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FOTD 29-10-12 (The Missing Minibrot [5.5])
by Jim Muth 29 Oct '12

29 Oct '12

FOTD -- October 29, 2012 (Rating 5.5) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when 1.5 parts of Z^(-1.24) are combined with 0.19 part of Z^(-7.26) on each iteration before (1/C) is added. This parent is a colossal sprawling thing hundreds of times the size of the default screen, which consists mostly of zig-zag filaments twisted into huge loops. Today's image is located in a more interesting area of the parent, not too far from the origin. I have named such scenes 'dry valleys'. From a distance it appears that minibrots might lie at their centers. The two-way symmetry is certainly there. But at the center of symmetry we find only saddle-shaped blank walls exactly as we find at the center of today's image. The name "The Missing Minibrot" refers to the disappointment at the centers of these dry valleys. The rating of a 5-1/2 indicates that the image leaves much to be desired. And the calculation time of 5 minutes also leaves much to be desired. A better time bargain may be found on the FOTD web sites. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Increasing wind and rain prevailed here at Fractal Central today. The wind and rain are the start of the big frankenstorm, which is not due to reach its peak until tomorrow morning. So far, the highest wind gust has been a not-too-impressive 37mph or 50kph, but winds of 70mph, 112kph are expected tomorrow. The rain so far has measured only 0.5 inch or 1.2cm -- also not too impressive. Up to 12 inches, 30cm is expected south of here however before it all ends on Wednesday. The temperature of 50F 10C was quite chilly for a tropical storm. Fractal cat Nicholas watched the goings on with interest, then viciously attacked his toy ball. The next FOTD is due in about 24 hours. If it fails to appear, don't wait up for it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= TheMissingMinibrot { ; time=0:00:05.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-3.959516711/-0.158776657/874/1/-27.5/0 params=1.5/-1.24/0.19/-7.26/0/0/0/0 float=y maxiter=1200 inside=zmag outside=tdis periodicity=6 colors=000fFnaLmXRlSXlOakJgjEmj9si5xi6te6pa7lY7hU8\ dR8`N9XJ9TFAPBAL8CKADJCEIEFHGGGHHFJJFLKENLDOMCQNBS\ OAUPAVADFBCEBCDBBDCBCCABCABD9AD99D89E88E77E77F66F6\ 5F65I59K5CM4FO4IQ4LS3OU3RW2UY2X_2_a1bc1ee0hg0ki0nb\ ATnT`zjhvlfrmdnncjoagp`cqZ_rXWsWStUPuTLvRHwPDxO9yM\ 6zL7uM8pM8kN9fN9aOAXOBSPBNPCIQCDQD8RD4RNOXXfaUg`Sh\ `Pi_Ni_Kj_IkZFkZDlYAmY8mY5nX3oX1oX6jZAe_E``IXaMSbR\ NcVIdZEeb9ff4gj0hk0jk0jm0km0mn0mp0np0pq0pq0qs0sx0t\ t0ss0sq0qp0qn0pm0pk0ph0ng0ne0md0mb0m`0k_0kW0jV0jzz\ 0zz0zz0zz0yz0xy0vx0tt0ts0sq0qp0pm0nk0mj0mg0ke0jd0h\ b0g_0eY0eW0dV0bS0`Q0_P0YN0YK0WJ0VH1TF1SE1QD1QD2PE2\ NF2MG2KH4JI4JJ4HK4GI5EG5CE5AC5AA5A84A62A51A41A30A2\ 0A10A00A00A00A00A00A00A00A00A00C00C00E20E40G50G92H\ A4HC7JG9JHCKJEKMHMNJMPMNSNNTQKTTMVSMVSNVSNVSPWQPWQ\ QWQQWQSWQSYPTYPTYPV`PV`PW`NW`NY`NY`N_`N_`M``M`aMba\ MbbMdbKdbKebKebKgbKgcJhcJ } 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 28-10-12 (Lake of Dreams [7])
by Jim Muth 28 Oct '12

