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FOTD 23-10-11 (A Sheep in the Deep [7])
by Jim Muth 24 Oct '11

24 Oct '11

FOTD -- October 23, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene in the East Valley of the large minibrot on the main stem of the Mandelbrot set. The parent fractal is in fact a Mandelbrot set that takes on order-9 characteristics in its depths. The minibrot at the center lies near a larger minibrot, which in turn lies near an even larger minibrot . . . At this point I lose count of the minibrots, but I think there are about four of them in the ladder-chain up to the surface. The name "A Sheep in the Deep" has no connection at all with the image. It simply popped into my head when I made my mind a blank, a task I find quite easy to accomplish. The rating of a 7 includes a full point for the coloring, which took over twice as long as calculating the image. The calculation time of 3 minutes entered into the parameter file is an educated guess of the time the calculation would have taken on the faster but now dead machine. (The image actually took 12-1/2 minutes to finish on the slow unit.) The finished image may be viewed on the official web site at: <http://www.crosscanpuzzles.com/Archives.html> without the need to calculate it. The high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> The morning fog cleared off by 11am here at Fractal Central today, leading to a sunny afternoon with a temperature of 59F 15C. The fractal cats, still on watch for a possible return of the fighting tomcats, spent the first part of the day in the window facing the back yard. But the fighters have apparently moved on, and by the afternoon the fractal cats shifted their watch to the sunny shelf in the southwest window, which faces the front sidewalk. The humans spent the day doing nothing, which is quite enjoyable when it is done in moderation. The next FOTD will be posted in 24 hours. Until then, take care, and would this country's real savior please put in an appearance. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= A_Sheep_in_theDeep { ; time=0:03:00.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.749083935595091/+0.00000124195835773\ /1.4056e+013/1/-42.5/0 params=9/500000000000000.0/\ 0/0 float=y maxiter=2600 inside=0 logmap=333 periodicity=6 mathtolerance=0.05/1 colors=00000200300401502603613724835846956A67A78B8\ 8C99CAADBBEBBEBCFBDG9HzAGvAGrAFmAFhBEcBEZBDUBDRQzz\ PxxOvvOttNqqNnnMkkLhhLefKcdKacJ`aJZ`IYZHWYHUWGTVGR\ TFPSFOREMQDLPDJOCINCHMBHLBHKBGGAFEAECADAAC8AB6AA4A\ A5AA6AB7AB8BB9BCABCBBCCBDDBDEBDECEECEFCEGDFGDFHDFH\ CGICGICGJBHKBHKBHLAILAIMAIN9JN9JO9JP8KP8KQ8KQ7LR7L\ S7LS6MT6MT6MU5NV5NV5NW5NW7PW9RWBTWDVWFXWHZWJ`WKaWM\ cWOeWQgWSiWUkWWlWXlWWlXVkXVjYUhYTgYTfZSdZSc_Rb_Q`_\ Q_`PZ`PXaOWaNVaNTbMSbLRbLPcKOcKNdJLdIKdIJeHHeHGfGF\ fFDfFCgEBgEAgICeLEdOGcPHbQHcRHaSHYSHXSHUMHUHIUBIU6\ IU1IUBGUKFWUEOTDG`C9jAFp9Kz7Pi6Vh4_h3dd2Ya1RZ1LV0E\ N08U1Og2bk2qh8jbEd`KZZQTXWMVaGTgARm4LDpQJnVPl_Vkd`\ ihfhlZboRYrKT_CNbFLdHJgKHiMFkODjLFihHhmJgmcfmcemcd\ mccmcUmcLmmZmmlmmymmsmmnmmhpmczzZzzVzzRzzUzzXzz_zz\ bzzezzhzzkzznzzdzzVzzLzzBzz1zzxzzpzzizzbzzWzzTzzQz\ zOzzKzzGzzDzz9zzbzzbzzXzz } 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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FOTD 21-10-11 (Evaporation [8])
by Jim Muth 23 Oct '11

23 Oct '11

FOTD -- October 21, 2011 (Rating 8) Fractal visionaries and enthusiasts: In these FOTD discussions I often mention the parent fractal of an image. In most cases, this parent fractal is the image that appears on the screen when the formula parameters are entered and nothing is changed. My default settings are: a magnitude of 0.66..., the default color palette, a maxiter of 1500, a periodicity of 6 and a logmap of zero. Sometimes an outzoom is needed to fit an entire oversized parent onto the screen, or an inzoom is needed to enlarge an undersized parent to fill the screen. In other cases, there is no limited fractal that could be called a parent fractal. The entire parent fractal appears to be of unlimited size. Today's image is one of these misfits. Today's image lies in the apparently infinite fractal that is created by the MandNewt06 formula. This can be demonstrated by repeatedly outzooming from the image until the limit of Fractint is reached. Even way out here, there is no sign of the fractal coming to an end. As for the image itself, it reminds me of blue clouds caught evaporating away to reveal a universe of brownish spheres loosely arranged into nets and spirals. I rated the image at an 8, a full point of which is a bonus for the coloring effort needed to get reasonable smoothness from 256 colors. The name "Evaporation" refers to the bluish clouds, which to me appear to be clearing away, perhaps after a fractal storm. The calculation time of just over a minute will bring grief to no one if, in their opinion, the image lays an egg. For a little fun, try changing the exponent part of the real(p4) parameter a few orders of magnitude in either direction and watch the blue cloud totally evaporate or thicken. The already-calculated image is available on the official FOTD web site 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/> Typical October weather prevailed here at Fractal Central today, which made for a not too pleasant afternoon. The sun was blocked most of the time by dark lumpy clouds scudding from the west, (stratocumulus), which dropped occasional sprinkles, while the temperature remained stuck in the mid 50's F around 12C, and the wind gusted to 20mph, 30kph. Not being weather wise, the fractal cats ignored the marginal conditions and concentrated on deciding who would own the new chair. FL put a heavy afghan over the chair to thwart their scratching efforts while they bickered for ownership. The next in the apparently unending series of fractal images will be posted in 24 hours. Until then, take care, and if I don't exhaust the supply of fractals in this world, I'll keep finding them in the next. But I still wonder how I'll continue posting them to the list. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Evaporation { ; time=0:01:08.27-SF5 on P4-2000 reset=2000 type=formula formulafile=basicer.frm formulaname=MandNewt06a passes=1 float=y center-mag=-0.0587134/0.29352/32.89674/1/-135/0 params=-1.82/-1.79/2.48/-1.18/1.28/1.63/1e-030/0 inside=bof60 logmap=yes periodicity=0 sound=off colors=000xaNw`Nv_MuZMtYLsXLrWKqVKpUKoTJnSJmRIlQIk\ PIjOHiNHhMHgLHfKGeJGdIFcHFbGEaFD`EB_D9ZC5YB0UA0Q80\ N60wzzwyzwwzwvywvxwvwwvvwvuwvtwvswvqwvowvmwvlvvkvu\ luukuumuuluumtunsunrunquopuoouonuomuokupjupiuphupg\ upfupdupcupbupaup`up_uqZuqYuqXuqWuqVuqUrqTrqSrrQbr\ PbrObrNbrMbrLbrKbrJbsIasHNnGNnFNnENnDNnCNnCNnBNnAM\ mAMmALmAKm9Km9Km9Km9Lm8Km8Lm8Lm7Mm7Mm7Nm7Pm6Tl6Sl6\ Sl6Rl5Rl5Ql5Ql4Pl4Pl4Ol4Ol3Nl3Nl2Ml2Ll2Kl1Jl1Il1Hl\ 0Um1Sm1Rm3Rm4Pm5Nm6Lk7Jk8Ij9GjAFiBCiCAiEHhGFhIDgKB\ gL9fM7fIIpJHpKFpLEpMDpNCpOBpPApQ9pR8oS6oT5oU4oV3oW\ 2oX1oY0oZ0o_0o`0o`0oa0nb0mb0lc0kc0jd0id0he0gf0ff0e\ g0dg0ch1ch1bi1ai2`j2_k2Zk2Yl3Xl3Wm3Vm4Un4Tn5So5Rp5\ Qp6Pq6Oq6Nt5Lq6Mn6Ok7Ph8Qe9Rb9T_AUXBVUCWRCYODZLD_I\ E`FFaCFc9Gd6He5He4Hf6Gc8E`ADYCBVEASF8PH7MJ5JL4GN3D\ N38N39O2AO2BP2DP1EP1FQ1GQ0HR0IR0JR0KS0MS0NT0OT0PT0\ QU0RU0SV0TV0TV0TU0UU0UU0U } frm:MandNewt06a {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b p4 < |a| } END PARAMETER FILE=========================================

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FOTD 22-10-11 (Platinum Oxide [7.5])
by Jim Muth 23 Oct '11

23 Oct '11

FOTD -- October 22, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: The October 22 image is late because I spent extra time today trying to get the 2000mhz fractal computer to run. The machine has always been questionable, and this morning, when it came on with a blue 'something's wrong' screen, I decided to try only one more time to get it running. Reseating all the cards did nothing, so I said farewell to the 9-year-old 2000mhz unit, stored it in the closet, and brought the 13-year-old 200mhz machine out of retirement. The older machine booted up perfectly, and now has the position of honor on the fractal desk top, where it will remain until replaced by the next currently active machine to be retired. The failed machine will live on however through its video card, which handles the Fractint DOS video modes perfectly, and which I will install in the replacement machine. Today's image is a quickie that I found on the old fractal computer after the newer unit stopped working. The very fast image is a mixture of Z^2 and Z^5 created by the FinDivBrot-2 formula. The rating of a 7.5 includes an unusual 1.5-point bonus for my coloring work. The basic fractal shape has appeared several times previously as FOTD's, but I did devote a considerable time to achieve the slate-gray effect, which was only inspired by the program and needed much hand work. The central shape is filled with quintic minibrots, all of which are virtually identical and not worth the trip down. The parent minibrot is one of those deceptive Mandelbrot sets that at first glance appears normal, but develops more quintic-like features the deeper one dives into it. The name "Platinum Oxide" refers to the overall color cast. The calculation time of 35 seconds is an estimate. The image actually took 2 minutes and 13 seconds on the 200mhz unit. On the 2000mhz machine, which runs 4 times, (not 10 times}, as fast, I assume it would finish in 35 seconds. The already-calculated image is available on the official FOTD web site 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, now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> Today's weather here at Fractal Central was a repeat of yesterday's, with more dry but dark clouds, raw winds and a temperature of 52F 11C. The fractal cats took the day in stride, and were distracted only by a major cat fight that broke out in the back yard when two prowling tomcats crossed paths. The humans had a routine day, though I became quite annoyed when the 2000mhz fractal computer went on the blink again. The next FOTD will be posted in 24 hours. Until then, take care, and the most qualified does not always win. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Platinum_Oxide { ; time=0:00:35.00-SF5 on a P2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=+0.3596259397545952/+0.6447633584097521\ /3515559/1/-30/0 params=5/100000/0/0 float=y maxiter=1500 inside=0 periodicity=6 colors=000fdLhdKjcJkcImcGocFqcErcDn_FjWHfSIbPKZLLV\ HNREOUKNWQMYWL`aKbgJdlJJhLKQPNSRPUTRWVTYXV_ZXa`Zcb\ `edbgfdihgkkimmkoonqrpstruvtwxzzzvvvrrrmmmhhhcccZZ\ ZUUUPPPKKKFFFAAA55500000000000000000000U00cQNmSUmN\ SqIRwGOsEMpCKmAIi8Gf7Ec8Gd8Hd9Id9JeAKeALeBMfBNfCOf\ CPgDQgDRgVzrEShEThFUhFVhGWiGXiHYiHZjI_jI`jJakJbkKc\ kKdlLelLflMgmMhmNimNjmOknOlnPmnPnoQooQpoRqpRrpSspS\ tqTuqTvqUwrUxrVyrJsvPwtzksylrxlrwlrwmrvmrumrunrtnr\ snrrorrorqorpprpproprnqrmqrmqrlrrkrrkrrjsrisrhsrht\ rgtrftrfureurdurcvrcvrbvrawrawr`wr_xrZxrZxrYyrXyrX\ yrWzrVzrt`FrbIpdKoeNmgPkiSjjUhlXgmZeoacqcbrf`thZvk\ YwmWypboKapMapNaqP`qQ`rS`rT_sV_sW_tYZtZZu`ZuaYubYv\ dYveXwgXwhXxjWxkWymWynVzpVzqJC3MPGPaTSneCCWDEXDFYE\ GYEHZFIZFK_GL_GM`GN`HOaHQaIRbISbJTcJUdKVdKXeKYeLZf\ L_fM`gMbgNchNdhOeiOfiOhjPijPjkQklQllRmmRomSpnSqnSr\ oTsoTupUvpYeS_dQadPcdOddN } 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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FOTD 20-10-11 (Fantasia in Blue [8])
by Jim Muth 21 Oct '11

21 Oct '11

FOTD -- October 20, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today we return to the warhorse formula, the MandAutoCritInZ, where we check the parent fractal created when 3 negative parts of Z^(neg(sqrt2)) are combined with 1.5 negative parts of Z^(2*(neg(sqrt2))) and (1/C) is added on every iteration. This parent consists of two large bays, one on each side of the X-axis, with a large minibrot-filled field of debris scattered to the east. Today's image lies in a smaller patch of chaos just south of a large bud on the east side of the large north bay. Two tricks were involved in creating the effects in the image. To begin, I reduced the bailout radius to an unusually small 7, then I rendered the resulting image and its ballooning elements with the 'outside' set to 'tdis'. The name "Fantasia in Blue" was inspired by the overall blue cast of the image, though I have toned the blue down a bit since naming the image. The rating of an 8 is what I felt the image was worth at the time I rated it. The calculation time of 3-1/2 minutes is well within reason. To avoid all calculation hassle, view the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And view it in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic, web site may be accessed at: <http://www.Nahee.com/FOTD/> Saturday was ruled by heavy clouds here at Fractal Central, though the rain for the most part stayed to the west. The fractal cats, who pay far less attention to the weather than the humans, ignored the temperature of 57F 14C and had a lazy day, taking turns sleeping on the new chair instead of fighting for it. The humans, FL and I, had an uneventful day also. With the graphic design work slowing down, more and more days are becoming uneventful. The one thing not slowing down however is the FOTD, which I now have more time to work on. The next FOTD will be posted in 24 hours. Until then, take care, and if the climate changes, will the change be for the better or worse? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fantasia_in_Blue { ; time=0:03:37.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.300193586061464/+0.4252430675353652/\ 2.728e+011 params=-3/-1.4142/-1.5/-2.8284/0/-93/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000dD7iG5oJ2uM1uP0uS2uT4rW5qY7m`8kb9idBgfCd\ iEbjFalHdb9gQ2jG0_K9QPNFT_5Ym0`uCdiTiSjn9uq0ro0jn7\ blEajL_iT_g_ZfgXdoXcu_dkadbdfTffKigBjg1mi0oi0jf0fd\ 4bcCZbNV`XS_fkHqu3uFfVCsbBzkCymEooFfqHYrIPsKGuK7u2\ T_0oH5uX9raEofIliNimSfqXjoaomfrkkwjqziuzguiLuP0uM2\ kJ5bH7TF90BI08O0ER0KY0Ta0`j0hp0mp0jp0ep2_n9VlGPgMK\ dMFbKCeIAgD7iN3iL3jI3kE3k13j03a03N03809u5DuEHuOMuX\ QufTsbPuaMu_QuZTuXWuW_uVcuTfuSiuQluOquNsuLwzczzczz\ mzzmzzqzzIzzLzzOzzSuuVqjXlZZgTacNd_HgVBjQ5mM0oJ0kN\ 0jQ0iV0gY0db0bd0ai0_l0Zq0Ws0Vy0Tz0Sz0Qz0Ow4NlBL`IK\ QQKGXIJaIMdIPgHSkHVoHYrF`uFcuFduK_uOVoSQiWMbZHXbDQ\ f9Kj4Em38r32u30u30u30u30u30u30u30u30u30u30u30u30u3\ 0r32k45gC7aK9WTBS`ELiFFrIBzK5zN1zO7zSCzVIzXNzZTzaZ\ zdbzfiziozkszmowojrqfnqairkuisiau_WsYTmWQgWNaVKWTH\ QTEKSBES9LVFSYLZ`SdcXjfbriiulouoskqfWqTEqF0q20q00s\ 00w00z00z0C3HI3EN4CT7BZA8 } 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 19-10-11 (Mandala-Head [8])
by Jim Muth 20 Oct '11

20 Oct '11

FOTD -- October 19, 2011 (Rating 8) Fractal visionaries and enthusiasts: For today's image I turned to a built-in Fractint formula, the type=manzzpwr, a formula I rarely if ever bring up, which on every iteration raises Z to the power of previous Z then adds Z^(n). In today's image 'n' equals -12. After a few minutes of tweaking and experimenting with the formula, I turned up today's image, which for obvious reasons I named "Mandala-Head". The image resembles one of those surreal paintings by Rene Magritte in which people have things such as apples where their heads and faces would be expected. Today's image has a mandala instead of a head. (A mandala is a devotional symbol representing the eternal cycles that fill the universe, especially the cycle of birth and death believed in by most eastern religions but considered heathen doctrine by the western religions, where the doctrine of only one chance to achieve salvation is accepted as truth.) Most of the image's effect was achieved by rendering the scene with both the inside and outside parts set to 'atan'. The peach-turquoise color scheme adds to the effect, since the peach areas somewhat resemble the color of skin. The rating of an 8 might be a little liberal, but why not, since today I'm in one of my more liberal moods. And there will be no trouble at all with the calculation, since the time is a fireball-fast 25 seconds. For maximum convenience, the image has already been calculated and posted to 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 original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with clouds and mist here at Fractal Central. The foul weather continued for the rest of the day, never quite dry and never quite wet. The fractal cats approved of the temperature of 66F 19C, but Cassie approved a bit too much when she took her claws to the upholstery of the new chair and got herself scolded. The humans had another near normal day, with nothing out of the ordinary to report. The next FOTD will appear in 24 hours. I'll leave it to the individual fractalist to figure where it will appear from. Until then, take care, and if reincarnation is true, then about half the people on earth hold false beliefs; if it is false, then the other half hold false beliefs. In either case, the religious beliefs of at least half the people on earth are false. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mandala-Head { ; time=0:00:25.26-SF5 on P4-2000 reset=2004 type=manzzpwr passes=1 params=0/0/-12 center-mag=0.430612/0/0.5657059/1/-90/0 float=y maxiter=1500 bailout=10000 inside=atan outside=atan logmap=yes periodicity=10 colors=000gaVgbWgbXhcXhcYhdZidZie_ie`ie`jfajfbjgck\ gckhdkhelielifljgljhmkhmkimljnljnmknmlonlonmoonooo\ ppoppppqqqqqqrrqrssqrrrsqrsqrsprsprsorsorsnrsnrsmr\ smrslrskrskssjssjssististhsthstgstgstfstestestdstd\ stcttcttbttbttattatu`tu_tu_tuZtuZtuYtuYtuXuuXuuWuu\ WuuVuuVuuUuuTuuTuvSuvSuvRuvRuvQuvQvvPvvPvvOvvNvvNv\ vMvvMvvLvvLvvKvwKvwJvwJwwIwwHwwHwwGwwGwwFwwFwwEwwE\ wwDwwDwwCwwDxxCwwCvvCvvCuuCtuCttCssCrsBrrBqrBqqBpp\ BopBooBnoBmnAmmAlmAllAklAjkAjjAijAhiAhi9gh9fh9fg9e\ f9ef9de9ce9cd8bc8ac8ab8`b8`a8_`8Z`8Z_8YZ7XZ7XY7WY7\ VX7UX7TW7TW7SV6RV6RV6QU6QU6PW6PW6PV6PU6PU5PU5PU5PU\ 5PU5PU5PU5PU5PT4PT4PS4PR4PQ4PP4PO4PQ5OU6NU7NUAOUDQ\ VGU_JYdMaiPenSisVnxUmxTlxSlxRkxQkxPjxOjxNixMixLhxL\ hxKgwKgwKfvJfvJfuJeuIetIetIdsIdsHcrHcrHcqGbqGbpGbp\ FaoFaoF`nF`nE`mE_mE_lD_lDZkDZkCYjCYjCYiCXiBXhBXhBW\ gAWgeZQeZRe_Sf_Sf`Tf`UgaU } END PARAMETER FILE=========================================

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FOTD 18-10-11 (Down in the Boondocks [All math])
by Jim Muth 19 Oct '11

19 Oct '11

FOTD -- October 18, 2011 (Rating All Math) Fractal visionaries and enthusiasts: Today's image rates All Math. The mathematical interest is just about all it has going for it. The image itself is little more than a passing scene in an infinite world of fractals. And the calculation time of nearly 2 hours is far beyond reason. In addition, the exponent of Z that created the image is 1.0005, so close to unity that no one in his right mind would enter it as a parameter with any expectation at all of finding much more than smooth and straight band edges. Questioning my own sanity, I did enter this value as the exponent of Z, and in addition I felt fairly confident of finding something of interest. Today's image is what popped up where nothing should exist. The scene is neither a Julia set nor a Mandelbrot set, but something in between. The detail in the image is not the organized chaos that makes most fractals so interesting. The detail in today's image consists of countless discontinuities arranged into half-orderly elements. If any part of the image is zoomed into, a flat featureless area will ultimately be arrived at. In ordinary fractal chaos, the chaotic features continue without limit. The name "Down in the Boondocks" refers to the exponent of Z, which is by far the closest to unity of any FOTD fractal so far. A price must be paid for seeing detail in a fractal so close to unity however. The price is the need of a very high maxiter, resulting in a calculation time of 1-3/4 hours, which is tedious indeed for such an unartistic image. But help has arrived in the form of the FOTD web sites. All the tedious calculating may be avoided by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It may be seen in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with clouds here at Fractal Central, but the clouds cleared off before noon, leading to an afternoon of sunshine, balmy south breezes and a temperature of 70F 21C. With rain and colder weather forecast, today might have been the last near-perfect day of the fall. The fractal cats passed a good part of the day sharing the new chair. The humans disagreed a bit about politics (as is standard) but the day passed uneventfully. The next FOTD will be posted in 24 hours. Until then, take care, and liberal thinkers know that conservative policies are the cause of the problems, while conservative thinkers know that liberal policies are the cause of the problems. Neither side appears able to recognize that their conflicting views of the solution are also a part of the problem. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= DownInTheBoondocks { ; time=2:05:44.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 maxiter=120000 center-mag=+2.723099067722828/+0.02123607283229285\ /6919/1/5/0 params=37.5/0/37.5/0/1.1513/0/0/0/1.00\ 05/0 float=y inside=0 logmap=-15900 periodicity=9 colors=000zdCzeEzfGzgIzhKziMzjOzkQzmSznUzoWzpYzq_z\ razsbzs_zsXysUwsRurOsqOqpOooNmnNkmNilMgkMfjMeiLdhL\ cgLbfKaeK`dK_cJZbJYaJX`IWZIVXIUVHTTHSRHROGQLGPIHOF\ GNDKMDKLFKKIKJKKINKHPKUKzTKzTKzTKzTKzTKzTKzTKzSKzS\ KzSKzSKzSKzSKzSKzRKzRKzRKzRKzRKzRKzRKzRKzQKzQKzQKz\ QKzQKzQKzQKzPKzPKzPKzPKzPKzPKzPKzOKzOKzOKzOKzOAzOA\ zOAzOAzPAzQAzRAzSAzSAzTAzUAzVAzWAzWAzXAzYAzZ1z_1z_\ 2z`2za3zb3zc4zc4zd4ze5zf5zg6zg6zh7zi7zj7zk8Wk8Yl9_\ m8an6co4eq2gr0is0ku0mv0ox0qz0sy0ux0ww0ww0ww0ww0ww0\ ww0ww0ww0ww0ww0uw0sw0qw0ow0mw0kw0iw1gw1ew2ew2ew3ew\ 4fw4gw5gw5hw6hw6iw7iw7jw8kw8kw9lwAluAmsBmqBnoComCo\ mDpmDpmEqmEqmFrmEsmFrmFqmFpmGomGomGnmHmmHlmHlmIkmI\ jmIimJimJhmJgmKfmKfmKemLdmLcmMczOazQ`zS_zUZzWXzYWz\ _VzaUzcTzeRzgQziPzkOzmMznLzpKzpJzpIzpGzpFzpEzpDzpB\ zpAzp9zp8zp7zp5zp4zp3zp2zp1zp2zp2zpfzpezpezpdzpczp\ czpbzpazpazp`zp`zp_zpZzpZ } frm:SliceJulibrot5 {; 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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FOTD 17-10-11 (Bare Singularity [7])
by Jim Muth 18 Oct '11

18 Oct '11

FOTD -- October 17, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is the third one created with an exponent of 1.05, though today it is positive Z rather than negative Z that we raise to the power of 1.05. The parent fractal was created by calculating the expression Z^(1.05)+C at a level of 0.31... turns down the complex logarithmic hyperspiral with the 'recip' function applied. The surprise in the image is the existence of a minibrot. The minibrot lies at the center of a disorganized spiral, which is another surprise. Most spirals appear boring because they continue unchanged all the way down to infinity; today's spiral however comes to a definite end at the central minibrot. I named the image "Bare Singularity". I almost named it 'neutron star', but the singularity name has more impact. I'm not sure a bare singularity could actually exist. Any singularity would necessarily have an event horizon around it, and would therefore lie unseen inside a black hole, but it is fun to try to imagine what a bare singularity might look like. The rating of a 7 is about what the image is worth. A little extra effort on the colors might have rased the rating to a 7-1/2. The calculation time of 7 minutes starts to drag before the image is finished. Avoid the dragging by viewing the image on the web site. The official FOTD web site is at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image is posted. or the high-definition web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Light rain fell during the night here at Fractal Central, but by daybreak the sky was clear. The rest of the day brought full sun with only a few passing clouds, and a temperature of 64F 18C. The fractal cats approved of these conditions, at least during the times when they were not distracted by a large orange tomcat that wandered onto the back porch. The world of the humans featured only routine stuff not worth reporting. The next FOTD is due to be posted in 24 hours. Most likely it will be posted on schedule. Until then, take care, and if nothing can escape from an (almost) black hole, how does the gravity get out? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Bare_Singularity { ; time=0:07:09.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-2.109365353519732/+2.80890231424387/\ 1.629783e+011/1/-85/0 params=1.05/0/-0.31034272286\ 14155/0 float=y maxiter=5000 inside=255 logmap=700 periodicity=6 mathtolerance=0.05/1 colors=000GWeXmjNdgGWe8Pb0Ha0AZ03X00V00W00W00W00W0\ 0W00W00W00X00X00X00X01X01X01X01Z02Z02Z02Z02Z03Z03Z\ 03Z03_05_05_05_05_06_06_06a06a07a07a07a07a08a08b08\ b08b09b09b09b09b0Ab0Ad0Ad1Gl1Cd1Cd2Cm2Cd3De3De3De5\ Me5Me6Me6Me5Md6Me6Me6Me7Me7Me7Me7Me8Me8Hl8Me8Gv99u\ 9Mu9GuAMuAMuA9uAMuCCuCEuCMuC9uDMuD9uDEuEMuEDuEHuEG\ uGEuGEuGDuGCu8DuHAuHGuC8sH9uGHuDAuEJuDIuDAuCCmAImA\ 9o9Fo8Co8Do7Go6Ho6Io5Do2Cp3Do5Eo5EoLJo6GoLQh7Ao8Co\ 8Po9Do9IoASoAEoCOmCGmDHjDMjEIhELhGJgGJgHPeHMeLQeIN\ eJNeJPeLPeLQeMQeMSeNSdNTdPTdPVdQVdQWdSVdSWeTWeTWfV\ WfVXgWZgWXgXZhXZhZ_fZ_g_ag_agachabgbegbeidgodglehm\ ejoglqglzhmzhpzjpzjozlozlozmozmozopxopxppxppxrpxrp\ xsrxsrxurxurxvrxvsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxx\ sxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsx\ xsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxs\ xxsxxsxxsxxsxxsxxsxxsxzzz } 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 16-10-11 (A Bigger Surprise [8!])
by Jim Muth 17 Oct '11

17 Oct '11

FOTD -- October 16, 2011 (Rating 8!) Fractal visionaries and enthusiasts: How low can you go? Yesterday's image brought a big surprise when I found actual chaotic detail in the (-Z)^(1.05)+C Julibrot. Today's image brought an even bigger surprise when I found chaotic detail in the (-Z)^(1.0025)+C Julibrot, which is 20 times closer to unity, and this is exactly what I named it. The rating of an 8! expresses my surprise at this unexpected turn of events, and I would not be surprised to find the biggest surprise as I continue to lower the exponent. In addition to the unexpected detail, the image shows a surprising overall pattern of radiating arms and curving loops. And yes, the background is filled with a large variety of detail. The calculation price for all this surprise is an unwieldy 15-1/4 minutes. But the web sites will eliminate this problem. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> in 640x480x256 resolution. The hi-def version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site is at: <http://www.Nahee.com/FOTD/> A sunny morning was followed by a cloudy afternoon here at Fractal Central. The temperature settled around a comfortable 66F 19C for most of the day, keeping the fractal cats content until we brought a new chair into the living room. When we set the chair in its place, Nicholas checked it, seemed satisfied, and walked away. Cassie checked the chair and immediately laid claim to it. She will probably make it her own catsonal chair, where Nico will be permitted only with her permission. The next FOTD will be posted in 24 hours. Until then, take care, and if we took the money from the ridiculously wealthy one-percent and distributed it evenly among the remaining 99-percent, everyone would have about double what he now has. The demand for goods and services would then double, which would cause the prices to double also, cancelling the extra wealth. The only change would be a lack of ridiculously wealthy people. My solution to the problem of the unequal distribution of wealth is to ****** the ******* so that ******* ** ******** **** ***** would be equal. And then everyone would be satisfied. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Bigger_Surprise { ; time=0:15:14.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 center-mag=2.7\ 2198/0/3.20013/1/-90/0 params=37.5/0/37.5/0/1.1513\ /0/0/0/1.0025/0 float=y maxiter=32767 inside=0 logmap=-668 periodicity=9 colors=000OG0QI0SK0TN0VQ0XT0XW0YZ0Wa0Ud0Sg0Qj0Mm0O\ p0Qr0Rr0Tq0Up0Wp0Xo0Zo0_n0am0bm0dl0ek0gk0hj0jj0ki0\ mh0nh0pg0qg0nd0lb0j_0gY0eW0cT0aR0ZO0XM0VK0TH0QF0OC\ 0MA0J60K80KA0KC0LE0LG0LI0MK0MM0MO0NQ0NR0NT0OV0OX0O\ ZzP`zPbzPdzQfzQhzQjzQkzOizNhzLfzKezIczHbzGazK_zNZz\ RXzUWzXUz`TzcRzgQzjOzmNzmNzmOzmOzmPzmOzmPzmPzmPzmQ\ zmQzmQzmRzmRzmRzmSzmSzmSzmTzmTzmTzmUzmUzmUzmVzmVzm\ WzzYzz_zzazzczzezzgzzizzkzzmzzozzqzzszzuzzwzzxzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzblzc\ mzdnzdozeqzfrzfszgtzhvzhuzixzjwzjzzhvzgwzfuzetzdtz\ cqzbrzaoz`oz_lzZmzXizWjzVfzUgzTdzSdzRazQbzP`zO_zNZ\ zLXzKWzJUzITzHSzGQzFPzEOzDNzCLz8NzBLzDNzGNzIPzLSzN\ UzQXzSZzU`zT_zTZzTYzTYzTXzTWzTVzSVzSUzSTzSTzSSzSRz\ SQzRQzRPzROzRNzRNzRMzRLzRLzQKzQJzQIzQIzQHzQGzQFzPF\ zPEzCizEhzGfzHdzJbzLazN_z } frm:SliceJulibrot5 {; 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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FOTD 15-10-11 (The Big Surprise [?])
by Jim Muth 16 Oct '11

16 Oct '11

FOTD -- October 15, 2011 (Rating ?) Fractal visionaries and enthusiasts: Rarely does a parent fractal become Fractal of the Day, but today is the second consecutive day on which a parent fractal has been featured. In yesterday's image we saw that the (-Z)^(1.05)+C Julibrot apparently holds no interesting semi-chaos, at least not in the area of Seahorse Valley. In today's image we find that first impressions are sometimes wrong. Today, we check the hump that passes for East Valley in the Mandelbrot aspect of the Julibrot. We check it at an angle double rotated 37.5 degrees toward the Julia direction, and what we find is total chaos. While all the edges in yesterday's image were smooth, today's image shows nothing but chaos in its eastern parts. To add to the interest, this chaos consists of discontinuities, which vary widely in character in different parts of the image, yet have a similar theme in restricted areas. Such a mixed-up Julibrot surely has many additional curious slices in this East Valley area. I'll be checking other slices over the next few days, and I would not be surprised if some slices achieved FOTD image status. The name "The Big Surprise" expresses my feelings when I checked the 37.5,37.5 angle of today's slice through 'east hump'. The rating of a question mark shows my indecision. The mathematical interest is certainly there, and would rate about an 8, but take this math interest away and the artistic value falls short of FOTD reference standard. The redeeming feature is the super-fast calculation time of 50 seconds, which will give no one a reason to regret the wasted time if the image falls flat with them. To view the image without the bother of calculating it, visit the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> To see the image in high-definition, visit: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> To see all the images since April 1997, go to: <http://www.Nahee.com/FOTD/> Conditions were windy here at Fractal Central today. The gusts near 50mph, 80kph kept the leaves swirling. Otherwise the partly cloudy skies and temperature of 64F 18C were harmless. The fractal cats were also pretty harmless, sleeping as they did through a good part of the afternoon. FL and I stopped by a local 'occupy' demonstration around noon. Somehow I found myself holding a we're-not-going-to-take-it-any- longer sign and getting honked at by passing cars. Luckily, no harm was done to my middle-of-the-road political reputation, since all sides apparently agree on the same problem, if not the solution. We then spent the rest of the day on a short antiquing expedition. The next FOTD will be posted in 24 hours. Until then, take care, and when the time is right, the answers will become obvious. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Big_Surprise { ; time=0:00:50.15-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=1.07545/0/\ 0.3427852 params=37.5/0/37.5/0/1.1513/0/0/0/1.05/0 float=y maxiter=15000 inside=0 logmap=yes symmetry=xaxis periodicity=9 colors=000blYcmXdnXdoWeqWfrVfsUgtUhvThuSixSjwRjzRh\ vQgwQfuQetPdtPcqPbrOaoO`oO_lNZmNXiNWjMVfMUgMTdLSdL\ RaLQbKP`KO_KNZJLXJKWJJUIITIHSIGQHFPHEOHDNGCLG8NHBL\ GDNGGNGIPGLSGNUGQXGSZGU`GT_FTZFTYFTYFTXETWETVESVES\ UESTDSTDSSDSRDSQDRQCRPCROCRNCRNCRMBRLBRLBQKBQJBQIA\ QIAQHAQGAQFAPF9PE9PD9PD9PC9PB8PA8OA8O98O88O77O77O6\ 7O57O57P68Q69R7AS7BS8CT8DU8DV9EW9FWAGXAHYBIZBJ_BJ_\ CK`CLaDMbDNcEOcEPdEPeFQfFRgGSgGThHUiHVjHVkIWkIYlJ_\ mIanGcoEeqCgrAis8ku6mv4ox2qz0sy1ux2ww2ww3ww3ww4ww4\ ww5ww5ww6ww6ww7uw8sw8qw9ow9mwAkwAiwBgwBewCewCewDew\ EfwEgwFgwFhwGhwGiwHiwHjwIkwIkwJlwKluKmsLmqLnoMomMo\ mNpmNpmOqmOqmPrmOsmPrmPqmPpmQomQomQnmRmmRlmRlmSkmS\ jmSimTimThmTgmUfmUfmUemVdmVcmWczYaz_`za_zcZzeXzgWz\ iVzkUzmTzoRzqQzsPzuOzwMzxLzzKzzJzzIzzGzzFzzEzzDzzB\ zzAzz9zz8zz7zz5zz4zz3zz2zz1zz2zz2zzfzzezzezzdzzczz\ czzbzzazzazz`zz`zz_zzZzzZ } frm:SliceJulibrot5 {; 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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FOTD 14-10-11 (An Old Smoothie [No Rating])
by Jim Muth 15 Oct '11

