May 2007 - Fractint - mailman.xmission.com

FOTD 23-05-07 (Something New [8])
by Jim Muth 23 May '07

23 May '07

FOTD -- May 23, 2007 (Rating 8) Fractal visionaries and enthusiasts: The four-dimensional HyperMandelbrot set is virtually ignored. And why not? Very little totally new stuff is to be found in it. But is it actually as devoid of new stuff as would first appear? Today's image answers that question with a resounding NO! Today's under-used formula draws the 4-D HyperMandelbrot set, and does some strange things with it. I do not fully understand all the things this formula does, but one thing is certain. It plays some very interesting tricks with the familiar elements of the classic Mandelbrot set. The familiar M-set has been quite well explored, at least down to the level where the slow arbitrary-precision math kicks in, and most of the features to be found in its upper depths have been well investigated. It would be curious indeed if something truly new were to be uncovered in this range. Well, today's image uncovers something totally new. As far as I know, nothing like it has ever been found in the familiar two- dimensional M-set. Today we are investigating the four-dimen- sional Hyper-M-set however, so it is no wonder new things are popping up. I named today's image "Something New" because that's what it is. I rated it at an exceptional 8 because it truly is something new. The calculation time of 55 seconds is on the P4-2000. On the P200 it would take about 3 minutes to finish. But why not forget inconveniences like calculating parameter files? View the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With full sun and a temperature of 75F 24C, Tuesday was not quite perfect here at Fractal Central; the sky was slightly hazy. But despite the lack of a pure blue sky, the day came so close to having perfect weather that only a professional weather observer would notice the deficiency. The fractal cats most certainly never noticed the gray haze. They were far too busy watching four squirrels that were running around in the yard all afternoon. My day was average. Only the above-average fractal saved it from being a dull day. The next FOTD will appear in 24 hours. Until then, take care, and reasoning about fractals could be unreasonable. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Something_New { ; time=0:00:55.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0.11351018609400590/+0.857731703162649\ 10/13846.92/1/-12.5/1.19338289250592311e-011 params=0.33/0.33/1/0/0/5e-015 float=y maxiter=980 inside=0 logmap=40 periodicity=0 colors=000GFp7Jp9LqANrBOrCQsDRsETtFUtGWuHYvIZvJ`wK\ awLcxMdxNfyPhzOjzOkzNlzNmzNnzMmzMkzMizLgyLexLcwK`v\ KYuKVsJSsJQrJOrIMqIKqGGrIJqKLqLNpNPpORpQUoRWoTYoV_\ nWanYdmZfm`hmajlclleqodnlcljbjgahe`eb`c`_aYZ_WYXUX\ VRXTPWRMVOKUMHTKFRGBTIDUJEVKFWLGYMHZNJ_OK`PLbQMcRN\ dSOeTQgURhVSiWTjXUkYVjZWiZXi_Yh_Zg`_g``faaeabebcdb\ dcceccfbdgadh`fgadhabia`jY_iUZiRZhNYhKYgGXgCWf9Wf5\ Ve2Ve2Xc2Yb2Za2_`2a_2bZ2cY2dX2fW2gV2hU2iT2kS2lR2mQ\ 2nP7mRClTHkVMjXQiYVh__gadfcgcchedhgdiheijeilejmfjo\ fjqfkrgktgkugksekrckqako_knYkmWklUkjTkiRkhPkgNkeLk\ dJkcHkbFk`Ek_CkZAkY8kW6kV4kU2nS0kT1hU1eU1bV1_W1XW2\ UX2RY2PY2MZ2J_2G_3D`3Aa37a34b32b3IT9XKEZMG_NH`OJbP\ KcQLdRNfSOgUQhVRjWSkXUlYVnZWo_YpaZrb`scatebwgdyiez\ kgzjfzifzhezgeyfexedwcdvbcuact`cr_brZbrYbrWarVarU`\ rT`rS`rQ_rP_rO_qP`pP`oP`nP`mQakQaiQagQaeRbcRbaRb_R\ bQTcZRbgPapOajX`dd_ZmZTuY } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 22-05-07 (Willy Wallies [7])
by Jim Muth 22 May '07