28 Oct '12

FOTD -- October 28, 2012 (Rating 7) Fractal visionaries and enthusiasts: We're preparing for a big storm here at Fractal Central, so I have little time for a detailed discussion. The parent fractal of today's image came about when I subtracted Z^10 from Z^11 and added straight C on each iteration. This parent is a lopsided, 9-1/2 lobed thing with most of the interest along the eastern edge of the large central bay. Today's scene is located in a kind of debris ring surrounding the northern bud attached to the 1-1/2 lobed bay on the east side. The terraced effect was achieved by rendering the scene with the outside set to 'tdis'. The deep-blue coloring adds a rather somber effect, contributing little to the overall worth of the image. The calculation time of 25seconds is no joke. The image really does finish that fast. For convenience if not faster viewing, check the finished image posted at: <http://www.crosscanpuzzles.com/Archives.html> And check the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Clouds, occasional rain, and increasing wind prevailed here at Fractal Central today, as the 'frankenstorm' approached. The temperature of 54F 12C was within reason. Fractal cat Nicholas had a restless day, apparently picking up the extra activity of the humans. The next FOTD will be posted before too much time has passed -- I hope! If the worst happens, it might not appear for quite a while. Until whenever, take care, and the gods are angry. Let's heed their message. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Visionary_Vision { ; time=0:00:25.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+1.205125057483229/+0.2232655114510676/\ 3.86445e+008/1/126.25/0 params=1/11/-1/10/0/0/0/0 float=y maxiter=750 inside=0 outside=tdis logmap=31 periodicity=10 colors=00053U65Y67a69d6Bh7Dl7Fo7Hs7Jw7Kz8Ly9LxALwk\ MhlOimRjo_zpczrhzsmztqzvzzwzzxzzrzzmtzhm_ccVYbPT`J\ O_DJZ8M`EObKRcQTeWVgaYhg_jmakrchneejfcfh`cjY_kWWmT\ SoQPpOLrLHsJEnKDiKDdLC_LC_KD`ID`HE`GF`FGaEHaDIaCJa\ BKaAKgHMlOOqUQo_cpZapZ`pY_qXYqXXqWWrVUrVTrUSU16Z7B\ cDFhJJmPNrl3rj5ri6rh8rg9rfBreCrdDrcFraGr`Ir_JrZKrY\ MrXNrWPrVQJkkVedf_Y2zP7wQBtQFrQJoQNmQRjQVhRZeRbcRf\ `RjZRnWRDsTRjSdaRvi2ug6ue97le8ne9Qe9SeAUeAWeGYZL_T\ Q`MVaG_XAYUEWRHVOKTLOSJRQGUPDYNA`M8cOBhPEmQHrRKwPI\ uNHoLGmKElIDjGCgFAdD9aB8ZA6W85T64Q53PJGSXSdjdgzzjz\ okrdkoZklTlEIpDAqC2qEAlFHhGOdHV_IaWTbHR`IP_INYJMXJ\ IRIFLHKPIOTISXJW`J_dKchKglLkpLosLpnJqiIreHr`GsXFtS\ EtNDuJCvEBvAAqDEmFIhHMdKQ_MUWOYUJbSEgRAkP5pO1tS6rW\ AqZEobIneMliRklVipZhsbfwfezjdxl_wmWuoStpOrrKqsGouC\ nv8lx4ky0ix2gx3ex4cw5aw6_w7Yv8Wv9UvASvBRsIQpPPmWPj\ bOgiNdpNbvKVoHNiEFcB8Y85W } 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 26-10-12 (Lake of Dreams [9.5])
by Jim Muth 27 Oct '12