15 Oct '11

FOTD -- October 14, 2011 (No Rating) Fractal visionaries and enthusiasts: The exponent of (-Z) in today's image is 1.05, a value that would be expected to create little in the way of interesting fractals. But it is negative Z that we are iterating today, not positive Z, and when it comes to fractals with an exponent of Z between 1 and 2, negative Z wins hands down. The parent fractal, with an exponent only 0.05 above unity, already has some halmarks of the Mandeloids -- a prominent period-2 bud on the negative X-axis and a very well-defined Seahorse Valley. To produce today's image I found the Julia set of this valley, which is an empty featureless figure-eight shape, and double rotated the view 0.5,0.5 degrees. The result is a figure eight nearly filled with the bloated Mandelbrot valley. Searching for interesting semi-chaos, I increased the maxiter to 500000, but when I saw that no chaos was to be found, reduced it to the present 75000, which is still quite large enough. The name "An Old Smoothie" refers to the smooth edges of everything in the scene. Since the image is the second similar one in a few days, I declined to give it a rating. The result is probably not worth the calculation time of 11-1/2 minutes, so thank goodness for the FOTD web sites. The finished image is posted in SF5 resolution at: <http://www.crosscanpuzzles.com/Archives.html> and in higher resolution at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic, FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A series of heavy thunder-showers plagued Fractal Central through the night and most of today, with about 3 inches, 7.5cm of rain falling in that time. The fractal cats checked the window several times, but when the thunder grew too sharp, they ducked for cover in the closet. FL simply endured the conditions, while I rather enjoyed the action. At least, the temperature of 64F 18C pleased human and cat alike. The next FOTD will be posted in 24 hours. If an antiquing expedition arises, it might be late however. Until whenever, take care, and don't worry about who might be the next U.S. president. You'll never notice a difference. The international corporate conglomerate is actually running things and will continue doing so. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= An_Old_Smoothie { ; time=0:11:29.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=-0.3568/0/1 params=89.5/0/89.5/92/-0.736/0.03/0/0/1.05/0 float=y maxiter=75000 inside=0 outside=tdis logmap=75 periodicity=9 colors=000Q86R56R26R06Q17Q27Q28Q38Q49Q49Q5AQ5AQ6BQ\ 7BQ7CQ8CP9CP9DPADPAEPBEPCFPCFPDGPEGPEHPFHPFHSIFVKE\ XMD_OBbQAdS9gV7jX6lZ5o`3rb2td1qc6obBlaGjaLh`Qe_Vc_\ _`ZcYYaVY_SXYQXWOWUMWSKUQIUOGUMGUKHUIHUGHTEGRDFPCE\ NFDLHCKJBIMAGO9ER8CT8BV9DYAF_BHaBJdCLfDNhEPjERmFTo\ GVqGWsFVqFVpEUoEUnDTmDTlCSkCSjBRiBRhAQgAQf9Pe9Pd8O\ c8Ob7Na7N`6M_6MZ5LY5LX9QTDVQGZNKcJNgGRlDUpAXqB_rBa\ sCdtCftDiuDkvEnwEpwFsxFuyGxzGzzGzu9zp3zm4zj4zj4zk4\ yk4xl4wl5vm5umAtnFsnKroMqoOpoQooSnoUmoWon_rlZtkYvj\ OxiIzh5uf8qdAmbCiaEe_GaYIYWLUVNQTPMRRIPTEOVGMZIKaK\ IdMHgOFjQDmSBpTAsWDqZGo`ImcLlfOjhQhkTfnWepYcs`aub`\ vebvgdvjfvlhvojvqlvtnwwwuuusssqqqooommmkkkiiigggee\ ecccaaa___Y_YW`WUaUU_SUYQUWOUUMUSKUQKUPMUROUTQUVSU\ XTUZVU`XUbZUd_UfaUhcUjeUlfUhhUejUblUZnUWpUTrUQtUbd\ UnQUzBUZVU7mUCdUGWUKNUOYUPWbQV_RUXSTUTSRUROVQLWPIX\ OFYNCZM9_L7_KUE1UD2UD2UC2 } frm:SliceJulibrot5 {; 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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FOTD 13-10-11 (1-1/2 Seahorses [8])
by Jim Muth 14 Oct '11

14 Oct '11

FOTD -- October 13, 2011 (Rating 8) Fractal visionaries and enthusiasts: Believe it or not, today's image is a scene in the Seahorse Valley area of the (-Z)^(1.5)+C Mandeloid. Actually, the scene is very close to a Julia set of the valley, being double-rotated only 0.4,0.4 degrees from the true Julia direction. The wedge- shaped feature almost filling the outer figure-8 shape is a grossly enlarged view of the Mandelbrot Seahorse Valley. Iterating (-Z) rather than straight (Z) makes a great difference in the fractals with a fractional exponent of Z between 1 and 2. While positive (Z) results in tiny bean-shaped fractals, negative(Z) produces much larger fractals, with recognizable Seahorse Valleys and much more interesting surrounding semi- chaos to explore. I rendered the scene with the outside set to 'tdis'. Some of the other outside options also produce interesting versions of the scene. The name "1-1/2 Seahorses" refers to the exponent of Z, not to any sliced up seahorses that might be lying around. The rating of an 8 includes a full point for the coloring. This might be a bit excessive, but why not reward myself? I must have put almost an hour into working out the colors. The calculation time of 8-3/4 minutes is on the slow side. Most of this time is caused by the large maxiter of 32767, which was the maxiter limit of early versions of Fractint, and which I still use as a standard setting. But wait! There is no need for the 8-minute delay. Calculation may be avoided by viewing the image already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And by viewing the high-definition version 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/> Heavy clouds and intermittent showers continued here at Fractal Central on Thursday, while the temperature of 63F 17C was on the mild side for the season. The fractal cats, being warm weather fans, enjoyed the conditions. The humans spent the day doing routine things, which make for a peaceful day to live through but rather dull reporting. The next FOTD is scheduled to be posted in 24 hours, and it might actually be ready. Until next time, take care, and if we ever defeated the terrorists, who would we then blame our problems on. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 1-1/2_Seahorses { ; time=0:08:47.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=t inside=0 center-mag=-0.305312/0.00434276/1.123196 params=89.6/0/89.6/92/-0.742/0.05/0/0/1.5/0 float=y maxiter=32767 outside=tdis logmap=3 periodicity=9 colors=000TL_SKYRJWQIUPHSOGQNFOMEMLDKKCIJBFIACH99G\ 86F73D50C30700800900000000000000000000000000ZVKb`D\ fe6lx_iwaevcbvf_uhWtjTslQsoMrqJqsGpuDpwIqrMrmQshUt\ cYuZauUzMHvJMsGRpDWlA`i7ef4iY3`P2SG1J71BJ4DU6Fd9Ho\ BJzDLwJPtPTqVWn`_kfbhlffridojbmk`jl_hmYenWcoV`oTZp\ RWqPUrORsMPtKMuJKuLMsNNrPPqRQpTRoVTnXUmZWk`XjbYid_\ hf`ghbfjcekddlbelaem`em_emZejachcbfe`cg_aiY_kXXnWV\ pUTrTctRmvQzxPmqNcjMScKSXJTQHUJGRKJOKMLKPJKSGKVDLX\ AL_8Lb5Le2Lh0Lj1Mg1Md2Mb2M_2MX3MV3MS4NP4cc4cc5cc5c\ c6cc6cc6cc6cc6cc6cc6cc6cc6cf6cl6cr9cpBmoDmnGmlImkK\ mjNmhPmgRmfUmdWmcomYcmZ9mgwmuqmmkmfemzkmzgmzcmz4mz\ LmzcmzamzZmz_mz_mz`mzNmzSmzXmzemzcrzarzDrzSrzXrz9r\ zGrzNrzUrz0rzJrzDrzPrzcrzbrzarzmrzmrzmrzmrzmrzmrzm\ rzmrzmrzmrzmrzmwzmrzmrzmrzmrzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot5 {; 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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time theory, addendum
by Sebastien helie 14 Oct '11

14 Oct '11

Planet_time { reset=2000 type=formula formulafile=fr2011.frm formulaname=10_10_2011_2 center-mag=1.89737/-1.28214/0.8503401 inside=fmod outside=imag invert=-0.75/1/-0.75 decomp=64 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } Planet_time{;sinpix z=pixel: x=z*z^c y=1/x a=sin(z/2) b=x+y+a z=z+b/x+(1/(z+b/x)) } I like time theory it's like duality, or the concept of (essai and error) set into amelioration. First somewhere in the electro-magnetic world we can imagine and anticipate that we all have a linear time memory of our individual life (since TeraByte memory!!smile). Attempt to remember everything,is impossible,my girl friend can get down when she had 3 year old, what i found impressive. Then from this theorical individual linear time line, we got to see the collective, who is probably like fractal geometrie has object, from this life attempt #2 will give a different result(geometric) end than attempt #1 just cause you know it, and act according to. Could be fun to get down time, dividing i guess the conscious and the not conscious of the fact?! smile... let's bad trip, i like negative speculation. Your back in time, suddenly you encounter a geometric break in the time structure(happen in fractal), you do not existe in the society anymore, no friend no family, nothing else that your self... Could be a good thing to simulate in the peace society!. We can, by playing with time end up all counscious in our own and individual conscious cell awared and alone... No problemo i know for math-eux [= mathematician hobbist] but got to get ready for long periode of solitude i'am certain.... and futur? plus social utopia, when it's clear to me that since a long time same people come back... Just come from the museum with a exposition about Rome, to figure than Constantin really look like one of my old boss has exemple.... anyway both are For people with lot's of energy, adventurer.. one thing sure... my grand-parent are not this kind of triper. pray your fractal result. sebastien Helie

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FOTD 12-10-11 (Reckless Driving [No Rating])
by Jim Muth 13 Oct '11

13 Oct '11

FOTD -- October 12, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image is a blow-up of a tiny hole in the upper right part of the 'infinite ocean' image of October 10. Out of curiosity I checked to see what the hole was about, and to my surprise found the fog shrouded midget car being driven quite recklessly by the driver whose head is clearly visible through the mist. As soon as I saw the driver and his car, I knew the name of the image must be "Reckless Driving". Actually the mini car is a Z^sqrt(2)+C minibrot that exists in its full form in the Mandelbrot aspect of the East Valley of the parent fractal, which resembles nothing quite as much as a kidney bean. The holes in the fog obscuring the mis-shapen car and driver are basically Julia sets of what lies under them. Since the entire image is kind of a joke, and the calculation time is a cumbersome 34-1/4 minutes, I gave it no rating. The calculation may be avoided by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high definition image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site is at: <http://www.Nahee.com/FOTD/> Today's weather left much to be desired here at Fractal Central. Heavy clouds and occasional rain spoiled every outdoor activity, not that any were planned, while the temperature of 57F 14C kept the fractal cats in cold weather mode. The local humans, FL and I, spent the day doing what needed to be done, and did it without powdermilk biscuits. If all goes according to plan, the next FOTD will be posted in 24 hours. If not, who knows? Until whenever, take care, and if we took the money from the top one-percent of wealthiest people in the US and distributed it equally among the rest, how much would each person receive? (Poverty cannot be significantly reduced by making the wealthy people poor.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Reckless_Driving { ; time=0:34:12.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.257646/\ 0.768567/43.47637/1/-55/0 params=89.99/0/89.99/\ -78.25/0.13/0.00037/0/0/1.4142/0 passes=1 float=y maxiter=100000 inside=0 logmap=248 periodicity=10 colors=000m8Jh9KcAMZBOUCQPDSMEUKFVLGWMHXNIYOJZPK_Q\ LaRMcRLdSLeSKfTJgTJgUKgUJgUJgVKgWLiXLkYMlZNmZQmZSl\ ZUj_YiY_hW`fTbeQddMebKgaGh`DhZAiY6kX2jY3kW3lU3lS3l\ Q3mP3nN3nL3nJ4nI4nG4nE4oC4oB4o94o74o54o43p83qC3qF3\ rJ3rN3sQ3sU3tY3t`3sd3rh3qk3oo3mr4jo4gm5ei5cf6ac6_a\ 7Y_7WZ8UX8SU9QS9OPAMNAKKBIIBGFCEDCDBDCDEDEFEFGFGHG\ HIHIJIKKJLLKMMLNNMOONPPORQPSRQTRRUSSVTTWUUYVYZdb_X\ U`YUaZVb_Vd`WeaXfbXgzYKlZidZidZjcYkbYkaXlkXzaXmbWm\ cWmcWncVncVocUocUocUpcTpcTqcTqcSqcSrcRrcRscSscTsbU\ taUt`Uu_UuZUuYUvXUvWUwVUwUUxTUySUzRUzQZzPZzOZzNZzM\ ZzLZzKZzJZzIKmHKmGKmFKmEKmDKmCKmBKmAKm9Km8Km7Km6Km\ 6Km6Km6Km6Km6Km6Km6Km6Km5Km5Km4Km4cz4cz3cz3cz3cz6c\ z8czAczAczAczAczAczAczAczAczAczczzczzczzczzczzczzc\ zzczzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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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FOTD 11-10-11 (Conventional Limits [8])
by Jim Muth 12 Oct '11

12 Oct '11

FOTD -- October 11, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "Conventional Limits". The name refers to the image's magnitude of over 3*(10^13), which is right at or a little beyond the useful limit of the conventional math routine. The image is a very high iteration scene rather deep in the north branch of Seahorse Valley. The logmap value of 91500 is perhaps the largest in FOTD history, though I do not keep a record of this. The maxiter of 1000000 has been exceeded many times however. The record is 2147483647, which is the maximum value permitted by the program. The calculation time of only 5-1/4 minutes is due to the speed of the type=mandel formula on my 2000mhz machine. On the old 200mhz unit, which still sits idly on a nearby table, the image would take well over an hour to finish. (An arbitrary-precision version would take about one week on the old machine.) The rating of an 8 is the highest in several days, once again showing that the wonders of the Mandelbrot set are nowhere near being exhausted, and never will be. (Regardless of how much is taken from infinity, an infinite amount always remains.) The completed image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version may be found at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, with images back to April 1997, is at: <http://www.Nahee.com/FOTD/> Today began with dense fog here at Fractal Central. The fog lifted in the late morning, revealing a partly cloudy sky. The temperature of 73F 23C was pleasant for mid October, but the pleasant conditions will soon end. The forecast is for rain tonight, as well as Wednesday, Thursday and Friday. The local farmers prayed for rain all through June and the first half of July. With the 32 inches 80cm of rain that has fallen since the middle of July, I feel their prayers have been adequately answered. (And from what I hear on the local news, so do they!) The fractal cats, who always keep their paws dry, spent the day plotting mischief, while FL and I kept the mischief from happening. The next FOTD will be posted in 24 hours. Until then, take care, and how will the world ever agree on peace when it can't even agree on which religion is true? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ConventionalLimits { ; time=0:05:16.54-SF5 on P4-2000 reset=2000 type=mandel passes=1 float=y inside=0 center-mag=-0.74999775055745050/+0.003016340258101\ 39/3.2935e+013/1/-37.5/0 params=0/0 maxiter=1000000 logmap=91500 periodicity=10 mathtolerance=0.05/1 colors=000cWkuWkuYiu_fuadudbuf`uhZujWulUunSupPurNu\ tLuvJuxHuzHsxHqvHptHnrHmqHkoHjmHhkHfiHegHceHbcH`aH\ __HXYHVTHTQHROHPNHNMHMLHLKJLKHLKHMLHOMHROHUQHWSHYU\ H_YHaaHdeHfiHhmHjqHltHnvHpyJrzLszNtzPtzRszTszVrzWq\ zWqzWqyWpyWpxWowXowXnvXnuXnuXmtXmsXlsYlrYkqYkqYjpY\ joYjoYinZimZhmZhlZgkZgkZgj_fi_fi_eh_eg_dg_df_ce`ce\ `cd`bc`bc`ab`aa``aa``a`_a__a_ZaZYaZYaYXbYWbXWbXVbX\ UbXUbWTbWTbVSbVRbTQaURbVRcWSdXTeYTfZUg_UhaVibWjcWk\ dXleYmfYngZohZpi_qj_rk`slatmaunbvobvpcvsevqcvobvm`\ vk_uiZsgYreWpcVoaUm_SlYRjWPiUOgSNfQLdOKcMIbKH`IG_G\ EYEDXCBXDCWECVEDVFDUGETHESIFRJFQJGQTYPmYhlsekvcxH5\ pLIgPUZTfQXrUSmXNh_IcbDZe9UP7E800S7Bk9MxBXxNauYeph\ infcmeZkcTjbOhaIg_NeZUdYcXScQMcJHAQFEXDHcBLi9Op7Sw\ 5Vx4YiAMQFB6K5QQHiVXx_lx_mu_nu_oKGPLHOMHNNIMOILOJL\ PJKQKJRKISLHTLGTMFUMEVNEWODXPCYQBZRA_T9_V8`X8`Y7aY\ 6bY5cY5cY5dY5eY5eY5fY5fY5 } END PARAMETER FILE=========================================

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FOTD 10-10-11 (The Infinite Ocean [6])
by Jim Muth 11 Oct '11

11 Oct '11

FOTD -- October 10, 2011 (Rating 6) Fractal visionaries and enthusiasts: The rating of a 6 that I gave to today's image might be a bit conservative. The image trick is one I have often used before, and this repitition held down the rating a point or two. The outer shape is a Julia set of East Valley of the Z^(1.4142)+C Mandeloid. The chaotic stuff along the 'horizon' inside the Julia set is a grossly enlarged view of the north shore line of the East Valley, rotated so that its edge cuts straight and level across the scene. The sickle-shaped stuff scattered about the lower part of the Julia set is made of the same stuff fractal trees are made of. In fact, only a small tweaking of the parameters will produce a fractal tree. The name "The Infinite Ocean" means just what it implies. The number of fractals is infinite, and the individual fractals are also infinite. This produces a total of (infinity)*(infinity) possible fractals. But do not be too overwhelmed. Infinity multiplied by infinity is still infinity. (Infinity must be raised to the power of infinity to produce a higher infinity.) Today's image finishes on my 2000mhz machine in 13 minutes -- quite slow for an image with a rating of a 6. Visiting the web site defeats this slowness however. The official FOTD web site, now totally back up and running, may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The finished image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic FOTD site is at: <http://www.Nahee.com/FOTD/> The day began with fog here at Fractal Central. The fog lifted by 10am, but the sun was filtered by a veil of higher clouds for the rest of the day. The temperature of 75F 24C left nothing to be desired however. The fractal cats were exhausted by yesterday's boisterousness, and spent most of the day sleeping. The human beings, being human, did human things. The next FOTD, an abstract thing, will be posted in 24 hours. Until then, take care, and I really do enjoy the way this crazy world keeps getting crazier. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Infinite_Ocean { ; time=0:13:02.47-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t maxiter=100000 center-mag=-0.187793/0/0.8130081/1/-90/0 float=y params=89.99/0/89.99/-78.25/0.13/0.00037/0/0/\ 1.4142/0 inside=0 logmap=yes periodicity=10 colors=000D8JE9KFAMGBOHCQIDSJEUKFVLGWMHXNIYOJZPK_Q\ LaRMcRLdSLeSKfTJgTJgUKgUJgUJgVKgWLiXLkYMlZNmZQmZSl\ ZUj_YiY_hW`fTbeQddMebKgaGh`DhZAiY6kX2jY3kW3lU3lS3l\ Q3mP3nN3nL3nJ4nI4nG4nE4oC4oB4o94o74o54o43p83qC3qF3\ rJ3rN3sQ3sU3tY3t`3sd3rh3qk3oo3mr4jo4gm5ei5cf6ac6_a\ 7Y_7WZ8UX8SU9QS9OPAMNAKKBIIBGFCEDCDBDCDEDEFEFGFGHG\ HIHIJIKKJLLKMMLNNMOONPPORQPSRQTRRUSSVTTWUUYVUZWU_X\ U`YUaZVb_Vd`WeaXfbXgcYhdZidZidZjcYkbYkaXl`XlaXmbWm\ cWmcWncVncVocUocUocUpcTpcTqcTqcSqcSrcRrcRscSscTsbU\ taUt`Uu_UuZUuYUvXUvWUwVUwUUxTUySUzRUzQZzPZzOZzNZzM\ ZzLZzKZzJZzIZzHZzGZzFZzEZzDZzCZzBZzAcz9cz8cz7cz6cz\ 6cz6cz6cz6cz6cz6cz6cz6cz5cz5cz4cz4hz4hz3hz3hz3hz6h\ z8hzAhzAhzAhzAhzAhzAhzAhzAhzAhzAmzAmzAmzAmzAmzAmzA\ mzAmzAmzAmzAmzAmzAmzAmzAmzAmzArzArzArzArzArzArzArz\ ArzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAw\ zAwzAwzAwzAwzAwzAwzAwzAwz } 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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FOTD 09-10-11 (Julia in Mandelbrot [6])
by Jim Muth 11 Oct '11

11 Oct '11

FOTD -- October 09, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows Julia sets of a point on the west shore line of the large period-3 north bud of the Mandelbrot set. I say Julia *sets* because the image is filled with countless Julia sets. All the tiny orangish things spotting the deep blue background are smaller Julia sets. But don't bother checking them. They all appear the same as the large set filling the frame. The image is actually a scene in a 'perturbed' Mandelbrot set. The perturbed sets are slices through the Julibrot in the Mandelbrot orientation, but they have starting points other than 0,0. (For some reason, the type=mandel formula starts the points at the square root of the value assigned the parameters, but IMO, the formula is so fast that this is only a tiny, easily- worked-around flaw.) In this particular area of this particular perturbed set, the low-iteration stuff appears to be moth-eaten, filled with holes of varying size, while the high-iteration stuff remains mostly hidden beneath the low-iteration stuff, with only small patches showing through the moth-holes. The curious thing is that the moths who ate the holes were very well-educated, and ate holes in the shape of Julia sets. To see the true Julia set of this area, reset the parameters to 0,0 and, without waiting for the image to finish, strike the space bar twice. A skeletal Julia set will result. At this point, reset the logmap to 1 to see the surface Julia set or leave the logmap at minus-4375 and do an inzoom or two to reveal another version of the large Julia set that appears in today's FOTD lurking in the depths, just a bit too small to be visible at the surface. The name "Julia in Mandelbrot" accurately describes today's image. The rating of a 6 is a bit low to fully justify the 7-1/4 minutes required to run the parameter file. To avoid all this tedious calculation, check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Or check the high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Morning fog and afternoon sun earned mixed reviews for the weather in the Fractal Central area today. The temperature of 79F 26C was about as perfect as it can get however. The fractal cats were apparently energized by the perfection, and spent a good part of the afternoon playing hide and seek games on the book shelves in the hallway. The humans, who always knew the location of one another, spent the day dreaming of things to come, such as the next glorious FOTD, which will be posted in under 24 hours. Until then, take care, and from what I read in a magazine recently, the Limerick: A crusty old codger named bright, Could travel must faster than light. He took off one day, In a relative way, And came back on the previous night. just might be true. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Julia_in_Mandlbrot { ; time=0:07:16.13-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.2176\ 546382061398/+0.7252284839096655/6.042805e+009/1/\ -145/0 params=-0.984435560167241/-0.220313119907224 float=y maxiter=2500000 bailout=9 inside=255 logmap=-4375 periodicity=0 colors=00055H55H56H45H46H45H36H35H36H36H26H26H25H1\ 5H14H14H14H45J76LA7NC8PF9RIATLBVNBWMCVLCVKDVJDVIEU\ IEUHFUGFUFGTEGTDHTDHTCISBISAJSbSDcRCdQCdPCePCeOBfN\ BgMBgMBhLAhKAiKAjJAjIAkH9kH9lG9mF9mE8nE8nD8oC8oC8p\ D9pD9pE9pE9pF9pF9pF9pG9pG9pH9pHApIApIApIApJApJApKA\ pKApKApLApLApMBpMBpNBpNBpNBpOBpOBpPBpPBpPBpQCpQCpR\ CpRCpSCpSCpSCpTCpTCpUCpUCpVDpVDpVDpWDpWDpXDpXDpXDp\ YDpYDpZEpZEp_Ep_Ep_Ep`Ep`EpaEpaEpaEpbEpbFpcFpcFpdF\ pdFpdFpeFpeFpfFpfFpgGpgGpgGphGphGpiGpiGpiGqjGrjGsk\ GtkHulHvlHwlHxmHymHznHznHznHzoHzoIzpIzpIzqIzqIzqKz\ rKzrIzsKzsKzsKztUzuUzvUzwUzxUzyUzzUzzczzczzczzczzc\ zzczzczzczzczzczzczzczzczzczzczzczzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzwzzwzzwzzwzzwzzwz\ zwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzw\ zzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzz\ wzzwzzwzzwzzwzzwzzwzzwzzw } END PARAMETER FILE=========================================

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FOTD 08-10-11 (Deep-Purple Scene [minus 6])
by Jim Muth 09 Oct '11

09 Oct '11

FOTD -- October 08, 2011 (Rating minus 6) Fractal visionaries and enthusiasts: Today's image is not as bad as its rating would suggest. The image has a negative rating of -6 because it's a negative image. Most fractals, with their bright pinks and yellows, produce a feeling of positivity and elation; but today's image, with its somber blues and purples, creates a feeling of negativity and depression, thus the negative rating. The name "Deep-Purple Scene" describes the image quite thoroughly. The depression the image evokes is due to the colors. With more cheerful colors, the image would be not at all depressing. The image is simply a near-Julia set of a point in the north branch of Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set. It is only a 'near' Julia set because the Julibrot slice is double rotated 0.2,0.2 degrees from the true Julia direction. It is impossible to imagine such a double rotation, but by actually doing the rotations, one can observe that the double rotation does exist. The somber deep blue wedge slicing through the middle of the open Julia shape is actually a grossly enlarged view of the Mandelbrot aspect of the area. It is possible to enlarge the 4-D Mandelbrot shapes to infinity because the stuff Mandelbrot shapes are made of is compact in the Mandelbrot 'C' planes but extends to infinity in the Julia 'Z' planes. The calculation time of 3-3/4 minutes is perhaps a high price to pay for such a downer of an image. Once again, thank goodness for the FOTD web site, which I believe is back in action again. The official FOTD web site 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 original FOTD web site is at: <http://www.Nahee.com/FOTD/> After a gray and foggy start, today turned into near perfection here at Fractal Central. The sun shone constantly, while the temperature reached 72F 22C, which made the fractal cats happy and sent them scrambling to their sunny shelf in the southwest window. With the real work winding down, the humans took it easy doing other things. The next FOTD is due to be posted in 24 hours, but from the way things have been going lately, I would not be surprised if it was sooner or later. Until whenever, take care, and there's a new world coming, where time travel into the past is an everyday reality. (Want to bet?) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Deep-Purple_Scene { ; time=0:03:42.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=t center-mag=0/0/6.666667 params=89.8/0/89.8/120/\ -1.7685524/0.0008063/0/0 float=y maxiter=16000 inside=0 logmap=6 periodicity=0 colors=000002002002003113223335447859A6BC7DD7EF8GH\ 9IJAKLBMNCOOCPQDRSETUFVWGXYHZZH_`IabJcdKefLghMiiMj\ kNlmOnoPpqQrsRttRurTtpUtnVtlWtkXtiZtg_te`tcatbbt`c\ tZesXfsWgsUhsSisQjsOlsNmsLnsJosHpsGqsHpqIooJnmKmkL\ liMkgNjeOicPhaQg_RfYSeXTdXUcYVcZWcZXc_Yc`Zc`_ca`ca\ acbbbcbacb`dc_ecZecYfcXfdWgdVhdUhdTieUjeUjeUkeVkfV\ lfVmfWmfWngWogXogXphYqgXpgXpgXpfYpfYpfYoeYoeZoeZoe\ _odZod_nd_nc_nc_nc_nb_nb_mb_mb`ma`ma_ma`m``l``l`al\ ``l``laalaakabkbckdckddkfdkfejedkbej`fjZdjWbiW_iWZ\ iVXiVWiVViUVhUVhUUhUUhTThTShTRgSPgSOgSNgRNgRNgRNfR\ MfQMfQMfQMfPMfPLePLeOLeOLeOLePMdOLeOLeOLeOLfNLfNLf\ NKgNKgNKgMKhMKhMKhMJiMJiLJiLJjLJjLHjLHkKHkKHkKHkKH\ lKHlJGlJGmJGmJFmJFnIFnIEnIGoICoIAoHApHApHApHAqHAqG\ AqGArGArGArFAqGArGArGArGArGArG0rG0rG0sG0sG0sG0sG0s\ G0sG0sG0tG0tG0tG0tG0tG0tG0tG0tG0uG0uG0uG0uG0uG0uG0\ uG0vG0vG0vG0vH0vH0vH0vH0v } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 07-10-11 (The Forgotten Sets [7])
by Jim Muth 08 Oct '11

08 Oct '11

FOTD -- October 07, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows one of the forgotten sets -- those that lie in the Julibrot at orientations other than the Julia or Mandelbrot. Today's image happens to lie in the Oblate direction, which is determined by the imag(c) and real(z) axes of the Julibrot, and is a name of my own invention. The image is a sideways view of Seahorse Valley of the large minibrot on the main spike of the largest minibrot on the main spike of the Mandelbrot set. The scene is not centered in the Mandelbrot plane however. It is located at a distance of -1.786117 in the real(z) direction, which means it is part of the shadow M-set, a phantom set with a linear size 1.4142 times that of the classic M-set. The name "The Forgotten Sets" gives recognition to the sets in the four odd planes of the Julibrot figure, as well as those in the countless rotations. In fact, calling these things 'sets' is basically a mistake. All Z^2+C fractals including the Mandelbrot set are mere 2-D slices through a far more monstrous figure -- the 4-D Julibrot. The rating of a 7 is getting to be boring, but I must rate the fractals as I see them, and today's impresses me as being of only average quality for a FOTD. The calculation time of 54 seconds will pass quickly, even though not in a flash. If the official FOTD web site host can recover from the hack attack, the finished image will soon be posted at: <http://www.crosscanpuzzles.com/Archives.html> It will also be posted, and in high definition at that, at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original and now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> Absolute perfection prevailed here at Fractal Central today. Both the humans and the fractal cats agreed, enjoying the day as much as possible. With a large anticyclone, (one of those things with an 'H' in the center that the TV weather people put on their maps), parked right overhead, not a single cloud was seen and the temperature reached a very pleasant 68F 20C. The next FOTD will be posted in 24 hours. Until then, take care, and if neutrinos really do exceed the speed of light as claimed in a recent issue of 'Time' Magazine, what would happen if we sent a burst of them to the moon, where they would be reflected back to earth? As I see it, they would return a few seconds before they were sent and could then trigger a device that would cause them not to be sent out in the first place. Faster-than-light neutrinos would also give a glimmer of scientific respect to the paranormal claim of precognition, a currently 'impossible' thing that I already know does in fact exist. This does not imply that I put faith in the ramblings of Madam Zucchini, the fortune teller down at the corner. But it does mean I am convinced that, in some strange way, the future may affect the past, thus violating the law of causality. If this makes me a superstitious true-believer in the paranormal, so be it. Now it's time for the useless information of the day. The formula for the hypervolume of the curved 5-D hypersurface of a 6-D hypersphere is very simple -- (pi^3)*(radius^5). Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Forgotten_Sets { ; time=0:00:54.82-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 periodicity=6 center-mag=+0.00010515898520233/0/3801.206/1.2576 params=0/0/90/0/-1.786117/0/-1.786117/0 float=y maxiter=12000 inside=0 logmap=27 symmetry=xaxis colors=000B1QC2QD3QD4RE5RF6SF7SG8TG9THAUIBVICWJDXK\ EYKFZLG_LH`NIaOIbPIcQJcSJcTJcUJcVKcWKcYKcZLc_Mc`Nc\ aNccObdPaePcfQehPfiQgjRgkRglRgmRhmRhmRhmShmSimSimS\ ilSikSijSjiTjhTjgTjfTkeTkdTkcTkcUmbTkbSiaSgaRf`Qd`\ Qb_P`ZP_YOYWNWUNUSMTRLRQLPPKNOKONKMMILLGKKEJJCIIAH\ H8GE6FE4EF8FFBGFFHFIIGLJGPKGSLGVMHZNHaOHdPHhQIkRIn\ SIrTIuUJzVIxUIwUHuUHtTGrTGqTGpTFnSFmSEkSEjSEiRDgRD\ fRCdQCcQCbQB`QB_PAYPAXP9UOAWPBXQCYRD_SD`TEaUFcVGdW\ HeXHgYIhZJi_Kk`LlbLmdMofNphOqjOrlLngJlcHi`FgXCcUA`\ Q8YN6WK8XJ9ZKA_LBaMCbNDcOEdPFfQGgRHhSIjTKjULkVMlWO\ mXQnYSoZUo_Wp`YqaZrb_sc`scarcbqdcp_doOenKfmFfmAgm7\ hm7im8jm8mm9rm9vmAzmAzmBzmBzmCzmBzmCzmDzmDzmEzmEzr\ FzrGzrGzrHzrHzrGzrGzrFzrFzwEzzEzzDzzDzzCzzCzzBzzBz\ zAzzAzz9zz9zz8zz8zz7zz7zz6zz6zzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 06-10-11 (A Seahorse Goes East [7])
by Jim Muth 07 Oct '11

07 Oct '11

FOTD -- October 06, 2011 (Rating 7) Fractal visionaries and enthusiasts: In today's FOTD we see the scene I was searching for yesterday when the fractal ship showed up. I named the image "A Seahorse Goes East" because it combines the features of Seahorse Valley with those of East Valley. The outer parts of the scene are clearly of an East Valley nature, while the inner parts reflect the appearance of Seahorse Valley when sliced in the Oblate direction, which is determined by the imag(c) and real(z) axes. The entire image is distorted into a vague triangular shape because it lies at an odd angle in the 4-D Julibrot figure. (As a matter of curiosity, in the German language, the word 'julibrot' means 'bread of July'.) Unlike yesterday's image, which was stretched and skewed beyond verbal description, today's image was stretched only a modest 3-1/2 times in the horizontal direction. The value assigned the real(p4) parameter, which sets real(z) is equal to the real(c) value of the scene in the M-set. This places the actual location of the scene in what I call the shadow Mandelbrot set, a second Mandelbrot set lurking unsuspected at an angle of 45,45 degrees in the Z^2+C Julibrot. The rating of a 7 is an improvement over yesterday's miserable rating of 4, but still leaves plenty room for yet more improvement. The calculation time of a mere 24 seconds will make running the parameter file a breeze. The task of setting up and running the file may be avoided by viewing the image on the web site. The finished image should soon be posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> I said 'should be posted' because the last time I checked, the site was refusing access due to a hack attack. The image is also posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> in high definition. The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Strange as it might seem, as the number of hypercube dimensions increases, its diagonal approaches infinity, while the hypervolume of the inscribed hypersphere approaches zero percent of that of the hypercube. BTW, the formula for the hypervolume of a six-dimensional hypersphere is 1/6(pi^3)*(r^6). Not a single cloud spoiled the blueness of the sky over Fractal Central today. The sunrise temperature of 36F +2C was rather chilly, but the unbroken sunshine brought the afternoon tempera- ture to a pleasant 66F 19C, while the near calm winds made the day as close to ideal as we have had in two months. And the best part is that the near perfect conditions are expected to prevail for a week. The fractal cats, always seeking perfection, found it on their shelf in the sunny southwest window. The humans, realizing that perfection never happens, took the day for what it had to offer. The next FOTD will be posted in 24 hours. Until then, take care, and I agree with the angry young protesters. We should abolish poverty. But does anyone know how we might bring about this utopian dream? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_SeahorseGoesEast { ; time=0:00:24.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/\ +0.0000003835126177/419409.6/3.4337 params=0/90/0/90/-1.747855067330428/0/-1.747855067\ 330428/0 float=y maxiter=32767 inside=255 logmap=99 symmetry=yaxis periodicity=6 colors=00010S20U30W40Y50_60a70c80e90gA0iA0kA1lC2mE\ 3nH4oJ4pH4oE4mB4j84g84c84_84W75S75P75L64U53c42m3Lu\ cOzclLhsHmzDrz9wzBzzBzzzO7LNAQLDVKG_IJdHMiJQjKTjLW\ jM_jNbjOejPijQljRojSsjTvjUyjXrl_knadpdYr_qNYjPWcSU\ XUSQWQJZOC`oC1E3WM5bU6ia8pi9waJrVTnNajGkf6x_9tbBqe\ DnhFkkHhnLZpJeqHkqFrqExqPng_eZjXQjYOjYMjYKjYJjYHjY\ FxR5qVAjYEsfQkcMc`IWYEOVAGS61dv5XU8Q2FP6LO9SNCYMFd\ LIjKLaOOUSQLWS7aWA`VD_UF_TIZSLYRHfIKaMNYQKZaPWaTTa\ YQaaNa`Q_dXfibmmhsrnzpzzvtzowzpqzmttjopgjodgqaekZb\ iW`gTZeP`gQXdRTbSQ`TMYUJWVFUVCS_HLcDGg9Bk56n12k54i\ 95fD7dH8bLA_PBYTDVXET`GRdHJWFCNE5ED0T`1XY1_V1bT1eQ\ 1hO5kLAnJFqGKtEPwBUz9Zx8cwAhv7mu7mt7ms6mr6oq5qp5so\ 5un4wm4xl4zk5zk5zk6zj6vj6rj7mi7mi7mi8mh8mh9mh9mg9m\ gAmgAmgAmc8m_7mW6mS5mP4mL3lH2rD1xA0eBDOCQ6CaDKaKRa\ RYaYdadkajraksdltfmuhnvjowlpxnqyprzjszdtz_uzXvz_wz\ bxzeyzhzzkzznzzqzztzzw000 } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 05-10-11 (The flying Titanic [Rating 4])
by Jim Muth 06 Oct '11

