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Two Pictures
by Brian Prentice 15 Sep '11

15 Sep '11

Here are two pictures of the same scene from the FOTD for 9/14/11: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_48a.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_48b.png Brian Prentice

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FOTD 14-09-11 (Terminal Iteration [7])
by Jim Muth 14 Sep '11

14 Sep '11

FOTD -- September 14, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that is created when 0.9 negative parts of Z^(3.8) are combined with 2.4 negative parts of Z^(1.2) and (1/C) is added. If this seems trite, be informed that the entire expression is a mistake. The exponents were supposed to be equal but negative values. I decided to go with what I had however, instead of taking 10 seconds to calculate the correct parent. This wrong parent fractal consists of a small Mandelbrot set with a disconnected crescent-shaped filament some distance east of it. A tiny M-set lies on this crescent, with today's scene located in the East Valley of this tiny M-set. I suspect that a scene almost identical to today's could be found with a minimum of effort in the standard Mandelbrot set, which adds nothing at all to the worth of today's image. The rating of a 7 means that the image is good enough to qualify for minimum FOTD honors, but that it will never win a prize. The name "Terminal Iteration" can mean anything the most radical fractalist would suppose. The calculation time of 2-1/3 minutes is about average. Since the image is also about average, this seems just about the right length of time. The official FOTD web site with the completed image may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD site, 14 years old, may be accessed at: <http://www.Nahee.com/FOTD/> A quite pleasant late summer day prevailed here at Fractal Central today. The temperature of 84F 29C and mostly sunny skies brought out the laziness in both man and beast. The fractal cats, who are offended at being called beasts, spent the day taking it easy in the windows with the least sun. The humans just took things as they came. The next FOTD will be posted in 24 hours. Until then, take care, and with many thanks to the Purple Cow: I've never seen a Boltzmann brain, I hope I never see one. But I can tell you anyhow, I'd rather see than be one. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Terminal_Iteration { ; time=0:02:20.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.410647617268638/-0.5399341480183459/\ 8.363451e+011/1/-127/0 params=-0.9/3.8/-2.4/1.2/0/\ 0/0/0 float=y maxiter=2500 inside=0 logmap=377 periodicity=6 mathtolerance=0.05/1 colors=000I6AJ8AL9AMAAODAPGARJCTMCVPIWRMYTRZWY`Ybb\ ZfcbmecrfewhhzjjzkkzcpzWtzOyzGzz9zw1zt0yp0voCtoZpo\ YmjWpeVrbTtYRvTRtPPrTPpVOoWOmYOkZMj`MhbLheLffLehJc\ jJbkI`mIZoIZpDWk9Th4Pc0O`0LW0IT0GP08D003000000tjyh\ ZkYP`MGOC8D1010001b40WA0RG0MM0IT0DZ09e03k00r00y00z\ 00y00r00k00e00Z00T00M00G00A004000000000j0Co01t00z0\ 3p00f00Y00O00F006000000000zV0zO0oI0eD0V80J10A0000m\ 00z0Gt0Cm08c03U00M00G00000k0ee0``0WW0RR0MM0II0DD0A\ 806301000000000000tvzGIJtJ8kF4eC1Y80R40J60DCAAPPIc\ ePpvYzzezzWzpRwfMoPIfJDZF9RA3I40A0030000000z0Ay08r\ 06k04f01`00V00O00J00D00800100000000000000000000zm0\ vT0eP0VL0PI0LD0GA0C608303000000000000000z00y00o00j\ 00c00Z00V00O00J00F009004000000000000000z00z00t00o0\ 0h00c00Y03T0AM0AG0IC0P60P10P00Y00e00mC0v90z80z60z3\ 0z1Az0Pz0ez0vz0vz0zz0zz0zz0zz0zz0zz8zz3zz0zz0zvzzv\ zzvzzvzzvzzvzzvzzvzzvzzvz } 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 13-09-11 (A Siegel Connection [8.5])
by Jim Muth 13 Sep '11

