has no escaping points. The points, which are all trapped, are colored by the bof61 inside fill according to which iteration comes closest to the origin. The result is curious, but too chaotic to hold long-term interest. Today's image will be the last in the present series of Mystic2 images. Like the previous images in this series, it is filled with many potential proto-themes, but none of them are sufficiently developed, giving an effect of untamed Fractal Wilderness, which in fact is what I named it. Studying the image, I see many spots that promise interesting zooms. Some of these spots may indeed hold images worthy of being declared FOTD's. Others likely lead to fractal dead ends. This tendency is probably why the formula never became a favorite of mine, as the MandelbrotMix4 formula did. As a result of the disorganization in today's image, I can rate it no higher than a 5 -- an average effort. But the render time of 4 minutes is fast enough to make seeing the average scene reasonably convenient. And as always, the pre-rendered image is available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The on and off showers continued into the afternoon Monday here at Fractal Central, spoiling the cats' day. The sun appeared by 3pm and raised the temperature to 84F 29C, but by then the duo were already sulking. Luckily, the tuna treat made things right. Today is again starting showery, so I had best have more tuna ready. The day's work load is average. But the next FOTD, which will appear in 24 hours, will be far from average. Until then, take care, and go ahead and be silly. Fractals are fun, and is the world not little more than a cosmic joke? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Wilderness { ; time=0:04:23.48--SF5 on a p200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cotan passes=1 center-mag=-0.06074811025606387/-0.993573573575838\ 00/1425.244/1/-25/1.08651629360245749e-011 params=3.4/6/-9/3.8/6.1/-2.4 float=y maxiter=95 inside=bof61 logmap=yes periodicity=0 colors=000mfWqqQrpZsogtnpumxmkueirYgpQemIcjAbhJU`S\ QT`QLRHDcI5cTBobHnlNnvTiwYewaawefwbkq_piXuaUyVRj8w\ iAuiBtiCriDqiEoiFncOiZWeUdaPlYKtULuSMvRNvQOwOPwNQw\ LRwKSwJTwHUwGVwEWwDXwCYwAZw9_w7`w6aw5dwAfwFhvKkrPm\ oUolZrhctehvbmx_qvZptYprXpqWpoVpmUpkTpjSphRpfQpeQp\ PJpcPpaOp_NpZMpXLpVKpTJpSIpQHpOGpAahB_iCYjDXjEVkFU\ kGSlHRlIPmJNnKMnLKoMJoNHpwhltfmrdmobmm`njZnhXneVnc\ To`RoZPoWNoULpRJpPHpxwNruSmnWgg_b`dXUhSNlDPWFN`HLd\ JJhLHlBKoEJpGIpJHpLGpHw_It`IraIobJmcJjdJheKefKcgKa\ hLZiLXjLUkMSlMPmMNnNKoNIpwCOuDQsDRrDSpDToDVmDWlEXj\ EYiEZgE`fEadEbbFcaFd_FfZFgXFhWFiUGjTGlRGmQGnOGo8hg\ 9fhAehBciBbiCajD_jDZjEXkFWkGVlGTlHSmIRmIPmJOnKMnLL\ oLKoMIpNHpD`8FWHHSQJOZLKg7pE9lIBhMCdQEaUFYYHUaJReK\ NiMJmGwWHuXHsYHqZIo_Im`IkaJibJgcJedKceKafK_gLYhLWi\ LUjMSkMQlMOmNMnNKoNIp8JCAIGBIKDIOEHRFHVHHZIHbJGeLG\ iMGmtqprnpplpnjplhpjfphdp } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-08-03 (Spots and Spotlets [5])
by Jim Muth 06 Aug '03