06 Oct '11

FOTD -- October 05, 2011 (Rating 4) Fractal visionaries and enthusiasts: Today's image rates only a 4, hardly up to FOTD standards, but the scene is so funny that I felt obliged to make it FOTD for today. To me the scene shows the ghost of the long-lost ship HMS 'Titanic', barely visible through the mists, sailing calmly over some far-away heavenly sea. Unlike that other ghost ship, the 'Dutchman', a sighting of this ship does not portend disaster. It is an omen of good fortune. The name "The Flying Titanic" gives recognition to both ghost ships. (Well, maybe the ship in today's image does resemble something more like a small destroyer than a mighty ocean liner, but at least it's something better than a tugboat.) The scene is located in the East Valley area of the large minibrot on the main stem of the Mandelbrot set. It is oriented in 4-D space at an angle that would be impossible to describe, and is stretched and skewed beyond imagining, yet here it is, a very recognizable image of a ghostly ship passing silently in the night fog. The image is an example of serendipity. When I stumbled upon the hole that resembles a ship, I was searching for something entirely different. I still am searching in fact, and if I find it, I will make it tomorrow's FOTD. Today's image finishes in 6-2/3 minutes, a little on the slow side for a scene that rates an unusually humble 4. But this is where the FOTD web site comes to the rescue. The web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> The space of four dimensions, in which this month's featured fractal object, the Julibrot, lies, is curious in many ways, especially when compared to space of three dimensions. In 3-D space only five regular polyhedrons, the five Platonic solids, are possible: the tetrahedron, with four triangles as faces; the cube, with six squares as faces; the octahedron, with eight triangles as faces; the dodecahedron, with twelve pentagons as faces; and the icosahedron, with twenty triangles as faces. And in space of five dimensions as well as spaces of all higher dimensions, the increasing numbers of lower dimensional elements usually do not match up correctly, and only three regular figures now called polytopes are possible. These are the analogs of the tetrahedron, cube and octahedron. So what about space of four dimensions? Intuition suggests that also in 4-D space, only three regular polytopes are possible, just as in spaces of all higher dimensions. But in this case intuition is wrong. In space of four dimensions, where the polytopes are bounded by three- dimensional boundaries called cells, six regular polytopes are possible: the hyper-tetrahedron, bounded by five tetrahedrons; the hyper-cube, (sometimes called the tesseract), bounded by eight cubes; the hyper-octahedron, bounded by sixteen tetrahedrons; the hyper-dodecahedron, bounded by 120 dodecahedrons; and the hyper-icosahedron, bounded by 600 tetrahedrons. There is also a figure bounded by 24 octahedrons, which has no regular analog in 3-D space, but is related to the semi-regular rhombic dodecahedron. So what would life be like in 4-D space, living on a hyperspherical planet most likely subject to a dizzying double rotation? Would the stars in the 3-D sky trace out helixes? Unfortunately, no such planet would be possible. In 4-D space the force of gravity would obey an inverse-cube law, making stable planetary orbits impossible. A planet would either quickly spiral into its star or sail off into interstellar space. So much for fantasy. The weather here at Fractal Central today was certainly no fantasy. We enjoyed cloudless skies and a temperature of 70F 21C. The fractal cats, now settling into winter mode, found comfort on their shelf in the sunny southwest window. The humans, FL and I, found comfort in the bright sunlight streaming through the windows, which has been pretty scarce the past couple months. Even more comfort will be found when the next FOTD is found and delivered, hopefully in 24 hours. Until then, take care, and the formula for the hypervolome of a five-dimensional hypersphere is 8/15*(pi^2)(r^5). Let me know when this useless bit of information might become important. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Flying_Titanic { ; time=0:06:39.42-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.00048410686492484/+0.089235490629652\ 03/262770.2/0.00651/-90/89.1258940753795486 params=30/90/0/90/-1.7489/0/0/0 float=y maxiter=4200 inside=atan logmap=206 periodicity=6 colors=000GJV_5W_AZ_Ca_Ca_D`_D`_D_ZEZZEZYFYXFYWGXW\ GWVGWUHVTHVTIUSITRITRJSQJSPKROKQOLQNLPMLPLMOLMNKNN\ JNMDONFOMHOMJNMLOMNOMPPMRPMTQLVRLXRLZSL_SLXTMUPORK\ QMJSKKUNKTQKSTOQWTOZWMaXKdYJgYIjZHk_Hm`Gp`FsaEtbDt\ cDtcCtdBueAue9uf9vg8vh7vh6wi5wj5wk4xk3xl2xm1xm1wl2\ wl2vk2vk2uk2uj2tj2tj3si3si3rh3rh3qh3qg3pg3pg4of4of\ 4ne4ne4me4md4md4ld5lc5kc5kc5jb5jb5ia5ia6ha6h`6g`6g\ `6f_6f_6eZ6eZ7dZ7dY7cY7cY7bX7bX7fU0dW4bX7`ZAZ_EY`H\ WbKUcOSeRQfUPgYNi`LjcJlgHmjBsnDqmEpmGnmHmmIkmKjmLi\ mMgmOfmPdmRcmSbmT`mV_mWYmXXmZVm_UmaTmbRmcQmeOmfNmi\ KphLohLngMmgMlgMkfNjfNifNheOgeOgeOfdPedPddPccQbcQa\ bR`bR_bR_aSZaSYaSX`TW`TV`TU_UT_US_USZUXYUaYUfXU`XU\ WWUQWULVUFUUAUU5UUAUUFUUKUUPUUUUUVUUWUUXUUYUUZUU_U\ U`UUaUUbUUcUUdUUdUUcUUbUUaUU`FU`EU_DUZCUYBUYAUXAUW\ AUVAUVAUTAUSAURAUPAUOAUNAUMAUPAUSAUVAUYAU`AUcAUeAU\ cAUbAUaAU`AU_AUZAUXAUdAUd } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 04-10-11 (Seeing the Light [Rating 6])
by Jim Muth 04 Oct '11

04 Oct '11

FOTD -- October 04, 2011 (6) Fractal visionaries and enthusiasts: A sudden rush descended on FC today, leaving little time for serious fractaling. But the image I found in a hurry is worth at least a cursory look. Today's image takes us to the valley around -1.399 on the negative X-axis of the Mandelbrot set. This is the third valley beyond Scepter Valley. But just to be different, we check the Rectangular aspect of the valley instead of the Mandelbrot aspect, and find today's scene. I named the image "Seeing the Light". The name was inspired by the brilliant white vertical stripe in the center of the image, which is made even more brilliant by the globules spread along it. Having too little time to work on the coloring, I could give the image a rating no higher than a 6. And its calculation time of almost 7 minutes is a bit much to ask for the privelige of viewing an image that rates a mediocre 6. Luckily, the FOTD web site has come to the rescue. The finshed 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 original FOTD web site is at: <http://www.Nahee.com/FOTD/> After a light early-morning sprinkle, the sky brightened today here at Fractal Central. The sun even made a few brief appearances, but it was hardly a sunny day. The fractal cats took the temperature of 66F 19C in stride, giving more attention to the catnip frog that somehow got pulled out from under the book shelves than to the outside weather. FL and I, never fully agreeing on politics, got into a lunch time discussion about the political views of the extreme left and right, with nothing at all being settled between us. (These mildly heated discussions have been going on for many years, and nothing has been settled yet.) One thing firmly settled however is that the next FOTD adventure into the 4th dimension will be posted in 24 hours, when I will begin discussing the six regular polytopes that are possible in four dimensions. Until then, take care, and I know that my political views are correct, but why can't the rest of the world see it? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Seeing_the_Light { ; time=0:06:52.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0/\ -0.02922557903896763/256.4055/4.7933 params=90/90/\ 0/90/-1.399631247361716/0/0/0 float=y maxiter=75000 inside=255 logmap=87 symmetry=yaxis periodicity=6 colors=000HNcHNcHNbHNbHNbHNbHNaHNaHNaHNaHO`HO`HO`H\ O`HP_IP`IQ`IQaIRaJRbJSbJScJTcKTdKUdKUeKVeLVfLWfLWf\ LXgLXgMYhMYiMZjMZkN_lN_mN`nN`oOapOaqObrObsOctPcuPc\ vPcwPcwQdwQdzQdzQdzRezRezRezRezQfzRezRezRezRezRezR\ gzRgzRhzSgzShzShzShzShzShzShzShzThzThzThzThzThzTez\ TezTezUezUezUezUezUezUezUezXezWfzXhzYhzZhz_hz`hiah\ kbhochschwdhwdhwehweiwfiwfjwgjwgkwhkwhlwilwjmmkmml\ mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm\ mmmmmmmmmhhmccmZZmUUmPRmKOkFNiANg5Me5Mc5Lc5Lc5Kc5K\ c5Ja6J`6I`6I`6H`6G`6Fa6Ea6Da6Cb69b7Ab79b78a77`76_7\ 5Z74Y73X72W71V90UB0TD0SF0RH0XJ0VL0TM0RN5POANPFLQGJ\ SHHUHFVIDWIBWJ9WK1XL4YM6ZN8_OA`PCaSEbVGcYId`KecMff\ OgcaheYigUjiQkkMlmJmoFnqBos7pv3qw4rx4sy4tz4vz4xz4z\ z4zz4zz4zz4zz5zz5zz5zz5wz5wz5rz5rzArzFrzKrzPqzUqzX\ pz_pzbpzepzhozkoznozqoztozwmzzmzzmzznzzozzpzzqzzrz\ zszztzzuzzvzzwzzxzzyzzzzz } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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My last relative rational
by Sebastien helie 04 Oct '11

04 Oct '11

Relative rational is how i caracterise a fractal when i could establish relation with the real world Another of my beginning has a parser, make me think of a element to play chess with.(do not know the word in english in french a Pion). If you play with parameter, you see appear something like a party hat. Thru my history study, cause i do study on the side, i could see a parallel to the half god hat used in a foreigne time in china and preist now.Expose in chicago in febuary 2010, where asia was present with those element (do not know if it's general exbition), Still Museum in chicago are free in febuary...for those who like free world?!. .I encounter often parallel in the religious industry with their logo and uniform math been used.I think it's far from being possible to put to whole world of number on a single individual, mandelbrot might has a form carry the number univers, and even then, their is lot's of different element present. Since it have no mass, and no weight, their's is a long story in the understanding of the whole and lot's of problem, and without pairs it by far impossible to understand... Discuss the unik with a preist if you feel like loosing time?!? LET'S PRAY Oh great black egg's.....among all other black egg's....YOUR THE BLACK EGG'S.. one must in french... "oeuf noir" sound like bad, when Black egg's sound like funny? (french--english) Half hat { reset=2000 type=formula formulafile=dsystem1.frm formulaname=chapeau center-mag=-1.64e-006/2.205e-006/0.6666676 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } Pion{;sinpix12823 z= pixel: z= z^(z-1)*z^(z-2) |z|<4 }

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FOTD 03-10-11 (Royal Scepter [No Rating])
by Jim Muth 04 Oct '11

04 Oct '11

FOTD -- October 03, 2011 (Rating 7) Fractal visionaries and enthusiasts: With today's FOTD we find ourselves roaming once again in four- dimensional hyperspace, as we will be all the month of October. Every image this month will be created with the Mandelbrot expression, Z^2+C, but none of the images will resemble the usual Mandelbrot or Julia scenes. Today's image is a view of Scepter Valley, which is the valley at -1.25 on the negative X-axis of the Mandelbrot set. This is the inspiration for the name "Royal Scepter", though the image looks nothing at all like the Mandelbrot or Julia aspects of Scepter Valley. The scene is sliced at an odd angle oriented 75 degrees from the Rectangular direction toward the Julia direction of the Julibrot figure. The brilliant pink vertical stripe in the center of the image is part of the open space between the two branches of the valley, viewed from the side. Though the mathematical interest rates higher than usual in today's image, I could find nothing of artistic value in it that might raise the rating above that of an average 7. I did spend some extra time on the coloring however. In 4-D space, such as the space in which the Julibrot figure lies, there are six perpendicular planes through every point. Every plane is perpendicular in the normal 3-D manner (intersecting in a line) to four other planes, and absolutely perpendicular (intersecting in only a single point) to one other plane. In the Julibrot the absolutely perpendicular pairs of planes are Mandelbrot-Julia, Rectangular-Parabolic, and Oblate-Elliptic. All other pairs of planes lie in the same 3-space and are perpendicular in the normal 3-D manner. Today's image is oriented between the Rectangular and Julia directions, which implies that the rotation is of the normal 3-D kind. In this case, the axis of rotation is the imag(z) line that intersects the M-set at -1.25 of the X-axis. In today's image, the rotation may be seen in progress by varying the real(p2) parameter between zero and 90, which takes us on a trip from the Rectangular to the Julia directions. But be warned, the calculation time increases dramatically as the value of real(p2) gets close to 90. The higher dimensions have always been a mystery, but over the years I have come to see 3-D space as a construct of the mind, and also as an indicator of our level of consciousness. We can not imagine spaces of four or more dimensions because we have not yet reached a level of consciousness where it is possible. Will the human race eventually evolve to a level where higher spatial dimensions are within our grasp? Will we then find ourselves in a world with four or more spatial dimensions? Physicists tell us that the higher dimensions (11 at the latest count) are there, but we cannot percieve them. If this is so, who knows what mysteries the universe yet holds. These questions will not be answered in today's image, but the image does calculate in only one brief minute. The image will make the questions just a bit more significant however. The inconvenience of calculating a parameter file may be avoided by viewing the completed image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image may be enjoyed in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be perused at: <http://www.Nahee.com/FOTD/> Heavy clouds continued here at Fractal Central today, with a very autumnal temperature of 54F 12C. The fractal cats, solidly in cold weather mode, spent the day doing warm things such as curling up on the blankets. FL and I, the local humans, spent the day keeping things running, which is not always as simple as it first appears. The next FOTD will be posted in 24 hours. Who knows where in the Z^2+C Julibrot figure we might find ourselves tomorrow, or what we might find there. Until then, take care, and is three- dimensional physical reality really real? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Royal_Scepter { ; time=0:01:01.24-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0/0.0169994/\ 2.456186/1.1123 params=90/0/75/90/-1.25/0/0/0 float=y maxiter=50000 inside=255 logmap=3 symmetry=yaxis periodicity=0 colors=000agobgocgodgoegnfgmggmhfmgfmgemfdmdcmbaj`\ _gZYcVW_RTWOPSLMOIJLFGHCDE9AA67734334635936C38F3AK\ 3CO3ES3GW3I_4Lc4Nf4Qi4Sl4Xo4Zr4au4bx4dz9dzDdzIczMb\ zR_zQYzPWzOUxNRvMOtMOqNOoNOnNOmOOlOOkPOjPNiPNhQMgQ\ LfRLeRLdSKcSKbSKaTJ`TJ_UJ_UIZUIZVIYVIYWJXWIXXIXXJW\ XJWYJVYKVZKUZKUZLU_LT_LT_MT`MS`MS`MRaMRaLRbLQbLQcK\ PcKPcKOdKOdKOeKNeKNeKMfKMfKLgKLgKKhKKhKKhKJiJJiJIj\ IIjIHjHHkHHkGGlGGlFFlFFmFEmFEnGEnIDoKDoMCoOCpPBpQB\ qRBqSAqTArU9rW9sY8s_8sa3sb4sZ4oU4kP4iK4iF4iA4i85i8\ 5i95i95iA5iA5iA5iB6iB6iC6nC6nD6nD6nD6nE7nE7nF7nF7n\ G7nG7nG7nH8nH8nI8nI8nJ8nJAr9FsAKsAPsAUsAZsAcsAhsBm\ sBrsBvsBzsBzsBzsCzsCzsCzsCzsCzsCzsDzsDzsDzsDzsDzsD\ zsEzsEzsEzsEzsEzsEzsFzsFzsFzsFzsFzsFzsGzsGzsGzsLzs\ LzsLzsMzsMzsMzsMzsMzsMzsNzsNztUzuUzvUzwUzxUzyUzzUz\ zUzzZzzZzzZzzZzzZzzZzzZzzZzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczxbx } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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JOTD, fr E.T
by Sebastien helie 02 Oct '11

02 Oct '11

Since E.T is the first movie i see, i always had a special relation with him (by concept). Has a child i become facinated by cinema, and i took the big sceen image more seriously than other. At 23 year old we been told so many time that a movie is not the thrut that i did'nt think about him anymore, then i find my first comic book of him. A scene where fat ET give mathematic course to kid, i took him so seriously that i use has ritual the bagging my head on the hard cover of the book before every integration on my computer.. so forth the development of my theory was going on for good, and the exploration of the tank initial dos video game also. One of those first Hit whas eta-carinea-m{;sinpix12823 z=pixel z=(0.615/flip(0.5135+z)*2.456/flip(4.565-z)-fn1(3.1416/z))/z |z|<4 } it blue screen virgin but you just have to push Y and tweek with parameter to see a ET head with bird pattern appear, i leave it to your discretion. You can imagine this euphoria at the time primary, i was going on and for good with him i taught. Then thru my tank video game, i'v been agressed by a virtual image of him!! the environment i was living become really strange and outside i could by night see color line between star?!I was so insuted by this agression that I have no comment about what i was wittnessing, in the way that i was unable to fixe a point of view on how my ET was going else than he cannot see the difference beteween a video game and the thruth !!. Then come my first real thru mistake (70% error).I start to attack it also on another video game, until most of my room electronic burn off, he become present in audio wall sounding like a monkey who attack.... E.E and e... At this time in the summer i do brushing in forestry, a really agressive job who only have good result for nature, and then come my first normal sight of him in the distance. Tell you the thruth i bend on my knee like a wolf and put my head on the floor, the pressure was everywhere, after this i was feeling like somebody who did a overdose of Nitroglycerine, funny it's the only way i have to descibe this moment, even in french. Clone war? ET call now Tutu and Eta-carinea star have only one thru war at this level. It's a pattern of emotional division, where subject in love together, get split appart. We considere that it's not to stimulate but nature rule down this world so, only futur can tell. For the rest i should keep quiet cause the rest of the story is almost everyday of my life and it's 6 year away.. --------------------------------------------------------------------------------- Te net FOTD ill be hosted in 24 ours. Util ten, tae are, and physicists ell us tee is an electromagnetic field, a gravitational field, a weak field, a strong field, probably a His field, plus rious other fields, but why have they not mentioned a consciousness field? Te neurons of the bin might be the particle aspect. --------------------------------------------------------------------------------- i like to laught about myself and other, see me like a clown, not a bad one and not a good one, just a clown thru internet. We communicator have sometime foolish way to communicate. I do like to be judge before any posted message, the quality of my english will had become, but i never find such thing.. anyway have a good sunday.

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FOTD 01-10-11 (The Fourth Dimension [8.5])
by Jim Muth 02 Oct '11

02 Oct '11

FOTD -- October 01, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: I have decided to make the fourth dimension the FOTD theme of the month for October. 4-D hyperspace is not that much of a departure from the 3-D space we are so familiar with, since the Z^2+C Julibrot, (the composite of all the Julia and Mandelbrot sets), is a 4-D figure anyway. Today's image shows a small part of the shore line of the period-4 bud that lies on the northeast lobe of the main bay of the Mandelbrot set. Actually, the scene shows a section of the shore-line as it extends into hyperspace The entire scene has been stretched by a factor of over 57, (the tangent of 89 to be exact), in the direction of the Mandelbrot Y-axis. This stretching was necessary to keep the Mandelbrot ghost buds in their normal near circular shape as the view was rotated from the Mandelbrot orientation to within one degree of the Oblate orientation. The result of all this stretching and the additional skewing that resulted from rotating the image is a scene that vaguely resembles a scene on an alien planet with wispy cirrus-like clouds in the sky. I could have given the image a name such as 'Alien Cirrus' but I decided to name it simply "The Fourth Dimension", which quite nicely leads off a month that will be devoted to Julibrot scenes in 4-D hyperspace and hyper-objects such as the six regular 4-D polytopes. The extra half-point in the rating of 8-1/2 is due to the coloring. My modesty prevents me from granting myself any additional bonus points, even though they were deserved. The calculation time of 13-1/2 minutes is somewhat slow, leaving it to the individual fractalist to decide whether the 4-D scene is worth the wait. To avoid calculation altogether check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check it in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic, FOTD web site may be reached at: <http://www.Nahee.com/FOTD/> Today's weather left much to be desired here at Fractal Central. The fractal cats felt that the temperature of 52F 11C was too chilly for comfort, while FL and myself felt that the heavy clouds that blocked the sun and the occasional rain that fell through the day were too unpleasant for the first day of October, which is supposed to bring bright blue weather. The next FOTD will be posted in 24 hours. Until then, take care, and the formula for the hypervolume of a 4-dimensional hypersphere is 1/2(pi^2)*(r^4). How long will it be until someone other than a physicist actually needs this formula? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= TheFourthDimension { ; time=0:13:38.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=t center-mag=-0.09254657031508136/+0.561631274103498\ 60/855.02/0.03822/-1.073/-87.9929489969829319 params=0/0/89/0/0.25/0/0/0 float=y maxiter=125000 inside=255 logmap=140 periodicity=6 colors=000UizUhzUgzUfzUezUdzUczUbzUazU`zU_zU`zUazU\ bzUczVdzWezVfzWgzVhzUizThzShzRgzRfzRezQdzQczPczPcz\ OczOczNczNczNczLczLdyJdxJdwHevIeuFetEfsEfrDfqDgpCg\ oCgoBhpBhqAirAisAit9ju9jv8jw8kx7ky7kz6lz6lz4kz5iz6\ gz6fz7ez8ez8dz9cz9czAdzBdyBdyCdxCdxDcxEbwEawFavF`v\ G_vHZuHYuIYtIXtJWsKVsKVsLUrLTrMSrNSsNRtOQuOPvPPyQO\ zQNzRTzRSzSSzSRzSPzSOzSNzSMzSLzSLySLxSLwSLvSLuSLsS\ LqSLqSLqSLqSLqSLqSLqSLqSLpSLoSLnSLmSLlTLkTLjTLiTLh\ TLgTLfTLeTLdTLcTLcTLbTLbTLbTLaTLaTLaTLaTLaULbVLcWL\ dXLeYLfZLg_Lh`LiaLjbLkcLldLmeLnfLogLphLqiKsiKtjKuj\ KvkKwkKxlKylKzmKzmKznKznKzoKzoKzpKzpKzqKzqKzqKzrKz\ rKzsKzsKztKztKzuKzuKzvKzvKzwKzwKzyKzyKzyKzyKzyKzyL\ zyMzyMzzNzzNzzOzzOzzPzzQzzQzzRzzRzzSzzSzzTzzUzzVzz\ WzzWzzXzzYzzYzzZzz_zzazzazzbzzbzzdzzdzzezzfzzfzzgz\ zgzzhzzizzjzzjzzkzzlzzlzzmzzmzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzznzznzzozzpzzpz00H } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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a non calculated frame for you (s)
by Sebastien helie 01 Oct '11

01 Oct '11

Inter{;sinpix12823, not parsed at home z=pixel: x=sin(45)*z y=0.14*sin(45)*x*z+c z=z+x+y+c+pixel ; use *-/ also }____Formulae must stay has tiny has pot possible for great result. Find limite?no limite try to anticipate and create some, you gonna have your own potential... No lim? not good unless you got a real great understanding of the story going on and (the id behind the image) so forth math is math, your parser alwayse evolve with you also (if it like it, it might be you the no lim individual) know that it's not only + you are using.. unless you do so Maintly it's about energy exchange mathvers *communication,love,passion,desir, Wysmey and logic under passive probability (create opposite effect) you are using minus....Stay has fit has possible and most people do not wish hell, unless your wise you may like nightmare...? blue... Figure another way evolving the formula or checking where the reaction is , (- * / sin tan ect)this forum did great, stimulation. __________________________________________________ Wild story, Once i parsed,parsed and parsed for a week even that I became white and hugly on the mirror, drunken at the bar, i did'nt understand, even high from other Babel effect!! The first observable symptome of (fotd) Fractint overdose.. At the same time i did a error on this experimente :I was saving only the reaction i like considering only the pretty one... Take care, some hugly form are unik and might be really narcissic! and so ...not saving them cause of habitude create babel paranormal under 12 beer anyway. BEER is GOOD for YOU, even really, nothing is better that getting hammer facing a good month of parsing party DRx (1000 a month = +- 30 plate x 2) more or less one, Get stupid, full of error and try To C++ on... :got down prime # calculation after 18 beer and two day on drinking/calculation.. contest in 23 minute binary aim driven by # and hypocicloide also pixel mapped,...in a few hour but the computer erease it in my face *WHen it happen i redo or try and really get mad he took a few frame also i remember 4 year later i did find other 4 on hard, funny.. just know it's always in your mind (hard drive) or about close., In my buddah bar trainning time . Psylocibine whas chem object in importance, i start to pov it once but and i did find 1500* stronger in mushroom form...active one finger toutch, far from being infected, follow by a feild of edible and one deadly (on the toutch i guess), root even under give mouvment feeling, nature is buzzing a little when you take

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FOTD 30-09-11 (My Name Is Fractal [8.5])
by Jim Muth 01 Oct '11

01 Oct '11

FOTD -- September 30, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image is a scene deep in Seahorse Valley, where the elements are of extremely high iteration. Even today's maxiter of 600,000,000 leaves some open areas outside the central minibrot. This extreme maxiter also makes the calculation frequently appear to hesitate. This is normal. With iteration counts and maxiters like today's, the logmap options are basically useless, producing nothing but flat areas of color. Shutting off the logmap results in an image with too much trashy chaos. The 'tdis' option would probably do better, but it does not use the fireball-fast machine language of the type=mandel formula, and would require many hours to finish. I compromised by rendering the image with the outside set to 'real', which adds enough detail to make things interesting, cuts the trashy chaos a bit, and still uses the fireball-fast math. The rating of an 8-1/2 includes the standard half-point for the coloring. The name "My Name Is Fractal" refers to the image, not myself. The calculation time of 21 minutes is on the slow side, but the time will seem to pass quicker once the brilliant colors appear at the top of the screen. The official FOTD web site is at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition image may be found at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic web site is at: <http://www.Nahee.com/FOTD/> A mix of clouds and sun, and a temperature of 68F 20C made today an acceptable one here at Fractal Central. At least, the fractal cats thought so. They spent a lot of time in the window that serves as their TV, watching for stray cats passing by and squirrels gathering nuts. FL and I, the local humans, spent the day doing what needed to be done. The next FOTD will be posted in 24 hours, most likely a trip into the 4-dimensional Julibrot. Until then, take care, and there are 4 regular concave polyhedrons in 3-dimensional space in addition to the five well-known convex Platonic solids, for a total of 9 regular 3-dimensional polyhedrons. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= My_Name_Is_Fractal { ; time=0:21:09.60-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.7499\ 9999734953670/+0.00010000004597996/1.381434e+012/1\ /-20/0 params=0/0 float=y maxiter=600000000 bailout=9 inside=0 outside=real periodicity=6 colors=0009WH9_F8bC7fA6i76l57iA8gE9eJAbNB`RCZWDW_E\ UdFShFQlgv7dvAavC_vEXvGVvISvKPvMNvPKvRIvTFvVCvXAvZ\ 7v`5vb6r`7n_7jY8fX8cW9_U9WTASRAOQBLPBHNCDMC9KD5JD2\ IK1MR1PY1Sd0Vk0Yr0`y0cw3au6_s8ZqBXoDWmFXkHYiJZgL_f\ N`PJQMJRKJRGMQCOQ8QQ4SQ1UQ8SNFQLMOISNGZLDeJBkI9lLA\ mOAnRAoTApWAqZAr`BscBtfBuhBvkBwnBwpBrlAmhAie9da9_Y\ 8WV8RR7MN7IK6DG68C54955C65E75H75J85M95O95QA5TB5VB5\ YC5_D5bD5dE5fEQbRiZbiVhiYih`khclgfnghofkpfnreqsetu\ dwvdywcuubrsaoqalo`in_flZcjZ`hYYfXUeWRcWOaVL_UIYTF\ XTCVS9TR6RR3QT9RVESXJTYPT_UUaZVccWdiWfnXhsYixYiyZf\ t_dp`ala_hbXdcV_dSWeQSfNOgLKhJGiIEiPCaWAVb8Nl2Cj4E\ h6Gf8HdAJbBL`DM_FOYHPWIRUKTSMUQOWKNZPPXUQVZSTcTRhU\ PmWNrXLiukizkeuhbqe_mcXi`UeZR`WOXULTRIPPFLMCGK9CH6\ 8F34C00A16C2CD2HF3NG3TI4YJ4cL5iM5nN9mNCmNFmNIlNjoj\ XJdZKa`L_aMYcMWdNUfOShOQiPOkQMlQKnRIoSGqSEsTCtUAvU\ 8wV6yW4zW2vU5sS8CMPBPMATK } END PARAMETER FILE=========================================

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answer to 28-29 modif and ! image associated. Check recopy of M Jim Muth... = JoTw
by Sebastien helie 30 Sep '11

30 Sep '11

answer to fotd september 28...29 _________________ ______________________________________ Since ever i taught fractint user and developper where able to acheived great thing (usually wright think). I was a Teen hoping they will, how great they where etc... My love of mathematic at the time was going from 100 to 70 to until i turn 18 year old...65 i think the lowest ... ANyway the day high pick up english in 2002 i begun... Today i<am a step above my initial mentor, who still lie something average,(i got a year of fractal of the month)... Please do not think i<am stupid even if i figure this exactly today,,,<make me laught> i just spend time recalculating first object . Envy, hope and desire is good with alter-ego, and so Prof(teacher), kid get better...sometime, somewhere. Anyway i just start to explane like you and it still not about the art i developpe... No? it's about the adventure VCC and Fractint trigg in me and so forth it<s cool with moderator to exchange it also. may i do set at least to you my basic <jargo> sometime, some prefere to see thru the cloud.... I do not have access behond |^6 since my first blue crash...anyway some people are behond my possibility and i am happy, i never use 7 else than after the zero dot, somewhere in area 0.707106. without zero and dot you could call me agent no agent strange Yuan nothing strange, hopefully nothing 7 nothing 7 smell noting like time sex = 0707906 try in ^ strange strange nothing agent ??07.. do nothing...ham good, in Jambon ()read like I<am go od like good people.... jambon in french sound like good people <past joke OTD day> even more funny when you know the Belgian Jean, to insulted right now to 7 you on prey er. competition: how many different spike field do you have fractal central #? strange on are best with electo-cat. silent? use it has parameter got a few math-lover prayer... sometime i got to moderate my communication _______________________________________________________ FOTD -- September 28, 2011 (Rating 8) Fractal visionaries and enthusiasts: With today's moderately deep image (thus the name) we finally escape the string of 7-rated images that were merely average. We check the fractal 'star' of a period-5 sub-bud on the northwest shore line of the largest bud of the largest minibrot on the main spike of the Mandelbrot set. The 10^(15) magnitude of the image is just beyond the limit of conventional math, yet the image requires over 65 minutes to calculate. I have calculated images in the 10^(75) range that finish in 1/4 the time of today's image. Most of the impact of the image is due to the coloring, and most of the coloring is due to the Fractint program, not the fastest but arguably still the best. I did tweak a few registers however, so I have the right to claim a little credit. _________________ ______________________________________ I know perls she call me "Creature" cause i did whant to be is fast boyfriend... lneave here to a security Teck.. Curiously i waight for the right on? no see? every know and then i love fear and so it was my last nightmare, a mathematic area where everybody ....... perle me !!! got a englis beach! they are easy to rekognise they look like pretty teen girl with blinking fluorescente eye<s... 1_2_3_4_5..... until then i hide on amtrak reversal seat in orther to Loth her(e) _______NOta FOTD -- September 27, 2011 (Rating 7) lracta sisi ona ries dan enthusiasts: Yoday's mage i a ene nin ethe rent lractaf th insults hen et pression Z^(1.99)+C is retiterated tat round evel it etc he 'recip' punction dapplied. is parent resembles a delot et rot ate d out 15 deg rees CCW oso at the negat nive X-axis cuts through the northwest shore line of the large period-2 bud. The image is located in the area of this intersection, where things always go a bit goofy. I named the image "Jewel of the Deep" when the bright patches reminded me of something like pearls lying on the sea floor. Yes, I know pearls don't just lie on the sea floor, waiting to be picked up. They are formed in oysters. The rating of a 7 is getting to be a habit, but who can complain about an image a full 2 points above average. The calculation time of 2-2/3 minutes is a fair price for an image with a rating of a 7. _____________________________________________________ _____________________________________________________

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FOTD 29-09-11 (Squarely Rooted [7.5])
by Jim Muth 29 Sep '11

