July 2008 - Fractint - mailman.xmission.com

FOTD 22-07-08 (Non-Mass Confusion [5])
by Jim Muth 22 Jul '08

22 Jul '08

FOTD -- July 22, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's image is found in the Z^(1.875)+C Mandeloid as it appears when calculated 25.5 levels up the log ladder with no function applied. This parent fractal reminds me of nothing more than a Mandelbrot set with a hernia, rotated 180 degrees. The exact scene is located in a small valley on the southeast edge of the parent's main bay. I named the image "Non-Mass Confusion" for some reason that I have now forgotten. I rated it at a 5 because I consider it worth little if anything more. The minibrot at the center is nearly an exact replica of its parent fractal. Considering the appearance of the parent, this is nothing to brag about. The image takes a little under 5 minutes to calculate on the fireball 2000mhz computer. This is the very first time this particular scene has ever been viewed by human eyes, so the calculation time is well within reason. But to assure that unreason has no opportunity at all to raise its ugly head, the finished GIF image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A fairly pleasant midsummer day at Fractal Central went un- noticed by the fractal cats, who were more interested in watching the local pigeons. My day was fairly average also. The next fairly average FOTD fractal will be posted in 24 hours. Until then, take care, and ask every question. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Non-Mass_Confusion { ; time=0:04:59.04-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.852267427778726/-0.442482399993808/\ 2523215/1/-172.5/0 params=1.875/0/25.5/0 float=y maxiter=5200 inside=0 logmap=333 periodicity=10 colors=000A0KE0MH0OM0QR0SU0V_0Yb0_g0fj0jo0lt0mx0oz\ 0qz0sz0tz0tzHozojzzeyz_szSlzNezHYz4_zC_zK_yR`u_`tg\ `smboubmzYhzblzeozjqzmtzqxzuyzyzxzzuzztzzqzzozzmzz\ lzzhzzestbzhhzlcjm_gj`ehbcgcbce`bgY`hWYjUWjSUlRRmN\ PoMNqKKsIItHHtb_WzR2uo7cz1ez5gzAgzEhzIjzNjzRlzWmy`\ ozlmzgmxcmo`mhYmbUmURmNNmHKjFNhEPeERcCS`AW_AYW9_U9\ `S7cP5eN5gK4hI2lF2mE1oH0zE0uC1qAAl9Kg7U`5cW4mR2uM2\ lW2bc2Ul2Yo2`q2bs2et2gu2jx0xz0qz2ly7gxAbxFWuIRtNMs\ RHsWAqz5zt1zt0zo0xg0mY0eP0YF0Q40450970E92IA4NC7SEA\ YFEbFFeHIjIMoKPtMRyNUzPYzR`zS`zjuzqszZtz_ozPcxNcsN\ cmNehMecMe_9PFFMNMeW0ocxzeSxb0yR0qW0h_4`bASeFKhAEc\ FChKClPCqUCtYCxbCzgCzlCzqCzx7ztCzsHzqMzoRzmWzl`uje\ shjmgohetecy`bzY`zSbz0`z4_zP0zzCzzIPxHRzHRzHSzHUzI\ MzHUzF`zEgzCmzAtx5yzAztFzmKzgzz`zzUzzNzzHzzAzz4zz0\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzz1zz1zz1zz1zz0zz1zz5zz\ 9zzEzzAzzEzzHzzKzzNzzRzzU } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 21-07-08 (Six Discontinuities [4])
by Jim Muth 21 Jul '08