13 Sep '11

FOTD -- September 13, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image in the Mandelbrot set lies within the range of conventional math, yet it rates an 8.5. This shows that the more accessible shallow parts of the M-set are not quite as thoroughly explored as some might assume. The image is located in the debris-filled radical of a remote bud on the northwest shore line of the main bay of the M-set. The name "A Siegel Connection" refers to the resemblance of the basins in the image to the so-called Siegel Disks of the siegel- disk fractals, the Julia sets with a C-value of -0.390541,+-0.586788i. Actually, I am not sure what is so special about Siegel Disk fractals. I assume the corresponding Mandelbrot points of the official Siegel Disks are on the exact edge of the M-set, yet an infinity of other points are also on the edge. Why then should these particular points be so special? As is usually the case with fractional ratings, the extra half- point is a reward for my coloring, which is the greater part of the image. The extremely brief calculation time of 45 seconds can be attributed to the relatively shallow magnitude of 3*(10^11), which is within the range of the high-speed conventional math routine. For the convenience of those who do not calculate fractals, the image is posted already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A near perfect day prevailed here at Fractal Central on Tuesday. The blue skies, puffy clouds, gentle breezes and temperature of 84F 29C were just what the fractal cats ordered. They spent the day in their window, wishing they could go out and be a part of the world. The humans passed the day just being human, which is sometimes not as easy as it appears. The next FOTD will be posted in 24 hours. For all I know, it might make it. Until then, take care, and are fractals animal, vegetable or mineral? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_SiegelConnection { ; time=0:00:45.15-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.3031762780813\ 251/+0.6219200633096369/3.178477e+011/1/72.5/0 params=0/0 float=y maxiter=300000 bailout=9 inside=0 logmap=1442 periodicity=6 colors=000DmdEneIodMpdQqeUrfYshatieukivmmwoqxqtyru\ yquypuypvyowyoxynyymwzmwzmwzrwzvwzzwzzwzzwzzwzzwzz\ wzzzzzzzzzzzzzzzzzvzzrvzmrvhmrchmZchUZcUUZUUWUUTUU\ SUUSUURUURUUQUUQoNhudztfvtgsshpsjlrkirlfrmcqo_qpXp\ qUpsQotNouKovHluKjtNhtQfsSdsVarY_q_YqbWpeUpgPfcLX_\ HNWDDS93O82R82U82X72_72a72d62g62j62l97jCBiFFgIJfKI\ hLIiMHjNHkPGmQGnRGoSFpUFrVEsWEtXEuWHsVKqVNoUQmTTkT\ WiSZgRaeRdcQgaPj_PmYOpWOsUGZV9KWBANDAEEA6FDAFCDFBH\ FBKFANF9RF8UG8YG7`G6cG5gc0mG4nG3qG3tH5sI6sJ7rK9rLA\ qMBqMCpNEpOFoPGoQInRJnSKmSLmQNlOOkNQkLRjJTiIUiGWhF\ XhL`fRcdWfbai`flZloXqrWspSunPwlMyjJziHziGziFziEziD\ zhBzhAzh9zh8zh7zg5zg4zg3zg2zg1vg0rh5mhAhhFchKZhPUh\ UPfSLdQKbOJaNI_LHYJGWIFUGDRECQDBNBAL99J88H67E46D35\ F45H45J44K44M44O43R43T43X42Z42bU2cU1dU1fZ1gZ1hZ2eZ\ 3cZ3aZAaZG`ZM`ZS`ZZ`Zd`Zj`sp`urYntWhvTbwRXoV_gZb`b\ dTfgMjiEnl7rnCsl8pGAoLBnQ } END PARAMETER FILE=========================================

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FOTD 12-09-11 (Circus Time [7.5])
by Jim Muth 12 Sep '11