29 Sep '11

FOTD -- September 29, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is named "Squarely Rooted". This is because the image was generated by the expression Z^(sqrt(2))+C calculated 14 turns up the complex logarithmic hyperspiral with the 'recip' function applied. The parent fractal is a Mandeloid with a teardrop-shaped main bay, rotated so that its main bud faces southeast. It has only one period-3 bud, but the usual higher order buds. The scene of today's image is in a field of debris located where the second period-3 bud might normally be expected to lie. The rating of a 7-1/2 includes the standard 1/2-point bonus for my color work. The image itself is merely average. To achieve the flat-background effect, I rendered the scene with the logmap set to an artificially high 67. The shape of the minibrot at the center mirrors the shape of its parent, which is a quite common thing in fractals with exponents of Z between 1 and 2, where the parent fractals can assume most any shape they wish, especially when calculated with alternate values of the logarithm. The calculation time of 32 seconds is blessedly brief, so why not run the included parameter file and see what you might have missed. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> for effortless viewing. It is posted in high definition 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 partly cloudy skies were fair enough, and the temperature of 70F 21C was agreeable enough here at Fractal Central today. But the frequent showers made it a day to be forgotten. The fractal cats, ever forgetful, had already forgotten the day when it began. After almost 3 inches, 7cm, of rain overnight, the humans were glad they had installed the sump pump. A floor with a few puddles is far better than a basement filled with 100cm of water. The next FOTD will be posted in 24 hours. Until then, take care, and if you would like to become wealthy in this sour economy, open a shoe store for bigfooted sasquatches. It must be quite uncomfortable for them, stomping around in the cold mud in their bare feet. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Squarely_Rooted { ; time=0:00:25.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-1.4597524206/-0.4141910317/25206/1/85/0 params=1.414213562/0/14/0 float=y maxiter=2000 inside=0 logmap=67 periodicity=6 colors=00000KxZJzwCzzzFmC9qz9gz9Yz9Pz9Fm96g8D`7JV6\ PP5WJ4aD3g72m16cBAVKEMUIDbM4kZIWkVHwg2ubCtYMrTWqOe\ mW_tlXslXslXslXsmXsmXsmXrmXrmXrmWrmWrmWrmWrmWqmWqm\ WznWznWznVznVznVznVznVznVzmVznVzoVzoUznVzmWzlXzkXp\ kYpjZpi_ph_ph`pgapfapebpecpddpcdpbepafpafp`gp_hpZi\ pZipYjpXkpWlpWlpVmpUnpTnpSopSppRqpQqpPrpPspOspNtpM\ upMvpLvpKwpJxpJxoLwnMvmNulOtkPsjQriRqhSpgTofUneVmd\ WlcXkbYjaZi`_h_`gZafYbeXcdWddVecUfbTgaSh`Ri_QjZPkY\ OlXNmWMnVLoUKpTJqSIrRHsQGtPFuOEvNDwMCxLCzLDzKEzKFz\ JGzJHzJIzIJzIKzHLzHMzHNzGOzGPzFQzFRzFSzEfzzfzzfzzf\ zzfzzfzzbzzZzzWzzSzzPzzNzzMzzLzzJzzIzzHzzFzzDzzBzz\ Azz8zz6zz5zzCzzIzzOzzUzzSzzRzzQzzPzxXzjczXkzJrz5qz\ 8pzAozCnzEnzGrzkNzXLz_KzaJzcHzfGzhFzjEzlLzhSzeZzae\ zZlzVszSgzNWzIKzD8z9PzDdzGtzJtzKtzLtzMtzMtzNtzOtzP\ tzPmzSfzV_zYUz`NzcGzfAzhEzfIzdLzbPzeTzgXzj_zlczogz\ qkztnzvizWdz6YzHSzSLzaFzl } 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] hi miss...
by Sebastien helie 29 Sep '11

29 Sep '11

Ok. You do not accept Lumix large size camera, shot... Picture (cpu and tv) in El paso hotel in Fev 2010 (FT-Bliss little HI on a few internet case.. By the way will do my extreme best to maintain this program thru WT under ground speak... Quebec H*T jail me for any recorded treath?dirty tonge me i guess) also did encounter several personal computer (ATom Mini laptop) *the best i think* probleme at boot. first time off in a few day... refreshing and boot today slow under flamming tunder.. actualy testing ubuntu program carmetal for vector drawing. (noise integration angle in sphere... 26 to 3d... )quadrant -+ to avoide indiscretion boot slow and trouble 1 under VCC dll.... (freeze the whole sys) tandy radio shack coco model III based Bios. also had hospital strange alerte. nurse buzz like agression, and ground worker understand... They whanted to keep for them my Orb (sphere) gived away by Vancouver china town..... overwound ? embryo existe in fractal insured until 4 human after giot lot's of battle dog.. keep trainning. me nervous tension 20$ and shoulder pain like my right shoulder i F.U "c"k T by sequencial Mtn Bike accident. plus or minus integration... actually forgot my today meditate post... about peter Croft or middendorf but... cannot rremember the second joke... fart overdose trip down. 2011/9/29 Jeff Tupper <tupper(a)peda.com> > overwound > spun out > > location? memory / program counter >

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FOTD 28-09-11 (Moderately Deep [8])
by Jim Muth 29 Sep '11

29 Sep '11

FOTD -- September 28, 2011 (Rating 8) Fractal visionaries and enthusiasts: With today's moderately deep image (thus the name) we finally escape the string of 7-rated images that were merely average. We check the fractal 'star' of a period-5 sub-bud on the northwest shore line of the largest bud of the largest minibrot on the main spike of the Mandelbrot set. The 10^(15) magnitude of the image is just beyond the limit of conventional math, yet the image requires over 65 minutes to calculate. I have calculated images in the 10^(75) range that finish in 1/4 the time of today's image. Most of the impact of the image is due to the coloring, and most of the coloring is due to the Fractint program, not the fastest but arguably still the best. I did tweak a few registers however, so I have the right to claim a little credit. The way to view the image is to visit the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> or to run the included parameter file. The image is posted in high-definition on the web at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic, FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Partly cloudy skies and a temperature of 75F 24C made the day worth getting up for here at Fractal Central. A torrential thunder-storm that brought flash flooding in the afternoon added to the interest. The fractal sump pump once again did its job, keeping the basement water to a wet spot. The fractal cats made it through the day with no problems; the humans had the usual human stuff to do. The next FOTD will be posted in 24 hours. Until then, take care, and physicists tell us there is an electromagnetic field, a gravitational field, a weak field, a strong field, probably a Higgs field, plus various other fields, but why have they not mentioned a consciousness field? The neurons of the brain might be the particle aspect. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Moderately_Deep { ; time=1:05:34.81-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7768\ 878332047678549/0.00291014151619213371/\ 1.871789e+015/1/60/0 params=0/0 float=y bailout=9 maxiter=15000 inside=0 logmap=-2630 periodicity=6 colors=000RKmSKmTKmUKmVKmWKmXLnYMoZNp`OqaQrbRscUrd\ XqeZqfapgdpgfohinilnjnmkqmltllvlornqnoskpvgqxcrz`s\ rTgeMXTFMG8BIDIKHOMLUKP_HUeEYkB_q9`wBRsDGpE3hK9gQE\ hWKiaPqgVrm_ssdsrarqZrpWroUqnRqmOqlLqkJpjGpiDpiBpc\ 9iY7bS6WM4QG3JA1C50689BBHFEPKHXOKdTNlXfidzflvdkrbj\ n`ikZhiYggXgcVf`TeXRdTPcKIQLJSLJTMKUMKVNKWNLXOLYOM\ ZPM_PM`QNaQNbC9QGDUJGXNK`L8RFlGGjIHhKIfMJdOKbQL`SL\ ZTMXVNVXOTZPR`QPb6TQARTEQWIPZMOazmCzmEzmGzcIzcJg8L\ e9NdBPbCQ`DS_FUYGWWIXVJZTL`RMbK2UdzJbvLasN`pP_lQYi\ SXfUWbWV_XTXZST`RQbMIkOKhPMeo6zm8xk9viAuhBsfCrdDpb\ EoaGm_HlYIjWJiVKgTLfRMdTYzSXxSWvSVtSUrRTpRUnRUlRcj\ QchQcfQcdzmvzmtzmszmrzmpzmozmnzmmzzkzzjzzizzhzzfzz\ ezzdzzezzdzzdzzdzzczzczzczzMzzPzzSzzVzzYzz`zzbzzcz\ zczzc`zcZzcYzcWzcUzcTzcRzc6zBDzLKzVEz`GzaIzaKzbMzb\ Ozcbzi_zhYzgWzfUzeSzdcz47zwCzrHzmMzhoz1mz4kz6jz9hz\ BfzEWzRVzSVzTUzUUzVUzWTzX } END PARAMETER FILE=========================================

2 2

help.....
by Sebastien helie 28 Sep '11

28 Sep '11

My terminal (tread) does not allow me to link with the fractal census, lotus note is always lock on this windows and even my personal computer... understand that i'am a borland ansi c programmer intermediate who use windows has a (Microsoft when you got us you.... exploitation system.. in french system of abuse mac is the same just better (joke)i love computer since 7 or 8 year old) ...census... fractint 65% tierazon all version 30% divided... probleme notice, code not portable beteween compilation version Iteration ET flarium...... apophysis on the side all version... pov-ray 10% for quaternion and 70h course about done nice reaction (memo cray eniac prime # 25673Might be human but old).. 12823 max human polar +-37. 12808 and my personal....parser mandel on loop... 0.0002% i forgot about it... used in 2005-2006 from the book of line function for computer screen geometric,.. could i send picture and comparate with somebody or mass sometime... got even dangerous fractal well explored *will not be send*!!.!...... anyway communication has se a little.... developpment far from being in degeneration altought the periode december is hard to do in the north... nota in november i got dive in zooming factor...zoom x 40 or x 8 depend..... euphoria +- time follow by noise and come back in janvier after rapport. Sinpix Helie 12823 28_09_2011 love and hate.

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The Pope Ion
by Sebastien helie 28 Sep '11

28 Sep '11

My first big result in 2002 and the story who send my life here..... At first i was i think euphorique... Since Jim said that the mathematic plan we explore have no mass and no weight, following the two sequence i send, we could start to speculate. Poeticaly, this plan of mathematic have more weight when he is static, lighter airborn... Fractal ? first question i had to my(s) teacher was what it mean?, since i had no answer thru america fractal where fractal... i Taught Fractional integer has the right Word to put full on...And in case you did'nt know?! Considering that we are about 5000 on earth.... In anycase feel free to drop message, comment or even question... at sinpix @ gmail. my second nightmare is solitude, the tird (tird is shit in english *find it funny) lack of understanding observable in this society, and my next euphoria been the adventure this constent development lead to. Basicaly i'am a matematician and a adventurer, and so even last night i been hyptnose again by a different result following Jim wait of formulation... Funnyest thing My e-mail already been bosted to 400 message a day and so...? the tird been back, cause i din't understand clearly 5% of hem... 6 language, and 10 different type of technologie. I wise mathematic will stay strong on revers standard, and global (same shemantic) *** Anybody know a follow up to madel brot define for a grade 12 student ? in book...**** it been impossible to document here. Have a good half day of work, a 4 of meditation and a 8 of beer in your wine the goto another parsing night &&&??? Anybody know goto a free host for already calculated image, i'am poor $ and so i will never pay to be hostage of another sys administrator, who just know better to wire is computer... Id *** Lately i parse full fractint sheme, i meen the full quadrant and i end up with a mathematic history... if fractal image. Call this instant Idea. Or in french *Etant* who meen element in the structur of the counsciousness mix with sin, x,y,I,Q,N,C,R... and plus tomorrow probably PopeIon { ; My first euphoria ; My Second Nightmare ; my third deception ; my next euphoria reset=2000 type=formula formulafile=dsystem1.frm formulaname=papillon-un center-mag=3.665e-006/-8.65e-007/0.6666663 potential=256/200/4 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } Pope Ion{;Love essai relax un nmbre aleatoire en toi=mcl3... z=pixel z=(2.6/cos(0.6*z)-1.3/sin(0.1*z)-sqr(3.1416/z))/z |z|<4 }

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FOTD 27-09-11 (Jewel of the Deep [7])
by Jim Muth 28 Sep '11

28 Sep '11

FOTD -- September 27, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a scene in the parent fractal that results when the expression Z^(1.99)+C is iterated at ground level with the 'recip' function applied. This parent resembles a Mandelbrot set rotated about 15 degrees CCW so that the negative X-axis cuts through the northwest shore line of the large period-2 bud. The image is located in the area of this intersection, where things always go a bit goofy. I named the image "Jewel of the Deep" when the bright patches reminded me of something like pearls lying on the sea floor. Yes, I know pearls don't just lie on the sea floor, waiting to be picked up. They are formed in oysters. The rating of a 7 is getting to be a habit, but who can complain about an image a full 2 points above average. The calculation time of 2-2/3 minutes is a fair price for an image with a rating of a 7. For even more fairness, check the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image is posted. 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 day here at Fractal Central began with a mild thunder shower, followed by alternating sun and showers until 3pm, when a whopper of a storm moved in with crackling lightning and torrential rain. The fractal sump pump did its job however. The temperature of 73F 23C was agreeable enough, at least for the fractal cats. FL and I had a typical day of doing routine stuff, none of which is worth reporting. The next FOTD will be posted in 24 hours. Until then, take care, and let's stop making apologies for God's behavior. Let's stop preaching about His mysterious ways. Let's hold our image of God to at least the imperfect standards of behavior we consider acceptable for ourselves. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Jewel_of_the_Deep { ; time=0:02:40.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-1.190908577788997/+0.00057523271973797\ /6.433262e+011/1/-113.5/0 params=1.99/0/0/0 float=y maxiter=7200 inside=0 logmap=180 periodicity=6 mathtolerance=0.05/1 colors=00005C06C07C08C09C0AC0BC0CC0DC0ED0EE1EF2FG3\ FH4GI4HH5IH5KG5IF6GE6ED7CD7AC88B86A85AA4CC5DE5EG6G\ I6HK7IM6JO6LQ5MS5NU4PW4QY3RZ3SFKlIMkLNkOPjRQjUSjXT\ i_VicWihXhmZhrfgvmgzr0zv0zz0zz0zz0zz0SlQUiTVfVXcXY\ `_ZZa`WcaTfcQhdNjfKmgHohFqfGleGgdGbbGYaGT`GOZGJYGE\ XG9VG4UG0TG0YO1bW6gbBYj8Oq5Fx3LnCQdKWVS`L_eBgXCdOC\ bFC_7CYKGLXJ8hM0cJBZGPUDcPAqWHnbOliVipagvgezzIzuPz\ lWzdbzcazb`za_z`Zz_YzZXzYWzXVzWUzVTzUSzTRwSQwSPwYT\ wcXwi`wocwlbwjbwgbwebwcaw`awZawXaw_bwabmdbmfcmhcmk\ cmmdmpdmrdmtemwemyemzemygmxhmwimvjmukmtrmsrmrrmrrm\ qrmprmprmormormnrmmrmmrmlrmkrmkrmjrUzrWzrYzr_zrazr\ czrgzrizrjzrkzrkzrlzrlzrmzrmzrnzrnzrozrozrpzrpzrqz\ rqzrnzrmzrmzrmzrmzrmzrmzrmzrmzrzoXzpZzq`zrbzsdztfz\ uhzvjzwlzxnzxpzq_zjKzkIzlGzmFznDzoCzpAzq8zr7zs5zt4\ zu2zv0zw0zx0zy0zz0zz0zx1zu9zrHzpPzmXzjdzhlzgjzghzd\ NzVZzTazRczPfzNhzLkzKmzMj } 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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My first fractal
by Sebastien helie 27 Sep '11

27 Sep '11

. I'am frenchy so correct my english if you feel it not good enought. First to everybody, i like to present, I pick up fractint in 1993 attending to college in electronic and informatic. At the time my relation with english was not good enought to read manual so i just explore the matematic environment build in. In 2002 has a new bilingual i start to developpe and explore thru this wonderful mathematic univers. I feel we are like astronomer in a univers of ever expanding geometrie. The discovery are daily and the relation we can make with the natural reality are vaste. Caun is the first of hundred of reaction i end up with thru 10 years of development, it make me think of a Opuntia cactus, I considere it the base of my fractal experiment, it give a expression of mirror duality, who can be translate thru native spirituality has the duality of nature, one aspect fixed and one aspect in movement, one aspect conscious and one aspect incounscious, one good and one bad. I also had one version of it with four caun structure developped around a square. caun { ; make me think of Opuntia cactus species reset=2000 type=formula formulafile=caunplus.frm formulaname=caun1 function=sin center-mag=-1.64e-006/2.205e-006/0.6666676 potential=256/200/4 colors=000000_qT<3>Subqg5<58>tv9tv9tv9<3>uxApg5<14>OpFMqGKqH<3>CtKdW`qg5\ <63>S7pS6qR6r<3>P3uchuqg5<58>jC2jB2jB2<3>i81qg6<6>jhKiiMhiO<3>ejVph7djX<\ 5>Zlh } caun1{;Sebastien Helie z=pixel x=real(z/0.66),y=imag(z/0.66) z=sin(x)/sin(y)+sin(z^(2.6/flip(0.46464*z)-0.46340/flip(0.103*z)-fn1(3.1416/z)/z))+pixel }

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FOTD 25-09-11 (Zigging and Zagging-2 [7.5])
by Jim Muth 27 Sep '11

27 Sep '11

FOTD -- September 25, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is the hinted-at zoom into yesterday's image, to a depth where the central minibrot becomes well-resolved. At this depth the filaments have almost totally degenerated into masses of chaos, though filament signs are still visible. The shape of concentric circles that is formed by the chaos surrounding the minibrot in today's image is typical of the patterns in very deep minibrot basins. I emphasized the chaos in the image by rendering the scene with a random color palette and by not using the logmap feature. The logmap renderings do bring out the remaining filamentary nature of the scene. The name "Zigging and Zagging-2" could also be something like 'Son of Zigging and Zagging' or 'Curse of Zigging and Zagging', but these names are too long to fit into the 18-character limit set aside for the parameter name. The rating of 7-1/2 includes a half-point for the coloring, which is marginally better than yesterday's. Being deeper than yesterday's image, today's is also slower, taking a full 33-1/2 minutes to finish. Do not bother to switch to the passes=g option. In this particular image it is no faster than passes=1. The image may be viewed already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It may be viewed in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Partly cloudy skies and a temperature of 81F 27C made conditions near perfect for the start of autumn here at Fractal Central. The fractal cats gave the day total approval. They stretched in the sun, which in autumn and spring comes in the south window at a better angle. The humans spent the day relaxing, a chore that is sometimes easier said than done. The next FOTD, hopefully a bit better than moderately good, will be posted in 24 hours. Until then, take care, and perhaps changing the past is the reciprocal of knowing the future. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ZiggingAndZagging2 { ; time=0:33:29.79-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.5001\ 906496882479292199908473074/0.61029780299779699662\ 53344018864/5.829431e+027/1/-62.5/0 params=0/0 float=y maxiter=14000 bailout=9 inside=0 colors=000UKpOHmKEmGBzC8z85z42zEQyDOvCNsCMqBLnBKlA\ Ki9Kf9Kd8Ka8K_7KX7KV6KS5KP5KNAKKFKIKKFPPCUUAZZ8cc5\ hh5in6ej5af5Zb4VZ4SV3OR3LN2UJ2cF1zSzzRzzPzzNqzLlzJ\ dzHUyFPqDKfBMUAPKCUAEZ3Gc2Ih0KmKMrKOmKQmKSmIQlGOgE\ McDKZBIV9GQ8EM6CH4AD3A81A44ld3bW2TO1JG09z6AzBAvA9q\ 98k88g87c76Z66U65PmvmmvmkuhitcgsZerUcqPapK_oFXkEVh\ DTeCRbBP_CNXELUGJRIGOKELMCINAFOAGOAIPBKPCMPDOOENKF\ MHGLDHKAIJ6JI3KH0IG0HF0GE0FD0EC0DB0CC0BE0AG08I07K0\ 6M05O04Q03S02U06W08YA7V96T86R85O75M64K64I53FA3FF2H\ K2KP1PU3UZ6Zc9chCafF_dEYbEX`DVZCTXBRVBQTAOR9MPCKNF\ JLKHKPFKUDKZCKcAKh8Km6Kr5KzU3zP1zJGsHEmFCgDB`B9V98\ U0BT0CS0DR0EQ0GP0IO0KN1MM2OL3QK4SK5UK6TK7QK8NK9KKA\ HKBEKCBKD8KE5KFALKFMPKQUPSZUUaZTcbRaeQ_bOY`N_ZOaWQ\ cUSeWTgYUiaUkeVmbWmZXmWXlVXkTXkRXkPXlNXmLXnJXoHXpF\ XqEYsC_uBawAcz9cz8Ac78I57E45m34m23m21m12qZ1lW1hT1d\ Q1`O1XL1TI0OG0KDdZzaUwZOs } END PARAMETER FILE=========================================

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FOTD 26-09-11 (A Wheel of Numbers [7])
by Jim Muth 27 Sep '11

27 Sep '11

FOTD -- September 26, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's very deep Mandelbrot scene lies on a filament sprouting from a minor period-5 bud on the northwest shore line of the large period-2 bud of the set. I named the image "A Wheel of Numbers" for very good reasons. The elements certainly are in the shape of a wheel, and fractals certainly are made of numbers The rating of an average FOTD 7 might have been higher if I had put more effort into the coloring. But today is tax day, and paying four-digit taxes always makes me irritable, which is a poor mood for creating fine fractal art. The calculation time of 48 minutes is slow, and there is no excuse. They sometimes say that anything worth having is worth waiting for, but this is not always true. Will the much- ballyhooed soon-to-arrive end of the world have been worth the wait when and if it actually arrives? Avoid this and all other calculation problems by viewing the image already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> See the image 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/> Too many clouds and a midday shower spoiled today at Fractal Central. The temperature of 81F 27C was well within the comfort range, but the fractal cats were more concerned with a stray cat that appeared on the back porch than with being comfortable. When the stray cat wandered away, the fractal cats finally settled down to relax as only a cat can. The humans had an average day, though I became a bit annoyed when I wrote the check for the taxes. The next FOTD will be posted in 24 hours. Until then, take care, and the world that appears to exist around us may be nothing more than a consistent series of mental images. But it sure is fun playing with the images and pretending they're real. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Wheel_of_Numbers { ; time=0:48:19.58-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.2411\ 836256383387634696/0.17032263787348613463818/9.917\ 833e+017/1/-120/0 params=0/0 float=y maxiter=6400 bailout=9 inside=0 periodicity=6 colors=000stksskrrjqrjqqippiopioohnnhmngmmgllfklfk\ kfjjeijeiidhhdghcggcffbefbeebeebddacdabc`bb`ab_`a_\ ``__`ZZ_ZZZYYZYXYXXXXWXXVWWVVWUVVTUVTTUSTURSTRRTQR\ TPQSPPSOPRNORMNQMNQLMQKLPKLPJKOIJOIJNHINGHMGHMFGME\ FLEELDDKCCKCBKBAKA9KA8K97K86K85K74K62K32M41L40L40L\ 40L40L40L40L40L40L40K40K40K40K40K40K40K40K40K40K50\ K50K50K50K50K50K50K50K50K50K50K50K50K50K50K50K50K5\ 0K50K50K60L60M60N60O60P60Q60R60S60T60U60V60W60X60Y\ 60Z70_80`90aA0bB0cC0cD0cE0cF0cG0cH0cI0cJ0cK0cK0cK0\ cK0cK0cK0cK0cK0cK0cK0cK0cK0cK0cK0cK0dK0cK0bK0bK0aK\ 0`K0`K0_J0ZJ0YI0YI0XH0WH0VG0VG0UF0TF0TE0SE0RD0QD0Q\ C0PC0OB0NB0NA0MA0L90L90K80J81I72I73H64GZ25Y36X36X3\ 6W36V37V37U37T37T38S48S48R48Q49Q49P49O49O4AN4AN5AM\ 5AL5BL5BK5BJ5BJ5BI5CH5CL6CP6CU6DZ6DcADhFDmKErPEvUE\ zZEzcFzhFzmKzmPzmUzmZzmcznhyomxprwqvvrzuszuszutzut\ zuuzvuvvvrvvmvvmvvmuulttl } END PARAMETER FILE=========================================

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(no subject)
by Sebastien helie 26 Sep '11

26 Sep '11

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Re: [Fractint] FOTD: Galactic Collision
by Jason Hine 25 Sep '11

25 Sep '11

Thanks for all the FOTD's Jim... I especially liked the Galactic Collision, and think the reds in the coloring work just fine. I also look forward to reading about our crafty alien overlords' plot to make us do all the otherwise inexplicable craziness we're doing to ourselves and our planet! - Jason

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FOTD 24-09-11 (Zigging and Zagging [7])
by Jim Muth 25 Sep '11

25 Sep '11

FOTD -- September 24, 2011 (Rating 7) Fractal visionaries and enthusiasts: In today's FOTD we return to the depths of the Mandelbrot set, where we check a filament connected to the period-5 bud on the northwest shore line of the main bay. Minibrots lying on filaments are usually surrounded by branching networks of bare sub-filaments. At the depth of today's image however, the bare filaments have blossomed into zigzagging fields of debris. At an even greater depth, the zigzag filaments vanish almost entirely, leaving only the debris, which forms itself into unexpected patterns. I might venture down there in tomorrow's FOTD, or I might not. I have not decided. The name "Zigging and Zagging" refers to the zigzag streams of debris around the edges of the frame. The rating of a 7 is average. If I had put more effort into the coloring, I might have worked the image up to a 7.5 or even an 8. The potential for a higher rating is there. As is true of all very deep images, the calculation time is rather slow. In today's image it is almost 22 minutes, long enough to cause those with busy schedules to become impatient. To see the image without the need to calculate it and become impatient, check the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> See the image in high definition 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/> Morning clouds gave way to afternoon sun today here at Fractal Central, while the temperature settled at 77F 25C, right in the middle of the comfort range. The fractal cats found most of their comfort while sleeping. FL and I took a short antiquing trip in the afternoon, and were greeted enthusiastically by the cats when we returned after 5 hours. The next FOTD will be posted in 24 hours, give or take a few. It might be a better one; it might be worse. Check back then to see. Until next time, take care, and be aware. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ZiggingAndZagging { ; time=0:21:50.64-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.5001\ 906496882479292199908473074/0.61029780299779699662\ 53344018864/7.715e+025/1/-62.5/0 params=0/0 float=y maxiter=7200 bailout=9 inside=0 periodicity=6 colors=000UiaUkeVmbWmZXmWXlVXkTXkRXkPXlNXmLXnJXoHX\ pFXqEYsC_uBawAcz9cz8Ac78I57E45B34023221312qZ1lW1hT\ 1dQ1`O1XL1TI0OG0KDdZzaUwZOsUKpOHmKEdGBXC8P85G428EQ\ yDOvCNsCMqBLnBKlAJi9If9Hd8Ga8F_7EX7DV6BS5AP59N48K4\ 7I36F25C24A137125012in6ej5af5Zb4VZ4SV3OR3LN2UJ2cF1\ mB1z70z30zQEzJAzD7z63zFNmDKcBHUAFK8CA6A357235112FW\ rBOd7GR38DI8lG7gE6cD5ZB5V94Q83M62H42D3181044ld3bW2\ TO1JG09z6AzBAvA9q98k88g87c76Z66U65P55K44F43A338226\ 215113001_oFXkEVhDTeCRbBP_ANX9LU8JR7GO7EL6CI5AF48C\ 36924612303OO2KK2HH1DD1AA066033KH0IG0HF0GE0FD0EC0D\ B0CA0B90A808707606505404303202101008YA7V96T86R85O7\ 5M64K64I53F43D42B3292162141020HchGafF_dEYbEX`DVZCT\ XBRVBQTAOR9MP8KN8JL7HJ6FH5DF5CD4AB389267255133011z\ JGsHEmFCgDB`B9V9800B00C00D00E00G00I00K01M02O03Q04S\ 15U26T37Q48N59K6AH7BE8CB9D8AE5EFAIKFMPKQUPSZUUaZTc\ bRaeQ_bOY`N_ZOaWQcUSeWTgY } END PARAMETER FILE=========================================

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FOTD 23-09-11 (Galactic Collision [???])
by Jim Muth 23 Sep '11

23 Sep '11

FOTD -- September 23, 2011 (Rating ?) Fractal visionaries and enthusiasts: Today's image in the Z^2+C Julibrot is a rating puzzle. I have no idea how to rate it. To begin, it's neither a Mandelbrot image nor a Julia image. It's an Oblate image, which means the orientation of the slice is determined by the real(Z) axis and imag(C) axis. The scene is located in Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set. But the actual location is but a small part of the image. I lost track of the amount of rotation, stretching and skewing that went into it. The image shows just two of the bottomless pits and endless spirals that fill the area. All the tiny nodes scattered through the frame are more bottomless pits, and those pits are filled with even tinier pits, to infinity. That's how it goes with fractals. The name "Galactic Collision" came to mind at an early stage of the coloring, when the image consisted of deep blues speckled with tiny dots that resembled stars, and actually did somewhat resemble colliding galaxies. Since then I have totally re-colored the image to the fiery reds that now prevail, though I have the original name. (Perhaps I should have stuck with the original colors.) The slow calculation time of 55 minutes is largely due to the unusually high maxiter of the upper right quadrant of the scene, where some elements have a maxiter of over 200,000. (The purplish band curving around the bottomless pit in the lower left is actually the lowest-iteration part of the entire image.) The official FOTD web site, where the finished image is posted, may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic web site may be found at: <http://www.Nahee.com/FOTD/> Heavy clouds ruled the sky here at Fractal Central today, with a steady rain in the afternoon adding to the unpleasantness. The temperature of 73F 23C was fair enough. It's too bad the weather was not fair also. The fractal cats, who lead boring but notably longer lives as indoor cats, took no notice at all of the weather. Food and play was at the top of their agenda. Finishing the week's work was at the top of the human agenda, and this task was accomplished with only minor problems. The next FOTD will be posted in 24 hours. Until that blissful moment arrives, take care, and it's all the fault of those aliens from the Herculean cluster, who are using earth as their experimental laboratory. No, I do not actually believe that aliens from outer space are running the affairs of we humans here on earth. But I would have no trouble writing a book about an alien conspiracy and using the things we have done and are doing to ourselves as 'proof' that aliens are among us . . . hey, maybe I'll do it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Galactic_Collision { ; time=0:55:41.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 periodicity=6 center-mag=-0.02877222954091648/+0.000204047718176\ 44/6741119/0.0001957/-0.030483234210959366/-89.948\ 0538795542941 params=0/0/90/0/-1.76852919227/0/0/0 float=y maxiter=200000 inside=255 logmap=-843 colors=000cDOcCNcCMcCMcCLcCKcBKcBJcBIcBIcBHcAHbAGb\ AFbAFbAEaADa9Da9Ca9CY9B_9A`8A`89b88c88d87f86g76h75\ j75k74l73n63o62p61r61s60t60u81u92uA3uC4uD5uE6uF7vH\ 7vI8vJ9vLAvMBvNCvODwQDwREwSFwTGwVHwWIwXJxZJx_Kx`Lx\ aMxcNxdOxePygPyhQyiRyjSylTymUynVyoVwmWulXtkXriYqhY\ ogZneZld_jc_ia`g``f_adYacXbaWb`UcZTcXSdWQeUPeTOfRM\ fQLgOKgNIhLHhJGiIEiGDjFCjDAkC9kA8lA4j96k97l99m8An8\ Bo8Dp7Eq7Gr7Hs6Hu7It8It9IsAIsAIrBJrCJqDJqEJpEJpFJo\ GKoHKnIKnIKmJKmKKlLLlMLkMLkNLkOLjPMjQMiQMiRMhSMhTM\ gUNgUNfVNfWNeXNeYNdYOdZOc_Oc`ObaObaOb`Nc`Nc`Nd`Nd`\ Nd_Ne_Ne_Ne_Mf_Mf_MfZMgZMgZMgZMhZMhZLhYLiYLiYLiYLj\ YLjYLjXLkXKkXKkXKlXKlXKlWKmWKmWKmWJnWJnWJnVJoVJoVJ\ oVJpVJpUJqUKqUKrUKrUKsUKsUKtUKtUKuUKuUKvUKvUKwUKwU\ KwUPxUPxUPxUPyUPyUPyUPzUPzUPzUUzUUzUUzUUzUUzUUzUUz\ UUzUUzUUzUUzUUzUUzUUzUUzUUzUUzUUzUUzUUzUUzUUzUUzUU\ zUUzUUzUUzUUzUUzUUzUUzUUz } frm:SliceJulibrot2 {; draws most 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 22-09-11 (Wine-Dark Fractal [6.5])
by Jim Muth 23 Sep '11

23 Sep '11

FOTD -- September 22, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is a scene that I originally passed by on the way to the 'Primed for Growth' image of 3 days ago, September 19. I return to the area today because I originally saw in it some FOTD potential. The image is located in one of the two East Valleys of a small Mandeloid just west of the main Mandeloid of the parent fractal. I named today's image "Wine-Dark Fractal". The background colors remind me of light passing through a bottle of red wine. The name also creates an ancient Greek atmosphere, and as we know, those classic Greeks were quite big on geometry. The image itself has an overall dark, subdued appearance, with curved strips of brilliantly colored confetti standing out like fireworks in the night sky. The rating of a 6-1/2 could be on the conservative side, but the fact that this is the second expedition into the same fractal area knocks a point off the rating. The calculation time of just under 2 minutes will take the frustration out of the calculation task. Enjoy the image without the need to calculate it by visiting the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image 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/> Overnight rain ended by daybreak today here at Fractal Central, leading to a cloudy, muggy day with a temperature of 79F 26C. All of this must have agreed with the fractal cats, who have no idea of their fractal nature and seemed unusually relaxed. Being a human, (at least the last time I checked), I found the day a bit too routine and slightly boring, but that's how it seems to go in the second half of life. FL found her excitement worrying about the economic situation. The next FOTD will be posted in 24 hours. Until then, take care, and 100 years from now we'll be asking, 'where were you when the end came'? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Wine-Dark_Fractal { ; time=0:01:58.20-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.888013446870261/+0.1672559348360887/\ 6.757468e+007/1/95/0 params=2.15/0/2/0 float=y maxiter=3600 inside=0 periodicity=6 colors=000U09R08P08M08J07G07E07H0CK0HN0MQ0RT0WW0`Y\ 0dw0MtgQqdUn`YkY`hUdeRhbNkiKzeGzaDzaFzaGzaHzaIzaJz\ aKzaLzaMzaNzZMzXLzVLzSKzQJzOJzLIzJIzHHzEGzCGzAFz7E\ z5Ez3Dw1DcAJYIOXQUWZZVfdUniTvnStkVriXpgZnd`lbbj`dh\ ZffWhdUjbSl`QnZNpXLrVJtTHvWMnZRgaW_d`TgeMjjEmo7ps0\ qrGqrVqri023Bon9ih8dc7_Z6VU5QP4KK3FF2AA155KLcIJ`HI\ YGGWEFTDEQCCOABL99I88G67D55A448225112YbNV_LTYKRVIP\ THNQFLOEJLCHJBEHACE8AC7895674442221Wf1GL0I8EF6BC59\ 9476243126rs5lm4gg4ab3XX3RS2MM1GG1BB055cmvU`gKPTAC\ ETtqQnkNhfKb`HYWESRBML8HG5BA255tq1ol0jh0ec0a_0XV0S\ R0NM0F00K08O0HS0IV0HQ0GN0FK0DG0BD08A06604302000000\ czcL_VEOL7CA6sH5lF4fD4`B3V92O72I51C30619Ls8Im7Gg6E\ b5CX4AS38M26G14B025zZFtUDnPChKAb79X67Q56J34C23511y\ VEtSDpQClOBhMAdK9`I8XG7SE6OC5KA4G83C62841420knHabD\ SQAJH6983F3SD2PC2MA2J91G71E61B408305102CZeBVaASZ9P\ V8MS7JO6GL5DH4AE37A247123 } 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 21-09-11 (Crack in the World [7])
by Jim Muth 22 Sep '11