21 Jul '08

FOTD -- July 21, 2008 (Rating 4) Fractal visionaries and enthusiasts: In today's image we return once again to the Z^(1.875)+C Mandeloid as it appears 26 levels up the complex-log hyperspiral with the 'floor' function applied. This Mandeloid closely resembles the Mandelbrot set. The main differences are the lack of a main spike and the 180-degree rotation. Today's scene is located on the west side of the south branch of Seahorse Valley of the parent, which becomes the north branch when the fractal is rotated 180 degrees to the 'normal' position. I named the image "Six Discontinuities" after the six almost- invisible discontinuities that interrupt the perfection of the spiral seahorse tails leading to the central minibrot. Unfortu- nately, these breaks are an inescapable part of all fractals created with fractional powers of Z. They must always spoil the sought-after fractal perfection. I rated the image at a humble 4, which can be considered no better than barely adequate. Let's face it, the image is basically nothing more than another scene in Seahorse Valley, the first place every tyro fractalist checks. Actually, this parent Mandeloid is basically a 'ground level' one, and can be created far more simply with any formula that can calculate (-Z)^(1.875)+C, which is another reason I was so stingy with the rating. The calculation time of 7 minutes on a P4-2000mhz unit just makes things worse. But with today's super-machines that move at the speed of a tachyon, that time may be cut significantly. The unlucky few with machines that have a panic attack when they see a DOS program can find the finished image posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Very summer-like weather prevailed here at Fractal Central on Sunday. The morning and first half of the afternoon were sunny, hazy, hot and humid, with a temperature of 93F 34C. But a thunder-shower moved in during the late afternoon with a wind squall and heavy rain that knocked the temperature down to 73F 23C, bringing welcome comfort to both cats and humans. The next FOTD will appear in 24 hours, so be right here when that paradisiacal moment arrives. Until then, take care, and fractals are never so good that they can't get better. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SixDiscontinuities { ; time=0:07:16.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=mandelbrotbc3 function=floor passes=1 center-mag=+0.7461139806164767/-0.0627672807415249\ 6/5.887638e+007/1/-10/0 params=1.875/0/26/0 float=y maxiter=5000 inside=0 logmap=652 periodicity=10 colors=000PFqOEpNDoMCnLBlKAkJ9jI8iH7hG6gG6fLCcQHaV\ N_ZSXcYVhbTlgRcdQVaPM_OQ`MTaKXbJ_cHbdGfbKjaOn_SrZW\ uYZrX_oX_mX`jW`gWaeWabWb_VbYVcVVcSUdQUdNUeLUeNVfOW\ fPXfQXfRYgSXgTWgUVgUUhUThTShSRhRShQRjOQkMPkINmFJoB\ GpEJoGMnIPmKSlMUlOXkQ_jSbiUdiNgjGjk9ml2pmAidIcXQXO\ YRGdL8ePCeSFeVIeYLe`OecRfgVfjYfm`fpcfsffvifylZxmSw\ nLvoEup7upBsnErlIqjLphOofSndVmbYl`akZdjXgiWheXhbXh\ _XhWYhTYhQYhMZhJZhGZhC_h9_h6_kCbmIepOhrUku_nweqyjs\ ultrmtonulouhpveqvbrw_twXuxTvxQwyNxyKyzHzzKywMytPx\ qRxnUxkWwhZwe`wccv`evYhuVjuSmuPotMrrJtpHslIrgIqcIp\ `JoZJnXJmVKlSKkPKiQLmOLlMLiILaMc_QdYUdWYeUZeSVfQUf\ PUgSTgVThXTm_jra`zcRqfDmh8cj9UmABoB6qB2jA3f93b83_7\ 3Z63Z53Y53X66W79V7CU8FR9IO9LLANIBQGFTFJWGNZHRaKVcN\ ZeQbgTfiWjkZkmakodjpgjpjipjipiiphhohhoggogiogmofro\ fwoexneyndznczncznbznbznazmzzmzzmzzmzzmzzmzzlzzlzz\ lzzlzzlzzlzzkzzkzzkzzkzzk } END PARAMETER FILE=========================================

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FOTD 20-07-08 (What's It All About [5.5])
by Jim Muth 20 Jul '08