06 Aug '03

FOTD -- August 06, 2003 (Rating 5) Fractal visionaries and enthusiasts: At the end of yesterday's discussion I stated that today's image would be a much better one. Actually, today's image is another perfectly average 5-rated one. I apologize for any bitter disappointment. The parent fractal of today's image was created by adding 0.018 part of Z^3 to Z^2, then adding 1/C instead of straight C, and increasing the bailout radius to 40000. It is a tiny Mandeloid, barely visible at the center of the default screen, shaped like a classic M-set with a greatly amplified negative stem. Instead of being a mere stick, the stem has broken apart into a new open area shaped much like a Julia set. But this area is not a Julia set, because it has Mandeloid buds and midgets on its border. One of the valleys holds today's scene. When studying the image for a name, I noticed the multitude of red-orange spots, and decided to name the image "Spots and Spotlets". The image is a pleasant one to view, especially on a video-tube monitor in subdued light, even though it rates only mediocre. Perhaps the image's greatest drawback is the 21 minutes required to render it from the attached parameter file. But that draw- back can be avoided by downloading the finished GIF image from Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The version of Fractint used by Scott on his site has been recently having trouble correctly rendering the images created with the 'Mystic2' formula. However, today's image returns to the 'MandelbrotMix4' formula, which has always worked properly, so Scott's site will have the correct image. A heavy thunder-shower at noon totally spoiled the cats' day Monday here at Fractal Central. When the sun appeared at 1pm, the yard was a puddle of mud and the holly trees were dripping, making it unfit for the delicate paws and ears of the dynamic duo, who spent the afternoon sulking on the porch. At least the temperature of 81F 27C was within their comfort zone. This morning is actually starting sunny, but more heavy rain fell during the night, and even more rain is forecast for this afternoon. Will things dry out in time for the duo to have a pleasant day? Find out in 24 hours, when the next FOTD will appear. Until then, take care, and pray for the rain to stop. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Spots_and_Spotlets { ; time=0:21:35.86--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.02416004980605908/+0.000316771873493\ 02/4.86578e+012/1/142.503194220881852/-0.009630602\ 08333854639 params=1/2/0.018/3/-0.9/40000 float=y maxiter=1600 inside=bof61 logmap=207 periodicity=10 colors=000MH`PHcRHgTHkWHoYHs_HvVMjQRZLWNJYOI_PH`QG\ bRFcREeSDfTBhUAiV9kV8lW7nX6oY5qZ4rZ7kW9eUCZSETQGRR\ IPRKNRMLROKRQIRSGRUERWCRXBRZAU_9X`8_a7bb6ec6g`AdZD\ bXH`VKYTOWRRUPVSNYPLaNJdLHhJFkGDoEBrC9uAAqBBmCCiDD\ eDEbEFZFGVFHRGINHJKIKGILCJM8KM5KR4JV4I_4Hc3Gh3Fl3E\ p3Dq2Bq2Aq29q28q27q26q25q24q23q22k95eG8_MAUTDOZGIe\ ICkL6rO0xQ4tO8qNBmMFjKJfJMcIOaKQ_MSYOUWQVUSXSUZQV`\ OXaMZcK`eIbgGdhEekA`n7Xq3Tt0Ps1Us1Zs1cs1hq2co3Zn4V\ l5QzcLz_HzWCzC7wD3sC2oB2kB2gA2cA2c92b91b91b91a91a9\ 1a91ZD6XHAVLFTPJRSOPWSN_XLc`JfdLefMegNehOeiPejRelS\ emTdnUdoVdpXdrYdsZdt_du`dvY`uVYuSVtPRtMOsJUsHYsgcn\ kgdndVqVMnXQlZUi`Ygbaddebfi_hmYjqWkt_lkcmcfnW`kUWi\ TRgSMdRGaPBZO6WN1TM5UO8UPCWRFYSJ`UMbVPdXTfYWh__j`b\ kbflcimelnfhoadoX`oTXpOTpJPpFLqAHq5Eq1FmBFiLFiVGkd\ GmnGowEqqCtkBwe9z_8zV6zP4zJ3zD1z70z24z48z5Bz7Fz8Jz\ AMzBQzDUzEXzG`zHdzJgzKKzX } 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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Re: [Fractint] FOTD irregularities & Jim Muth's Mystic2 formula
by Jim Muth 05 Aug '03

05 Aug '03

At 08:38 AM 8/5/03 -0500, Scott Boyd wrote: >Hi all, > >I was looking at Jim's .par files for the last four days to try to see why two >out of the four days, the FOTD did not generate properly on my Linux >computer. The only difference I see, is that the days it didn't generate >correctly, Jim used the 'cos' function. (Aug. 2 & Aug. 4) Strangely enough, >the 'cosxx' function that Jim used Aug. 3rd, did work correctly. And this is >the function that Jim says has an error in it! (The Aug. 1 .par file >generated correctly, but Jim used the 'atanh' function that day.) > >So it's possible that the 'cos' function is broke in Xfractint.... I doubt that this is so. If it were, none of the Mystic2 images would generate correctly. A 'cos' function is hard-coded into the fifth line of the formula. Jim M.

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FOTD irregularities & Jim Muth's Mystic2 formula
by Scott D. Boyd 05 Aug '03

05 Aug '03

Hi all, I was looking at Jim's .par files for the last four days to try to see why two out of the four days, the FOTD did not generate properly on my Linux computer. The only difference I see, is that the days it didn't generate correctly, Jim used the 'cos' function. (Aug. 2 & Aug. 4) Strangely enough, the 'cosxx' function that Jim used Aug. 3rd, did work correctly. And this is the function that Jim says has an error in it! (The Aug. 1 .par file generated correctly, but Jim used the 'atanh' function that day.) So it's possible that the 'cos' function is broke in Xfractint.... Scott Boyd -- sdboyd56(a)swbell.net http://sdboyd.dyndns.org --------------------------------------- No Microsoft or other proprietary products were used in the creation of this email.

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