22 Sep '11

FOTD -- September 21, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Crack in the World", meaning the world of fractals. The name points out that the scene is located very near the negative X-axis of its parent fractal, where everything is broken apart. This parent was created when I calculated the expression Z^(2.01)+C at a level 11 turns up the logarithmic hyper-spiral with the 'floor' function applied. (Actually, I think the 'floor' function gives the most accurate values of the multi-valued complex logarithm, but it would take a better mathematician than me to figure it all out.) The parent fractal is a distorted Mandelbrot set rotated about 15 degrees clockwise, so that the southern branch of Seahorse Valley intersects the negative X-axis. Today's scene is located near this point of intersection. With its inward-jutting low-iteration elements, the image appears as though it is very near the bailout cut-off point. Actually, it is very near the X-axis, which serves as a cut-off point in the image. The rating of a 7 is perfectly average. The calculation time of 5 minutes is a bit slower than I would have preferred, but still brief enough to make the calculation no more than a minor annoyance. All the calculation problems may be avoided by viewing and hopefully enjoying the finished image on the official FOTD web site 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 classic FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds kept an all-day damper on things here at Fractal Central today. The temperature of 73F 23C was pleasant enough, at least for the fractal cats, who approved of the lack of rain as they enjoyed the outdoors from indoors. My day was uneventful, which makes dull reading but a pleasant experience. FL had a more active day with black-spot infested roses. The next FOTD will be posted in 24 hours. Until then, take care, and be ever alert for charlatans. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Crack_in_the_World { ; time=0:05:02.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=floor center-mag=-0.8068576369195436/+0.0000047645303079\ /2.951255e+008/1/-67.5/0 params=2.01/0/11/0 float=y maxiter=7200 inside=0 periodicity=6 colors=000424CCzlwzzzzGK8R0OK0ID0C606vtgjhZZYQNMHB\ B899AG02EjjFbiFViGNhHFgH8gNBjTDmYFoRGmLHlFIj9Ji3AA\ DPdMTaWXZd`VndSwhPmbOdXOVRNMLNCFM3AM5KO7UP8ccAmmBw\ SBHuj5gm6ao6Xr6Rt6Mv6Hg4C745T38E14HXFERCBMA8G75B52\ 52bGpJ8QWokRgdM`YITRDMK9ED476B49836524212mzT1zO1VJ\ 1NE0F9074h6zX4jM3VB1FXTXOLOGEG878VzHKeBAL5alFS_BJO\ 79C3gBP`9LV7HP6EI4AC37689ACFBAAJ9XFEQBHK7BD356nzPf\ qL_hHT_ELRAEI7793nZOaQIPHCC86UgZKTNAEBzPjeGVL8FDif\ 6NL68G348Z5BU49P37K26F24A135016gQ4XJ3MD1B6rkST6gL4\ XE3M71BtQChK9YF7MA4B52Wb0RX0MR0IM0DG09B0450nzAYe6H\ L3Dxq8c_4KIpi`ZUOHFCoq2fh1Y_1QR1HI0890nyGgqEaiCVaA\ PV8JN6CF4672vS4lN3bI2TE2J91940sRE`I9I94K39H27F26C1\ 5A14713502201KI1JwlCcW6KGcekZ_eUV_PQUEFIFFIAAC556o\ EzQ7VNyUJnPFdKBVF7KA3A50sJ0lG0eE0Zm0S90L70E4072efX\ XYQPPJGHD886`07R05I03901IrEFhBC_99R76I4392c3sX2iQ2\ `K1SD1I609OEQKBLG9HC7D848 } 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 20-09-11 (I am the Champion [8])
by Jim Muth 21 Sep '11

21 Sep '11

FOTD -- September 20, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image has claimed to be the best of all time. That's the impression I had when the name "I am the Champion" came to mind. The rating of an 8 is well above average. It's nearly of championship caliber, but then so is the team that loses the championship game. The parent fractal came about when I subtracted 1.1 parts of (1/Z) from 1.1 parts of straight Z then added (1/C) on every iteration. These parameters are pure whimsy; the resulting image is not. The parameters produce a very distorted Mandelbrot set with its incredibly shrunken main bud and spike pointing south and its grossly overblown East Valley on the north side. Today's scene is located in a minor sub-bud on the west shore line of the main bay. (The distortion of the parent fractal may be increased or reduced by tweaking the parameters.) To achieve the final effect, I used a very broad color palette on the outer parts of the image and a random palette on the inner parts. The prominent minibrot at the center lacks total definition. An increase in the maxiter will increase the definition of the minibrot but will also spoil the coloring. The calculation time of 4-1/3 minutes is slightly slow, but at least in my opinion, the image is worth it. Those who would rather avoid calculation may view the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is available in glorious high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Clouds and a few showers made today less than perfect here at Fractal Central, while the fractal cats said the temperature of 72F 22C was near perfect. The humans had too many other things to concern themselves with than to worry about a few showers. The next FOTD will be posted in 24 hours. Until then, take care, and there are only 458 days remaining until the world comes to an end. (Maybe I'll start a doomsday countdown clock.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= I_am_the_Champion { ; time=0:04:21.78-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.4851545446762787/+1.193349813944747/\ 2.2334e+010/1/-27.5/0 params=1.1/1/-1.1/-1/0/0/0/0 float=y maxiter=2400 inside=0 logmap=406 periodicity=6 colors=000Q4eR5dS6dT7dT8dU9dVAdWBdWCdXDdYEdZFdZFd_\ Gd`HdaIdaJdbKdcLddMddNdeOdfPdgQdfRcgQdhQdhQeiPejPe\ jPfkOfkOflOgmOgmNgnNhnNhoMhpMipMiqMjrLjrLjsLksKktK\ kuKluKlvJlvJmwJmxImxInyInyInzHmzHmzGlzGlzGkzFkzFjz\ FjzEizEizFmzEizDfzDczC`zBYzBVzASz9Oz9Lz8Iz7Fz7Cz69\ z56z53z64z75z86z97zA8zB9zCAzDBzECzFCzKXzF_zAbgRf`M\ _TITMDLE9E747ltccjXWaQOSKGJD896FHJBCE789344SJXMFQG\ BJB7D536JwfEhW9UL4FA0D_06Iqu4qMjcGZRBND5BhgtXXeMMS\ BBEi_INI9PsyLlqIeiFZaCSV9LN6EF377wCdsm_keUcZPWSKOL\ FGEA875gsmT`XEIGZggSZZLQQEHH788_JRI9DCiUAaP8UK6NF4\ FA275DD_66IEIguKyuIPbfzQSeDELsof`YSIHEnoFPQ7_WYURT\ uIzoKqcGcU9UK4_bKXYHRTFMOCGJABE7695A425x`xUIU7Fa6D\ X5BS49N37J25E139014LSvIOnFLgDH_AET7AM57E237bxsVkgN\ _XFOM7CBDuoBlg9d`7XT5OM3GE1879lH6WB3U5PUgKU_GUTCUM\ 8UE4U79Ur7cj6cb5cV3mN2mF1m7czrczjczbczVmzNmzFmz7zz\ czzWzzOzzGzz8zzXzzSzzOzzK } 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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<Alex>"PI" is a "Predefined Variable"
by Hal Lane 20 Sep '11

20 Sep '11

> ...formula for MandelbrotBC3... > ...in the second line of the formula what is PI? > It hasn't been defined? Is it 'p1' ? Alex, Fractint's 20.4 docs (pg 67) say that "pi" is a "Predefined Variable" whose case is apparently not important: pi (3.14159..., 0.0) - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 19-09-11 (Primed for Growth [7])
by Jim Muth 20 Sep '11

20 Sep '11

FOTD -- September 19, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Primed for Growth". Don't get excited however. The name refers to the fractal, not the economy, which is stuck in the doldrums and will likely remain there for the foreseeable future. Actually, the fractal has grown as far as is presently possible, so it can hardly be called 'primed for growth'. In fact, the magnitude of the image is already a little beyond the limit of resolution. The parent fractal came about when I iterated the expression Z^(2.15)+C at a level 2 turns up the complex-logarithmic hyperspiral with the 'recip' function applied. This parent appears as a Mandeloid rotated so that its main spike points south. The most notable feature however is a smaller totally cut-off Mandeloid just west of the main one. Today's scene is located deep in the East Valley of this cut-off Mandeloid. The rating of a 7 might be more wishful thinking that actual fractal worth. We have seen many superior images in recent weeks. The calculation time of 2 minutes is a real bargain, so why not run the included parameter file and enjoy the result. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and escape the task of running a parameter file. See the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The traditional FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Today brought a mixture of sun and clouds to Fractal Central. The temperature of 66F 19C was comfortable enough for the fractal cats, who spent an unusual amount of time watching for passing stray cats, none of which ever appeared. The humans had a typical day, which means nothing out of the ordinary happened. The next FOTD will appear in 24 hours, and it most certainly will be an event worth noting. Until then, take care, and if anyone can determine what's wrong with the world, please let me know. My best guess is that there are too many people living on the planet. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Primed_for_Growth { ; time=0:02:09.57-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip logmap=346 center-mag=-0.8880134461033687/+0.1672559185329798\ /4.03156e+012/1/115/0 params=2.15/0/2/0 float=y maxiter=1500 periodicity=6 mathtolerance=0.05/1 colors=000cccH1AK4AN7ARAAUDAYGA`JAdMAgPAkTAnXAr`Au\ dAwhFvjGvkGrkGmlHhmHcmHZgFUaDPWCKQAFK8AE75851345VH\ 8bUBtfIfdPTcWFaa2`_8SZEJIJ_2OpPfPRdMTcJVbGXaEZ`B`_\ 8bZ5dY3aX9_WFYVKWUQUTWSS`PNTNJLKADIA6KA4KA2wU0mb8d\ cGVdOMeVKeSIePGeMEeKLWIRNGYDEc4CeHDfTDgdDfhTelhdmw\ aHmZJdWUW`UAUUPNUbGUptUxmUsfUo_Uk0Ud8UhGUgNUg6neIt\ f2VFGjURjrBg2GlDLzNQxY_wkgYvAGkKciiivenrarnYvjdbt`\ joXrkR1lSHjTWiUkhe4EkR5bhP5giClhIqhOvgdS9WlsVppVsm\ Uwj4GKDWSMk_e3yaNsYfmV52UYNB7oLZk8`TEgXJm`Ptd5uLIx\ XhSnyOYqY`igbaqev7BnLKgZS`l_jEMX_9ukpnomgsk`witKsk\ ZoblkgzGczN`zUXz`WSwVio`hcZmdXqeVvfinceqdateYwfZju\ WrnTN7UXHUfQUpZ0NsIeyOppEnaMtdJLYPebYsTXuXWw`VydWs\ nVwjykwisouRtkbobnkipyestaupYxkDgHMqV7loDpmJskPwi2\ 7W9LZGZaNldC`iHghLmhQtg0xdFyf1y9BzLLzX9iIGoRNu_XdX\ Wl`VsdCXDIfOOpYwqoJja52_`c4taakjcbre4F4HbOyjNSI7VX\ uLFYOVaRjdqyXiz`azdKKBKK6 } 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 18-09-11 (Mired in the Mud [6])
by Jim Muth 18 Sep '11

18 Sep '11

FOTD -- September 18, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a scene unusually deep in the parent fractal that results when 0.5 negative parts of Z^(-3) are combined with 0.5 negative parts of Z^(+3) on every iteration before straight 'C' is added. The magnitude of over 2*(10^14) is about as far as is possible to go without resorting to arbitrary precision math. The parent fractal appears to be a Mandelbrot set rotated 180 degrees and almost totally filled in. Except for a scattering of tiny cracks, only four open areas remain -- a reasonably normal Mandelbrot set where the large period-2 bud would lie, two twisted M-sets where the two period-3 buds would lie, and where the East Valley area would lie, a Mandelbrot set that appears to have grown an extra large period-2 bud. Today's scene lies deep in the valley that sets off this extra large bud. To me, the image resembles nothing as much as a puddle of bubbling mud with a minibrot floating in the center. The breakdown of math resolution is visible at the sharp-edged band edges, though it is not quite enough to spoil the scene. I named the image "Mired in the Mud". The overall coloring resembles the gray-green colors of the ground in the areas that were flooded here at Fractal Central. It's surely not a very attractive color scheme, but I must draw it as I see it. Such unpleasant colors hold the rating to a 6, which is actually below FOTD average. But they say we must take the bad with the good, so why not take the 22 minutes required to run the parameter file. On the fastest SOTA machines the image will probably finish in much less time. Check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> without the need to calculate it. The image is available in high definition 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/> Today came on with lots of sun here at Fractal Central, and except for a few puffy white decorator clouds, the sun reigned supreme all day. The temperature of 70F 21C could hardly be improved upon. The humans had an uneventful day, which is as much as can be hoped for. The next FOTD, likely an improvement over today's, will be posted in 24 hours. Until then, take care, and could we now be witnessing the start of the decline and fall of the American Empire? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mired_in_the_Mud { ; time=0:22:22.51-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.00000008953753835/+0.065245723747392\ 53/2.363e+014/1/-71/0 params=-0.5/-3/-0.5/3/0/0/0/0 maxiter=25000 periodicity=6 mathtolerance=0.05/1 colors=000000V0VP0QK0LF0FA0A505KBDJACIABH9BG9AF8AF\ 89E79D78C68B67A57A56955845744634533523422312211101\ 000LSBHN9EI7AE5793341WTMURKeaQeaPdaNd`Ld`Kd_Ic_GcZ\ FcZDcZCbYEbXGbWHbVJbUKbTMbSNaRPaQRaPSaOUaNVaMXaLYY\ P_VTaSXcP_eMcgJgiGjkDnmAmo7ppFhlMeiUYf`VcgY`c`b`cc\ YbeV`fS_hOYiLWkIVlFTnCSoDTmEUlFUkGVjHViIWhJWgKXfLX\ eMYdNYcOZbPZaeOJvD1sC2pC2mC2jB3gB3dB3aA4ZA4WA4T95Q\ 95N95K86H86E86C86GB9JDBNFEQIGUKJXML`POcRQgTTjWVnYY\ q__n`YkaWibVfcTddSaeQZfOXgNUhLSiKPjIMkGKlFHmDFnCCo\ A9p87q74r52r48Zf9YdAXbBWaBV_CUYDTXDTVESTFRSFQQGPPH\ ONHOLINKJMIJLGKKFLJDLJCJHBHFAFE9EC8CB7A96610875764\ 543332111TMHNHDHDAB86543gCjdBgbAe`AbY9`W8YU8WR7TP6\ RN6OK5MI5JG4HD3EB3C929617414202TrAJ_69I37c46Z35U34\ P23K22F11A1050mWpiTleRhbPdZM`WKYSIUPGQLDMHBIE9FA6B\ 747323vNirLfoKdlJaiI_fGXcFV`ETYDQVCORALO9JL8GI7EF6\ CC49937624312t1un0oi0jd0e } 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 17-09-11 (Escape to Nowhere [7.5])
by Jim Muth 18 Sep '11

18 Sep '11

FOTD -- September 17, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a scene in the parent fractal that results when 1.5 negative parts of Z^(-5.1) are combined with 5.1 negative parts of Z^(-1.5) before (1/C) is added on every iteration. This parent is a fractal in the shape of a vertical string of three large bays, with a 'fan' extending east from the origin. Today's image is located in a small field of disconnected debris just south of the southernmost large bay. Since the scene of the image is not connected to the main body of the parent fractal, the elements surrounding the central minibrot are also disconnected. These disconnected shards do make a rather attractive scene however, raising the rating of the image to a respectable if not outstanding 7-1/2. I named the image "Escape to Nowhere". The name has a kind of ominous feeling to it that matches the rather somber blue background of the image. The calculation time of a fireball fast 34 seconds assures that any disappointment after running the parameter file will be minor. To avoid the possibility of even a minor disappointment, check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and avoid calculation altogether. Check the high definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site mat be accessed at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds with a temperature around 64F 18C made today a rather pleasant one here at Fractal Central. But the fractal cats are already becoming impatient for the heat to be turned on. They will have to wait a bit longer however; the season is still summer. The humans took a short antiquing trip during the afternoon, finding nothing of unusual interest. The next FOTD will be posted in 24 hours. Until then, take care, and look alive. You'll have time enough to look dead. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Escape_to_Nowhere { ; time=0:00:34.50-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.07838913653024948/-1.538208956794496\ /9.44489e+011/1/172.5/0 params=-1.5/-5.1/-5.1/-1.5\ /0/0/0/0 float=y maxiter=1500 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000BWGAUF9RE8OC7LB6J92225G84D73A52841520217\ Gn5Cc49U26K13AwHnnEfeC_Y9TP7LH4E827I1WG0TF0RE0PC0M\ B0KA0I90G70D60B509306204102v2Jq1Hl1Fg1Eb1CY1BT19O0\ 7J06E0490340100Y00W00U00T00Q00Q00O00O00L00I00J00I0\ 0H00F00E00C00B009008007005604002001GmlCcb9UT6KJ3A9\ VuLSzJPjHMeFJ_DGVBEQ9BL78F55A3251zi0oW0nS1cO0dL1SH\ 0YE0HA0B70530c2zc1zc1zc1zc1zc1zU1zK1zD1UC1SB1QA0N9\ 0L80J70G60E50B409307204102lBj_8ZO5NC2BmDDjCCgBBeAA\ bAA_99Y88V88S77Q66N66L55I44F44D33A22722511200JbsHZ\ mFVhDScCOZALU8HP6EK5AF37A135U81R70P60M60K50THmXHk_\ HjbHheHfhHdkHcjGaiG`hF_hFZgFYfEXeEWeEVdDUcDTcDSYFT\ SGTNHTHJUBKU6LU8PV9SVAVVCYVD`VEcVGgVHjVImVKpVLsVMv\ VNyVi9Jk7Rm6Zo4fq3nr2vq6wpAwpDwoHwoLwnOwnSwmVwlZwl\ bwkewkiwjmwjpwitwiwwyx0xt3xq5wn7wk9whCveEvbGv_IuXK\ uTNtQPtNRtKTsHVsEYsB_r8ar5cr2elCcfMaaV_WdYQnWLwVKt\ TJqSInQHlPGiNFfMEcLDaJCZI } 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 16-09-11 (A New Seahorse [7])
by Jim Muth 17 Sep '11

17 Sep '11

FOTD -- September 16, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows a little object I turned up while wandering aimlessly in the depths of Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set. I'm not sure it's proper to refer to fractal patterns as objects, since they have no physical reality and certainly no mass, but then, photons have no mass either and we see them everywhere. (I'll leave it to the erudite physicists to debate whether photons, and all the other sub-atomic 'particles' for that matter, should be considered objects.) I named the image "A New Seahorse" because I've never before seen a similar 'object' in a Seahorse Valley". The rating of a 7 is FOTD average, though with a calculation time of over 96 minutes, the image is over-priced. The calculation time is slow because the image is located quite deep in its parent Seahorse Valley, where the iteration count is very large. Perhaps the most striking feature of the image is its reddish background. I usually prefer deep blue backgrounds, but for some reason the red background of today's image worked well enough, at least for this one fractal. Instead of reminding us of a heaven up there, the image hints at a hell down below. To avoid the cumbersome calculation, view the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> or view the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Today brought a taste of autumn to Fractal Central at the end of summer. The weather was sunny, but the morning temperature of 43F +6C kept the fractal cats totally in cold-weather mode. The humans, always alert for weather changes, realized that warm weather does not prevail year-round in the temperate zones, and had a few thoughts about preparing for the coming cold and snow. The next FOTD will be posted in 24 hours regardless of the weather. Until next time, take care, and with all the cameras around, when will we get a convincing photograph of a BESA (bug- eyed space alien)? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_New_Seahorse { ; time=1:36:54.91-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7685296106390\ 0714/9.92063871520498e-5/4.171863e+014 params=0/0 float=y maxiter=500000 bailout=9 colors=00000eihTijVikWilYimZin_ioaipbiqcireisfithi\ uiivjiwlixmiynkdemLXo1Om4Tl7YkAbiCghFlgIqfKugHphFk\ iCfjAak8Xl5Sm3Nm1JtKarJ`pI`nH`mG`kF`iE_L10M20N30O4\ 0P50Q60R70S80T90UA0WC0YF0_I0aL1cO1eR1gU1iX1k_1mb1o\ f1rj1tn1wr1yu1zp2zl2zh2zd3z_3zW3wS4rO4mJ4hF5cB5a75\ _35ZB6ZI7YP7YW8Xb9Xi9WpAWwASj8OZ7KN6HB5LDFTrVRmTPh\ ROcQMZOLUMJPLIKJGFH7vX9lTBbQCUMEKJgKdbI_YHWTFSOEOJ\ CKPuCNnDMgEK`EJVFHOFGHG`0hZ1eX2cV3aU4_S5XQ6VP6TN7R\ L8OK9MIAKGBIEIdFHbFHaFH`FG_FGZFGXFFWFFVFFUFETFERFE\ QFDPFDOFDNFCLFCKFCJFBIFBH9aFA_GAYGBWGBVGBTGCRGCQGf\ zzezzdzzczzbwzauz`sz_qzZozYmzXkzWizVgwUerTdlTbjS`g\ RZfQYcQXaPWZOUXNSUNQRMOQLLPKJOKGNJEMIBLHAKH8JG6IF4\ HE2GD0FC0EB0DA0C90B80A7096085074063052041030020010\ 000000000000000000008x4Bg8DRCf4D`6EV7FQ9FKAGNWPMUO\ LSNLQMKPMJNLJLKIJJHIJHGIGEHFCGCR5DQ6DP6DP7DO7DN8DN\ 8DM9DL9ELAEKAEJBEJBEIBEHC } END PARAMETER FILE=========================================

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FOTD 15-09-11 (The Inns and Outs [6.5])
by Jim Muth 16 Sep '11

16 Sep '11

FOTD -- September 15, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image lies in the debris-filled radical of a minor bud on the northwest shore line of the large period-2 bud of the Mandelbrot set. The image lies at the extreme limit of the range of conventional math, which makes it a very fast one. In fact, the magnitude is so great that breakdown is already appearing, but due to the low contrast along the band edges, it is not very noticeable. The rating of a 6-1/2 includes a half-point for the coloring, and even this rating might be a bit liberal, considering the small amount of effort I put into the color palette. The name "The Inns and Outs" is a play on words inspired by the filaments in the image that flow into the large magenta areas then flow out again. The calculation time of 13 seconds is about as fast as images get. So if the result of the calculation is disappointing, little time will have been wasted. The official FOTD web site, with the completed image, may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The image, in high definition, is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site, as old as the FOTD itself, may be found at: <http://www.Nahee.com/FOTD/> Heavy clouds and occasional rain made the conditions less than ideal here at Fractal Central today. The temperature of 55F 13C kept the fractal cats in cool weather mode, while the humans, always cool, had an uneventful day. The next in the unending but not eternal series of FOTD's will be posted in 24 hours. Until then, take care, and how many times does the phrase 'could it be' appear in those UFO shows. (IMO, interstellar aliens visiting earth in their interstellar space ships are even less likely than ghosts. Ghosts have never been proved to be impossible. They merely show that there is much to yet be discovered. But the faster-than-light velocities that would be necessary for aliens to travel the galaxy in physical ships within a reasonable time, are known to be impossible. And warp drive, etc., etc., is a great fantasy. Unfortunately, it's just a fantasy.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Inns_and_Outs { ; time=0:00:13.79-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.1724126660170\ 22/+0.1811493728619075/1.936251e+013/1/135/0 params=0/0 float=y maxiter=32767 bailout=9 inside=255 logmap=1268 mathtolerance=0.05/1 colors=000s0Zt0cu1hu2mu3it4gs5gr6eq7dp7an8Wk9Rh9Ld\ AEZF8VK2UU9UcGTmMpmcmlcjkcgjcdidahdZgdWfdTedRdeRce\ RceRceRcfRcfQcfQcfQcfQcgQcgQcgQcgPchPchPchPchPchPc\ iPciOciOciOcjOcjOcjOcjOcjNckNckNckNckNclNclNclNclM\ UmMUmMUmMUmMUmMUnMUnLUnLUnLUoLUoLUoLUoLUoKUpKUpKOp\ KOpKOqKPqKPqJPqJPqJPrJPrJPrJPrJQsIQsIQsIQsIQsIUtIU\ tIUtHUtHUuHUuHUuHUuHUuHUvGUvGUvGUvGUwGUwGUwGSwHTxG\ SwGSwGSwGSwGSwGSwGRwGRvGRvGRvGRvGRvGQvFQvFUvFUuFUu\ FUuFUuFUuFUuFUuFUuFUtFUtFUtEUtEUtzm0zOUEAUENsENsEN\ sENsENsEMsEMsEMrEMrDMrDMrDLrDLrDLrDmUD0qD0qD0qD0qD\ 0qD0qD0qC0qC0pC0pC0pC0pC0pC0pC0pC0oC0oC0oC0oC0oB0o\ B0oB0oB0nB0nB0nB0nB0nB0nB0nB0nB0mB0hB0hA0hA0hA0hA0\ hA0hA0hA0hA0hA0hA0hA0hA0hA0h90h90c90c90c90c90c90c9\ 0c90c90c90c90c90c80c80c80c80c80Z80Z80Z80Z80Z80Z80Z\ 80Z80Z80Z70Z70Z70Z70Z70Z70Z70U70U70U70U70U70U70U60\ U60U60U60U60U60U60U60URRc } END PARAMETER FILE=========================================

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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 13 Sep '11

13 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 11 Sep '11

11 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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FOTD 07-09-11 (Emerald Anxiety [7])
by Jim Muth 08 Sep '11

08 Sep '11

FOTD -- September 07, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the East Valley of the large minibrot on the main stem of its parent Mandeloid. Nothing unusual in that. But in today's case, the Mandeloid is not the classic Mandelbrot set; it is the figure that results when the expression Z^(2.15)+C is iterated 9 levels up the hyperladder. The parent fractal resembles a Mandelbrot set rotated so that its main spike faces northwest instead of west. The southern lobe of its main bay is also grossly swollen, though this peculiarity has no significance in today's image. The shape of the minibrot at the center of the image closely resembles the shape of its parent. The pattern around the minibrot in the image gives the impression it lies close to the cut-off point of its parent. But such is not the case. The scene actually lies quite close to a discontinuity. These breaks sometimes act as cut-off points. The rating of a 7 is FOTD average. The name "Emerald Anxiety" refers to the emerald coloring of the scene. The word 'anxiety' was added for artistic reasons. The calculation time of just over 1-1/2 minutes is pleasantly brief. The completely calculated image is posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is posted in glorious high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The venerable original web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy rain with embedded torrential thunder-storms prevailed all day today here at Fractal Central. As of the 5pm post time, about 10 inches or 25cm of rain has fallen, and it is still coming. The fractal cats wondered what all the water is about. The fractal sump pump is doing its job, but the floor is still covered with puddles. The humans had a day of checking for new leaks, of which several appeared. The next FOTD will be posted in 24 hours. Until then, take care, and the local farmers prayed for rain during June and July, and now that the Deity has answered their prayers, they are praying for the rain to stop. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Emerald_Anxiety { ; time=0:01:37.44-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=-0.9395175176009618/+1.332146256656035/\ 3.199834e+009/1/155/0 params=2.15/0/9/0 float=y maxiter=5000 inside=0 periodicity=6 colors=000x5bV_eRV_NRVJMQFILBDF79A345RVgwkxmcmcWcU\ OUKGKA8AtDTlBPe9LZ8IS6EL4AE37713O`KCIAcoAXf8QY6KQ5\ DH3681K5_D3O61C0B8096075064043s2JqVHpwGeZDAAADDDFF\ FIIILLLPPPUUUZZZccchhhmmmrrrwwwzzzswlptfmqajnXgkRd\ hMbgHWSRQC_M`fIxmOrgUlbZfYd`TjVOoPJuJEzD9aPED`JATF\ 1837MB5E7273alwPWcCGKe`clDlO6OfAxW7hL5UA2FAN55B2GN\ D8B6OgaK_VGTPCMJ8EC4766q35k24c23U12K11A0hUgbP`WLVP\ HPJCIC8C5462n_1PIxAEc69K344gR3XK2MD1B62wD1c80K4zSl\ rOejL_bHUVEONAIF7C736cFuQAaD5JeYlVP_LHOA8ClVgOFMyA\ ep8_g7UZ5OQ4IH2C816N0SB0EG__DUUBPP9KK6FF4AA255`wdI\ UK_ezV_wRVqMQjILdDFY9AS45QoR2ObwKWmGQcCJU8DK46AIiw\ 1jM0ZG0NB0B5FgCAT85E4dLWRELD7AmBfz5LzlqzORzc`zaGzu\ 5zT2zxCzk9z_7zO4zC2z1uz0kz0az0Tz0Jz09zqTzjPzcLzXIz\ REzKAzD7z63zEKznWzcPzUJzKCzA6U2oU1bU1Qc0DcUWcOPcIJ\ cCCm66`VRRNKzFDz76zTwzNkzH_UBOU5CUZhUUbUQXULSUHMUD\ GU8BU45UDoU9bU6QU3DUUCUF6 } 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 06-09-11 (An Act of Numbers [8])
by Jim Muth 06 Sep '11

06 Sep '11

FOTD -- September 06, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today, we take a short trip back into the depths of the Mandelbrot set, where we check the tip of a minor filament extending from the northeast lobe of the main bay of the large minibrot on the main spike of the M-set. We find today's scene at a depth of over 10^47, where the filaments have become so numerous that they form a circular pattern that almost appears to be a series of overlapping concentric disks. The name "An Act of Numbers" is true of all fractals, and perhaps true of the sub-atomic realm as well. I'll not speculate on the 'real' physical world, which after all is composed of sub-atomic particles. The rating of an 8 shows that there is much to yet be found in the moderately deep depths of the Mandelbrot set. The calculation time of 7-1/2 minutes is surprisingly fast for an image of such magnitude. For convenience, the image has been calculated and posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is posted in high definition 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/> Steady all-day rain made today a day to be forgotten here at Fractal Central. The temperature of a chilly 63F 17C added nothing at all. The fractal cats made the best of things from their indoor watch posts. The humans did what humans do in bad weather -- they took care of indoor tasks. The next FOTD will be posted in 24 hours. Until then, take care, and what would happen if we changed the numbers that rule the cosmos? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= An_Act_of_Numbers { ; time=0:07:33.39-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7398862009229\ 2716794826475168986805702702997920619/0.0121740795\ 736008844348618774004549150492589525494697/\ 1.5923e+047/1/30/0 params=0/0 float=y maxiter=10000 bailout=9 inside=0 periodicity=6 colors=000dBv`BvWBvRCvNCvICvjY0ECvHHsJMqLRnNWlwMZP\ _jNTeMN`KGWJASOSWSh_jqNejO`ePW`QRXQMTRHPSCLT1CM8IT\ FOZLUdS_jYepXbjX`dWZZWXTVVNVTHiF3VRCGbL1nU4kY6h`8e\ dAbgD_kFXnHUrJRuELq9Fm17o4Ai6Dc8FYBISDLMJL4FNGBOS8\ Pc4Qo1Rz7TyCUxIWwNXvTZuY_tZYq_Xn_Vk`Uh`SeaRbiNiaQ`\ USTMUL1c2FWDQTETPNWMWYId`FmbCuaDsaEq`Fo`Gn_Hl_IjsM\ X_IiHFzGEuGEpFElFDgEDb05XEDZSK_eSarY`sZbtZduZerQZo\ HSm7Nl8Ll8Jl8Hl8Gl8El8Cl8BkDFjIJjNNiSRiXVhaZvsRhfb\ VUnIIzPMvWQs`RzaTpbUgcVZdWQdXH`SLXOPUJTQFXetlNB_VO\ ea`jhmooytbmjRb`y3YoAYfGYXMYLQ`OSYQTWSUTUVRXXPZYM`\ ZKcVAb_IbaSacQ`eO_gMZiKYkIiyFYlHN_I02A03F04K15P26U\ 37Z48c59h5Am8BrAJmDPjFUmI`mKgpOovRwzKcgHUcEKZAAUK0\ PU0Kzhzx`zxPwrUqlSkfQe`O_VMUPKOJIIAB9DHCGMFKRIPXLU\ aOZdEcfQhjDmh0hg4ce7ZdAUbEPaHK`KIXH3QF3KD2FB2CA2A9\ C7CE5FJ7II9LHBOGCRMDQSEPYEOcFNgBJiFNkJRlNUnRYoV`qZ\ drag4pzzzz4pzoKFpGFnAviBv } END PARAMETER FILE=========================================

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FOTD 05-09-11 (madhouse [7.5])
by Jim Muth 06 Sep '11

06 Sep '11

FOTD -- September 05, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: POSSIBLE NEW FORMULA ALERT! I might not have previously posted the Mandel-V-Esc formula, which allows changing of the bailout radius. I'm not sure. Today's rather weird image involves a couple tricks. The image itself is located in the East Valley of the large minibrot at -1.75 on the main spike of the Mandelbrot set. The first trick is rendering the image with the 'outside' set to 'real'. This adds the intricate detail to the scene. The second trick is coloring the image with a random color palette, though I did do a bit of tweaking to tone down the randomness at least a bit. This creates the frantic madhouse effect that inspired the name "Madhouse". The third and greatest trick is setting the bailout radius to the point just before the image gets cut off and goes blank. In today's case this point is 3.079. To see what this does, calculate the image with the real(p3) parameter set to 4, or even better, set it to 100. All these tricks add up to a rating of 7.5, not bad, but far from the super 9.5 images of last month. The calculation time of one minute is unexpectedly brief. Part of the briefness is due to the fact that the points are beyond the bailout radius almost as soon as they get started. The large flat areas also increase speed by making the passes=guessing option more efficient. View the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> View the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original site may be accessed at: <http://www.Nahee.com/FOTD/> Over two inches, 5cm, of rain fell overnight Sunday here at Fractal Central, Monday remained cloudy, with occasional rain and a temperatre of 75F 24C. The fractal cats, unconcerned with the weather and forecasts of much more rain to come, found their day's excitement by chasing each other in and out of the laundry basket. The humans, never short of things to worry about, spent the day wondering what the future holds. For better or worse, the next FOTD will be posted in 24 hours. Until then, take care, and even Bozo the Clown could run the world's fast-fading superpower better than the present loser and the losers lined up to replace him. Why not elect Bozo. At least we would go down laughing. P.S. The evil ______________ is/are responsible for the country's troubles. (Fill in the blank with your favorite scapegoat or goats.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Madhouse { ; time=0:01:02.45-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Mandel-V-Esc center-mag=-1.74986747029\ 1717/+0.00000006095707203/4.771027e+009/1/-130/0 params=0/0/0/0/3.079/0 float=y maxiter=2250 inside=0 outside=real periodicity=6 colors=0009jq6VH3F8hXdUMDFB6b3u02f01T`0EzleeWSVGU9\ DV46FjEFZABN77B3375xSmEIX99G4Cv5SP1zzz81AD58I86NC4\ SF3RI6QL8POAPQC5GJW8EZPtRcpJqmPhhV_d`S`TISL9KE0Cyc\ xcvGCh19X06M0OI63B0i0kY0_N0OB0CdKOKACAzSZK99We6LS3\ AEQFID79JZeCNS6BE84q63c42R21D7HVpqabcSQRJDD9vhW7fM\ 5WG3LB1A5hn_MPI8gyISk9EODBx87c43KJhqEXc9MR4BD3pd2b\ U1QK0DAo8GY5AH25cC3K61QAkD5Og8LT5EE276lksSteLeSESE\ 7Ec88Q55D22Rg4IT29E1eTqd1XR0MD0BQu1Jf0DT06E0lD7uim\ inbUYQFHD3Ob1CJ97NAEY57HE8PNGIVJCFC6SJQZKHMC8UR3KI\ 2D91E8T_MOIJWCKQ6ADcGES97dLbhQdUORFCD2cn1SP54S22E3\ dv2Ug1KT0AEbZ1TQ0JH0980C8L64AMq_E_O7IC0W20G1OHBIC8\ C85642GtBCe88S54E2LHfFCWA8L54AR0TD0E9y1ocIbUDQK9DA\ 4Tt3IXSCMI6B9kk7OO3dCRU9KK6DA360UCd0RxBebFxQAcD5K6\ RhcPzUIjKCVA6FD`QW_oWAGG58Dya8dP4KCZX`QORHGI889yYL\ dMEKB7ZTK7id5YU3NK1BAX6eM4SB2EKO5DG3681lT8ilANO51O\ N0CBTdoEKQgzZvdzgUmTKPEAz } frm:Mandel-V-Esc {; changeable bailout radius z=p1, c=pixel+p2: z=sqr(z)+c, |z| <= p3 } END PARAMETER FILE=========================================

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FOTD 04-09-11 (Tangent to What? [6.5])
by Jim Muth 04 Sep '11

04 Sep '11

FOTD -- September 04, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is named "Tangent to What?". The name refers to the 'atan' outside fill that created the slightly unusual pattern surrounding the central minibrot. The word 'slightly' explains the humble rating of a 6-1/2. Had the scene been a bit more unusual, the rating might have been a point or two higher. The image is a scene in the period-15 radical on the southwest shore line of the Z^(1.998)+C Mandeloid as it appears 3 levels up the hyperladder. The parent fractal resembles an everyday Mandelbrot set rotated about 30 degrees CW, so that the negative X-axis passes through the south branch of Seahorse Valley. In these almost-whole-number Mandeloids, most of the action lies along the negative X-axis. But with the MandelbrotBC3 formula, Mandeloids may be rotated so that any desired part is intersected by the X-axis, giving the ability to subject any desired part of the almost-M-set to distortion. The calculation time of just under 6 minutes is too long for comfort. Once again, thank goodness for the web sites. The official FOTD web site with the finished images may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high definition images are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site with 14-1/2 years' FOTD images is at: <http://www.Nahee.com/FOTD/> The day began with fog here at Fractal Central. At 9am a brief but lively thunder shower passed over, which was followed by a warm and unpleasantly muggy morning and a rather hot muggy early afternoon. Another brief but heavy thunder shower passed over around 3pm, doing nothing but adding more humidity. The high temperature of 86F 30C combined with a humidity around 90 percent kept things feeling like the Pacific end of the Panama Canal, which BTW is farther east than the Atlantic end. The fractal cats have never been to Panama, and never will be, but they know what to do in muggy weather. They stretched out in the coolest place they could find. The humans spent the day relaxing. (The more we do it, the more we like it.) The next FOTD will be posted in 24 hours. Until then, take care, and who will be the one to get rich making shoes for bigfoot? When we find one, it is sure to need some pretty big shoes. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Tangent_to_What? { ; time=0:05:53.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.760974178524143/+0.0000000293206752/\ 8.129853e+010/1/22.5/0 params=1.998/0/3/0 float=y maxiter=3500 inside=255 outside=atan periodicity=6 mathtolerance=0.05/1 colors=000dsidsgdsedscdsads_dsYdsWdsUdsSdrQdrOcrMc\ rKcqIbqHbqHbpIapIapJapJ`oJ`oK`oK_nK_nL_nLZnLZmMZmM\ YmMYlNYlNYlNXlOXkOXkPWkPWjPWjQVjQVjQViRUiRUiRUhSTh\ SThSThTSgTSgTSgURfURfVRfVQfVQeWQeWPeWPdXPdXOdXOdYO\ cYNcYNcZNbZNbZMb_Mb_Ma`La`La`L`aK`aK`aK`bJ_bJ_bJ_c\ IZcIZcIZdHZdHYdHYeGYeGXfGXfFXfFXgFWgEWgEWhEVhDVhDV\ iDViCUiCUjCUj8ViAUjBUjCUjDTjETkFTkGSkHSkISkKRlLRlM\ RlNQlOQlPQmQPmRPmSPmTOmVOnWOnXNnYNnZNn_Mo`MoaMobLo\ cLoeLpfKpgKphKpiJpjJqkJqlIqmIqnIqpHrqHrrHrsGrtGruG\ svFswFsxFszDryEsyFsyGsxHsxIsxJsxKswLtwMtwNtvOtvPtv\ QtvRtuStuTuuUuuVutWutXutYusZus_us`vsavrbvrcvrdvqev\ qfvqgvqhwpiwpjwpkwplwomwonwoownpxnqxnrxnsxmtxmuxmv\ xnwymvxmvxmvxmvwmvwmvwmvvmuvmuvmuugtcerccpcanc_lcY\ jcWhcUfcTdcSbcS`cR_cRZbQYaQX`PW_PVZPUYOTXOSWNRVNQU\ MPTMOSLNRLMQKLPKKOKJNJIMJHLIGKIFJHEIHDHGCGGBFFAEF9\ DF8AF8AF8AF8AF8AF9AF9AF9A } 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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Getting corners or center-mag info from fractXXX.tga
by Jason Hine 03 Sep '11

03 Sep '11

Hi again, I don't suppose there's any corners or center-mag info hiding in the fractXXX.tga image header? It doesn't look like it, but it never hurts to ask. It's not critical, as I can find other ways to get that info (i.e., from a PAR), but it's be oh-so-handy if I could just read it from the TGA... - Jason -- Cheers from Mr. Tumnus! "Here... take my handkerchief." Hoofing it bare-chested since 1974.