27 Oct '12

FOTD -- October 26, 2012 (Rating 9.5) Fractal visionaries and enthusiasts: Today's image is a rerun, but it is such a good rerun that I gave it a superior rating of 9-1/2. The image is a scene in the Seahorse Valley area of the Z^2+C Julibrot, sliced in a direction about halfway between the Oblate and Rectangular orientations. The reason for the name "Lake of Dreams" will be obvious once the image is viewed. The ripples on the 'water' appear in perfect perspective, while the coloring so closely resembles water that it makes me thirsy. The calculation time of 45 seconds will add to the enjoyment. Enjoy the serenity of rippling water by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> without the inconvenience of calculating it. A high-definition rendering is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images are available at: <http://www.Nahee.com/FOTD/> The clouds hung tough here at Fractal Central today. Fractal cat Nicholas carefully checked the hall closet to be sure Cassie was not in there, then settled on the scratching post for most of the afternoon. The humans once again made it through the afternoon with nothing to report. The next FOTD will be posted on Sunday. On Saturday I'll be in Baltimore, checking Old Fractal Central to see it it's prepared for a big storm expected early next week. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Lake_of_Dreams { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.130564/0/\ 2.314276/1/90/0 params=40/90/0/90/-0.75/0/0/0/2/0 float=y maxiter=100000 inside=255 logmap=yes periodicity=10 colors=000Q0hR2iS5jT8kUPnVSmWTnXVoYXpZZq_`r`bsadtb\ fuchvejwfkwglxfkzekwdjvciubhtagrafq`ep_doZcnYbmXak\ X`jW_iVZhUZgUYgTXfSWdRVcRUbQTaPS`OR_NQYMPXMPWLOVKN\ UJMSILRHKQGJPGIOFHNEGLDFKCEJBDIBCHABG9AE89D78C67B5\ 6A55944733622511400320640860A80AA09C09E08G07I07K06\ M36O65Q94SB4U93W83Y62_41a31c10c6Ib5Ha5Ha5H`5G_5GY5\ GY5GX5FW5FW5FV5FV4EU4EU4ET4ET4DS4DR4DR4CQ4CQ4CP4CP\ 3BO3BO3BN3BM3AM3AL3AL3AK39K39J39J39I28H28H28G27G27\ F27F27E26D26D26C26C15B15B15A15A1491481481371371361\ 3602502502402301301201201100100000AKQAKmAKmAKmAKmA\ KmAKmAKMAKLAKKAKKAKJAKJAKIAKIAKHAKGXKGWKFVKFTKESKE\ RKDQKDPKCOKBNKBLKAKKAJK9IK9HK8GK7EH7DG6CF6BD5AC59A\ 4893683562452341221110AK`AK_AKZAKYAKXAKWAKVAKUAKUA\ KTAKSAKRAKQAKPAKOAKOAKNAKMAKLUYKTXJSVIQUIPSHORGNPF\ LOEKNDJLCHKCGIBFHAEF9CE8BC7AB68A678567455334222111\ 0ENuDMsDLrL4dL4dL3eL3eAAA } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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You folks are asleep at the switch. You let me...
by Hal Lane 26 Oct '12

26 Oct '12

You folks are asleep at the switch. You let me post the parent (and zooms into it) of Jim's FOTD for October 3rd, 2012 with a 16 color EGA-type color map -- instead of his colors. For comparison -- here's an example of the parent fractal with the color map I had previously used for the parent: http://www.emarketingiseasy.com/TESTS/FOTD/F121003YwrongMap.jpg and the same fractal with Jim's colors: http://www.emarketingiseasy.com/TESTS/FOTD/F121003Y.jpg The October web page has the correct color map in all the images for the 3rd now: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html Jim's FOTD for October 3rd, 2012 has always had the correct color map on my page: http://www.emarketingiseasy.com/TESTS/FOTD/F121003J.jpg - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Some zooms into Albrecht's Strange Beauty Multifractal_10
by Hal Lane 26 Oct '12

26 Oct '12

Here are some zooms into Albrecht's Strange Beauty fractal that uses his Multifractal_10 formula. The fractal has quite a bit of nifty, colorful variety in it. All 640 x 480 non-anti-aliased. They're arranged in increasing zoom depth, with the 2nd and later fractals each a zoom into the previous one: Albrecht's original Strange Beauty fractal: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBUT.GIF And zooms into it: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU2.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU3.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU4.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU5.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU6.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU7.GIF http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU8.GIF Has numerical loss of precision: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBU9.GIF Has extreme numerical loss of precision: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGB10.GIF The parent fractal: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGBUP.GIF And a zoom into the parent: http://www.emarketingiseasy.com/TESTS/FOTD/STRNGB11.GIF - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 25-10-12 (Starriest Night [9.5])
by Jim Muth 25 Oct '12