12 Sep '11

FOTD -- September 12, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: The most recent image, the one for September 10, shows a minibrot very near the cut-off point of the truncated Mandelbrot set that remains when the bailout is set to 2. Today's image shows a minibrot many orders of magnitude smaller and even closer to the cut-off point. In fact, the minibrot is well out of sight. Only the outer fringes of its surrounding pattern are visible. I chose a 'reset' point to add variety. I could rate the image no higher than a 7-1/2. These very deep images are starting to develop a boring similarity, and a new approach must be found to keep the ratings high. I did put a bit of extra effort into the coloring, though the image has such an over-abundance of fine detail that no coloring would be totally satisfactory. The calculation time of 1-1/5 hours is quite slow, especially for an image that rates a mere 7-1/2. Thank goodness for the web sites. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The high definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The FOTD for September 11 is admittedly late, because this FOTD is, or was, it. But I cured the lateness by renaming the FOTD for the 11th, the FOTD for the 12th. The delay was caused by the 120-pound, 55kg, front door of FC, which jammed shut due to the dampness, and needed work. At latest report, the door was looser, but still quite sticky. Morning clouds gave way to afternoon sun and a temperature of 73F 23C here at Fractal Central on Sunday. The scene was repeated on Monday, much to the pleasure of the fractal cats. The humans found enough things to do to keep them busy on both Sunday and Monday. The next FOTD will be posted in 24 hours. At least it is scheduled to be posted. Check back then to see if it actually appears. Until whenever, take care, and is it true that fractals will dissolve in water but not in carbon-tetrachloride? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Circus_Time { ; time=1:12:30.15-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y bailout=2 center-mag=-1.414213559000246436257000092131178840\ 044418020153333969/0/3.311132e+050 params=0/0 maxiter=32767 symmetry=xaxis periodicity=6 colors=000KitGmuCqu8uw4ywAtpEnjJjcNeZS_SXXNaRGgPCe\ NBbLB00A00A00B00C00E00F00G00H00J00K00L00N00O00P00R\ 20R20R20S20V20V20V20V20V20W20Y20Y20Z20_20`20a20a20\ b20b30c40c60e70e80gA0gB2iCBjEFlFKjGPiHUjJZmWamYdmX\ gmcjmgnmmommpmmrmmtmmxmpzmuzTzzezzszzzzzszzezzXxzS\ uxOsuNptLmsKjpJgnHemGbjF_iE_gC_eBZcAZb8Z_7ZZ6XS0YV\ 2ZY6__A_bEacHbfLbiPclTemYepafseguiiyngwlguigsggqef\ nbfmaflZfiXegVeeSecPeaOc_LcZKcXHcVFbSEbRBbO8bN7aL4\ aJ2aH0aF0_E0_B0_A0_80ZB0YE0XF0VF0TF3SL6RS8PZBOeENl\ GLpJKtLJxNPzPUzSXzZ_zcbzhezlbyh_xcXv_UuVRsTOqSLpRI\ nPFmODlNBjLBiNBgLBfKBeJBcHBbGBaFB_EBYCBVBBS8BP7BN7\ BK6BH7BF7BE7BB8BA8A76B88BAABACBBEBBFBCHBEJBEKBFNBF\ OBGRBHSBHTCJXCJYCKZCLaCLbCNeCNfCOgCPjCPlCRmCRpCSqA\ TuCSsESqGRpHRmKPlLPjOOiPOfSNeTNcXLbYL__KZaKYcJVeJT\ gHSiHRlGOmGNpFLtFKyEHzEGzCFzCAzB6yCExCLwCSuE_tEgxA\ msEnnHpjLpfPqaTqYYsTasPet } END PARAMETER FILE=========================================

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<Mike>Really nice great spiral & color mapping
by Hal Lane 11 Sep '11