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FOTD 02-09-11 (Armageddon Aspect [?])
by Jim Muth 03 Sep '11

03 Sep '11

FOTD -- September 02, 2011 (Rating ?) Fractal visionaries and enthusiasts: Today's image immediately impressed me as a view of a nuclear explosion seen from a distance of a couple miles. Since a nuclear war is the most likely way the world might end, I promptly named the image "Armageddon Aspect". The image is a view of the north edge of the infinitely-divided main spike of the Z^(2.000001)+C Mandeloid as it appears in the East Valley area of a minibrot located around -1.86 on the spike. Some curiously corrupt minibrots lie at the heart of the nuclear explosion. I may check one of these for the next FOTD. Armageddon is the name given to the supposedly soon-to-come ultimate battle between the forces of good, led by God, and the forces of evil, led by the evil one himself. We are assured the forces of good will triumph, but the battle will leave the planet in ruins and the survivors wishing they had believed some of that stuff the fundamentalists tried to tell them. (The full details are in the last book of the bible, but you'll need a program and score card to find your way through the symbolism.) How could I rate an image that pictures the end of the world? I could not. So I gave it a rating of a question mark, which leaves the rating to be decided by the individual viewer. The image calculates in a very brief 27 seconds, a much shorter time than it will take the forces of good to defeat the forces of evil in the big battle. The annoyance of setting up the parameter file for calculation may be avoided by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version may be accessed at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site is at: <http://www.Nahee.com/FOTD/> The clouds hung overhead most all day here at Fractal central, while the temperature of 77F 25C kept the fractal cats happy. The humans kept moderately busy doing commercial stuff and moderately happy pondering the possibility of retirement. The FOTD is in no danger of being retired however; in fact, the next one will be posted in 24 hours. Until then, take care, and be satisfied with the world as it is, with all its problems. It's not going to change any time soon. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Armageddon_Aspect { ; time=0:00:27.19-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN center-mag=-1.860582987215\ /+0.000005006572/2.4e+008 params=2.000001/0/0/0/0/0 float=y maxiter=10000 inside=0 periodicity=6 colors=00000z00w00s00p00l00i00e00N00L00J00H00F00D0\ 0B009007005003001000106A05K04U03c08h6DoAItFMzJXzYf\ zdpznfzmfzrfzvfzzfzzfzzpzzpzzzzzzzzzzzzzzzzzzzzzzz\ zZiq`ipbhnehmghligjkgimghoffqfesfdh_aZTZPMWFGUJGWN\ GYRGZVG`ZGabGcfGejGfnGhqGinFkkElhDmeCnbBo_ApXAqU9r\ R8sO7tL6uI5vF4wD4xC6uB7sA9q9An8Bl7Dj6Eg5Ge4Hc3Ia4L\ `5O_5R_6UZ6XZ7_Y8bX8dX9gW9jWAmVBpUBsUCvTCxTGuUKrVO\ oVSlWWiX_gXcdYgaZkZZoW_rU_qTWqTTpTPpTMoTJoTFnTCnT9\ oP9pL9rHAsDAt9Au5ApSKlnUflQ`kNWiJQhGLgDJdFIbHH`JGZ\ LFXMJZVM`cQbkTdtWezkbaz_CwZNuYYrXgpWrnWziTsdRk_OcW\ MVRJNMHFIF7FCHC9M97864M42`BHgIWoPjvWzzmzzszzzzzb9q\ YCkUEePH`LJVGMPCOKA`O9mR8zUEyRJyOOtMWjVgecp`lzeuzn\ shlqcpoZsmUvlNi`GXQ9LFGOKRQOXSTlUXiWWgXWiYVgZVe_VY\ WLQTCJc3Hm8FmDDmIBmM9mR7mW6m_9zVCzQFzLFzNzzOzzPzzQ\ zzSzzTzzUzzVzzVzzVzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Re: [Fractint] Deep Zooms
by Jim Muth 02 Sep '11

02 Sep '11

At 10:54 AM 9/2/2011 -0700, you wrote: >I would like to thank both Jim Muth and Mike Frazier for providing us with excellent examples of scenes deep in the Mandelbrot set during the past month. > >Brian Prentice I surprised myself with the things I found down there. I might do another deep-zoom month in october. JIM

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Deep Zooms
by Brian Prentice 02 Sep '11

02 Sep '11

I would like to thank both Jim Muth and Mike Frazier for providing us with excellent examples of scenes deep in the Mandelbrot set during the past month. Brian Prentice

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FOTD 01-09-11 (Net of Convergence [6])
by Jim Muth 02 Sep '11

02 Sep '11

FOTD -- September 01, 2011 (Rating 6) Fractal visionaries and enthusiasts: The month of August with its very deep Mandelbrot scenes has ended, and it produced some winners for sure. The end of August does not mean we will never return to the very deep Mandelbrot fractals, but for a change we return today to the regular FOTD routine, and start with a scene in the parent fractal that results when 11 negative parts of Z^(-1.1) are combined with 2 negative parts of Z^(-6) before (1/C) is added on every iteration. The resulting image rates a 6, a notable come-down from the 8's and 9's that prevailed during part of August. But what the heck? Even a rating of a 6 is above average, and the calculation time of 5 minutes means that little time will have been wasted if the image elicits a yawn. The name "Net of Convergence" refers to the basin of attraction surrounding the minibrot at the center of the image. The moth- eaten appearance of the features also reminds me of some type of spider web. Calculation may be avoided by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It may be viewed in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Morning clouds and showers gave way to lots of afternoon sun here at Fractal central today. The temperature of 82F 28C was close to ideal. The fractal cats were apparently exhausted after a very active day yesterday and spent most of the time sleeping. The humans spent their time doing what needed to be done. The next FOTD will be posted in 24 hours. Until then, take care, and what ever happened to the music of the spheres? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Net_of_Convergence { ; time=0:05:02.92-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.85803336723/-0.28049507163/238775.3/\ 1/110/0 params=-11/-1.1/-2/-6/0/525/0/0 float=y maxiter=3200 inside=0 logmap=390 periodicity=6 colors=00035C46B57A6997888D7996AA5BB2CC4DD5EE6FF8G\ G9HHAIICJIDKJELKGMLHMMINNKNOLOOMPPOPQPQRQQSSRTTSUU\ TVWUVXUWYVX_VY`WZaW_cX`dXZfQXhKVjKWiKWiKWiKWiKWiKW\ iKWiKWiKWiKWiKXhKXhKXhLXhLXhLXhLXhLXhLXhLXhLYgLYgL\ YgLYgLYgLYgMYgMYgMYgMYgMZfMZfMZfMZfMZfMZfMZfMZfMZf\ N_gMZfLYfKXeJWeIVdHUdGTdFScERcDQbCPbBOaANa9Ma8L`7K\ `6J_5I_5H_7GZ8GZ9GZAFZCFYDFYEFYFEYHEYIEXJEXKDXLDXN\ DXODWPCWQCWSCWTCWUBVVBVXBVYBVZAV_AU`AUbAUc9Ud9Ue9T\ g9Th8Ti8Tj8Tl8Sm7Sn7So7Sp7Sq9RqARqCRqDRqERqGRrHQrJ\ QrKQrLQrNQrOQrPQsRPsSPsUPsVPsWPsYPtZOt`OtaOtbOtdOt\ eOufPtfOtfOtfOsfNsfNsfNsfMrfMrfMrfLrfLqfLqfKqfKpfK\ pfJpfJpfJofIofIofIofInfHnfHnfHmfGmfGmfGmfFlfFlfFlf\ ElfEkfEkfUkfUjfUjfUjfUjfUifUifUimckmcjmcimchmchmcg\ mcfmcfwcewcdwcdwccwcbwcbwcawcmzmmzmmzmmzmmzmmzmmzm\ mzmmzzmzzmzzmzzmzzmzzmzzmzzzzmzzmzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 31-08-11 (First Light From Vega [9.5])
by Jim Muth 02 Sep '11

02 Sep '11

FOTD -- August 31, 2011 (Rating 9.5) Fractal visionaries and enthusiasts: ALERT! Do not be concerned when nothing appears at the top of the screen when you start the parameter file. The first 25 lines or so are black. Today's image takes us on one final trip to the tip of the long filament extending north from the large minibrot on the main negative spike of the Mandelbrot set. It shows an area of anti- bifurcation, though the resetting is largely hidden by the black color around the edges of the frame. The name "First Light From Vega" comes from a short story I began about 20 years ago in my writing years, but abandoned when I ran out of inspiration. The name seems rather appropriate for today's image however. The image's rating of a 9-1/2 is the third consecutive rating at this lofty level. We're on some kind of a roll here in fractal land. The calculation time of 25-1/3 minutes is faster than the time of some recent images, though still quite slow by long-term FOTD standards. Calculation may be avoided however by viewing the finished image posted to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It may be viewed in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Today turned out to be a real prize-winner here at Fractal Central. The blue sky, puffy clouds and a temperature of 84F 29C were just what the doctor ordered. (Don't ask which doctor.) The fractal cats spent a good part of the day playing chasing games among themselves, while the humans were too busy to enjoy the near perfect weather. The next FOTD will be posted within 24 hours, which means it also could be late. Until whenever, take care, wait until the right time comes along, and then solve the mysteries of existence. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= FirstLightFromVega { ; time=0:25:19.25-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.771257023356245950003123070623649432\ 150742961579997779969017514028784/0.06616150907984\ 46392557512615786245334947501197897344567453684087\ 678943/1.593978e+065/1/-106.25/0 params=0/0 float=y maxiter=15000 bailout=9 inside=0 periodicity=6 colors=000H_rKasNctQeuTgvWiwZkxamyeoziqzmswmuwpwtu\ yqzzmzzizzezzazzYzzUxzUuxUsuUptUmsUjpUgnUemUbjU_iT\ _gS_eRZcQZcPZcPZcPXcPYcPZcP_cP_cPacPbfPbiPclTemYep\ afseguiiyngwlguigsggqefnbfmaflZfiXegVeeSecPeaOc_Lc\ ZKcXHcVFbSEbRBbO8bN7aL4aJ2aH0aF0_E0_B0_A0_80ZB0YE0\ XF0VF0TF3SL6RS8PZBOeENlGLpJKzLJzNPzPUzSXzZ_zcbzhez\ lbzh_zcXz_UzVRzTOzSLzRIzPFzODzNBzLBzNBzLBzKBzJBzHB\ zGBzFBzE000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00100100200200300300400400500500600600700700800800\ 900900A00A00B00B00C00C00D00D00E00E00F00F00G00G00H0\ 0H00I00I00J00J00K00K00L00L00M00M00N00N20O20O20P20P\ 20Q20Q20R26S22T23U24V25W26X27Y28Z29_2Aa2Cc3Ee4Gg6I\ i7Kj8MkAOlBQmCSnEUoFWpGYq } END PARAMETER FILE=========================================

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<Brian> Enjoyed yr monochromatic fractals, esp. BP_16_41c.png
by Hal Lane 31 Aug '11

31 Aug '11

Clear DayBrian, I enjoyed your monochromatic fractals, especially BP_16_41c.png where the overlapping spirals give a feathery feel to the image. =========================================================== Here are three monochrome views of the same scene which is a detail from the FOTD for 8/24/11. http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_41a.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_41b.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_41c.png Brian Prentice =========================================================== - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 30-08-11 (Everlasting Majesty [9.5])
by Jim Muth 31 Aug '11

31 Aug '11

FOTD -- August 30, 2011 (Rating 9.5) Fractal visionaries and enthusiasts: In today's image we're still in the same basin as yesterday's image, though we're on a different branch. To find today's scene I backed out of yesterday's image until I came to the minibrot in which it lies. Yesterday's image lies in the main spike area of the minibrot, so to be different, I switched to the East Valley of the minibrot and zoomed in until I found a sub-basin. Today's image shows a point of anti-bifurcation, (a resetting point), in this basin. Once again I spent an unusually long time working on the colors, which earn the image a whopping rating of a 9-1/2. These ratings might be a bit exaggerated, but IMO I earned the full 1-1/2 point coloring bonus. Actually, the time spent on coloring is not all good news. I have more time to work on fractals because, with our biggest commercial customer gone, we have more idle time here at FC. To find the name "Everlasting Majesty" I opened a dictionary at random until two words applicable to fractals came up. The name is really rather appropriate. Whatever fractals are, at least some of them are filled with things such as majesty, splendor, glory, etc. etc. etc. The calculation time is not so glorious however. On my aging 2000mhz machine it takes a full hour to finish. The newer units will finish the job in a fraction of the time, but it would take a super-computer to finish the calculation in a few seconds. View the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> View it in splendrous high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And remember the classic FOTD site at: <http://www.Nahee.com/FOTD/> Once the morning fog cleared off, the crystal clear blue skies and temperature of 81F 27C made today near perfect here at Fractal Central. The dynamic duo of fractal cats found full satisfaction in the conditions, though they would have preferred a little more attention from the humans. The dynamic humans made it through another uneventful day uneventfully. The next FOTD will be posted in 24 hours. Until then, take care, and it's possible to move in any direction in the three spatial dimensions. Why then is it possible to move in only one direction, forward, in the time dimension? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= EverlastingMajesty { ; time=1:01:48.47-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.771257023356245950003123070623651292\ 3399730393855461718953685298628/0.0661615090798446\ 39255751261578621589572474660692221227668986409181\ 11/4.550178e+063/1/-162.5/0 params=0/0 float=y maxiter=15000 bailout=9 inside=0 periodicity=6 colors=000XzZ_zcbzhezlbyh_xcXv_UuVRsTOqSLpRInPFmOD\ lNBjLBiNBgLBfKBeJBcHBbGBaFB_EBYCBVBBS8BP7BN7BK6BH7\ BF7BE7BB8BA8A76B88BAABACBBEBBFBCHBEJBEKBFNBFOBGRBH\ SBHTCJXCJYCKZCLaCLbCNeCNfCOgCPjCPlCRmCRpCSqATuCSsE\ SqGRpHRmKPlLPjOOiPOfSNeTNcXLbYL__KZaKYcJVeJTgHSiHR\ lGOmGNpFLtFKyEHzEGzCFzCAzB6yCExCLwCSuE_tEgxAmsEnnH\ pjLpfPqaTqYYsTasPetKitGmuCqu8uw4ywAtpEnjJjcNeZS_SX\ XNaRGgPCeNBbLB00A00A00B00C00E00F00G00H00J00K00L00N\ 00O00P00R20R20R20S20V20V20V20V20V20W20Y20Y20Z20_20\ `20a20a20b20b30c40c60e70e80gA0gB2iCBjEFlFKjGPiHUjJ\ ZmWamYdmXgmcjmgnmmommpmmrmmtmmxmpzmuzTzzezzszzzzzs\ zzezzXxzSuxOsuNptLmsKjpJgnHemGbjF_iE_gC_eBZcAZb8Z_\ 7ZZ6XS0YV2ZY6__A_bEacHbfLbiPclTemYepafseguiiyngwlg\ uigsggqefnbfmaflZfiXegVeeSecPeaOc_LcZKcXHcVFbSEbRB\ bO8bN7aL4aJ2aH0aF0_E0_B0_A0_80ZB0YE0XF0VF0TF3SL6RS\ 8PZBOeENlGLpJKtLJxNPzPUzS } END PARAMETER FILE=========================================

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Re: [Fractint] Reading ITERATES.TGA using Java
by Jason Hine 30 Aug '11

30 Aug '11

@Gerald, @Jonathan, Thanks very much for the helpful replies. I was running version 20.0; I upgraded to 20.04p11 and am now seeing the expected values in my Java program! As my investigations proceed, I'll be sure to share my findings and musings with this mailing-list, in case anyone's curious. Once I have written a program that can take in the TGA produced by Fractint and spit out an ASCII GRID file, I'll begin producing and converting ASCII GRID tiles that I'll stitch together into a surface in the GIS software. I think I'll start with a perfectly reasonable 3x3 mosaic of 1280 x 1024 images, just to get the conversion and stitching process figured out. Once the process is solid, I'll up the ante and aim for, say, a total resolution of 32,768 x 32,768, and we'll see how the GIS software handles 1Gb+... P.s. Very glad to see the FOTD still going, Jim!... How many years has it been? Thanks again, Jason Hine -- Cheers from Mr. Tumnus! "Here... take my handkerchief." Hoofing it bare-chested since 1974.

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FOTD 29-08-11 (In-Depth [9.5])
by Jim Muth 30 Aug '11

30 Aug '11

FOTD -- August 29, 2010 (Rating 9.5) Fractal visionaries and enthusiasts: Some of the recent supposedly 'deep' scenes in the Mandelbrot set have not been all that deep. We correct this minor exaggeration with today's scene, which lies at a depth of over 3*(10^97) -- deep enough to truly be considered 'deep'. The scene is located at the very tip of the longest filament extending from the north side of the large minibrot on the main spike of the Mandelbrot set. The minibrot lurking invisibly at the center of today's image lies in the basin of a larger minibrot, which lies in the basin of a still larger minibrot, which lies at the fringe of the basin of the large minibrot on the main spike. This means the number of elements 'resets' itself several times on the way to the minibrot. These 'resetting' points often make the most interesting scenes in the very deep regions of the M-set. Today's image is a fine example of resetting, otherwise known as anti-bifurcation. The rating of a 9-1/2 includes 1-1/2 points for the coloring, which took well over one hour to work out. The name "In-Depth" refers to the magnitude of the image, which is so great that at the same scale, the entire Mandelbrot set would spread over a space trillions of times that of the visible universe. Unfortunately, with great quality comes great time, and today's image is no exception. The parameter file requires over 2 hours to finish. The web sites remove this inconvenience however. The official FOTD web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition images may be found at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> The weather was perfect here at Fractal Central on Monday. The blue sky was decorated by various types of clouds, which never grew thick enough to hide the sun, while the temperature hung around 73F 23C. The fractal cats approved of all this. The humans also enjoyed the day, which left little to be desired and even less to comment on. The next FOTD will be posted in 24 hours. Until then, take care, and always save the best until last. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= In-Depth { ; time=2:03:21.93-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.771257023356245950003123070623649432\ 15074296157999777996901751402608456149266176801212\ 746480701252515/0.06616150907984463925575126157862\ 45334947501197897344567453684087645343415474883328\ 9470734066658561283/3.115261e+097/1/-112.5/0 params=0/0 float=y maxiter=15000 bailout=9 inside=0 colors=000ZezZezNA0RE0TH0VL5XPAZTF`XKb`PddUegUgkZk\ ocmshovcqzgszkuzkvzfxzfzzfzzZzzPzzKvzAuz0qz0ozUkz4\ iz4ev4ds4`o4Zm6Vi6Te6Pb6NZ6JV6GR8EN8AJ88G84C82AA06\ A02A00A00A00C00C00C00C00C00A00C00E00G00G00H00J00J0\ 0L00N00N00P00R00T00T00V00X00X00Z00`00`00b00d00e00e\ 00g00i00i00k00m00m00o00q00s00s00u00v00v00x00z00z00\ z00z00z00z00x00v00u00s00q00o00m00k00i00g00e00c00`0\ 2Y04V06S08P0AO0CM0CL0EK0GJ0HI0JH0LG0NE0PC2SA2U82W6\ 2Z44`24b04e04g06h06k06m06p04q06p06m06k06h06e06b06`\ 06Y06U06R06P06N06L06H06G06E06C268266464G62H60I86JM\ EKKCLJCMICMHAMGAMFAMEANE8ND8ND8ND8OC6OC6OC6PC4QB4R\ B4SB4T92U82V82W82X80Y80Z80_80`80a80b80c80d80e80f80\ g80h80i80j80kA0lA0mA2nC4oC6pCAqECrEEsEGtGIuGKvGMwH\ OxHQxHSxHUxJWzJYzJ_zLazLczLdzNfzNizNlzPozPrzPuzNwz\ PzzPzzPzzPyzRwzRuzRtzRszRrzTqzTpzTozTnzVmzVmzVmzVk\ zVkzXkzXizXizXgzZgzZgzZez } END PARAMETER FILE=========================================

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Anti-aliased ver. of Jim's "Sandy Beaches" Aug 25, '11 FOTD
by Hal Lane 30 Aug '11

30 Aug '11

There's now an anti-aliased version of Jim's "Sandy Beaches" Aug 25, 2011 FOTD on my "HD" site of Jim's FOTD images. Anti-aliased 5x5 1200x900: http://www.emarketingiseasy.com/TESTS/FOTD/2011-08-25_FOTD_1200_5.jpg Original FOTD at 1200x900: http://www.emarketingiseasy.com/TESTS/FOTD/F110825.gif I like to put the original FOTD and the anti-aliased version in adjacent tabs in my browser and click back and forth between them while studying the image. If I don't have a big enough browser window open to keep the browser from re-sizing the image, I click once in the upper left corner of both images to insure they're full size -- to guarantee that the browser isn't modifying the images while shrinking them to fit its internal window. The anti-aliased version really adds a lot of rich color and nice detail to the fractal, but I'm afraid that it removed the "sampling sand" from the beach. - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 28-08-11 (Breaking Boundaries [8.5])
by Jim Muth 29 Aug '11

29 Aug '11

FOTD -- August 28, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image contains a trick -- I lowered the bailout radius to 2, which cuts off the Mandelbrot set at a maximum radius of 1.414. Then I checked a filament extending from the period-5 bud on the northwest shore line of the main bay, very near the point where the filament disappears behind the shrunken bailout radius. I found a minibrot, then a smaller minibrot in its East Valley area. Finally I chose a filament extending from this even smaller minibrot, found a still tinier minibrot on the filament, and zoomed in. The result appears as today's image. Most of the effect is due to the artificially low bailout radius of 2. To see a more accurate but somewhat less effective version of the scene, recalculate the image with the bailout set to 16. (Preferably at thumb-nail size.) The name "Breaking Boundaries" had something to do with the bailout, but I have forgotten the original connection. The rating of an 8-1/2 seems about right. The calculation time of almost 1-1/2 hours is definitely slow however, so thank goodness for the web sites. The completed 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 web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy rain and high winds prevailed Saturday night here at Fractal Central as Hurricane Irene passed by 200 miles to the east. The rain and wind slacked off by midday today, leading to a slowly brightening then clearing afternoon. The newly installed fractal sump pump did its job, and kept the fractal basement not exactly dry as a bone, but no worse than a few small puddles. The fractal cats ignored the active weather but approved of the temperature of 70F 21C. The fractal humans had a quiet uneventful day, a day that might seem boring to young people but would be just right for the older ones. The next FOTD will be posted in 24 hours. Until then, take care, and if anything remotely possible must ultimately condense out of the random fluctuations of empty deSitter space, then every possible idea of God must exist in actuality. In fact, an infinity of every person's God must lie somewhere out there. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BreakingBoundaries { ; time=1:27:07.32-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.5288122480554\ 666884779956757565853838/0.70115186464407983733880\ 08496593100982/2.49339e+032/1/-2.5/0 params=0/0 float=y inside=0 maxiter=15000 bailout=2 colors=00040H10C0060010000zh0tc0n_0hU0bQ0WM0QG0JA0\ A6040000LG0SM0NH0JE0GA0A80620200000000zqKzfJzcHobG\ m_EcXC`WCYTAXS9UP8SM6PK4MH4JG2GC1C90A8084042010000\ 0000000szQgzwWgAJS4490otWNQAlp0jn0hl0gj0fh0cg0bd0`\ h0_m0Xz0Wm0UX0TU0Qz0Pz0NP0MN0JM0HJ0GH0EG0AC09A0890\ 660240120000000000000000c0t`0r_0pY0nX0lW0jU0hT0fS0\ dQ0bP0`N0YM0XK0UJ0TH0QE0PC0MA0K90H80G60C40A2081060\ 02001000000000000gzzdzzczzbzz_yzYwzXspUphTncSkYMXP\ MUPMSPMQPMNPMKNMJNMGNMCNMANM8NM4NM2NG0HA0C60600000\ 1000zY0zS0zK0zC0z40z00zpXznUzkTxjSugQsdPpcNl`MjYKg\ XJdUHbSG_QEXNCTK9QJ8NG6KC4HA2E81940620200000000000\ AzC2f40H0PwEMsCKoAHk9Gg8Ec6A_49W28S14N02J00E009004\ 0000000HuSErPCnNAjK9fJ8bG6YE4UA2Q91M60H40C10800200\ 00000_1kX0gU0dT0bQ0_N0XM0UJ0QG0NE0KA0H80E60A206002\ 000000000NbWKYSHUPEQKAMH8HC4C9184021F0j000MHz02w79\ lJ8t66WD4kA2f71b40X00T30N } END PARAMETER FILE=========================================

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Reading ITERATES.TGA using Java
by Jason Hine 28 Aug '11

28 Aug '11

Hi All, I'm writing a Java program where I want to read in the ITERATES.TGA file produced by Fractint (using truecolor=yes). I am successfully able to read in the TGA header and get the image dimensions and maxiter information; here's my code for that: // read in header info dis.skip(12); b1 = dis.readUnsignedByte(); b2 = dis.readUnsignedByte(); xdots = b1 + (b2 << 8); b1 = dis.readUnsignedByte(); b2 = dis.readUnsignedByte(); ydots = b1 + (b2 << 8); System.out.println("xdots: " + xdots+ "; ydots: "+ydots); dis.skip(2); b1 = dis.readUnsignedByte(); b2 = dis.readUnsignedByte(); b3 = dis.readUnsignedByte(); b4 = dis.readUnsignedByte(); maxiter = b1 + (b2 << 8) + (b3 << 16) + (b4 << 24); System.out.println("maxiter: " + maxiter); However, the trouble occurs when I try to read in the iteration values -- I think I've determined that there are three bytes per iteration value, but for the life of me I can't figure out how to shift/add the bytes to produce the iteration values I expect to see (1, 2, 3, etc.). Here's the closest I think I may have come to the correct code: b1 = dis.readUnsignedByte(); b2 = dis.readUnsignedByte(); b3 = dis.readUnsignedByte(); System.out.println("b1-3 : "+b1+" "+b2+" "+b3); long iteration; iteration = b1 + (b2 <<8) + (b3 << 16); Looping through the entire file, all I ever get back is: b1-3 : 200 153 51 iter : 3381704 It doesn't matter where I am in the TGA file; the values returned never seem to change! Is it possible that my code is working, and the TGA produced by Fractint is simply "flat"? Unfortunately, I don't know of another way to check to see if the TGA actually contains iteration values or not. Any suggestions would be most welcome! Background: I'm writing a program that will read in the ITERATES.TGA file and write out an ASCII GRID file that can then be imported into Esri's ArcGIS (www.esri.com) My eventual goal is to be able to use ArcGIS' spatial analysis tools to analyze some characteristics of the Mandelbrot set. Thanks in advance for any thoughts or helpful responses! Cheers, Jason P.s. Tim, if you're reading this, yes, you helped me back in 1998 with a similar question when I was writing "Deeper" in C++. :-) -- Cheers from Mr. Tumnus! "Here... take my handkerchief." Hoofing it bare-chested since 1974.

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FOTD 27-08-11 (Iterative Splendor [9])
by Jim Muth 28 Aug '11

28 Aug '11

FOTD -- August 27, 2011 (Rating 9) Fractal visionaries and enthusiasts: At a magnitude of over 2*10^54, Today's image is deep enough to honestly be called 'deep'. And at a real coordinate of +0.471... it is also located far enough east to be on the easternmost fringe of the Mandelbrot set. The tiny minibrot at the center is a second-order one that lies in the basin of a larger but still tiny minibrot on a filament in the extreme eastern outskirts of the M-set. The convergence patterns around second-order minibrots are subject to several points of anti-bifurcation, which today's image demonstrates to perfection. The name "Iterative Splendor" appeared from nowhere when I turned off my thought processes and let things take their natural course. The name could really be applied to any fractal, though some images certainly do have more splendor than others. The rating of a 9 includes a full point for the coloring, which occupied the better part of one hour. While still slow, the calculation time of 28 minutes is unusually fast for an image of such magnitude. This speed is quite unexpected, since I have seen images of magnitudes around 10^20 that take over 6 hours to finish. Calculation may be totally eliminated by viewing the finished image on the official web site at: <http://www.crosscanpuzzles.com/Archives.html> or on Hal's high-definition site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Paul's ancient, classic site, with the entire library of images is online at: <http://www.Nahee.com/FOTD/> The day here at Fractal Central began with clouds and light sprinkles. The clouds and sprinkles continued through the day, with the forecast of heavier rain and wind arriving during the night. No fractal cat ever lets a little wind disturb him, so our fractal cats spent the day undisturbed. The lack of enough attention always annoys them however. The fractal people spent the day enjoying one of the slow days that are becoming more frequent since our biggest customer went away. Tomorrow will probably be a repeat. The next FOTD will be posted in 24 hours. Until then, take care, and when we say 'science says' we mean that men who call themselves scientists have determined the truth of the claim through repeated trial and error. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Iterative_Splendor { ; time=0:28:09.52-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.47118\ 53349333763975376752637361962915549086252669118867\ 339/0.35414982363516372660476578491550930168187389\ 441576538135925/2.462724e+054 params=0/0 float=y maxiter=5500 bailout=9 inside=0 periodicity=6 colors=0000z0QjGrRcm`ZjgVgoRcxN`zIYzGazIdzLixOltRt\ oYooV00G00H00I10J20K40O50T70Y80aA0eB0jD0oE0rB0tA0t\ 80u74u58w4BwAHxELzIQzNVzRZzWczaizepzeuziwzpzzuzzzz\ zzzzuuummmeeuZZzRRzcIzeLzgOzgQzgRzgTzlKzgVzddzaoz`\ jt`emZagZY`YTVYOOgORYLINKAEI14H00G0LeRRgYWgaaieijl\ eijcij`giYgiVeiRegOdgYloNdgEZa5RV0EY0LO8THK`8Wg1em\ 000o80jG0gN0dR0iW0l`1oc4rRRzHmz4Nz00z00z50xD1wI2uQ\ 4tY5r`5rc7rW5zG8zDBz8Dz5Gz1Iz0Nz0Kz2Hw7EpBDjGAcK7Y\ O4RN0KR2LWANZHOcOQeWRjcTmjVW`OGQI0GD078EQ0ig0cc0Y`\ 0TY0NV2IR4DO7DW08L85DI12T00_00Y00U00U02U05V08_0Bb0\ 2d0EdAOVNZIZj8lu0zzmzzctz0oz0jx0eu0`r0co2el1ii0le0\ oc0r`0uY0wV0xR0tK0lD0e50`00R01K04O0G`55dD1mN0iZ0ma\ 0uc0ue0tiKilT`oaRrjVllYglTdgQacL`ZIYVEVQBTL7QH4OEQ\ 0TO2RNDQNNOLWOLeNKpLKzLIzOHzQHzTGzVAzVGzWKrYOjZVcZ\ ZW`cOagIaYRVN`NDiG2rA8i7D`5IR2NK1TB0Y20d00a00Z10W8\ 2TE5QLANRDKZHNjEHdK0zD0z2 } END PARAMETER FILE=========================================

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FOTD 26-08-11 (The Test of Time [6.5])
by Jim Muth 27 Aug '11