22 May '07

FOTD -- May 22, 2007 (Rating 7) Fractal visionaries and enthusiasts: Today's semi-glorious fractal image was created by combining 5 negative parts of Z^(-1.5) with 1/2 negative part of Z^(-6.5) and adding (1/C). The parent fractal consists of 4 main bays with a scattering of isolated rings to the north of the main fractal. Today's scene lies in one of the smaller rings. As is obvious from the one-googol value of the imag(p3) parameter, the image is an evaporated one brought to life by the bof61 inside fill. I named it "Willy Wallies", a nonsense phrase for a non-sensical reason. The rating of a 7 means that at least in my opinion, the image is a bit above the FOTD average. And I can justify the rating because of the extra 15 minutes I spent working the colors. The calculation time of the image on the fireball P4-2000 is 33 seconds. On the P200 it finishes in 2-2/3 minutes. Of course, the calculation time may be ignored by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image there. A near-perfect sunshiny day with a temperature of 70F 21C here at Fractal Central on Monday made the fractal cats wish they could get outside to enjoy the conditions along with the lucky squirrels and people. Unfortunately for their feelings, it appears they will be indoor cats for the rest of their lives. My day was busy enough to keep me occupied, but not so busy as to preclude a trip to fractal land. The next FOTD fractal image will appear in 24 hours. Until then, take care, and dine out with a fractal. They eat very little. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Willy-Wallies { ; time=0:00:33.41-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.62778255764460900/+2.877258062006794\ 00/7.169358e+010/1/20.0025100081782341/0.000116997\ 977210396564 params=-5/-1.5/-0.5/-6.5/0/1e+100/0/0 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000DOTDOUCNVCNVCNWBMXBMXBMYBMYKOcTPiaQnjRtr\ SynRxjQwgPvcOu`NtXMtULsQKrNJqJIpGHpJGoMFoOEoRDoTCo\ WCoYBo`Aob9oe8og8oi9nj9mkAllAknBjoBjpBiqChsCgtDfuD\ evDelQTcbHVo5Sj6Qe7O`7MM8KS8INPVC9I3Nm9AC0Sc9B000X\ 8CC8CztWpzzqpgjo_cbSXmKQpCzk5Se8Z`AYWAXRAWMAVHZUCA\ SI9RN9PT9OY9Mb9Lh9Jm9rz9dW8eQ7eL7eG6zBmf65f15dFJbT\ X`fj_sxbqydoygmyilykzznhzpfzrezvjcyoHqkKjgNcdQX`TP\ XWIUZBQa4NcOTRfZFyc3XnM5xcTgSpSHjRNdRSZQXTQaNQfHPk\ BPp5PudyqarrZksWdsTYtQRuNKuKRpIYlGdgEkcCq_FbUIOPL9\ KHHIDOG9WE5bCBfHGiLLmPRpUWtY`wabqbckbefcf`chVdiQdk\ KelFebMhUTkLZnCeq3ksAhpGenNbkT_iZXfeUdkRaqO_gUeZZk\ QcpR_lRXiRTfSQbSM_SJXSGUTHWTIXTJZTJ_UKaULbUMdUMeYI\ daEddAdh6dk3dj8bjC`jHZjLXjPVjUTjYRjaQc1h_9cXGZTOUQ\ VPMbKJiFFqACx6HhGLTQPEZDJP1OGfrGdfKbWNaLQTFHVJMWNQ\ YRUZUZ`YbaafbdjXelRfmMfnGgoBgpBhpBiqBjrBjrBksBlsBm\ tBnuBouBpvBpvAqqArm9si9se } 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 21-05-07 (Beneath the Shadow [6])
by Jim Muth 21 May '07