20 Jul '08

FOTD -- July 20, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image is not so bad for such a hurried one. But due to being out in the Poconos having fun all day Saturday, I have little time for the fractal discussion. Surprisingly, at level 26 of the hyperladder, and with the function set to 'floor', the fractal created by the formula Z^(1.875)+C closely resembles a Mandelbrot set with X-axis symmetry that has been rotated 180 degrees. The scene of today's action is located in a minor valley on the eastern shore line of the large southern bud. (If the parent fractal is rotated 180 degrees to the 'normal' position, this is the western shore line of the northern bud.) I was a bit generous when I rated the image at a 5.5. It really has little going for it other than coordinated confusion. When I named it "What's it all About", I was thinking of the 'real' 'objective' world, which we all assume to be really 'out there'. The older I get, the more I doubt that the world is actually 'out there' rather than 'in here', or more likely a combination of both. The calculation time of 7-1/2 minutes is more than the image is worth. I strongly recommend visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and saving the effort of running the parameter file. If, due to the unusual hour of this posting, the image is not yet posted, check back in a few hours or bite the fractal bullet and run the parameter file at once. Typical midsummer weather prevailed at Fractal Central on Saturday, and it is prevailing again today. The fractal cats are ignoring it. The next FOTD will be posted in about 8 hours. Until that brief time passes, take care and search for the elusive truth. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Whats_It_All_About { ; time=0:7:30.00-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=+0.09083559731196626/-0.751949802458988\ 10/3.635092e+009/1/-165/0 params=1.875/0/26/0 float=y maxiter=7500 inside=253 logmap=420 periodicity=10 colors=000SDfUEgWFhYGi`HjcIkfJliKmlLnoMor0pu4qzBhz\ HZzFYzEWzEWzCVzCUzBUzBSz9Rz9Rz8QfrBfqBhq9ho9io8in8\ jn7jn7iq8hs9fv9eyBdzCbzCazEazErPzmVziawdhs`mnWsiRz\ eNz`JzWfIzdQzaYsZenWmhUuaRzWWvaaqfekjjhoobusYyySzz\ PzzMzyLswJmuIfsH`rFSqEMnCFmB8k91j80iC0iF0iJ0iM0iQ0\ iS0iW0iZ0ia0ie0ih1ik1in1ir3iu3iw3eu5as7Yr8Vo9RnBNm\ CLjEHiFChH9eI5dJ1bL0aM0jP1sR3zSHyZSvddsi3zd8zeEzeJ\ zePzfUwfYvfbshhqhmnhrkiwiizhizikzjmzknzmqzzzwwztsz\ qoznlzkjzhhxeeubbq__kXXdUUaRR`OP_LO_ILZFITCCOZFQ`E\ PbCNv9Lo8JzPIz5HzVFvBJvRNiPQhVUh`Yhf`fmdzzhmyjYnmQ\ dnIUq9Jr18u00v4SmEudRqbdmaziaqaMqV5jY7e`7Zb7Ud8Nf8\ Ii8Bj95m90o90q90oE0oI1nM4nQ7mU9mYCkaFkdIkhLjkNjoNi\ sSiwVhzYhzZhzbkzenzhqzksznvzqzyuzwwzvzzuzzszzkvzeq\ zYjzRhzJazCVzLPzSIzZJzfQznVzuazzfzzdzzazwZzrWzmUzh\ RzbPzYMzRJzMHzHEzBBz58z05z07z08z08z19z3Bz5Bz7Cz8Ez\ BEzCFzFHzHHzIIzHJIFLzFMzE } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 19-07-08 (Green Dumplings [6?])
by Jim Muth 19 Jul '08