25 Oct '12

FOTD -- October 25, 2012 (Rating 9.5) Fractal visionaries and enthusiasts: Today's fractal rates an honest 9.5. A full point and a half is due to the coloring, which is about all the image has going for it. The scene lies in the parent fractal that comes about when the Mandelbrot set is corrupted with Z^(0.94145506) energies. This parent is mostly cut-off beyond the too-small escape radius. What shows of it is shaped like a large teardrop. A larger escape radius would have revealed more of the parent, but would have lost today's scene. The sky part of the image is all outside stuff made visible by the 'bof60' outside fill. The lower part is everyday inside stuff. The name "Starriest Night" was inspired by a well known painting. The calculation time of 3-1/2 minutes will pass slowly at first, but will speed up notably once the calculation reaches the distant horizon about 2/3 of the way down. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering plus other goodies is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> Heavy clouds permitted only a few peeks of sun at Fractal Central today. The temperature of 66F 19C was all right, but it would have been more enjoyable if there had been more sun. Fractal cat Nicholas spent most of the afternoon on the shelf in the southwest window, waiting for the sun that never came. The humans made it through the day as best they could. The next FOTD will be posted soon. Until whenever, take care, and who said fractals cannot be art? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Starriest_Night { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=FinDivBrot-2 function=recip logmap=yes passes=1 center-mag=-0.05596778/+0.5609443890/568/\ 1/-91.1/0 params=0.94145506/1.5/1000000/0 float=y maxiter=15000 inside=bof60 periodicity=10 colors=000bzz_nzXgzU`zRVzPPzMLzJJzGHzDFzBDz8By59t5\ 7q53p53n43k33h23e13c03a03_03Y03W03U03T03S03R03Q03P\ 03O03N03M03Mn4rp4ur4xt4zs5xr5wq6vq6up7to7sn7rn8qm8\ ol9nk9mk9ljAkiAjhBihBhgCffCeeCdeDcdDbcEabE`bE_`KUZ\ POYUIWZCVc7Td8Sd9Rd9QdAPdBOeBNeCMeDLeDJeEIeFHfFGfG\ FfGEfHDfICgIBgJ9gK8gK7gL6gM5hM4hN3hO2hO1hP0hP1iQ2i\ Q2iQ3iQ4iR4iR5iR5iR6iS7iS7iS8iS9iT9iTAiTAiTBiUCiUC\ iUDiUEiVEiVFiVFiVGiWHiWHiWIiWIiWGjZEl`CmcAoe8pgCne\ FlcIjaLh`PfZSdXVcWYaUL58M48M39N3968978A88E98FA8GB8\ MCBUEEcGImIOrNRvTVzWYzZ`zadzdgzejzdjz0WU0UT0RT0PS0\ NR0LQ0IQ0GP0EO0CN09N07M05L03L0BO0IQ_PTaWVcbYei_eh_\ ef_eeZedZecZeaZe`Ze_YeYYeXYeWYeVXeTXeSXeRXeQXfOZgM\ `gKbhIdhGfiEhiCjjAlj8nk6pk4rl6o08m09k0Bh0Cf0Ed0Ga0\ H_0JY0KV0MT0NR0PO0RM0SK0UH0VFuXDuXBiXLZXVN`dCanB_o\ BYoAWoAUo9Sp9Rp8Pp8Np8Lp7Jq7zq6zq6zq5zr5zr5zr4zr4z\ r3zs3zs2zs2zs2zs5zt7zt9zt } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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I'm able 2 calc Albrecht's The_Miracle w the comments in; Dev. Q.
by Hal Lane 25 Oct '12

25 Oct '12

I'm able to calculate Albrecht Niekamp's: "The_Miracle" (that uses Multifractal_10) with all the comments in it in the form he posted it on the [Fractint] list serve Oct 23, 2012 -- in VESA video mode 640 x 480 with DOS Fractint v 20.04.4 under WinXP SP3. The video chip built into the system board of my computer only supports VESA video mode: 640 x 480, and the DOS environment for Fractint is able to allow the calculation of his fractal using that video mode. However, when I try to use the 640 x 480 (or 4k x 3k) Disk Video modes, I get: "Insufficient memory to run fractal type 'formula'" Invoking Disk Video mode apparently allocates some additional memory that "breaks the camel's back" -- despite using the hard drive to write the image to. The version of Multifractal_10 *without* comments has this same problem. Here's Albrecht's "The Miracle" at 640 X 480: http://www.emarketingiseasy.com/TESTS/FOTD/T_MIRACL.GIF and a zoom into it: http://www.emarketingiseasy.com/TESTS/FOTD/T_MIRAC2.GIF Question: Any of the developers have any idea of how to get around the Disk Video modes not leaving enough memory for multifractalll-10 to run? Any debug modes lurking around that might help -- say, specifying the allocation of smaller Disk Video buffers? - Hal Lane ######################## # hallane(a)earthlink.net ########################