21 May '07

FOTD -- May 21, 2007 (Rating 6) Fractal visionaries and enthusiasts: To generate today's parent fractal I combined some negative Z^(-0.95) with about 1/5 as much negative Z^(-6.1) and added (1/C). This parent fractal is an oversized thing consisting of a large area of chaos with one large and somewhat distorted Mandelbrot set. An even larger open area extends from the East Valley of the Mandeloid. Today's image is located where this large open area merges into the Mandeloid. I named the image "Beneath the Shadow" because I like the sound of the words. I rated it at a 6 because I think it's just a bit above average. The calculation time of 3-1/4 minutes is true on the fireball P4-2000 machine. On the old P200 machine the image would take over 20 minutes to finish. Relief for any remaining frustration may be found at the FOTD web site, where the image will momentarily be posted for instant gratification. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A partly cloudy day with a temperature of 70F 21C here at Fractal Central on Sunday made conditions near perfect for outdoor activity. But the fractal cats' activity is limited to the indoors, so they could not appreciate the good weather. My day was kept active with yard work. The next in the seemingly unending series of FOTD fractals will appear in 24 hours. Until then, take care, and know that every- thing from atoms to the universe is ultimately an abstraction. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beneath_the_Shadow { ; time=0:03:16.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-7.244795676089/-2.026205433111/8.2041\ 2e+007 params=-5.5/-0.95/-1/-6.1/-0.8/0/0/0 float=y maxiter=2700 inside=0 periodicity=10 colors=000lZRnbXqfbsjhvnntmpzvyuosvnqtjmrfipbenZbl\ X_kWYjVWiUUgTSfSPeRNUJ5dQLbOJaNH`ME_LCYKAXJ8WI6ZOG\ YNFYMEYMDXLCXLBXKAWK9WJ8WJ7VI6VI5VH4rHblHUfHL`HCay\ I_pFZgCXZ9WQ6xnvsoonheiaXdVN_ODQA2RB3RB3RC3SC3SD3S\ D3TE3TE4TF4UF4UG4UG4VH4VH4LWOPRHSMA7seJ_Ney8du7cr7\ bn7ak6`g6_d6_`5ZY5YU5XR4WN4VK41jt4go7djAaeC_`FXWIU\ SLRNNPIQMDTJ8GL3JK4MJ4PI4SH4wqWtnTrkRphPneNkbLi_Jg\ YGeVEbSC`PAZM8XJ6cJbbI_aIYaIW`IU`IS_IP_INZILYHJYHH\ XHEXHCWHAWH8VH6jNxhMrfLleLfcKabKW`JQZILYIFWH9zVzxU\ vvTrtSnrRkpQgnPclO`jOXhNTfMQdLMbKI`JFZIBXH7yU2iN3y\ QPcAqZETUdZVSiVbJMSg2`d6V_AWVDTRHRMLOHOMDSJ8_`BZZA\ ZX9YW9YU8XS8XR7XP6WN6WM5VK5VI4sy3lm4fb4`S4azc_nVYc\ MWSDHEGIFFJFEKFDLFDMFCNGBOGAOGAPG9XfjUenVejSclTdiR\ bkRchQajQagR`cR``SYYSZUSWRTXOYUbRUeKQg4Ph8MfCKdGIb\ KG`OEZSCXRAWR9WR8WR8WR7WR7WQ6VQ6VQ5VQ5VQ4VQ4VS7SU9\ PWCMYEK_GHaJEcLBdN9gRFiVL } 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 20-05-07 (Fractal Test [4])
by Jim Muth 20 May '07