19 Jul '08

FOTD -- July 19, 2008 (Rating 6?) Fractal visionaries and enthusiasts: Today's fractal image reminds me of green dumplings. I can't help it. That's what I see, so that's what I named it. I could not decide on a rating, so I let the image go with a rating of a questionable 6. The parent fractal was created when I calculated the formula Z^(1.875)+C just 3/4 of one level up the logarithmic ladder with no function applied. This fractal resembles nothing that one is likely to see in what is commonly known as the real world. In fact, it consists of several separate Mandeloids, with today's scene located in the East Valley area of a small Mandeloid lying to the west of the main Mandeloid. The image is one of the most jagged I have yet found. It almost looks a bit sinister. A good part of it consists of inside stuff colored a deep blue. A better coloring might have been possible if I had put a bit more effort into it. The calculation time of the included parameter file is 3-1/2 minutes, but the wait to see the image can be reduced substantially by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. The 91F 33C heat and high humidity here at Fractal Central on Friday was not broken by a shower in the evening, as it was on Thursday, thereby making the fractal cats irate. And irate fractal cats are certainly no fun. Except for the irate cats, my day was pleasant enough, and with a similar day expected tomorrow, FL and I might plan a little outdoor enjoyment. If so, the FOTD for July 20, might be 15 hours or so late. Until next time, whenever that is, take care, and search for reality in the least likely place -- your mind. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Green_Dumplings { ; time=0:03:31.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.820586956762904/+0.1116182311689719/\ 7.098603e+007/1/92.5/0 params=1.875/0/0.75/0 float=y maxiter=3600 inside=255 periodicity=10 colors=000Q7KL5JG3HB1F60EA3OE6XI9eMBnYHgiN`uTVnVVg\ WV`XVUYVNZVG_VSYWbWXmUXlS_jRaiPcgOeKMe2LeaJeZIfYGa\ YFZXD`XCaWAbW9cU8aT7`S7`R6`V6aZ5bY5bX4cW4cR7cM9UHC\ PCEK7HA2J06L39N6CP8FQBJSEMUGPWJSXMWZOZ`RabUdcWeaSf\ _PfYLgXIgVEhTBhS8ro6ujBweGyaLxbMxcNxcOxdOwePweQwfR\ wfRvgSvhTvhUviUujVujWukXukXvd_wZbwSexMhxFky9ny3pBA\ iGAjKAkOAkTAlXAl`AmeAniAnmAorAovApzApyLnxVlwejvoiY\ IiWMfUPdSSbQV`OYZM`XLcVJfTHiRFlPDoNBrL9uJ8xHHvOQtU\ Zr`gpfpnmylsymtyntyotyotyptyqtyrtyrtystzzzwzzzztxr\ qxoowllwijvfhvceu`cuZatWZtTXsQUsNSrKQrHNqELqCJqFMq\ IOqLQqNSqQUqTWqVYqY_q`bqbdqefqhhqjjqmlqpnqrpppnonm\ nmlnkkmjjlhikfgkefjceibdh`ch_b_aZSbVJcRBdOEeRHfTJg\ WMhYPi_RjbUkdWlgZmiankconfpphqrkokmmdokYqiRsgKfQYh\ OajMdlKgnIkpGnrErtCuvBxvDuvErvGovHlvJivKgvMdvNavPZ\ vQWvRUiUNXXHK_A8b4Da5I`6N`6S_7XZ8`Z8eY9jXAoXAtWBxW\ BwZAv`Avc9ue9ug8tj8tl700P } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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Re: [Fractint] FOTD->AOTD
by JackOfTradeZ＠comcast.net 18 Jul '08

18 Jul '08

. Animation of FOTD 7/9/08 (fractal black hole) is posted: http://www.fractal-animation.net/vid/blackhole.zip 12 Meg download. Noone commented on the last few - does that mean they suck? Hope you like this one. .

6 5

FOTD 18-07-08 (Too Much Too Early [5.5])
by Jim Muth 18 Jul '08

18 Jul '08

FOTD -- July 18, 2008 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image takes us back to the Z^(1.875)+C Mandeloid. This time we examine the version that appears 1 level down the complex logarithmic ladder when the 'floor' function is applied. At this basement level, the formula produces a fractal shaped like a puffed-up kidney bean with a large bud hanging from its bottom. Today's image is located in a curiously striated area on the western shore of this bud. When I delved into this area, I did not find the infinitely divided striations I expected. I found an area exceedingly rich in random detail but with no unifying theme, leading me to the name "Too Much Too Early". The rating of 5.5 indicates my dis- satisfaction with the plethora of detail, while including a half- point bonus for my modest coloring effort. The calculation time of 7-3/4 minutes is somewhat slow, so why not speed up things by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished GIF image there. An uncomfortably muggy day here at Fractal Central on Thursday was mitigated by a brief but heavy thunder-shower in the late afternoon. The rain dropped the temperature from 90F 32C to 73F 23C, and made the fractal cats happy in the process. My day was once again on the busy side, but better things could happen tomorrow, when the next FOTD fractal appears. Until then, take care, and now, even some physicists are saying that the universe, as well as empty space itself, might be a great fractal. Maybe the skeptics and Atheists are wrong when they claim it's all a meaningless accident; maybe the believers are wrong when they claim that a supernatural God did it. Or, maybe I'm wrong when I think the answer lies far beyond the ability of the human intellect to comprehend. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Too_Much_Too_Early { ; time=0:07:48.57-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.331401349423654/-0.801267905838342/\ 2.180413e+007/1/-10/0 params=1.875/0/-1/0 float=y maxiter=7200 inside=0 logmap=725 periodicity=10 colors=000NASOASPASQASRASSASTASUASVASWASXASYASZBS_\ CS`DSaCSbBSbASc9Rd9Qd9Pe9Oe8Nf8Mg8Lg8Kh7Jh7Ii7Hi7H\ WQBNRMCQVFRWIRWLRWOSWRSWUSWXSWZTWaTWdTWgTWjUWmUWpU\ WrUWhWW_XWQZWH_WN0RT7NZ8JaBFl88jGBiNDhVFgaIfiKepMd\ wOetPerPeoPemPejPehPeePecPdcQeaPe_OeYNeWMfULfSKfQK\ fOJgMIgKHgIGgGFgEFhGJhINiKRiMViOZjQbjSfjUjkWnkYrjY\ ykZvk_sk`qkanlbklcildfledmfamgZmgXmhUniRnjPnkMnlKo\ mHonEooCop9op7loAjnDhmGelIckLajOZiQXhTVgWSfYQe`Odc\ LceJbhHakE`mC_pAZs7Zy8Yu9XrAWnBVkCUgCQZDUdEYiEanFe\ sFhxGcuH_rIWpJSmIPnJOkKOiKOfLOdLObLO_NOYNOWNOTOORO\ OPRRRUTSXVT_XUbZVdXXgcYjeZmg_pi`tt`rvaqkapwankbmkb\ ljbkjbischjcgjcfjcdidvndbid`ie_ieZheYseWhfVhfUZfQf\ hThfVieXjdZkc`mbbnado`fp_hrZjsYltXuuanvWgwQ`xKUyEO\ z9QzBVzDZzFczHhzJmzKrzMvzOzzQzzSzzUzzVzzRzzOzzLzzI\ zzFzzCzz2zz9zzFzzLzzRzzXzz`zzbzzdzzfzzhzzizzkzzmzz\ ozzpzzLzzMzzNzzOzzPzzQzzR } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 17-07-08 (Eastern Lights [7])
by Jim Muth 17 Jul '08