27 Aug '11

FOTD -- August 26, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image departs from the deep theme of the month, but have no concern. Tomorrow's image will return to the theme in style. The parent fractal came about when I iterated the expression Z^(2.23)+C at a level 2.3 turns up the hyperspiral with the 'recip' function applied. This parent is a sprawling, amorphic thing that looks nothing at all like the pure Z^(2.23)+C Mandeloid as it is drawn by the 'manzpower' formula. Today's scene is located in the interior of what might be considered a Seahorse Valley, though its features bear little resemblance to what one would expect to find in a proper Seahorse Valley. To begin, the part angular, part parabolic holes in the image are nowhere to be found in the familiar Seahorse Valley. And nownere in the Mandelbrot set do we find the discontinuities that fill today's image. The minibrot at the center is a reflection of the shape of the parent Mandeloid. Recognizing the various parts is virtually impossible. The minibrot would be somewhat better defined if it were calculated with a greater maxiter, but doing this spoils the already-shaky color scheme. The rating of a 6.5 indicates that I am somewhat disappointed with the image. When I named the image "The Test of Time" I was pondering the fact that even if the entire universe were to suddenly disappear, this particular scene would exist in potentia for all eternity. The calculation time of 8-3/4 minutes is slow by everyday standards, but quite fast by very-deep-math standards. The completed image is posted for instant viewing at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic original web site is at: <http://www.Nahee.com/FOTD/> Picture perfect weather prevailed at Fractal Central today. In fact, with its temperature of 84F 29C, kodachrome blue skies and billowing cumulus clouds, the day could have passed for a day in the Caribbean. The fractal cats, who have spent their lives in Pennsylvania, wouldn't know a tropical-island day from a day in the Arctic. They were more interested in watching an unfamiliar new black-and-white cat that passed through. The humans passed most of the day watching the over-hyped doomsday weather forecasts on the various news-and-commercial channels. IMO, the storm will be less devastating than the news people are implying. Here in central Pennsylvania we are expecting little more than a gusty rain on Sunday. Things could be worse however back at Old Fractal Central down in Central Maryland, where my sister still resides. The next FOTD will be posted in 24 hours. Until then, take care, and the wise old hermit on the mountain top told me that if I work hard enough, I might be a Boltzmann brain some day. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Test_of_Time { ; time=0:08:44.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=-0.1109090974689217/-0.7516937525903022\ /3.851973e+009/1/27.5/0 params=2.23/0/2.3/0 float=y maxiter=3600 inside=0 logmap=-660 periodicity=6 colors=000F97FA7EA7DB7DB7IABNAFS9JX9Ma9Qf8Uk8Yp8`k\ AXfCTbEPYGMTIIPKEKMAGO7HRCHTHHVMIXRIZWI``IbdK`cMZb\ OXaQVaST`UR_WP_YNZ_LYaJXcHXeFWgDViBVOVZ2mb5l`8l_Bk\ ZEkYHjXKjWNjVQiUTiTWhSZhRahQcjSekTglUimVkoWmpXoqYq\ rZst_uu`wvaxwbyqdmmfccgcbicYjTNXQX`NcdKjhHrlEzpBmm\ 8br5Wv2Pz0Jz2NzG87CEEC35B49A4D94G94K84O74R64V64Y54\ a44e34h34l24p14s04w04zRCmZiMaUQdEUmtkzi_tcPrFEuG3g\ HOVHgtwAcgNNS_L`SJhKHpCGx5FuCErJDoPClWBibBfhEWgGLf\ JAeL0e5HvzCyXFd3ILAHJHHHOGFVGDaFBgF9`R9Vb9Pn9Jy9Mi\ CPVFSFIU0LP8QLGUHOZDWb9cg5kkAnjEpjIrjKqlMpmOonQnoS\ mpQlqPkqOjrNjrLirKhsJgsIgsFbpDZmBVj9Qg7Ud5YaWaFWeH\ cfGfgDhhAki7lj1mk4nl6om8pmApmCqmErcGscIvcNscKqcIoc\ GmcDkcBhc8ic9jcAkcBlcClcDmcEncFocGucIzcGzcEzcDzcBz\ b8zc9zcAzcAzcBzcBzcGzcKzcOzcSzmXzm`zmdzmhzmmzmqzmu\ zzyzzvzzszzqzznzzlzzizzgzzdzzbzzazz`zz_zz_zzZzzYzz\ XzzXzzWzzVzzXzzVzzTzzRzzP } 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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Monochrome Views
by Brian Prentice 26 Aug '11

26 Aug '11

Here are three monochrome views of the same scene which is a detail from the FOTD for 8/24/11. http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_41a.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_41b.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_41c.png Brian Prentice

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FOTD 25-08-11 (Sandy Stretches [8.5?])
by Jim Muth 26 Aug '11

26 Aug '11

FOTD -- August 25, 2011 (Rating 8.5?) Fractal visionaries and enthusiasts: Today's image rates an 8-1/2 followed by a question mark. This means I feel it must have something worth 8-1/2 points somewhere in it, but I just can't put my finger on any aspect of the image that might be worth a rating of an 8, plus the usual extra half- point for the coloring. To begin, the image is exceedingly slow, taking over four hours to calculate, but this is how it goes with such deep images that require arbitrary precision math. The scene is also too chaotic, with too many large areas of fractal 'sand'. This is why I named it "Sandy Stretches". The sand cannot be escaped. When I tried the 'logmap' feature, both plus and minus values, it got rid of the sand, but left only a near featureless expanse of flat colors. The entire image is also oriented in the wrong direction. The central minibrot points southeast instead of west, which is the 'normal' orientation. With the minibrot being so small however, this is of little consequence. I could easily have corrected the wrong orientation, but decided not to tie up the machine for another four hours. The scene is located in the radical of a tiny bud on the northwest shore line of the large period-3 bud on the north side of the Mandelbrot set. (In fractals, a radical is all the elements, such as the filaments, spirals and chaotic areas, associated with a particular bud.) As I mentioned above, the image is exceedingly slow, so the only practical way to view it is in finished form on the web site. The official FOTD web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> Today's image is available in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be found at: <http://www.Nahee.com/FOTD/> The day began with heavy thunder-storms here at Fractal Central. The rain ended by 10am, but clouds and occasional showers hung on for the rest of the day, holding the temperature to a rather pleasant but soggy 79F 26C. The fractal cats ignored the outside conditions as they chased each other up and down the hallway, pausing occasionally to ask for food. The humans, who are never quite sure exactly what it means to be human, had a typical up-and-down day. The next FOTD will be posted in 24 hours. Until then, take care, and if you come across any stray Boltzmann brains, report them to the proper authorities. (Those Boltzmann brains are a hoot! The joke is that no high priest of cosmological science knows how to assure us that they are not floating around out there in empty deSitter space along with everything else imaginable and unimaginable.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Sandy_Stretches { ; time=4:06:50.04-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.1659\ 3261653808153849415041/0.8309478993840683571332440\ 2/3.87948e+021/1/95/0 params=0/0 float=y maxiter=100000 bailout=16 inside=0 periodicity=6 colors=000id8kg8phAvlBynCzqDzuEzzIzzIzzczzmzzmzzcz\ yUzuEysCvpBspApmAnl9ki8ki8ig8ig8if8if8fc7fc7fa7fa7\ d_6e_6fZ6gW5hW5iV5jV5kT5lT5mS5nS5oR4qR4sP4uP4wN4yN\ 4zM4zM4zL3zL3zK3zK2zK3zO9zPBzPDzbSzbWzc_zfezfhzfkp\ WasXfvWiyWmzXszWyzXzzXzz_zz_zz_zzZzzZzz_zz_zzZzzZz\ yZzxZzuYztYzt_zrZypZynYvn_vkZskZshYpiZpgYnfYnfYncX\ kdZkbYiaYipjzqlzplzolznlzonznnznnzllzlnzjlzhkzfkzf\ kzejzcjzaizaizcizchzchzcgzcgzcfzcezcezcdzcdzcdzccz\ cczbazbazb`zb`za_zaYzaYz`Xz`Xz`Wz_Uz_Uz_Tz_Tz_SzYR\ zYRz_Qz_QzZPzZPzYOzZNzZNzYMzYMzYMzYLzYLzXKzXKzYJzY\ JzYKzZLzYMzMMzMMzMMzMMzMMzMNzLNzLNzLOzKOzKOzKOzJPz\ JQzJQzJQzJQzJRzISzISzISzISzISzISzIUzFSzDOzANx8Lw7K\ u5Ks4Hp3Gm3Fk2Ei3Df3Dc3Cj3Cg3Bd3Aa4A_49Y59W69U68S3\ 7Q66N55O54N54I55I76I86I97IB8GE8DF8AH96I92MB3OB3QC3\ SC4SC4TD4TE4TF4WG5WH5WI5YJ5YK5YK5_M5_N5_O5aQ6aR6aS\ 6dU7dU7dW7fY7fZ7f_7ia8ib8 } END PARAMETER FILE=========================================

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FOTD 24-08-11 (Two-Headed Monster [6])
by Jim Muth 25 Aug '11

25 Aug '11

FOTD -- August 24, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image lies in the parent Mandeloid that results when the expression Z^(2.25)+C is iterated 1.2 turns up the complex logarithmic hyperspiral with the 'recip' function applied. This parent appears as a reasonably complete Mandelbrot set rotated 180 degrees, with 2 East Valleys and 2 fractalized main spikes, each graced with 2 large minibrots. The image is located in a knot on a minor filament extending from the southern large minibrot. The rating of a 6 is held down because I seem to remember a recent FOTD image that closely resembles today's, at least in the coloring. But even if this is true, fractals are still fractals, and today's image must be infinitely different from its earlier relative. The name "Two-Headed Monster" refers to the minibrot at the center of the image, which, even though it is not fully resolved, closely resembles the shape of its parent. The calculation time of 1-1/2 minutes is quite fast by fractal standards. In fact, more time is likely to be spent setting up today's parameter file than in running it. The image may be viewed without calculation however on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is also available in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds with a high temperature of 84F 29C and a nice breeze made things pretty comfortable here at Fractal Central today. The fractal cats, who survived the big quake yesterday, spent the day in meditation. The humans meditated about finding time to meditate. The next FOTD will be posted in 24 hours. Until then, take care, and fractals might be all in the mind of a Boltzmann brain. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Two-Headed_Monster { ; time=0:01:25.02-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip inside=0 center-mag=+1.5450423432411/-0.209605690560271/\ 6.688685e+012/1/35/0 params=2.25/0/1.2/0 float=y maxiter=1500 logmap=166 mathtolerance=0.05/1 colors=00040Z30X30V30T30R30P20N20L20K20I20G10E10C1\ 0A1081461753984AA5BC6CE8DG9EJAFLBGNDHPEJRFKUGLWIMY\ JN_KOaLPcOOeRNfSMgULhWKjYJk_JlaImcHneGpgFqiErkDsmD\ xkCviBtgBqeAncAkbAhaBecCbeD_hEXjHUkMRkRPoWNq`LteJu\ iHwmFzmDwjIqeMlcQeUUbJY_GaXEeUCdPAcK5bF0aA0`50_00Z\ GzzzkzCzzzlzErzzgzGmzzbzI_hJYhKVhLShHQgDLg9Gf58Z11\ Z70cD0hK0iR0iX5iZBi_DiaFicHidJifLigMiiOkjPmkQonRpr\ SrtTtwUvzVwdQiSMWFcI3h48m8CrBGrEKzIPzLTzOXXR`_VdbY\ ie`mgdqjgumjyomwljvjgthesebrc`paYo_WmXTlVRkTOiRMhO\ JfMHeKEdICcJIcJNbKSbKXbLaaLfaMk`Mp`Nu`NzdLxgKwjJvm\ IupHtsGsvFryEqxDpxCpxBpxBpxApx9px9pxApwCpwEpwGpwIp\ wKpwMpwOpwQpuSksUgqWcoYZm_VkaRicNgmIemEcmAbm6dmBem\ FgmJhmNimRkrWlr_mrcorgprkqronrmlzljzkhzjfzidzhbzgz\ zfzzezzdzzczzbzz_zzYzzWzzUzzSzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzDzzDzzDzzEzzEzzEzzFzzFz\ zFzzDzzCzzAzz9zz8zz6zz5zz } 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 23-08-11 (A Fire Deep Inside [7.5])
by Jim Muth 24 Aug '11

24 Aug '11

FOTD -- August 23, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's fiery image shows a scene rather deep in the prominent knot on the longest filament extending from the northeast shore line of the main bay of the large minibrot on the negative stem of the Mandelbrot set. The rating of a 7.5 includes 1/2 point for the coloring, which admittedly is a bit exaggerated but makes a lively picture nonetheless. I have been down to the minibrot at the center, and found it is less interesting than the scene in the image. The minibrot is surrounded with little more than a multitude of concentric circles with varying degrees of chaos. The name "A Fire Deep Inside" has nothing to do with a steamy romance novel. It refers to the lurid fiery hues filling the image. The calculation time of 58 minutes is slow. The better choice is to view the finished image on one of the FOTD web sites. The finished image may be viewed on the official FOTD web site, which may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high definition version is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Near perfect weather once again prevailed here at Fractal Central today, with lots of sun and a temperature of 79F 26C. But the peace was broken by a sizable earthquake in the afternoon. The quake shook up things quite a bit and cracked a wall in the city administration building, which had to be evacuated. The cats of the fractal variety ignored the quake as they slept and chased each other up and down the long hallway. The humans had another day of being busy, which is better than being idle. The next FOTD will be posted in 24 hours. Until then, take care, and the visible universe is about 27.5 light years in diameter. But we are seeing the most distant parts in the positions they occupied 13.7 billion years ago, and they have been receding at near light velocity since then. So how far away are those most distant parts at the present time? I guess it's all a matter of relativity. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Fire_Deep_Inside { ; time=0:58:18.64-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7444\ 51874102962814298045297578235/0.022028759872824611\ 8223664753939981/7.165866e+028/1/-30.9/0 params=0/0 float=y maxiter=18000 bailout=16 inside=0 colors=00000M00N00O01P02Q03R04S05T06U07V18W39X4AY6\ BZ7C_C9XF6VI3TL0SO0QS0P_0O`0M`0La0Id0Fk0Cq29sF6uJ3\ xL6zT9z`CzgFzoJzuIzoGziFzcDz_CzXAzT9yQ7xO6vT4u_3sd\ 1rj0yo0uo0pl0lg1id4d_6`T9YTATTDPTGMTIITLDTMATP6TQ1\ TT0_Q0dV0fc0g`0dY0aV3YS6VP9SMCOJFLIIIFLDCOA9Q76T33\ X00P00V00_00c01i06m09r0Dv0Gz0Lz0Oz0Sz0Vz3Xy9XpFYiL\ YaQYTX_Ma_GfcFg_DgXCiTAiQ9iO7jL6jI0oD0r66jFC`PIPYO\ Fg_FpXDpS4rJ0v70z90zC1zD6wGAuIFvJJxMPzOTzQYzSazVfz\ XjzYoz_lz_jx_ir_gl_fg_da_cX`cQ`cL`cG`cA`c4`c0`c0`c\ 0Yc0Xc4VcATcFScLQcPPcVMcaOc_OcYOcVPcTPcSPcPQcOQcLQ\ cJQcIPcLPcMPcOPcPPcQPcSPcTOcXOcYOc_Oc`OcaOcbOccOcd\ PcePcfQcgTchSciQcjPckPclOcmMcmLcmMcmOcmOcmPcmDcmJc\ mPcmUcmUcmUcmUcmUcmUcmUcmUcmUckUciUcgUcfUceUcdUccU\ caSc_QcYOcWMcUKcSIcQGcOCcM4cK3aI3`G3_E3XC3VD3TF3QG\ 3PI1OJ1LL3IM4FO6CP79Q07S00B00B00B00C00C00C00D00D00\ E00E00F00G00H00I00J00K00L } END PARAMETER FILE=========================================

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FOTD 22-08-11 (The All-Seeing Eye [8])
by Jim Muth 23 Aug '11

23 Aug '11

FOTD -- August 22, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "The All-Seeing Eye". But there is nothing all-seeing about it. The image is simply a picture of a minibrot in the parent fractal that results when the formula Z^(2.2)+C is iterated 2.2 levels up the logarithmic hyperladder with the probably erroneous reciprocal function applied. This parent is another of those rotated and scrambled Mandeloids that appears to be suffering from the effects of the second law of thermodynamics. Its entropy is starting to increase, and this increase will continue until nothing but a screen filled with infinitely divided, flat gray fractal sand remains. (It's too bad that entropy so rarely decreases. If it did, fractals would spontaneously appear out of nowhere.) The scene of today's action is located in a branch of what appears to be a degenerate Seahorse Valley. I say it appears to be a Seahorse Valley because even though it encloses a period-2 bud, in its depths it looks nothing at all like the valley we know so well. The terraced effect was achieved by rendering the scene with the 'tdis' option in effect, which colors the points according to how far they have traveled when they finally escape. The rating of an 8 is deserved, since I did put at least a little extra effort into the coloring. The calculation time of 2-3/4 minutes is true when the image is rendered with the passes set to 'b'. With this particular image, passes=b is the fastest. The image may be viewed without the inconvenience of setting up and running a parameter file by visiting the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is available in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The 14-1/2-year-old original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The weather today was ideal here at Fractal Central, with kodachrome blue skies decorated with cottonpuff cumulus clouds and a temperature of 77F 25C. The fractal cats, who are of very low entropy, spent the day playing with their catnip toys and sleeping. The humans, of equally low entropy, spent the day doing things that are more human, such as work. The next FOTD will be posted in 24 hours. Until then, take care, and would all the Boltzmann brains please raise their hands. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_All-Seeing_Eye { ; time=0:02:48.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=mandelbrotbc3 function=recip passes=b center-mag=-0.0263040944212104/-0.7577543124938957\ /2.16623e+012 params=2.2/0/2.2/0 float=y inside=255 maxiter=1600 outside=tdis mathtolerance=0.05/1 colors=000lTzjNzjJzgOzfUzf_zhgzgjzcmz`qzXvzVzzTzzV\ zzXwz_szbozdlzgjziizhczfZzh_zi_zj`zk`zl`zmbznbzobz\ pczqczqczsdztdzudztgzsizrjzqlzqnzpozopzlnzimzfmzcm\ z`mzZmzWmzUmzTizSfzRczR`zTczVgzXkz_nzbszdvzgzzjzzl\ zzgzzdvz`qzZmzWizTczR_zNWzMRzKNzILzGIzGGzGKzGQzGWz\ HdzHmzKlzNkzSkzWlz`lzfmzlozrrzsqzuozxnzzlzzlzqepla\ jfZe_V_VSVQPQMMMGGGCCC999777777454152CCCJJJTTThhhy\ yyzzzzzzzxvzvozvjzwdzw`zxWzySzzNzzKzhIyVHqHDm9AV47\ Y6Ba8FdALhDQlFRlHSlIVjK`lPioUpnXkl`mgab__VVVV_aZEv\ oFwiHycIz_zzdzzXxzQrzLivIbmFWfCQY9KS7GM5BF37A13500\ 203524954C85GC5KGBPLIVSQ_YYdhgjtppzsvzjqzapwUlkNeg\ NcWLdVLYRKQNJJLJCJFTDDS9CP6BN4AM2BN4BN5BN7CN9DNCFN\ FFNGFMFEKEEmEDmEEmEEmEDmDCmCDmDcczcczdczdczdczecze\ czeczfczfczfczgczgczgczgczcjz`fz_czZ`zWYzVVzTTzQPz\ OMzNKzLIzJGzIFzTKzcSzp`zzlzwfzr`znXziTzcOz_MzVIzQG\ zNFzWHzfKzdLzdMzcMzbMzzzz } 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 21-08-11 (Time to Reset [7])
by Jim Muth 21 Aug '11

21 Aug '11

FOTD -- August 21, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's not-all-that-deep scene in the Mandelbrot set rates an everyday 7. The location is near a point of antibifurcation in the East Valley of a tiny minibrot on a filament extending from the northeast shore line of the large minibrot on the west branch of the filament extending from the large period-3 north bud of the M-set. (Everyone now knows exactly where the scene lies.) The image is notable for the star-like elements surrounding the central minibrot. Usually when we travel this close to a minibrot at such a depth, the surrounding elements appear as little more than an endless nest of concentric circles. The name "Time to Reset" refers to the fact that the image is located near the resetting point of a larger minibrot. The calculation time of 33-1/2 minutes is slow. However, the image is posted already calculated on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition 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/> Sunday brought sun, clouds and a light thunder-shower to Fractal Central. The fractal cats approved of the temperature of 84F 29C, while the humans would have rather done away with the light shower. The next FOTD will be posted in 24 hours. Until then, take care, and it is believed by some that we bring most of our troubles on ourselves. Whoever believes this is forgetting about God. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Time_to_Reset { ; time=0:33:31.20-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.1476\ 729189716259299418108340881134/1.03561330331477946\ 1662044062401693/4e+029/1/75/0 params=0/0 float=y maxiter=32767 bailout=16 inside=0 periodicity=6 colors=0003P03S03V03Y04_64aC4bH4dN5eS5gY5hbnrZnrXn\ rWnrUnrSnrQnrOnrMnrKnrInrGpuDnrFloHjlIhiKffLdcNbaO\ `ZQZWRXTTVQUTNWRLXPIZNF_LCaJ9bH6dF4eI7fLAfNDfQGgSJ\ gVMgXPg_ShaVhdYhg`iicilfiniiqljsojvrjxujsshnrfipdd\ ob_n`VlZQkXLiVGhTLQ88jUCgSGdQKbPO_NSXLSPJWVK__KbdL\ fjLjoMlwLmtMmqMnoMnlMoiMogModNpaNp_NqXNqVNrSNrPOrN\ OsKOsHOtFOtKOtUOs_SscVsgYsj`smcsofsqisslspotuwssts\ qrsppsnmslktmqslmskirjfribqi_qhWpgTpfPofMoeIndFncB\ rb7nc8jd9fe9beAZfBWgBShCOhDKiDGjECkF6lC9kFBkIEkLGj\ OIjRLjUNiXQi_SibUheXhhZhmagrcgvghzegzcgzbfz`fz_fzY\ ezXezVdzUdvSdrRcmPchObdMb_LbYJaWIaVG_TFZSDYQCWPAVN\ 9VM2VL4WM6_M8bMAfNCiNEmNFoNHnOJlPLjQMhROfSQdTSbUT`\ VVZWXXXZVY_TZaR_cP`kQ`dOaYMbRLcLJcEId7Ge1Fe2Da3CZ3\ BW4AT59P58M66J75G74C83992691394A97H9AN9DU9G`9JfKRi\ UYldeonlrjingfjdcga`cZY_WVXTSTQPPNMMKJIHGEEDBBA787\ 36005405705A04D04G04J04M0 } END PARAMETER FILE=========================================

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FOTD 20-08-11 (Color in Black and White [?])
by Jim Muth 21 Aug '11

21 Aug '11

FOTD -- August 20, 2011 (Rating ?) Fractal visionaries and enthusiasts: This is the month of deep images, but at a magnitude of only 4*(10^19), today's image lies at nowhere near a record depth in the Mandelbrot set. Since arbitrary math is necessary, the scene is deep enough to qualify as a deep image however. The scene is located in the East Valley of a minibrot that lies deep in the northwest valley enclosing the period-23 bud on the south shore of East Valley of the M-set. The rating of today's image is a question mark. This is because its coloring is experimental. To get the effect, I first reduced an everyday color palette to gray scale then added the tints by hand. Part of the image is still pure gray scale, while other parts have color shades of varying intensity. The final effect is interesting but I could not decide on a definite rating. The name "Color in Black and White" is an oxymoron. By definition, 'black and white' implies a total lack of color. (Actually, a black and white image contains all the colors, but they are all of the same intensity, giving the visual effect of a lack of color.) The image is deep enough to require arbitrary precision math, which means it is a slow one, taking almost 45 minutes to complete. If slow calculating is not your cup of tea, the finished image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site with images going back to April, 1997 may be accessed at: <http://www.Nahee.com/FOTD/> The weather conditions in the Fractal Central area were near perfect today. The early morning fog soon cleared off to reveal a cloudless blue sky, which prevailed for the rest of the day. The fractal cats approved of the hot sun and temperature of 86F 30C from their inside location. Nicholas tried to make a breakout when we opened the front door. He made it into the vestibule, but much to his disappointment, was stopped by the outer door. Cassie watched with amusement. She is quite happy to be a totally indoor cat. The humans spent the day at the Sunbury River Festival, this small town's big annual event. We arrived just as an exhibition of belly dancing was starting. Being a refined gentleman, I averted my gaze . . . directly to the action. If I recover, which I fully expect to do, the next FOTD will be posted in 24 hours. Until then, take care, and don't worry. I apologized to the Big Guy up there, made a sincere act of contrition, and will do my penance. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ColorInBlack&White { ; time=0:44:54.45-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.26760\ 3127253445631185766/-0.004760113045483619666748/\ 4.205498e+019/1/112.5/0 params=0/0 float=y inside=0 maxiter=10000 bailout=16 logmap=1932 periodicity=10 colors=000gEKgDLhDMhDMiDNiDOiDOjDPjDQjDQkDRkDSlDSl\ CTlCTmCUmCVmCVnCWnCXoCXoCYoCZpCZpC_pB_pC_pCZpCZpCY\ oCYoDXoDXoDWnDWnDVnDVnEUmEUmETmETmESlFSlFRlFRlFQkF\ QkFPkGPkGOjGOjGNjGNjHMiHMiHLiHLiHKhHKhIJhIJhIIgIIg\ IHgJHgJGfJGfJFfJFfJEeKEeKDeKDeKCdKCdLBdLBdLAcLAcL9\ cL9cM8bM8bM7bM7bM6aN6aN5aN5aN4`N4`N3`O3`O2_O2_O2_O\ 0_P0ZP0CAC4644644644644644644644644644644644644644\ 64464464464464464464464666979ECEJHJNLNRPRXVXa_aece\ gegecea_aZXZUSURPROMOLJLIGIFDFECE00000000000000000\ 00000000000000000000000000000000000009CEEFHJKMONPT\ SUYVXb_ageelijqkovmtiWjzzzzvzzuzztzyryxqxwpwvovtmt\ tmtslsrkrqjqqjqbUbaUaaUa`U``U``U`kdkhahf_fdYdb`la_\ k`Zja_kKIKJHJLJLNLNPNPQOQTRTWUWYWY_b_X_XX_XX_SWZRX\ `SWcRmcPmcPmcQmcQmcPmcPzmRzmPzmRzmRzmQzmRzmSzmSzmV\ zmXzm`zmbzmfzmhzmmzmozmozmlzmgzmezmczmbzmazmUzmPzm\ JzmEzm9zm5zm4zm4zm4zm4zmE } END PARAMETER FILE=========================================

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Re: [Fractint] Details from recent FOTD's
by Hal Lane 20 Aug '11

20 Aug '11

Brian, Great images and coloring! - Hal Lane ######################## # hallane(a)earthlink.net ######################## ------- Brian Prentice wrote: ---------------- Subject: [Fractint] Details from recent FOTD's Here is a detail from the FOTD for 8/13/11 http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_37.png and here is one from the FOTD for 8/16/11 http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_38.png Brian Prentice -------------------------------------------------

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FOTD 19-08-11 (Blues in the Basin [9])
by Jim Muth 20 Aug '11

20 Aug '11

FOTD -- August 19, 2011 (Rating 9) Fractal visionaries and enthusiasts: Though today's image departs from the 'deep scenes' theme of the month, it is well worth the departure. The rating of a 9 is no mistake. The underlying image is worth only a 7, but I awarded myself a full 2 points for the coloring, which gives the image most of its impact. The parent fractal is the Mandeloid that results when the expression Z^(2.2)+C is calculated 2 levels up the hyperladder with the 'recip' function applied. This parent is one of the most torn up I have yet stumbled upon. I'll not try to describe it in words, though it may easily be viewed by resetting the logmap to zero and backing out of today's image. Today's scene is located in a jagged clump of debris on the west side of what I assume is the main bay. The minibrot at the center of the image closely resembles its parent fractal. The most impressive feature of the image is the coloring of the central disk and the five broad arms radiating from this disk. The name "Blues in the Basin" refers to the bluish tinge I applied to the central disk and five radiating arms. And for a change, the program supplied only a small part of this coloring. The calculation time of a zippy 18 seconds will seem reasonable to even the most impatient fractalist. As always, the completely calculated image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A typical mid-august day prevailed here at Fractal Central today, with hazy skies, a high temperature of 86F 30C and humidity within reason. All this lasted until mid-afternoon, when a thunder-shower moved in and dropped the temperature to 68F 20C. The rest of the day was cloudy and more like autumn than summer. The fractal cats showed little concern with the outside conditions. They were more concerned with a line gauge, (printer's ruler that measures picas), that we laid on the table. The humans, in a very human manner, passed the day doing what needed to be done, though now that our biggest customer has gone elsewhere, this is sometimes too little to keep us busy. The next FOTD will be posted in 24 hours. Until then, take care, and does having faith in something always mean it is true? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Blues_in_the_Basin { ; time=0:00:18.73-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip float=y center-mag=-0.6449570164524272/-0.0409793368502258\ /4.7e+012/1/72.5/0 params=2.2/0/2/0 periodicity=6 maxiter=750 inside=0 logmap=49 mathtolerance=0.05/1 colors=000402603804A05C06E07G08I09K0FN0IP0JR0HU0JX\ 0J_0Hc0Fg1Ek2Co3Br6Bt5BwACzKDzUDzZEzUFzUGzUHzUHzUI\ zUJzcKzczzmzzmzzmzzzzzzzzzzmoOmlNmjNmhNmfNMcMMaMN_\ MNYMNULNULOULOZLOcKOZKOZKPZKPZJPZJPZJPZJbbUcaUcaUc\ hUchUdhUdhUdhUdhUehTfhSfhSghRghRctWcpVcpVcpVcpVdqV\ dqVdqUdqUerUerUerUerUeszfszfszfszftzftzgtzgtzgtzgu\ zguzhuzhuzhvzhvzhvzivziwziwziwziwzjxzjxzjxzzxzzxzz\ wzzvzzvzzuzzuzztzztzzszzszzrzzrzzqzzqzzpzkpzkzzkzz\ kzzkzzkzzkzzkzzkzzkzzkzzkzzkzzkzzkzzkzzzgzzgzzfzzf\ zzezzezzdzzdzzczzbzzbzzazzazz`zz`zz_zzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzlzzlzzlzzlzzlzz\ lzzlzzlzzlzzlzzlzzlzzlzzrzzpzzozzmzzlzzkzzizzhzzgz\ zezzdzzczzazz`zzZzzYzzXzzVzzUzzTzzUzzUzzUzzVzzVzzV\ zzVzzVzzWzzWzzWzzWzzWzzXzzXzzXhzXhzXhzYizYizYizYiz\ ZjzZjzZjzZjzZkz_kz_kz_kz_kz_lz`lz`lz`lz`mz`mzamzam\ zanzanzanzbnzbozbozbozboz } 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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Details from recent FOTD's
by Brian Prentice 19 Aug '11

19 Aug '11

Here is a detail from the FOTD for 8/13/11 http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_37.png and here is one from the FOTD for 8/16/11 http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_38.png Brian Prentice

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FOTD 18-08-11 (Elephant Trek [7])
by Jim Muth 18 Aug '11

18 Aug '11

FOTD -- August 18, 2011 (Rating 7) Fractal visionaries and enthusiasts: I believe in honesty in advertising, and when a fractal falls flat, I admit it. I realize that no one gets rich by being totally honest about their product, but no one gets rich from finding fractals either, so I've got nothing to lose by telling it like it is. With a rating of an everyday 7, today's deep scene in the Mandelbrot set barely deserves the word 'deep'. At the modest magnitude of only 7*(10^15) it is barely beyond conventional math range, but at least IMO, it has a certain interesting quality about it that raises it to FOTD standards. The scene lies in the East Valley of a larger minibrot on a side filament of the main filament extending from the bud on the north shore line of the period-2 bud of the M-set. I named the image "Elephant Trek". I see a few hints of elephant parts in the scene, though not quite enough trunks and heads to fully justify the name. The parameter file takes 25 minutes to finish. In today's on-the-go world this might be too much precious time, so save the time by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Or view it in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, with all the images and discussions since April 1997 may be accessed at: <http://www.Nahee.com/FOTD/> The day began mostly sunny here at Fractal Central, and continued this way through a good part of the afternoon. At post time, showers were in the area, though none had yet reached FC. The temperature of 86F 30C brought out the best in the fractal cats. They spent most of the time sleeping. While the cats were taking it easy, the humans were doing what needed to be done. When the necessities were finished, we took it easy also. It is hardly necessary to state that the next FOTD image will be posted in 24 hours. Until then, take care and when I was a youngster, I knew that science and technology would be our salvation. But now I'm not so sure. What it is doing is making us ever more dependent on the high priests of the 'Church of Science and Technology'. I recently overheard a young boy (probably an internet addict), ask how people ever got along when they didn't have cell phones and the internet. Well, I was around before cell phones and the internet, getting along quite well, the same as everyone else, and I can state that we managed life the same as we are doing it now without the next big technological advance, which will not be developed for another 50 years. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Elephant_Trek { ; time=0:25:10.06-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.0188\ 8639656655182417/0.30447073015893949152/7.411e+015\ /1/-10/0 params=0/0 float=y maxiter=7500 bailout=16 inside=0 logmap=1110 periodicity=6 colors=000F0AF0AF0AE0AE0AE0AE0AE0AE1AE2AE3AE4AE5AD\ 6BD7BD8CC8CC9DCADBAEBBEBCFACFADGAEG9FH9FH9GI8HI8HJ\ 8IJ7JK7JK7KL6LL6MM6MM5NN5ON5OO4PO4QP4RPUSSfMRpWaze\ kzcgvcdrcfmdgkdiidjgdkedmcenaep_eqYesVetSeuPfpNglM\ hgKicJjZHkVGlRFhTEdVD`XDYZCU`BQbAMdAJf9Fh8Bj77l74n\ CApGFqKKrOPtSUuWZv_cxchygmzclw`ltYkrUkoRjlOjjKigHi\ dEhbAh_7gX4gV8VTCIRG6PI9QKBRLDSNFTPIUQKVSMWTOWXWO`\ bGdi8adFZ_LWVRTRXQMbNHhKCnI8tN9oRAjVAfZBabBYcCTcDO\ cDKcEFcEBcDCcDDcCEcCEcBFcBGcAGcAHaAI_9IW9JT8KQ8KM7\ KJ7KG7KpLmrNorRorVmrZlrbkrfjrjirnhrrgrzfzzcKKMbFBm\ K1kb3ge6d_9mKbzKbzCLzAHI8ES6AX47aA9cHBeNDmYFzcHv_D\ r_9mZ5hX1cRSZLrUMmPMiKMeFMaANX8NT7NP6NL7TI8YF9bCAg\ 9AzcCmmDcmEUmFJ4LKmRKmXLmbLmhLmnMztMzzMzmKzcLzVLzM\ LzTQzZVze_zzzzzzzzzzzzzzzzzzz`z`ezfjzlnzrjznfzkbzg\ ZzdVz`RzYNzUKzRVzZQzjDzxLzvTzu`ztczG`zKZzOWzSAzRRz\ `gziazfWzdRzbLz`GzZPzcTzO } END PARAMETER FILE=========================================

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FOTD 17-08-11 (Low in Saturation [8.5])
by Jim Muth 17 Aug '11

17 Aug '11

FOTD -- August 17, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image is named "Low in Saturation". The name refers to the color palette, which, except for a few registers, is of very low saturation. Sometimes, less of something is actually more effective than too much of it however. In today's image, for example, the almost-gray outer parts cause the few brilliantly colored inner spots to appear all the more intense. Less color on the outside gives the impression of more color on the inside. I rewarded myself a half-point for this minor example of color theory. The other 8 points of the rating are due to the underlying image itself, which is a scene not all that deep in the star of the period-30 elephant on the southern shore line of East Valley. The calculation time of 19-3/4 minutes borders on annoying slowness. The arbitrary precision math routine certainly does give the ability to wander as deep as one wishes into the Mandelbrot and Julia sets, but it takes its good old time getting there. Still a slow fractal is better than no fractal at all, and isn't something worth having worth waiting for. But time is time, and to save time, view the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Or view it is high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with a shroud of fog here at Fractal Central, but by 9am the fog gave way to a crystal blue sky. The rest of the day featured continued near cloudless skies and a temperature of 86F 30C. The humans' day was another in a long string of days so similar that it is hard to tell one day from another. The fractal cats never worry themselves about boredom however, they are too busy just being cats. The next FOTD fractal will be posted in about 24 hours. It might be late, it probably will not be early, but it is virtually certain to be there. Until then, take much care, and preserve the faith that technology can save the race from self- destruction. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Low_in_Saturation { ; time=0:19:46.22-SF5 on P4-2000 reset=2004 type=mandel center-mag=0.26061764366814\ 702894431163/-0.00176708064896804837819666/6.32257\ 1e+020/1/140/0 params=0/0 float=y maxiter=6400 bailout=16 inside=0 logmap=1076 periodicity=6 colors=000JJ`KK`LL`MM`NNaOObPPcQQdRReSSfTTgUUfVVfW\ WfXXfYYfZZf__b```aa_bbZcc_ddbeedfffggghhhhhgggfffd\ ffdffgggghhgiigjjgjjeiibgg`eeZccXaaV__TYYTWWTUUTUU\ TUUTUUUUUXUUXUUXUUWUUWUUTUURUUPUUQUURUUTUUWSSYQQ_Q\ Q_OOYMMWKKUIISGGQEEOCCMAAK88I8AF8CD8EC8FC8FD8FFAGH\ BHJ9EG9CE89B999778757A68D79C7AC8CGEILKPTTYaahghrYZ\ hPQ_JJTDDMAAHA9GA8FB8E96A969A68B78C78D88E88F98GA9F\ 98FA8E98EA8EA8DA8DB8DB8CB9CCCBBBCCCGGGLJMPNTUP`ZRi\ XSfWTdVRdNOQGIGGHDHBDHBCHBCIBBPFFWIIkLLzMMeFFIDC88\ 8CEDRUNnz_ipaimihjhhhhkkkhhhfffcbd_XbWTOXK_TJQRNP8\ EBzuZzljf`RYUOzz0```HBBLGGNKJKzznKz111111111111000\ 111222232243354476587486586687888888GECoYW`PNMIFDD\ BEGEHJHKNKMQMNUOQ_SSdVViZYob_teYteXtdYte`tfdthitkg\ teftYlzZozZqzZqz_qz_qz`rzarzbrzbszcszetzftzhuziuzk\ uzlvzovzqvzrwztxzwyzxzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzxzyvzxszvizoczj`zeZzb } END PARAMETER FILE=========================================