20 May '07

FOTD -- May 20, 2007 (Rating 4) Fractal visionaries and enthusiasts: The FOTD seems to be slipping. I could rate today's image no higher than a humble 4, which actually is a bit below average. I made almost no effort at all to find and color it. The name "Fractal Test" demonstrates this fact. The formula behind the image is Z^(1.2)+C as it appears at ground level of the logarithmic ladder. Actually today's image lies at -3.14159... of the ladder, since the number PI is the actual ground level. I could make a slight change in the MandelbrotBC2 formula to set the ground level at PI, but if I did this, the old parameter files would no longer calculate correctly. The image itself shows a Mandeloid midget that lies in the chaos that exists on the north side of the main bay of its parent, which is little more than an egg-shaped oval with a pimple on its south end. There is little to say about the image, so I will say only that it reminds me of a greenish shield. The calculation time of 2-1/4 minutes on the P4-2000 machine and 7 minutes on the P200 may be bypassed by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image there. Sunny skies in the morning gave way to cloudy skies by afternoon here at Fractal Central, but the temperature reached a very pleasant 70F 21C. The new Fractal Cats, whose lives are not nearly as adventurous as the lives of the old fractal cats, spent the day examining a garden beetle that somehow got into the kitchen. My day was rather busy. But if all goes as planned, tomorrow will be much slower. The next FOTD will appear in 24 hours, give or take a few hours. Until then, take care, and where does yesterday go? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Test { ; time=0:02:17.31-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.1105933609727138/+1.520866940519481/\ 5.918391e+010 params=1.2/0/0/0 float=y maxiter=5000 inside=0 logmap=214 periodicity=10 colors=000GJNDIIAHD7G9AJDDMGGPJJSMMVPPYSS`VVcYYfa`\ idclgfojirmlupoxsrzvnxqkvlhuhescbr_ZpVWnQTmMQkHNjD\ PlERmEToFVpFXrGZsG`uHavHYuNVtTRtZOsdKsjHrpErvIpsMn\ pQmnUkkYihahfefcieafb`d`_bYZ`WYYUYWRXUPWSNVQKUNIUL\ GTJDSHBRF9RGCTHFUIIVJLWKOXLRYMUZNX_O_`PbaQebRhcRjd\ MeSH`GCX4F_6Ia8Ld9OfBRiDUkEXnG_pIbrJhnQnkXtgczdisb\ bl`XfZR_XLUVFNT9HS3MV4QY5U`6Yc7af8ei9il9TkFCjLoDSn\ GQmIPlKOkMNjOMiQLhSKhUJgWHfYGe_FdaEccDbeCagBaiA_gE\ ZfIYdLWcPVbTU`WT__RZcQXfPWjOVmLUnJUnGUoEUoCUp9Up7U\ q5UqCNeJHUQAIX46YARYFkORoFbs6mv8kr9ioBhk96m75p65sA\ 4qE4pI4oM4mP4lT4kX4j`4hd4gg4fk4eo4cs4bw4az4`x8bwCc\ uGetKfsOgqSipWjo_kmcmlgnkkoioqhsrgwsZnuRfvJZxBRyEQ\ vHPsKOqNNnQMlTLiWKgZJd`IbcH_fGYiFVlEToDQrCOuBLwBJr\ CInCIjDHfDHbDHZEGVEGREGNFFJFFFFFBGE7GE3GE4FG4FH4FI\ 4FJ4EK4EL4EM5EN5DO5DP5DR5DS5CT5CU6CV6CW6BX6BY6BZ6B\ _6B`8Da9FbVQjSPePN`MMXJLS } 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 PARAMETER FILE=========================================

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FOTD 19-05-07 (The Ear of God [5])
by Jim Muth 19 May '07

19 May '07

FOTD -- May 19, 2007 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is named "The Ear of God". Surprisingly, God's ear looks quite like a human ear that has been colored celestial blue. The resemblance is not surprising, since God is said to have made us in His image. And quite an ear it is! It has heard every word that has ever been muttered or ever will be muttered through the entire history of the multiiverse. I leave it to the individual to decide what the deity will do with all that scandalous knowledge gained by eavesdropping. As for today's image, it was created by combining 11 negative parts of Z^(-1.1) with one negative part of Z^(-11) and adding (1/C). The fractal was given added interest by rendering it with the outside set to 'tdis' and the inside set to 'fmod'. If a midget were at the center, the image might have rated a 6. As it is, the image rates only a 5, which is average. The calculation time of 2-3/4 minutes is true on the new fractal- dedicated computer, a P4-2000mhz unit. On the old P200 it would take about 14 minutes. But incidentals such as calculation times can be ignored by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the divine ear there. A partly cloudy and rather chilly day with a temperature of 64F 18C here at Fractal Central on Friday went totally un-noticed by the fractal cats, who were more concerned with chasing each other up and down the hallway. My day was totally average. With any luck, tomorrow will be the same. The next FOTD will appear in 24 hours. Until then, take care, and watch your words. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Ear_of_God { ; time=0:02:48.51-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.397995/-3.53557/4.956733/1/150/3.269\ 9953855797048e-012 params=-11/-1.1/-1/-11/0/525/0/0 float=y maxiter=1500 inside=fmod proximity=1 outside=tdis periodicity=10 colors=000KoOLoOMoOOnNPnNQnNRnNTmNUmNVmMXlMYlMZlM_\ lMakMbkLckLejLfjLgjLhjLjiKkiKliKnhKohKphKqhKliOhiS\ djV_jZWkbPmlRlhSkeTjbUi_ViXWhUXgRYfOZeL_eIYoWzmGWc\ GVbFTbESaERaDQ`CP`CN_BM_ALZAKZ9IY8HY8GX7FX6EO6CP5B\ Q4AR49S37T18U39V4AW5BX6CY7DZ8D_9E_BF`CGaDHbEIcFIdG\ JeHKfILgKMhLNhMNiNOjOPkPQlQRmRSnTSnUToVUoWVqXWrYXs\ ZXs_YrZZqZ_pY_oY`nYamXbmXblXckWdjWeiVehVfhVggUhfUh\ eUidTjcTlgRjcTi`UhYVgVWfSYePZdM_cJ`bGbaKc`Pd_UeZZf\ _ag_dh_gi`ii`kj`mkaolaqlarmbsnbtobuoYvpYwt`wtYwtYv\ tYvtXutVutTttRttPstNstLrtJrtHqtFqtDptBotAot9nt9mt8\ lt8kt7jt7it6ht6gt5ft5et4dt4ct3Zt3Yt3Xt5Vr6Uq8Tp9So\ BRnCPmDOlFNjGMiILhJKgKIfMHeNGdPFbQEaRC`TB_UAZW9YX8\ XY7WW9UVBTTDSSEQQGPPIONJMMLLKNKJOJIQHGSGFUFDVDCXCA\ ZB9_97a86c75d6Dd8LdAOd5SaCL_IEMP7DV04`A7YF9WKBUPDR\ UFPZINcKLhMImOGpQEsQApSCkTEgVGcWI_YJWZLS`NOaPKcQGd\ SCfU8gW4hXIiPEkPGmOHoOIpO } 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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Heart Shaped Orbit Traps
by Paul N. Lee 18 May '07