11 Sep '11

That's a really nice spiral and color mapping, Mike. I usually think most spirals are "ho hum" but this one is great -- probably because it has so many "arms" and such a gentle curve to each arm.. It also responded nicely to the anti-aliasing. Was it 5x5 anti-aliasing? (I'm guessing from the "_5" in the image's name that it was.) - Hal Lane ######################## # hallane(a)earthlink.net ######################## ------- Mike wrote ---------------------------- Author: Mike Frazier Date: 2011-09-10 16:26 -400 To: Fractint and General Fractals Discussion Subject: [Fractint] Down the Drain This fractal started with Jim Muth's FOTD for April 28, 1999. I added the central 32 arm interleaved spiral to the image by zooming in on a spiral in the original. I tried many color palettes before settling on this one with the sqrt mapping. It was hard to find a coloring scheme that didn't break up the long arms of the central spiral. If you continue to zoom deeper down the center of the spiral you will see the number of arms repeatedly double until you reach the minibrot at the center. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/down_the_drain_640_5.jpg . . . --------------------------------------------------

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FOTD 10-09-11 (Squarely Rooted [9])
by Jim Muth 10 Sep '11

10 Sep '11

FOTD -- September 10, 2011 (Rating 9) Fractal visionaries and enthusiasts: The X-parameter of today's main-spike image is very close to sqrt(2). This is no coincidence. I intentionally set the X-value to sqrt(2) when I chose the parameters. The bailout radius of the image is 2, which cuts off the set at a radius of 1.414... Today's image shows the closest minibrot to this cut-off point that I could find. Today's minibrot is not the actual one closest to the cut-off however. There are an infinity of smaller ones closer than today's. It is simply the closest one that I took the trouble to find. The rating of a 9 appears justified. The coloring alone makes the image worth the brief time required to run the parameter file. Almost all the colors were randomly chosen by the Fractint program, though I did slightly tweak a few registers. The name "Squarely Rooted" refers to the X-value of the image. The calculation time of 8-1/2 minutes is surprisingly fast for an image created with arbitrary precision math. For the convenience of those who dislike the task of setting up and running parameter files, the finished image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is posted in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The weather has been changeable here at Fractal Central lately. On Thursday it rained; on Friday the rain changed to showers; on Friday night a very noisy thunder-storm passed over; on Saturday we saw more showers. But during all this time the temperature hovered around 72F 22C, with little change. The fractal cats disliked the activity when we prepared for possible flooding, and they disliked the activity as we restored FC to normal when the flood water stopped four blocks short of FC. The next FOTD will be posted in 24 hours. Until then, take care, and river, stay away from my fractals. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Squarely_Rooted { ; time=0:08:33.83-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.4142133491632\ 888307967678939/0/2.307799e+024 params=0/0 float=y maxiter=32767 bailout=2 inside=0 symmetry=xaxis periodicity=6 colors=000GMMEJJDHHBEE9CC799577344122QlbNgZLcVIZSG\ VOEQLBMH9HE7DA487243PQ9MN8KL7IJ6GH6EF5CD4AA3883662\ 4412205zE3e91L4UMTRKQPIOIcrJfsKitLluMovOpuPquQruRs\ uStuTutUvtVwtmzzXytUtoSojPjeNeaK`XIWSFRNDMJAHE8C95\ 743201sp0ol0kh0gd0c`0_Y0WU0SQ0OM0KI0GF0CB087043rUz\ lRsgOmaLgXI`RFVMCPG9IB6C536kHufFobDjYCeUA_Q9VL7QH6\ LD4F83A415aLyZJtWIpUGlRFhPEdMC`KBXH9SF8OC7KA5G74C5\ 28214vONqMLmKJiIIeHG`FEXDDTCBPA9L88G66C54833411Z0s\ W0oU0kR0gP0cM0_K0WH0SF0OC0KA0G70C508204FIOEGMDFKCE\ JBDHACG9AE89C78B679568446334223111UfdP_ZLUTHONCIH8\ CB465APLORcLNZIKUFGPCDK9AF66A33529b17W16Q14J03D016\ QaeDJLjr1fn0cj0`g0Yc0V_0SX0PT0LP0IM0FI0CE09B067033\ 0P6qM5kJ4eG4_D3UB2O82I51C2068lr7ek6_d5UY4OR3IK2CD1\ 66x0vs5bl4Ye3TZ3OS2JL1EE19704KHGGDCCA9866433CBFA9C\ 87A668546334112iRRu48p37l36g36c25Z24V24Q13M13H12D0\ 1801400S``QYYOWWMTTKRRIOO } END PARAMETER FILE=========================================