17 Jul '08

FOTD -- July 17, 2008 (Rating 7) Fractal visionaries and enthusiasts: Due to an excess amount of real work, the fun work of fractals was cut short on Wednesday. But I did find time to delve into the parent fractal that results when the formula Z^(1.875)+C is calculated 36 levels up the logarithmic ladder with the 'floor' function in effect. This parent fractal resembles a Mandelbrot set that has been put through a wringer. Its most interesting feature is a much smaller distorted Mandelbrot set just to the east of the main set. Today's image is located in the East Valley area of this mini-M-set, which curiously lies on the mini's west side. There is not much more to be said about the image, though there is much to be seen when viewing it. I named the image "Eastern Lights" because it's on the eastern side of its parent, and rated it at a 7 because that's what I think it's worth. The calculation time of a nominal 2-1/2 minutes may be avoided by viewing the finished fractal on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With added haze, higher humidity and a temperature of 88F 31C, Wednesday was a comedown from the previous day here at Fractal Central. The fractal-cat duo showed their displeasure by camping most of the day under the cool-air vent. My day was busier than I would have preferred. With any luck at all however, tomorrow, when the next FOTD will ne posted, will be an improvement. Until then, take care, and speak softly with nature. I hear that, at its smallest scale, it may well be a fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Eastern_Lights { ; time=0:02:27.61-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=+0.786337062833908/+0.5106500816556531/\ 70165.7/1/40/0 params=1.875/0/36/0 float=y maxiter=2400 inside=0 logmap=175 periodicity=10 colors=000AAwAAtAApAAlAAhAAdAA`AAX8AU7AQ57M43N55L6\ 7M78Q8AP8BR9DTAEUBGVCHWCJYDK_EIbFNbGPcGJgHLcIMbJKa\ JI`KG_LEZMCYMAXKCVJETIGRHHPGJOELMDMKCOIBQGARFCTHDV\ JEXKFZMG_NHaPIcQJeSKgULhVMjXNlYOn_Po`WdVaUQhJKn9Fl\ BIjCLhDOfERdFTbHW`IZZJaXKdVLfTNiROlPPoNQrMRtKPrJOq\ INpGLoFKnEJmDIlGMkJPjMSiPVhUZgZafcdehgdmjcrnbvqazt\ `zw_zz_zwYztXzqWvnVrkTmhShfRccQ``PYYNWVMUSLSPKQNJO\ QKMTLKVMIYNG_OEbPDdQCgRCiSClTCnUBjYBg`BddBagHeZNiR\ SlJTkIUjIUjIViIWiIWhIXhIYgIYfIZfI_eI_eI`dI`dIgZRnT\ _tNhpPelRciT`eUZbWXZYUWZSS`PPbNLcLIeIEgGBhEDeHFbJG\ `LIYNJVQLTSMQUONWQLYRI`TFbUDdWAfX8hZAi`CibEjcGjeIj\ gKkhMkjOllQlmSloUmqWmrYmp_jo`gnbdmcakeZjfWihThiRfj\ OelLdmIcoFapC`r9_s6Zt4asAcsFfrKhrPjrUmqZoscquhtwmv\ xrxzwrzvmzvgzubzuXzuzztzztzztzzlzzezzYzzRzzJzzCzz4\ zz1zz2zz6zzAzzFzzJzzNzzKzzH_zEWzBSz9QzBPzCNzEMzFKz\ HJzIHzKGzLEzMDzOBzPAzR8zS } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 16-07-08 (Naturally Fractal [7])
by Jim Muth 15 Jul '08