6 8

FOTD 24-10-12 (Nuclear Newton [8])
by Jim Muth 24 Oct '12

24 Oct '12

FOTD -- October 24, 2012 (Rating 8) Fractal visionaries and enthusiasts: There was no FOTD for October 23 because FL and I spent the day searching for a companion for fractal cat Nicholas. We found a calico cat named Callie, who will be the next fractal cat when she gets her shots and if she gets along with Nico. For today's image I returned to the MandNewt series of formulas, number 10 to be exact. Amidst all the confusion I dredged up today's scene, which despite the off-coloring, still reminds me of a nuclear explosion. I named the image "Nuclear Newton". The most notable feature of the image is the unusually smooth coloring -- smooth, that is, by 256-color GIF standards. The unexpected smoothness earns the image a rating of an 8. The calculation time of 1-2/3 minutes will pass in a flash. With the passes set to 'g' the image will finish even faster, but a few minor bits of detail will be skipped over. Relieve nascent boredom by checking the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And don't miss the high-definition rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at> <http://www.Nahee.com/FOTD/> Today here at Fractal Central seemed more like a day in May than a day in late October. The temperature of 75F 24C was mild enough for any outdoor activity, while the cloudless skies and light breezes made things near perfect. The fractal cat spent much of the time in the sun and the rest of the time hoping for food. The humans made it through the day with nothing to report. The next FOTD will be posted when it is ready. Until whenever that might be, take care, and protest ambiguity. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Nuclear_Newton { ; time=0:01:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt10 passes=1 center-mag=-0.115\ 184/0/2.9/1/90/0 params=5/-1/1/0.5/1/5e-031 float=y maxiter=430 inside=255 logmap=yes periodicity=0 colors=0000020020020020020010010010010011212423634\ 845A56C67E66G56H56I56J56K56L56M56N56O56P56Q56R56R5\ 6R56S56S56T56T55T45U45U45U45V45V45W45W45W45X45X45X\ 45Y45Y45Z45Z45Z45_44_34_34`34`34a34a34a34b34b34c34\ c34c34d34d34d34e34e35f36f27f28g29g2Ag2Bh2Ch2Di2Ei2\ Fi2Gj3Hk3Ik3Jl4Km4Ln4Mn4Oo4Qp4Sq5Uq5Wr5Ys5_s5`t6au\ 6bv6cv6dw6ex6fy7gy7hz7iz7iy8jy8jy8jy9ky9ky9lx9lx9m\ xAmxAmxAmxAmxAmxBmxBmxBmwBmwCmwCmwCmwCmwCmwDmwDmwD\ mwDmvDmvEmvEmvEmvEmvEmvFmvFmvFmvFmvFmuGmuGmuGmuGmu\ GmuHmuHmuHmuHmuImtImtImtImtImtJmtJmtJmtJmtJmtKmsKm\ sKmsKmsKmsLmsLmsLmsLmsLmsMmsMmrMmrMmrMmrNmrNmrNmrN\ mrOmrOmrOmqOmqOmqPmqPmqPmqPmqPmqQmqQmqQmqQmpQmpRmp\ RmpRmpRmpRmpSmpSmpSmpSmoSmoTmoTmoTmoTmoUmoUmoUmoUm\ oUmnVmnVmnVmnVmnVmnWmnWmnWmnWmnWmnXmmXmmXmmXmmXmmY\ mmYmmYmmYmmYmmZmlZmlZmlZml_ll_kl_jm_im_hnfgoheooeo\ odqmeqmfqmgqohqqiqtjqwkqz } frm:MandNewt10 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-g j=c*z^d+g z=z-e*h/j, f <= |h| } END PARAMETER FILE=========================================

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Multifractal_10 - The Big Ball
by Albrecht 24 Oct '12

24 Oct '12

Hi, as it seems nobody has bothered to check or zoom into "Unexpected_mandel" sofar. Other wise you would have detected that something extraspecial is hidden. I enclude two zooms, as different as can be. Also the total view, even that is impressive. To make it clear: This fractal is one of the most unbelievable ones I have ever seen, and I?ve seen a lot. There is beauty, symmetry and diversity everywhere. In addition: Up to now I have seen no cuts or inconsistencies, although it is made up using five different formulas. The reason for that are the various reset commands I used. Only today I enclude the "FRM" just in case somebody has not yet downloaded it. Sorry for beeing a bit drastic but I want to create some curiosity and action in this forum. I?m thrilled to view your reactions. ---------------------------------------------start pars------------------------------------- 1536705 { ; Strange_Beauty ; secant-mmods-bees-phoen-newt ; time 0.05.49 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50137769253409600/+0.100910670672261\ 60/6855.058/1/165.000000000015433/-4.8305803801440\ 5611e-013 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR } 1536704e { ; Inside_View ; secant-mmods-bees-phoen-newt ; time 0.33.55 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50145147245682100/+0.100169185289958\ 60/843407.3/1/74.9999999981563263/2.46247487678541\ 432e-009 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<3>000000304<8>X0a_0dc0h<3>p0w<4>_0dX0aU\ 0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3\ >4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000<43>00\ 0<4>000330<11>110110110<3>000KA4<7>gcOjgRmjT<3>zzc\ <9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0C<3\ >A08004000<26>000 } 1536705d { ; The_Big_Ball ; secant-mmods-bees-phoen-newt ; time 0.02.44 XP Dos shell ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.0231296/0.0288228/0.5500051/1/92.499\ 9999999409539/2.09411585294638769e-011 params=-0.05825983458967864/0.3785210730307932/153\ 67.64595767025/14235.4911030602/152048.0404808048/\ 384.1604894048/384.00482000595/256.1007683001/512.\ 1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\ b8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiOD\ jQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE\ 6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2C\ K2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1\ ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotv\ sww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XC\ AaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI\ <3>UnXRm_NlcJkgFfpAaz<6>_5fc0ce7_jFR } frm:Multifractal_10 { ; Albrecht Niekamp Jan2005 ; ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2: 2digits_many-mods 2digits_phoenix 2digits_spider ; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp ; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl ;fn(1) shared by many-mods+bees ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ----------------------------------------------------------end par-----------------------------------