18 May '07

Greetings, Recently Stephen C. Ferguson posted some of his latest images to the A.B.P.F. Usenet Newsgroup <news://alt.binaries.pictures.fractals/>. Those images had been created with his "EmberJ" Java program. One particular image caught my attention because Steve was experimenting with orbit traps and came up with a heart shape method. Here is part of the formula: // Hearts xtmp_ = Math.sin(xtmp+ytmp)+ytmp*ytmp; ytmp_ = Math.sin(ytmp+xtmp)+xtmp*xtmp; xtmp = xtmp_; ytmp = ytmp_; It is very simple math that creates the heart shapes. I thought I would pass this along to those that may find it interesting and useful for their own images. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 18-05-07 (Rare Flowers [6])
by Jim Muth 18 May '07

18 May '07

FOTD -- May 18, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today we journey to the land that is created when 7 negative parts of Z^(-1.07) are combined with 0.7 negative part of Z^(-7.1) and (1/C) is added, and then the fractal is brought to a state just short of being totally 'evaporated'. The unevaporated parent fractal is an immense thing consisting of several huge bays, a prominent 'fan' and countless 'rings'. Today's image is located in a bit of cut-off debris near the fan. I named the image "Rare Flowers", even though it bears little resemblance to any flower I am familiar with. Considering the overly-brilliant values, the rating of a 6 seems appropriate. The calculation time of 41-1/2 seconds is true on the P4-2000 machine. But regardless of how fast a parameter file is, running one is always a minor task. But this task may be eliminated by viewing the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 66F 19C made things pleasant for both humans and cats here at Fractal Central on Thursday. The cats spent several hours in the sunniest window, but when the sun kept coming and going between clouds, they finally decided to keep warm under a lamp. My day was quite busy again, but as today's image shows, a day is rarely too busy for a trip to fractal land. My next trip will happen in 24 hours. Be sure to check back here at that time to see what I find there. Until then, take care, and if life serves you a fractal, make . . . . fractalade??? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rare_Flowers { ; time=0:00:41.36-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+9.8008552903/+3.1509873292/742801.7/1/\ 157.5/0 params=-7/-1.07/-0.7/-7.1/0/1.2e+014/0/0 maxiter=1500 inside=bof61 periodicity=10 colors=000rinoillijiihfifcid`ibYjaVj_SjYPjWMjUJjSG\ jQDjPHfSKbVOZYRV_VRbYIe`JhdFjgBmk7pn3sq0urAksJbsTU\ taKukBut2pp8llDhhIddN``SWXYSTbOPgKLlTH`CEvFGrHIoJK\ lLMiNNfPPcSR_UTXWUUYWR_YOa_Lc`IbYHaVG`SF_PFZMEZJDY\ GCXDCWABP7AU49U19X9EZHI`PNbWRecWkk_ssdzzhvvirrimoj\ tpjngkoiko`lpalpUmqQmqNntJnrGnoIolJplKpfLqcMr`NrYO\ sVPtSQtPRuMSuLWrKZpJamIdkHghGjfFmcEzaEs_KpSQmLmzE`\ g7ee0GQuy`7tKXo4ul8piClgGhdKdbO`_RXYVTVZPTbLQfHOiD\ zzGSdJUbMV`OXZRZXU`UXaSZcQaeOdgMgIYtmJlhKicLgZLdVM\ bQN_LNYGOVDINCLQCOTCRWCTYCW`CZcBafBchBfkBinBlq1ss6\ psBnsFlsKjsOhsTfsXdsabspczjave`s`_pVZmQYjLXgFWdAVa\ 5iD5aO5UZ1Jo3Ll5Ni7Of9QdBSaDTZFVXHXUJYRL_ONaMPbJRd\ GTeEIgL5gR8hSAhSChTEhTGhUJhULhVNhVPhWRhWUhXWhXYhY_\ hYahZchZfeWhcUk`RsnOpfPmZPkSQhKQfDQlMXrVcwbjxdYyfM\ yhAu`LqTWnLehK`bKWXKR7I1HJCRKMP3EVCN_KWeScj_logtmd\ plalkZijWebefgfilgkqhnuhp } 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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Martian Fractal
by Lee H. Skinner 17 May '07