15 Jul '08

FOTD -- July 16, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image returns us to the complex logarithmic hyperspiral, which we have not visited in about a month. The parent fractal was created by the formula Z^(1.875)+C as it appears 33 levels up this abstract spiral when the 'floor' function is used. This parent resembles a ragged, somewhat squashed Mandelbrot set rotated so that its main spike points northeast. I chose the exponent 1.875 because it is 7/8 of the way from 1 to 2, which is close enough to 2 to create minibrots resembling recognizable quadratic ones, yet far enough from 2 to create fractals of infinite variety. Today's scene is located in a filament extending from the period-5 bud on the southwest shore line of the large minibrot on the main spike of the parent fractal, very near the point where the hairline filament emerges from the chaos. I named the image "Naturally Fractal" in recognition of the fact that nature is filled with and possibly made of fractals. I rated it at a 7 because it not only leads to pondering, it also is attractive in its own way. And no one will complain about the calculation time of a mere 30 seconds. For added convenience, the finished image is posted for fast if not instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect midsummer day went unrecognized by the fractal cats of Fractal Central on Tuesday. The temperature of 86F 30C was made quite bearable by the low humidity. My day was a bit too busy for total enjoyment, but I still managed a half-hour under the mulberry tree, pondering the mysteries of the outer world and man's pathetic efforts to comprehend it. The next FOTD, which BTW is still a mystery, will be posted in 24 hours. Until then, take care, and fractals can cause deep thinking. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Naturally_Fractal { ; time=0:00:29.98-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor center-mag=+1.298046570238266/+1.385392696646682/\ 1.09e+007/1/65/0 params=1.875/0/33/0 float=y maxiter=1200 inside=0 logmap=70 periodicity=10 colors=000OKOOKNOKNOKLOKKOKKOKKOKKOKKNKJMKILKEKKAJ\ J9II8HH7GG7FF6EA5B54814K46P77V99bCAgJCiHDzfCoJEzzD\ f3Fh0JimNj2Qk2Ul2Xm2`p1_n2cm2fl2ij3mi3ph3sg3va8uXc\ tSGsMLrHcrCTv1mz7mvCXrHWmMWhRWRWVL`VEdY3eV8fSCfPHg\ MLgJPiKRkKSmKUoKVzXNpKWb6og8dlAVqCKvEAzF0qO3iW5ad8\ UlAMdMEYYIZVMZTP_RT_PX_N_`Lc`Jf`HlRQrHYqMXpQXoUWnZ\ WmbVlfVqhPljVhl_cnd_oiVqnRssNtxHskBs_5rO0rC2cQ4Qc0\ Aw5CpAEjFGcE6XKHYPRYU`YswSZjY5eiEYbMQXUIQ`CGaAKa8N\ b6Rb5Uc3Yc1`c0cbDgaPk`ao_ms_ywfyjmyYtyLzy82i7czQ`r\ RZjSXbTVVUTOUTOUTOUTNTTNTTNTTNTTMTTMTTMTTMTTLTTLTT\ LTzLTzKTzKTzKTzKTzWkzTfzQazNXzgfzfeueetddscdrccqbc\ zabz`bz`az_azZazY`zX`zX_zW_zVZzUZzUYzzYzzXzRXzzXzQ\ WzzWzzVzzVzzUzMUVzTzzTzz2zz3Cz3Cz4zz4zz5zS5zz5zR6z\ z6Ez7Fz7Fz8zz8zz8zQ9Gz9zzAHzAHzBzzBzQBzPCzzCzPDJzD\ zPEJzEzPEzOFKzFKzGLzGLzHLzHLzHzzIMzIzzJzzJzzKNzKzz\ KzzLzzLOzMzzMPzNPzNPzNQzO } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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FOTD 15-07-08 (Hyper Ultra Hyper [6])
by Jim Muth 15 Jul '08