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FOTD 22-10-12 (Snake Resurrection [No Rating])
by Jim Muth 22 Oct '12

22 Oct '12

FOTD -- October 22, 2012 (No Rating) Fractal visionaries and enthusiasts: The very first FOTD image was posted 15 years ago on April 11, 1997. It was named "Snaketree". Today's image is a slight reworking of that old image. In an attempt to improve the original image, I zoomed in on the central tree and recolored it. The result IMO is a somewhat improved image, with more contrast and a more prominent center of attention. The name "Snake Resurrection" has nothing to do with snakes rising from the dead. It is simply a comment on the nature of the image. Way back in the prehistoric era of 1997 I wrote a new formula for each image, giving the formula the same name as the image. Thus today's fractal is the only image ever created by the SnakeTree formula, which calculates (-Z)^(1.095) then adds 3.4 instead of (C) on each iteration. The image is a fast one, finishing in its full glory in a modest 33 seconds. The glory is gloriously reflected on the FOTD web sites. The glorious finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> A super-glorious high-definition rendering is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online in total glory at: <http://www.Nahee.com/FOTD/> Today was absolutely perfect here at Fractal Central. The temperature of 68F 20C was perfect, the cloudless sky was perfect, and the gentle wind from the west was perfect. The only improvement I could think of would have been a few puffy clouds to add interest. Fractal cat Nicholas spent a good part of the afternoon in the sun on his shelf. The humans simply spent the afternoon. The next FOTD, maybe a trip into the FOTD past, maybe not, will be posted when it is ready. Until whenever, take care, and let's all drive to Syracuse to join the protest against the obscene profits the greedy big oil companies are making from their unfair gasoline prices. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Snake_Resurrection { ; time=0:00:33.00 SF5 at 2000MHZ reset=1950 type=formula formulafile=apr-97.par formulaname=SnakeTree passes=1 center-mag=1.79478/\ 0/3.110565/0.929/90/0 float=y maxiter=500 inside=0 logmap=yes bailout=100 periodicity=6 sound=off colors=000b8zY3zY0zQ0zY0zg0zo0zY8zHUz0tz0zz0zz0zo0\ zY0zH0zU0zg0ztCzzbzzxjzzQzz3zz0zz0z30z30z000000000\ 000000000000000000000000000000JA9000H97000F86000E7\ 5000D64000C53000B42000A3100092000081000000000Y00Y3\ cY3cYQcYQcYQcYMczMczMczHmzMmzMmzMmzMmzMmzMmzMmzMzz\ QzzQzzQzzQzzQzzQzzQzzQzzUzzUzzUzzUzzUzzUzzUzzQzzUz\ zYzzbzzbzzgzzjzzozzozztzzxzzzzzgzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzz0ozz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zt0zz0zz0zz8zzMzzYzzozzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzjzzbzzUzzQzzHzzCzz3zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz3zz3tz3xz8zz8zzCzzCzzHzzHzzHzzMzzMzzQzz\ QzzHzzQzzUzzYzzbzzgzzjzzozzxzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzozzbzxQzgC\ zQ0z80z00z00z00z30z80zC0zH0zM0zQ0zU0zU0zY0zb0zg0zj\ 0zo0zt0zx0zz0zz0zz0zz0zU0z00zC0zY0zt0zz0zz8zzHzzQz\ zQzzYzzjzzgzzgzzgzzbzzbzz } frm:SnakeTree {; Jim Muth z=pixel: z=(-z)^1.095+3.4 |z| <= 100 } END PARAMETER FILE=========================================

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