17 May '07

Hi, All While looking at Mars images this morning, I snipped this portion of one showing an unusual combination of two craters. (I didn't even rotate the image!) Paul Lee has put the photo on his website at: http://home.att.net/~Paul.N.Lee/Mandelbrot_Crater.png The full image is at: http://hiroc.lpl.arizona.edu/images/PSP/PSP_003273_1675/PSP_003273_1675_RED… Cheers, Lee Skinner

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FOTD 17-05-07 (Satellite TV [6])
by Jim Muth 17 May '07

17 May '07

FOTD -- May 17, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image reminds me of a ring of satellite TV dishes, so I named it "Satellite TV". It is actually a scene in the grossly oversized parent fractal that results when 5 negative parts of Z^(-1.3) are combined with one negative part of Z^(-3.1) and (1/C) is added. When it is finally squeezed onto the screen, this parent fractal is seen to be a single large Mandeloid bay with 3 large buds, each competing to be the prominent bud. A filament extends from each of these buds and terminates in a ring. The largest rings are located northwest and east of the large bay, with today's image located where the filament joins the large eastern ring. The rating of a 6 does justice to the image, and the calculation time of only 53 seconds on the almost-S.O.T.A. P4-2000 machine makes calculating the included parameter file a breeze. And those who would rather avoid high winds may view the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Things were much less pleasant here at Fractal Central on Wednesday. The day began with sunshine, but by late morning the clouds moved in, and light rain fell through most of the after- noon, while the temperature hovered around 70F 21C. The fractal cats paid scant attention to the rain. They were more involved in watching for squirrels. My day was quite busy, but I kept things under control. The next FOTD will appear in 24 hours. Until then, take care, and be at ease with the intricacies of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Satellite_TV { ; time=0:00:53.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+51.82836052591048/-42.36598795380647/\ 1.507148e+010/1/-32.264893292778666/-0.08747463235\ 98468573 params=-5/-1.3/-1/-3.1/0/3500/0/0 float=y maxiter=1600 inside=0 logmap=214 periodicity=10 mathtolerance=0.05/1 colors=00000G11H22I43J64M85MA6QC7PE8UG9TIBYKDYMFaO\ HbQJeTMcVOfYQc_TcaVadX_f_ZiaXkcVnfUpdSrjRpgOoiLniI\ miGkhDjhAih8hh5ff2ed0dc0cb0ba0``0__0ZZ0YY0XX0WW0VV\ 0UT0TR0SP0RN0QL0PJ0szbrwYquTpsOoqJnpEmn9lm4mk0mj0n\ h0ng0oe0pd0pb0qa0r_1rZ1sX1sW1rW3qX4pY6pZ8o_9n_Bm`D\ maElbGkcIkcJlcNyeVvdUcGW_ORWWMTcHPkCMr7GkJAeU5_dC`\ aIa_g_NOaYVbW`bUfcSLGYPJXSMWWPVZSUbVTeYSi`RWLK_PMD\ 20C30A309407506604603701800801D12I33M54R75W96_B7dD\ 8hEG4hLAZQGPULFZR5bW0dU0eS0fQ2gO4hN6iL8jJAkHClGEP`\ PT_PXYPaWQeVQiTQnRQrQQvOQzNQyORyPRyQRyRSySSxTSxUSx\ VTxWTxXTxYTtYQpYOmYLiYJeYHbYEZYCVY9SY7OY5KY2HY0DY0\ 9Y06Y05X05X04X04W04W23W43V62V72V92UB1UD1UE0TG0TI0T\ J1VL2WN2YP3ZQ4`S4aU5cW5dX6eZ7g`7hb8jc9ke9mgAniAojC\ nkDnkEnkFnkHmkImlJmlKmlMllNllOlmPlmRkmSkmTkmUkmRjl\ PjlNilKilIilGhlDhkBgk9gk6gk4fk2fk0fk8VhFKfM9dTVUZp\ JWnHUlGRkFPiEMhDKfCIdBFcA } 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 16-05-07 (Sanctified Station [6.5])
by Jim Muth 16 May '07