15 Jul '08

FOTD -- July 15, 2008 (Rating 6) Fractal visionaries and enthusiasts: I spent most of the time on today's philosophy, which appears below, so I have little time for the fractal discussion. Today's image is from the same parent fractal as yesterday's image. This parent was created by combining 0.4 part of (1/Z) with Z^100 and adding C. Whereas yesterday's image is located on the west side of the open area of its parent, today's is found in a vestigial East Valley on the East side. I named the image "Hyper Ultra Hyper", which means nothing. I rated it at a 6, which is a half step down from yesterday's image. The calculation time of one minute will bring only happiness. And that happiness may be assured by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished GIF image there. Out of the blue Monday afternoon, FL made one of her comments that are intended to be innocent, but really get me pondering. She commented that she thinks I might be losing faith in science. How insightful a statement! Science is supposed to work in exactly the opposite way from faith. The claims of science must be objectively provable and falsifiable, while faith is based on unverifiable and unfalsifiable doctrines stated by priests, plus lots of hope, and yes, a bit of wishful thinking. When one loses faith, it means that the person can no longer believe a particular religious doctrine. A person may lose faith in the existence of a supernatural creator God because so much of the universe has been shown to have a perfectly natural explanation. They may lose faith in the existence of an immor- tal soul because the conscious mind is known to be intimately connected with a healthy functioning brain. Or the person may simply be unable to believe in things he cannot observe. But at the same time, science also requires us to have faith in things that we cannot observe. No one has ever directly seen an atom or any of the sub-atomic particles. We see only the written scriptures of physicists serving as high priests, who claim to have observed some high-energy phenomena that only they can interpret for us. We have the words of the religious priests written in the holy scriptures of religion; we have the words of the physicist priests written in the holy scriptures of published scientific papers. We have apologists for religion; we have apologists for science. The religious faithful are quick to defend their religious beliefs; the scientific faithful are just as quick to defend their scientific beliefs. I see little difference. In my case, my greatest doubt is that it is possible for a theory of everything to even exist, much less be worked out mathematically. Not the least problem is that the concept of 'everything' is an unrealizable ideal, not an objective reality. Finding a theory of everything is as likely as finding every possible fractal. Physicists have been chasing a chimera for over a century. But the chase is fun, and the chasers get their books published, and their shows fill the television channels, so the futile chase will likely continue well into the 22nd Century. But even then, the number of calculated fractals will have yet to scratch the surface of the total number of fractals that potentially exist. Monday opened with clouds here at Fractal Central, but by late morning the clouds had cleared away, leading to one of the most delightful afternoons of the summer. The fractal cats were too busy watching a tailless cat hanging around the area to bother with the 84F 29C weather. In my department, the real work was finished early, leaving ample time for today's image, which, despite sufficient time, still fell short. The next FOTD image will be posted in 24 hours. Until then, take care, and keep the faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hyper_Ultra_Hyper { ; time=0:01:02.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.5274268482159935/-0.0000290600313758\ 7/6.88186e+009/1/-166/0 params=1/100/0.4/-1/0/0/0/0 maxiter=1500 inside=0 logmap=116 periodicity=10 colors=000`UK_UKZUKYUKXUKWUKVUKUUKTUKRUKPUKNUKLUKJ\ ULHVMFXKDZIBaF9cD7eB6g99jCBlEDnGGpJIrLKtNNvQPxSRzU\ Pz_OziOzsMzzKzzKzzauzqeUzP0z90z20zU0sc0wm0zm0zm0zK\ 2zR9zYGzeMzkPoIMO0Kc0Oq0Rz0Wz0Yz0Uw0Rm0Oc0MU0IK5G9\ 9DRGYiKqzOz00z00z9DzOWz_mzz09z0Gz5KzBPzGUzMYzRczYg\ zakz_gzYczW_zUWzRRzRPo55e000c00Y00RG0MU0Ie0Bs05z00\ z0Bz0Mm0WY0eI0o00y00m07cGIRUPIg_5ug0zq0uy0gz0Uz0Gz\ 00z00z02z5IzGWzPiz_wwizqszkzzayzRwzIuu7qi0oW0mI0k5\ 0oD0sK0wR0zY0zc5zk9zqDzw9zm5sc0gU0WK0M9G50_00q00i0\ 0a00U02M0D052MG9cOGwWKzcPzkUzcYzYasPceKgUDiOOyDyz9\ zcOz0Iz0Bz5Oz9IzDBzI7zKmzDzz7zzPzzezzuzzmYzg2za0zW\ Gz0Oz0WzGczUkzeKz0Rz9YzOczaizmuz_zzMzz7zz0QKPXPKbT\ GiYCoazuezeRzQDzPPzP`zPlzTVzXDzTGzPIzMKzINzEPzBRz8\ Yz5dz2kz4hz5ez6cz7`z8Yz9WzATzBRzTYzidzzjzthzogzifz\ ddzZczUbzTdzRfzQhzPjzNlzMnzKpzJrzIszOszTszYszbszhs\ zmszrszwsztmzrhzpcznZzlTz } frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================