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Flood danger has passed
by Jim Muth 10 Sep '11

10 Sep '11

Fractal fans: The flood danger has passed here at FC and things are returning to normal. The FOTD for today will appear in a few hours. JIM

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Down the Drain
by Mike Frazier 10 Sep '11

10 Sep '11

This fractal started with Jim Muth's FOTD for April 28, 1999. I added the central 32 arm interleaved spiral to the image by zooming in on a spiral in the original. I tried many color palettes before settling on this one with the sqrt mapping. It was hard to find a coloring scheme that didn't break up the long arms of the central spiral. If you continue to zoom deeper down the center of the spiral you will see the number of arms repeatedly double until you reach the minibrot at the center. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/down_the_drain_640_5.jpg The parameter file used to make the image: Down_the_Drain { ; Exported from Fracton. ; time = 26 min 48 sec at 640 x 480 with no aa ; on a Mac Pro 2 x 2.8 Ghz Quad-Core Xeon ; by Mike Frazier, public domain reset=2004 type=mandel passes=1 float=y center-mag=0.2510741463378246509490302634487064524\ 58685130735208872490198850774986748159870717220750\ 85801942767767307/0.563759715033491421452401420767\ 15267715765961288320347597715980467217970405679051\ 286432019075377948720496/1.33333335e+92/1/46/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=50000 inside=0 logmap=-23131 colors=pH6rH5vH3zH0vH2rG3mE2hD2cB2ZA2U81P71K51F41A\ 30510000330760BA1ED1IG1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3\ ql4tq3wu1zz0ww1tt2pp3mm5jj6gg7cc8``9YYAXVBURBROBOK\ BLHBJDBGABD6CA3C80CC4CHH8MJ9RLBWNC`PEeSFkWInZHqaHt\ cGwfGziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDTGDQDCNBCK8C\ 413000443775BB8EFAIIDLMFPQISUKWXNZ`PbdSegUikXloZpr\ asvcsvcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZP`XO_UMYRKW\ PJUMHVKGWJGXHFYGFZEF_DEaBEbAEd9Dg9Cj8Bl8Ao89r78u77\ r67p67n68l68i59g59e59c5A`5BZ6CW7EU8FR8GP9IMAJKBLMC\ IOFKQHNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljlolornrulprk\ mnikkgihffdddabbZa`W_YSYWPWUMVRITPFRNCQK8OI5RK7TN9\ WPBYRD`TFbWHeYJg_LiaNkcPneRpgTsiVulYxn_zpawn`tk_pi\ YmfXjdWgaVcZT`WSYURVRQROPOLOKJNHGMDDLAAKADMAGNAIPA\ LQAOSARUBUWBXYB__CbaCecChfCkhDnjDqlDtnCqlBmjBjiAfg\ 9cf8_d8Xc6SY5NS4IM3EH29B145000311632943D54G75J87MA\ 8QB9TCAWEBZFCbHEfHBjH9nH7 } -- Mike Frazier www.fracton.org

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Jim's Recent Formulas
by Brian Prentice 09 Sep '11

09 Sep '11

Here are two more details which use Jim's recent formulas. The first from FOTD for 9/5/11: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_46.png and the second from FOTD for 9/7/11: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_47.png Brian Prentice

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High water threatening FC and cancelling the FOTD
by Jim Muth 09 Sep '11

09 Sep '11

Fractal visionaries and enthusiasts: We're under a major flood warning here at Fractal Central. I don't think the water will reach FC itself, but we are taking precautionary measures. Due to the confusion there will be no FOTD until the threat has passed. JIM

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