16 May '07

FOTD -- May 16, 2007 (Rating 6.5) Fractal visionaries and enthusiasts: With today's fractal we return to the well-used MandelbrotBC2 formula and examine the Z^(1.618)+C Mandeloid as it appears 74 levels down the logarithmic ladder. At this level it resembles a Mandelbrot set with its main bud facing southeast and its East Valley flattened out and filled with chaos. Today's image is located in some of the farther-out debris in the area of what passes for East Valley. The name of the image has nothing to do with a blessed railroad station. When I shut off my mind in search of a name, the phrase "Sanctified Station" popped into my head. So this is what I named it. When struggling for a rating I was undecided between 6 and 7. I resolved the conflict by giving the image a rating of a 6-1/2. If the central midget were a bit more prominent, the rating would have been a 7. The calculation time of 2-1/3 minutes is true on the ancient workhorse P200 computer. The more S.O.T.A. P4-2000 unit would finish calculation in about 30 seconds. But calculation time will be no problem for those who visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted for instant and easy viewing. Wednesday proved to be unusually warm here at Fractal Central. The hot sun and temperature of 88F 31C kept the fractal cats away from the sunnier windows. My day was busier than average, but not excessively so. The next FOTD will appear in 24 hours. Until then, take care, but stop taking care long enough to enjoy the Fractal of the Day. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sanctified_Station { ; time=0:02:23.08--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.8449604577846213/+1.512609951022948/\ 1.830674e+007/1/22.5/3.0546204665693466e-006 params=1.618/0/-74/0 float=y maxiter=12000 inside=0 periodicity=10 colors=000IGNHELGDKECIDBGCAFA9D98B86A6585464352231\ 111wf0qa0kY0eU0_P0UL0OH0IC0C8064xL_tJYqIWnHUkGSgFQ\ dEOaDMZCKWBIS9HP8FM7DJ6BG59C47935623311iz``ljWfdSa\ _OWVKRQGLKCGF8AA455nhzkevhcse`obZl_WhYUeVRaSPZPMVM\ KSJHOHFLECHBAE87A557223_`bUUWOOQIIJCCD666l_9Oz4KGX\ IFVHETGDRFCPEBNDAMC9KB8IA8G87EzXJzVKzUKzTLzRMzQMzS\ NzUNzWOzYPz_PzaQzcQzeOzg1pENmDLiCKfBIcAH_9FX8EU8DQ\ 7BN6AK58G47D35A246123012mm1hh1cc1ZZ1UU1PP0KK0FF0AA\ 05538i26_14R13I019R3KM2GI2DD1A916403Wq9Un8Tl8Sj7Qh\ 7Pe7Oc6Ma6L_6KX5IV5HT4GR4EO4DM3CK3AI39F28D26B15914\ 61240120lxbgrZclVZgSVaOQXLMRHHMEDGA8B7453rVumSohPj\ cMeZJ_UGVPEQKBLF8FA5A5258hn6Xa4MP2BChLEeKDcJCaIC_H\ BYGAWFAUE9RD8PC8NB7LA6J96H85F74C64A53842632421210r\ mmniikffgccd```YYYVVUSSRPPOLLKIIHFFDCCA99666333TBL\ RAJP9IO9HM8GK7FJ7EH6CG6BE5AC49B4893783562441331210\ 1Y9gSOZQMXPLVOKUMJSLIQKHP } 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 PARAMETER FILE=========================================

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