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FOTD 14-07-08 (Hidden Jewels [6.5])
by Jim Muth 14 Jul '08

14 Jul '08

FOTD -- July 14, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image lies in the curious fractal that results when 0.4 part of (1/Z) is combined with Z^100 and straight C is added. This parent fractal appears as a circle with an open bay filling the right quarter of its interior. Today's scene is located on the X-axis in the rich detail at the left edge of this bay. I named the image "Hidden Jewels" for no good reason, and rated it at a 6.5, allowing myself a half point bonus for the extra coloring effort. The calculation time of a minute will seem more like 10 seconds once the scene starts to appear on the screen. For added convenience, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A hot muggy morning with ample sunshine led to clouds and rain showers in the afternoon on Sunday here at Fractal Central. The dynamic cats slept through most of the non-excitement. The next FOTD will be posted in 24 hours. Until then, take care, and for insomnia, read "Finnegan's Wake". Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hidden_Jewels { ; time=0:01:08.12-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.03805276306469168/0/198852 params=1/100/0.4/-1/0/0/0/0 float=y maxiter=1500 inside=0 logmap=32 symmetry=xaxis periodicity=10 colors=0000iM0eO0cO0_P0WR0RU0PU2OcMMmaKkmIcsGczGcz\ Pcy_viizUszDzz0zz0zz7zzUzzozzzzzzy0Dm09c05R00I0050\ 0000000009O7UzGRzUPz_OziOzsMzzKzzKzzauuqeUzP0z90z2\ 0zU0sc0wm0zm0zm0zK2zR9zYGzeMzkPoIMO0Kc0Oq0Rz0Wz0Yz\ 0Uw0Rm0Oc0MU0IK5G99DRGYiKqzOz00z00z9DzOWz_mzz09z0G\ z5KzBPzGUzMYzRczYgzakz_gzYczW_zUWzRRzRPo55e000c00Y\ 00RG0MU0Ie0Bs05z00z0Bz0Mm0WY0eI0o00y00m07cGIRUPIg_\ 5ug0zq0uy0gz0Uz0Gz00z00z02z5IzGWzPiz_wwizqszkzzayz\ RwzIuu7qi0oW0mI0k50oD0sK0wR0zY0zc5zk9zqDzw9zm5sc0g\ U0WK0M9G50_00q00i00a00U02M0D052MG9cOGwWKzcPzkUzcYz\ YasPceKgUDiOOyDyz9zcOz0Iz0Bz5Oz9IzDBzI7zKmzDzz7zzP\ zzezzuzzmYzg2za0zWGz0Oz0WzGczUkzeKz0Rz9YzOczaizmuz\ _zzMzz7zz0zz0zz0zz00z07zUKzzUzz_zmezRkz5wzDzzKzzP0\ z70zM7zYIziRzuizazzIzz0zz2zz7zz9zzYzzszzzzzzazzWzz\ RzzOzzKzz7zz0zgIzoczwyzzzzzozzOzz0zz0zi0zBRzWszozz\ zyzsMzPgzePzRKz07zz0zI0zK } frm:MandAutoCritInZ {; 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 PARAMETER FILE=========================================

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