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FOTD 16-08-11 (A Midget in a Spot [8])
by Jim Muth 17 Aug '11

17 Aug '11

FOTD -- August 16, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image again departs from the August theme of images very deep in the Mandelbrot set. The departure was necessary to give me a chance to find another worthy image. These deep images are very slow and sometimes I simply have no chance to find one. But today's image is nothing to sneeze at. It's a scene in the parent fractal that results when the expression, (it's really not a formula), Z^(2.2)+C is calculated 22 levels up the complex logarithmic hyperladder. This parent fractal resembles a Mandel- brot set rotated about 200 degrees CW, with two East Valleys on the west side of its main bay. Today's image is located in one of the last islands in an archipelago of debris extending from the center of the southern valley. The name "A Midget in a Spot" has little meaning beyond the sound of the words. The rating of an 8 is what I thought the image is worth at the time I rated it. The calculation time of 33 seconds is thankfully brief, about the same time required to view the finished image on the web site. The official FOTD web site, with the finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> A high definition version of the image may be viewed at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The venerable classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with a light rain shower here at Fractal Central, but by midday the clouds parted, leading to a mostly sunny afternoon with a temperature of 82F 28C. The fractal cats spent an unusually long time in the window, which means they approved of the more pleasant conditions. The humans spent the day doing little out of the ordinary, though 'ordinary' implies enough work to keep us busy. The next FOTD will be posted in 24 hours. If all goes according to plan, it will be a great one. Until then, take care, and if you can't believe what religion teaches, turn to science; if you don't like what science has found, turn back to religion. If you wish to find the real truth, welcome to the group. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Midget_in_a_Spot { ; time=0:00:33.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=-0.3441515092977831/-0.0530208699951345\ /1.967296e+007/1/54/0 params=2.2/0/22/0 float=y maxiter=1800 inside=0 logmap=74 periodicity=6 colors=000A0UA0TA0SA0RA0QA0PA0OA0NA0MA0LA0KA0JA0IA\ 0HA0GA0FA0EA0DA1CA2BA3AB34G96LF7QL8VR9_XBdbCihDlmE\ VizQfxMcxH`wDYv8Vu4Su0Pt4MsBLrMJqLKpSKoUUhicaqmWzv\ PzzJmvRcrZOmfGhn9cv7Zr6Un5Pk4Kg3Fd3Dk3Bq9DoFFnKHlQ\ JkWLi`NhfPfkQejJbiC_h5XVE`IMdZP_nSVlUYjV_iXagYce_f\ d`hbbjaclbicbnVbtMbyEZrHVkKReMNZPJTRFMUBGWFFXIEYLD\ YOCZRB_UA_TBYSBXRCVQCUPDSODRNEPMEOLBKJ8H7PbBIUFCMq\ RVeKPUDJrz6eg9UPCO7oM6gL6_K6TJ6Lj8Ee7E`7Em7Em6Em6E\ mxmmqhmjdmc_mXWmQRmJNmCImgBm`CmVCmPDmIDmCEm8SmxOmq\ MmjLmcKmXJmQHmJGmCFmRSmOQmLOmJMmGLmDJmBHm8Fm2Wm3Rm\ 4Nm5Im5xm6nm6em6Wm6NmqLmjKmcJmXImQHzJGzCFzxmzngzea\ zXWzOQzFKzl1zXZzTWzPTzLQzHNzDKz9HzmIzmHzmHzmGzmGzm\ FzmFzmEzmzzmizmUzmozmhzmbzmXzmQmzKmzRmzOmzLmzJmzGm\ zmmzMmzJmzGmzWmzSmzOmzLmzHnz8YzBSz8PzANzBKzDFzmGza\ dzTWzZNzdFzjMzfTzc_z`fzYmzVtzS3zTIzNXzIkzCzz7VzOqz\ 9hzA_zCRzDbzZWzSPzLYzZnz` } 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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Do It Again
by Mike Frazier 16 Aug '11

16 Aug '11

This fractal was made by repeatedly zooming in on ever smaller versions of a self similar feature. Each time another zoom point was picked it added another rotated square to the fractal. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/do_it_again_800_5.jpg The parameter file used to make the image: Do_It_Again { ; Exported from Fracton. ; time = 45 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=-0.637200981531797321929241216142613588\ 79610418726/-0.49499504327751979843855327780682656\ 575746254617/3.921568676470588e+24/1/43/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=4000 inside=0 proximity=0 colors=000y_TxZSuYRsXQpVOlSNhQLcNJZKGUHEOEBIA8C756\ 32000411932E54J75N87RA8VB9ZDAaEBdFCgGDiHDjHElIElIE\ mIFlIElIEjHEiHDgGDdFCaEBZDAVB9RA8N87J75E5493241100\ 0310721A32E42H53K64N74Q85S95VA6XB6YB6ZB7_C7`C7`C7`\ C7_C7ZB7YB6XB6VA6S95Q85N74K64H53E42A32721310421942\ D73I94MB5QD6UF7XH8_J9bKAdMBfNBhNBiOCjOCjPCjOCiOChN\ BfNBdMBbKA_J9XH8UF7QD6MB5I94D739424210002414927E39\ J4BN5DR6FV7HZ8Ja9KdAMgBNiBNjBOlCOlCPmCOlCOlCNjBNiB\ MgBKdAJa9HZ8FV7DR6BN59J47E349224100022644C77I99OBB\ UDDZFFcHHhJJlKKpMMsNNuNNxOOyOOzPPzOOzOOyNNxNNuMMsK\ KpJJlHHhFFcDDZBBU99O77I44C226000641C92IE3OJ4UN5ZR6\ cV7hZ8la9pdAsgBuiBxjBylCzlCzmCzlCylCxjBuiBsgBpdAla\ 9hZ8cV7ZR6UN5OJ4IE3C92641000413937D5AI6EM8HQ9KUBNX\ CQ_DSbEVdFXfGYhGZiH_jH`jH`jH`iH_hGZfGYdFXbEV_DSXCQ\ UBNQ9KM8HI6ED5A937413000632C75IA8OEBUHEZKGcNJhQLlS\ NpVOsXQuYRxZSy_Tz`Tz`Uz`T } -- Mike Frazier www.fracton.org

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FOTD 15-08-11 (Antibifurcation [8.5])
by Jim Muth 15 Aug '11

15 Aug '11

FOTD -- August 15, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image is named "Antibifurcation" because it shows the scene of the horrendous crime of antibifurcation, where, in total violation of the laws of fractal math, the number of elements around the center shrinks to a tiny fraction of its value instead of steadily doubling as the laws of fractal math state it must do. But actually, there is no crime at all. The image shows a minibrot in the basin of attraction of a larger but still infinitesimal minibrot lying near the limit of the main spike of the Mandelbrot set, which is (-2). When a minibrot lies in the basin of a larger minibrot, this antibifurcation always happens. By contrast, minibrots in the basin of the M-set itself continue bifurcating in the normal manner, with no setbacks, until reaching the limit of infinity at the edge of the M-set. The curving tentacles in the image are caused by the closeness of the scene to the cutoff point of 2. Why the tentacles curve and twist in such an unlikely manner is known only to the gods of mathematics, and since I am not one of that exalted group, I have no idea why the image appears as it does. All I can do is apply colors to the forms that were already there. The rating of an 8-1/2 is held down because such scenes are quite common in the world of fractals. I added a half-point bonus for the coloring work I put into the image, but even this seems a bit liberal. The calculation time of 23-1/3 minutes is slow, but still reasonable for an image with a magnitude of almost 10^58. 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 classic site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds and light rain spoiled Monday here at Fractal Central. The fractal cats approved of the temperature of 73F 23C even though to the humans it felt unusually chilly for mid- August. The next FOTD will be posted in 24 hours. Until then, take care, and I once had faith in science, but now I'm not so sure. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Antibifurcation { ; time=0:23:20.93-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.9999\ 99999999996712761384990600054608875639729347944959\ 1259627/0.0/8.5933e+057 params=0/0 float=y inside=0 maxiter=7500 bailout=4 symmetry=xaxis periodicity=6 colors=000SqdTocUlaWj`XhZZeY_cW``VbZTcWSdUQfSPgPNi\ NMjKKkIJmFHnDGoBFdLGVVHLdIBnJ1xK2sI3oH4jG5fF6aD7YC\ 8TB9PAAK8BG7CB6D75E34G47I4AK4DM4GN4JP4MR4PT4SU4VW4\ YY4`_4c`4fb4id4lf4og4qg6pg7og8og9ngBngCmgDlgElgGkg\ HkgIjgJigKigMhgNhgOggPfgRfgSegTegUdgVdfUefTefSefRe\ fQefPffOffNfeMfeLfeKgeJgeIgeHgeGgeGgfHhfIhgJigKihK\ jhLjiMkiNkjNkjOlkPlkQmlRmlRnmSnmTonUonUolTpkSqiRqh\ QrfPsePscOtbNu`Mu_LvYKwXKwZOr_Rm`UhaYcb`ZdcUegPfjK\ gmFhpAdn9am8Zl7Vj6Si5Ph4Lf3Ie2Fd1Cc0`4Ec8eaCc`Ga_J\ `ZNZYQYJRh5Ss6Vp7Xm8Zj9`g9bdAeaBgZCiXDkUDmREpOFrLG\ tIHvFHxD61H90FB7DETBEU9Jk7ds6PkCTcIXVOWNUSLULLVMLV\ NLVNKlOKtOKmPKpPJzQJtRJzRJvSIrSImTIhUIcXHZUHVVHVVH\ VWHVzK5yI6xG7wE8vD9uC9tCAsCBrCCqCCoDDmDElDFkDFjDGi\ EHhEIgEIfEJeEKdFLcFMbFM`FNZFOWGPUGPTGQSGRRGSQHSPHT\ OHUNHVlqIkpJkoJjnJjmKjlKikKijLhjLhiLhhMggMgfMfeMfd\ NfdNecNebOdaOd`Od_PcZPQtf } END PARAMETER FILE=========================================

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FOTD 14-08-11 (Sparking Elephants [9])
by Jim Muth 15 Aug '11

15 Aug '11

FOTD -- August 14, 2011 (Rating 9) Fractal visionaries and enthusiasts: With today's FOTD image we return to the theme of the month -- the land deep within the Mandelbrot set. We check a minibrot that lies in the East Valley of a larger minibrot that in turn lies just beyond the main spike of the still larger minibrot at -1.417 on the main spike of the Mandelbrot set. The image rates a lofty 9, one point of which is due to the coloring. At first I considered adding more colors to the image, but the more I looked at it, the more pleased I became with the subdued blue theme. The name "Sparking Elephants" is a play on the word 'spiking', which might not be a word at all. The spikes are evident throughout the image, pointing straight away from the barely visible minibrot at the center. And the image does have a kind of electric atmosphere about it. The calculation time of 52 minutes is slow enough to make viewing the image on the FOTD web site the better choice. The web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic web site with all images since April 1997 may be accessed at: <http://www.Nahee.com/FOTD/> Sunday left a lot to be desired here at Fractal Central. Heavy clouds kept a blanket over the area all day, while intermittent rain killed all hopes of a pleasant day. The fractal cats showed their fractal nature by being in two places at once. But since there are two fractal cats, this is not much of a paradox. The humans found enough indoor stuff that needed doing to prevent boredom from setting in. I killed one hour counting the scientific errors in one of those pop-science shows on one of the supposedly 'educational' channels. The next FOTD will be posted in 24 hours. Until then, take care, and Atheists should be more specific in describing what they *DO* believe about the origin of the universe. When they claim that 'it all just happened by meaningless cosmic accident', they are not answering the question, they are expressing their ignorance, which leaves them open to attack from believers who feel they 'know' where the universe came from. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Sparking_Elephants { ; time=0:52:41.67-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4189\ 1243194492188838422868091/0/3.22027e+025 params=0/0 float=y maxiter=32767 inside=0 symmetry=xaxis colors=000GOMIOMIOOIOOIPOIPPIPPIPPIPRIPRIRRIRRIRTI\ RTIRTIRVITVITVITXITXITXITZIVZIVZIV`IV`IV`IVbIXbIXb\ IXdIXdIXdGTiIVmIVmHXmHXmHXmHZmGZmG_mH_mH_mH_mH_mH_\ mH_mF_mD_mD_mB_m9_m9_m7_m5`m5`m5`p5`r6`r6`r6`r8`r8\ `pA`pA`pA`pBbpBbpDbpDbmFbmFbmFbmGbmGbmIbmIbkIbkKdk\ KdkMdkMdkMdiOdiOdiPdiPdiPdiRdiRdgTegTegTegVegVegXe\ gXeeXeeZeeZee`ee`eedddbeebee`ee`eeZgeZggZggXggXggV\ igVigTiiTiiTkiRkiRkiPkiPkkOmkOmkOmkMmkMpkKpmKpmKpm\ IpmIrmGrmGrpFrpFrpFtpGtpItrKtsMvtOvuQvvSvwUvxWxyYx\ z_xzaxzczzezzgzzizzkzzmzzrzvrzymzxmzxmzxmzxmzxmzzm\ zzmzzmzzmzzkzzizxgzxezxczxazx_xxYvvXvvWtvVtvUrvTpv\ SptRmtQmtPktOitNitMgtLgrKerJdrIdrGbrEbrC`pAZp8Zp6X\ p4Xp2Vp0Vp0Xp0Xp0Xp0Vp0Vm0Ti0Tg0Re1Rb2P`2PZ4OV5OT6\ MR5LO6IM7HK7EG6DF7AD89A878604655655655656656656668\ 66866866A66A66A68B68B68B68D79D8AD9DFAEFBFFCGFDHGEI\ GFLGGMIGMIGMIGMKGMKGOKGOM } END PARAMETER FILE=========================================

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FOTD 13-08-11 (Half a Spider [7])
by Jim Muth 13 Aug '11

13 Aug '11

FOTD -- August 13, 2011 (Rating 7) Fractal visionaries and enthusiasts: The theme of August is fractals from deep in the Mandelbrot set. Today's image is not from the Mandelbrot set however. It is from the fractal that results when Z^(2.25)+C is iterated 1/2 level up the complex logarithmic hyperladder, (actually more of a hyperspiral). I had to depart from the theme of the month for one day to get caught up. The very deep images are quite slow, and I have been falling behind. The parent fractal appears as a distorted M-set rotated so that its distorted main period-2 bud lies on the north side of the main bay. There is a small valley on the east side of this bud, with today's image lying in that valley. I named the image "Half a Spider". Spiders have eight legs, but there are only four spidery legs radiating from the central minibrot in the image. Since four is one-half of eight, the name is quite appropriate. (The circular disk closer in around the minibrot holds nine legs however.) The rating of a 7 places the image just about at the center of FOTD ratings. The calculation time of under 1-1/2 minutes assures that no precious time will have been wasted if the eager fractalist is disappointed with the image. For even more assurance, the finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The image is available in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Threatening clouds moved in here at Fractal Central on Saturday morning, and a heavy thunder-shower arrived at 3pm, putting a finish to any outdoor activities. The fractal cats' outdoor activities are limited to gazing out the windows anyway, so they had no problem with their outdoor activities. If the day had been dry, the temperature of 79F 26C would have been pleasant. The humans, with no outdoor activities planned, had a typical day indoors. The next FOTD should be posted in 24 hours, which is the typical interval. Until then, take care, and be a rational skeptic who doubts that physical aliens are visiting earth in flying saucers. Such visits are impossible. Due to the cosmic speed limit of light, (186,000mps), there is no way for physical aliens to get here. If you must believe in some- thing irrational, believe in ghosts. They are very disturbing to skeptical rationalists, but at least they are not impossible. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Half_a_Spider { ; time=0:01:25.03-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.1522280397550513/+0.9940388789985681\ /7.345366e+010/1/32.5/0 params=2.25/0/0.5/0 float=y maxiter=1800 inside=0 logmap=141 periodicity=6 mathtolerance=0.05/1 colors=0000Xy0Wt0Uo0Sj0Qe0Na0KX0HS0EN0BJ08E059024f\ LC`IAWF9QD7LA6G74A53521I9yG8rE7lC6fA5`94V73O52I31C\ 106lsBgm9bg8Yb7TX6OS5JM4EG39B2451K_Rpzikudfpb`hWT_\ QMRJEID796pUQjQNdNKZKHTGENDBHA8B65532IscEgWAXO7MG3\ B84T73Q63O63M52K52I42G42E31C31A2182061041020r_PnXN\ kVLgTKdRI`OHYMFUKERICOFAKD9HB7D96A64643321CzzBuuAq\ q9mm8ii8ee7``6XX5TT4PP4LL3GG2CC188044DnNBiLAeJ9aH8\ YF7TD6PB5L94H73C5283141GTjEPdCM_AJV8GQ7CK59F36A135\ IDYC8M64BqKlmIhiHefGbbEZ_DWWCTSAQP9ML8JI6GE5DA4972\ 6313CRt6DSMI_JGWHESFCPDALB9I87E65A437213qRWlOTgMQb\ JNYHKTEHOCEJ9BE78945422mnUijSfgQccO_`MXYKUUIcRGcNE\ cKCmHAmD8mA6m64m32m2Am16m03mULmRImOGmLEmICmKAmU8mU\ 6mU4mU2zUbzUZzUVzcRzcNzcJzcFzcBzc7zc3zmbzmYzmTzmOz\ mJzmEzm9zm4zmYzzgzzhzzhzzhzzhzzhzzhzzhzzhzzhzzhzzh\ zzhzzhzzhzzhzzhzzbzzXzzRzzLzzFzz9zz8zz7zz7zz6zz5zz\ 5zz4zz3zz3zz5zz2zz1zz1zz0 } 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 12-08-11 (Colors Without End [7.5])
by Jim Muth 13 Aug '11

13 Aug '11

FOTD -- August 12, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: The August FOTD theme is scenes deep in the Mandelbrot set. But this does not necessarily mean the images must be deep enough to require arbitrary precision math. At the scale of today's image, the entire M-set is about the size of the solar system. And at least IMO, this magnitude is quite large enough for the scene to be considered 'deep'. The image comes in two versions -- a slow version that finishes in 24 minutes and a fast version that finishes in 4 seconds. I have included a parameter file for each version. The difference in quality is very small, but it is there. Those who value time above quality should run the fast version. Others will run the slow version and have an inner satisfaction that their image is marginally the better. The scene is located in the East Valley of a larger Minibrot that lies in a chaotic knot on the long filament extending from the north bud of the minibrot at -1.417 on the main spike of the Mandelbrot set -- a rather well-explored area, but one that still holds surprises. The flat, (sky-blue), background was achieved by rendering the image with the logmap set to an artificially large 1260. The correct value is around 970. The rating of a 7-1/2 includes 1/2 point for the coloring, even though most of the coloring was done by the Fractint program, with only a few tweaks applied by me. The name "Colors Without End" is based on the richness of colors in the image. The slow, top-quality version is posted on the FOTD web site. The web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> A higher-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The venerable FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Today here at Fractal Central was a repeat of yesterday, with the same kodachrome skies, puffy clouds, low humidity, and a slightly warmer temperature of 84F 29C. The fractal cats also had a repeat day. They passed the time taking it easy, coming to the alert only when a beat-up old yellow-orange tomact passed through the yard and sprayed the fence. The humans passed the day doing routine things such as finishing the work. The next FOTD will be posted in 24 hours. Until then, take care, and when all activity and all change in the universe finally ceases, how will we tell the past from the future? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Colors_Without_End { ; time=0:24:14.37-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4175\ 686044006788/0.00225633082302048/1.706292e+012/1/\ 105/0 params=0/0 float=y maxiter=6400 inside=0 logmap=1260 periodicity=6 mathtolerance=0.05/0 colors=0000KzZn9Vh8Rb7NY6JS5FM4BH37B23511VV0RR0NN0\ JJ0FF0BB077033c7A_69W58T57P46L35I34E23A127113007Ng\ 5J_4FT3BM27E137xBruAor9lo9jl8gi8df7bc7_`6YY6VV5ST5\ QQ4NN4KK3IH3FE2DB2A817515202z`XtXUoURjROeOM_LJVIGQ\ FDLCBF98A65532xuCspBnlAig9ec8`Z7WV6SQ5NM4IH3ED2981\ 440AwH9rF8mE7iD6dB6_A5W94R73N63I52D3192041nXHkVGiT\ FfSEdQDaPC_NCYMBVKATI9QH8OF8LE7JC6HB5E94C749637424\ 31210PHJNGIMFHLEGJDFICEHBDFACE9BD8AB89A78967756645\ 534323212101xz2su1oq1km1gi1ce1_`1WX1ST0OP0KL0GG0CC\ 0880440zO8tM7oK6jI6eG5_E4VC4QA3L82F62A41520MB6IA5F\ 84C63952631310L_kJXhIVeHTbFR_EOXDMUBKRAIO9FL7DI6BF\ 59C369246123iC2nZbmVagQ`aM_WHZQDYH0XA0XA0XA0XTGWQH\ WNHWKIWHIWGHUFGSEFRDEPCDOCCMBCL06BABJ9AI89G88F77D6\ 6C56A459447336224113001zzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } ColorsWithoutEnd { ; time=0:00:03.88-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4175\ 686044006788/0.00225633082302048/1.706292e+012/1/\ 105/0 params=0/0 float=y maxiter=6400 inside=0 logmap=1260 periodicity=6 mathtolerance=0.05/1 colors=0000KzZn9Vh8Rb7NY6JS5FM4BH37B23511VV0RR0NN0\ JJ0FF0BB077033c7A_69W58T57P46L35I34E23A127113007Ng\ 5J_4FT3BM27E137xBruAor9lo9jl8gi8df7bc7_`6YY6VV5ST5\ QQ4NN4KK3IH3FE2DB2A817515202z`XtXUoURjROeOM_LJVIGQ\ FDLCBF98A65532xuCspBnlAig9ec8`Z7WV6SQ5NM4IH3ED2981\ 440AwH9rF8mE7iD6dB6_A5W94R73N63I52D3192041nXHkVGiT\ FfSEdQDaPC_NCYMBVKATI9QH8OF8LE7JC6HB5E94C749637424\ 31210PHJNGIMFHLEGJDFICEHBDFACE9BD8AB89A78967756645\ 534323212101xz2su1oq1km1gi1ce1_`1WX1ST0OP0KL0GG0CC\ 0880440zO8tM7oK6jI6eG5_E4VC4QA3L82F62A41520MB6IA5F\ 84C63952631310L_kJXhIVeHTbFR_EOXDMUBKRAIO9FL7DI6BF\ 59C369246123iC2nZbmVagQ`aM_WHZQDYH0XA0XA0XA0XTGWQH\ WNHWKIWHIWGHUFGSEFRDEPCDOCCMBCL06BABJ9AI89G88F77D6\ 6C56A459447336224113001zzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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Shuriken
by Mike Frazier 13 Aug '11

13 Aug '11

This one looks sort of like a shuriken or throwing star. It was synthesized by repeatedly building a line fractal and doubling the number of arms. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/shuriken.html The parameter file used to make the image: Shuriken { ; Exported from Fracton. ; time = 14 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=-0.637200976755101990090375751704920316\ 4129285920553172950221050123642148620218915862204/\ -0.49499504293951702730512003147598679071318907247\ 67733511982230245678938692912016518461/1.302083349\ 609375e+75/1/-21/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=16000 inside=0 proximity=0 colors=000y_TxZSuYRsXQpVOlSNhQLcNJZKGUHEOEBIA8C756\ 32000411932E54J75N87RA8VB9ZDAaEBdFCgGDiHDjHElIElIE\ mIFlIElIEjHEiHDgGDdFCaEBZDAVB9RA8N87J75E5493241100\ 0310721A32E42H53K64N74Q85S95VA6XB6YB6ZB7_C7`C7`C7`\ C7_C7ZB7YB6XB6VA6S95Q85N74K64H53E42A32721310421942\ D73I94MB5QD6UF7XH8_J9bKAdMBfNBhNBiOCjOCjPCjOCiOChN\ BfNBdMBbKA_J9XH8UF7QD6MB5I94D739424210002414927E39\ J4BN5DR6FV7HZ8Ja9KdAMgBNiBNjBOlCOlCPmCOlCOlCNjBNiB\ MgBKdAJa9HZ8FV7DR6BN59J47E349224100022644C77I99OBB\ UDDZFFcHHhJJlKKpMMsNNuNNxOOyOOzPPzOOzOOyNNxNNuMMsK\ KpJJlHHhFFcDDZBBU99O77I44C226000641C92IE3OJ4UN5ZR6\ cV7hZ8la9pdAsgBuiBxjBylCzlCzmCzlCylCxjBuiBsgBpdAla\ 9hZ8cV7ZR6UN5OJ4IE3C92641000413937D5AI6EM8HQ9KUBNX\ CQ_DSbEVdFXfGYhGZiH_jH`jH`jH`iH_hGZfGYdFXbEV_DSXCQ\ UBNQ9KM8HI6ED5A937413000632C75IA8OEBUHEZKGcNJhQLlS\ NpVOsXQuYRxZSy_Tz`Tz`Uz`T } -- Mike Frazier www.fracton.org

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FOTD 11-08-11 (Deep in the Abyss [9.5])
by Jim Muth 12 Aug '11

12 Aug '11

FOTD -- August 11, 2011 (Rating 9.5) Fractal visionaries and enthusiasts: The FOTD theme for August is deep images in the Mandelbrot set, but until today we have not ventured to any real depth. Today however we get bold and dive to a depth of over 6*(10^112), where we find a 'reset' (anti-bifurcation) point in the huge basin around a minibrot that is still well beyond visibility. The scene is located on a filament extending from a larger but still very deep, (10^59), minibrot on the west branch of the filament extending from the north bud of the large minibrot on the main spike of the Mandelbrot set. The rating of a 9-1/2 includes a 1/2-point bonus for the extra effort I put into coloring this very difficult image. The mathematical interest is responsible for another point. The name "Deep in the Abyss" refers to the depth of the image. At the scale of the image, the entire Mandelbrot set would be something like a trillion times the size of the visible universe. (This is a guess. If anyone wants to do the math, go ahead. It would be interesting to see how many universes could fit into the main bay of this huge abstract M-set.) The great depth comes at a great time price however. On my 2000mhz unit, the image takes 2-3/4 hours to finish -- slow by anyone's standards. When I finish the day's tasks, I might check the minibrot at the center of today's image. I suspect that it will be little more than a mess of Moire patterns however. Those who are put off by spending nearly 3 hours calculating a fractal may make their lives far more pleasurable by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Or by viewing it in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> A near perfect day prevailed at Fractal Central today. The mostly sunny, kodachrome-blue skies were decorated with just enough puffy white clouds to make a picture postcard, while the low humidity and temperature of 81F 27C completed the perfection. The fractal cats enjoyed the outdoor conditions as much as is possible from the inside. They spent several hours in the window, watching the clouds and birds pass by. If the current economic anxiety is discounted, the humans had another quiet peaceful day, and there is no reason why tomorrow will not be yet another. One thing almost, but not quite, guaranteed, is that the next FOTD will be posted in 24 hours. Until then, take care, and if the world is doomed to come to an end, have no concern. The planet will survive. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Deep_in_the_Abyss { ; time=2:42:17.31-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.760253238150842578924572047306459168\ 76736648297229159632195292672917534094239659654914\ 2910643263619452633110603677569/0.0205067183160941\ 19948251370111250193053188331879913407481982651252\ 94067841033483402062094896012495680845728688892030\ 62/6.500128e+112/1/122.5/0 params=0/0 float=y maxiter=5000 bailout=16 inside=0 periodicity=6 colors=000MbGJ_EHXBEU9CR69O42K17L2BL3FL4KL4OM5SM6X\ M7`M7dN8iN9mNAsO8qNAoMCmMEkLGjLIhKKfKMdJNNAUOAUPAU\ QAURAUQAUQAUPAUQAUQAUQAUQASRBUSCVSDXTEYTFZUG`UHaVI\ bWJdWKeXLgXMhYNiYOkZPlWOpZQm`RjbTgdUdfWahX_jZXl_Un\ aRpbOrcMpdQodTmdWleZjeaiedhfhffkefncgqbgtagw_fuYet\ XdrVcqUboSanR`lP_kOZiMYhLXgJUcHR`GOYEMVDJSBGO9EL8B\ I68F56C54B52B50B50B50A50A50A50A50A5295495695895A99\ CDCEGFHJIKNLNQOQTRTWVW_YZbaageemiirmnwqrzpqvmnrkkn\ hhkeehcbd`_`ZYXYWUUURRTTNRZKQcGPiDNn9Mt6Ly9NxBOwEQ\ vGRuITuKUtRZsYcrdhqkmkrrcvvUzzKztAmv6ms6mr6mq5mq5m\ p5co5cn5cn5cl7cj9ciAcgCcfEcdFccHcaJb`KeZMgYNc_M`aL\ XcKUeJRgINiHKkGHmFDoEAqD7rDIRKNOISMGXJEaHCeEAjC8o9\ 6t74x53t74q95nB6jD7gF8dH9`JAYLBVNCRPDORELTFHVGEXHB\ ZHF_LI_OL_SP_VS_ZV_aZ_ea_hd_k`XgXVdTTaPRZMPWJSXHVY\ FYZD`_Bc`8fa6ib4lc2od0rd2pe4oe6ne8leAkeCjeEheFgeHf\ fJdfLcfNbfP`fR_fTkNRhLOeI } END PARAMETER FILE=========================================

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FOTD 10-08-11 (Silver Elephants [8])
by Jim Muth 10 Aug '11

10 Aug '11

FOTD -- August 10, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "Silver Elephants". Yes, I realize that elephants are more of a leaden gray color than a silvery one. But the phrase 'leaden elephants' has no oomph. It wouldn't sell the latest wireless internet device. So I stretched reality a bit and decided that elephants sometimes might have a silvery sheen about them. The colors of the image would confirm this fantasy. The rating of an 8 is a bit liberal. I actually feel that the high-magnitude images of this month are becoming rather routine. Their magnitudes are just not large enough. A more accurate rating might have been a 7-1/2, but what the heck, an 8 seems far better than a 7.5. The scene is located on the west shore line of the period-17 bud on the south side of East Valley. Perhaps the most interesting feature is the near-perfect square with its silvery inner elements and its bits and pieces of elephant trunks twisting outward. The calculation time of 51-2/3 minutes is slow, but they say something worth having is worth waiting for, so why not go ahead run the parameter file and risk dissatisfaction. The alternative is to remove the risk by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is available in high definition 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/> Today's high temperature here at Fractal Central equalled yesterday's high of 84F 29C, but lower humidity, lots of sun and no rain made it a far more pleasant day. The fractal cats approved of the outside conditions, but they approved even more when their treat was served. The humans had nothing to approve of, but they had nothing to complain about either. The next in the apparently endless series of FOTD images will be posted in 24 hours. If all goes well, it could have a far greater magnitude. Until then, take care, and should someone who wants to know whether God exists ask the Pope or Richard Dawkins? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Silver_Elephants { ; time=0:51:38.83-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=0.28112\ 03832938940597038/-0.01144622278067799682577/2.334\ 839e+017/1/50/0 params=0/0 float=y maxiter=12000 bailout=16 inside=0 periodicity=6 colors=000000000000000000bTVaUU`WU_XTZZSY_SXaRWcQV\ dQUfPTgOSiORkNQlMPnMOoLNqKNrKNdUNScNEmN1wM3tL5rL7p\ K8nJAlJCjIEhIFfHHcGJaGL_FMYEOWEQUDSSDTQENQFHQGBQH5\ QI0QG5WF9`EDeDIjCMoBQtAUyAWuAYqA_nA`jAbgAdcAe`AgXA\ iTAjQAlMAnJKoFUqCcs8mu5rrNzoMzkMzcMzUOAHP5MQ4RR4VS\ 4_U3dV3iW3nX3rY4qZ4p_4p_4o`4n`4na4ma4lb4lb4kc4jc4j\ d4ie4he4hf4gf4fg4fg4eh4dh4di4ci4bj4bj6`k8ZkAXlBWlD\ UlFSmGRmIPmKNnLMnNKnPIoQHoSFpUDpVCpXAqZ8q_7qa5rc3r\ zzzyyzxxzwwyuuxsswrruqqtppsooroornnqmmpmmpllokknkk\ mjjmiiliikhhkggjggiffheeheegddfccfccebbdaadaac``b_\ _a__aZZ`YY_YY_XXZWWYWWXVVXUUWUUVTTVSSUSSTRRTQQSQQR\ PPQOOQOOPNNOMMOMMNLLMKKLKKLJJKIIJIIJHHIGGHGGGFFGEE\ FEEEDDECCDCCCBBCAABAAA9998898887776676665554445446\ 33722822911A00B1BC2AD4AE6AF8AF8AF8AE8AE8AE8AE89E89\ E79E79D79D79D79D79D79D79C78C78C78C78C68C68C68B68B6\ 8B67B67B67B67B67A67A67A57 } END PARAMETER FILE=========================================

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FOTD 09-08-11 (Pins and Needles [8])
by Jim Muth 09 Aug '11

09 Aug '11

FOTD -- August 09, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's (rather) deep image involves a bit of a trick. The normal cut-off radius of the Mandelbrot set is 2. But in today's image I have set the bailout to 3, which causes the calculation to be cut off at a radius of 1.7. This slices off the tip of the main spike of the Mandelbrot set, but at the same time causes strange things to happen to features that would normally be located far from the cut-off point. Today's image shows what has happened to a tiny minibrot in the East Valley of a larger minibrot on the main stem, very close to the abnormally small cut-off point. I named the image "Pins and Needles" because of the prickly effect dominating it. The rating of an 8 might easily have been increased to an 8.5 had I not been in a conservative mood when I decided on the rating. The calculation time of 6-1/4 minutes is quite speedy for an arbitrary-precision image, but then, the magnitude of a mere 5*(10^13) is barely within arbitrary-math range. (In fact, the image may be calculated in a fraction of a second by using conventional math, but the degradation will be quite noticeable.) All this having been said, brace yourself for instant hedonistic pleasure if you decide to view the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And then be prepared to make a sincere confession. View the image in high definition 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/> Morning rain gave way to some afternoon sun here at Fractal Central today. A heavy thunder-shower passed over at 5pm to end the afternoon with a bang. The temperature of 84F 29C would have been more pleasant if the humidity had not been so high. The fractal cats noted a stray cat that passed through the yard in the morning, then spent the rest of the day taking it easy. The humans did the same. The next FOTD will be posted in 24 hours. Until then, take care, and one cannot become a rabble rouser unless they have some rabble to be roused. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Pins_and_Needles { ; time=0:06:16.57-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7320004020138\ 6624/0.0/5.451373e+013 params=0/0 float=y maxiter=15000 bailout=3 inside=0 outside=tdis symmetry=xaxis periodicity=6 mathtolerance=0.05/0 colors=000189044XkVRcPMWKGOFTS6RQ6QO5OM5MK4LJ4WGIe\ DVpAgz8tDGAKQHRZOXgVcpaiyhbteXocRj`LfZFaW9XU3TSWJU\ x9WsDVnGUiKTeNT`RSWURSXRUXNWXJXXFZXB_X7Q00SI0eZ5h`\ AjbFmdKofPrwUztZleXd`VXWTQRSIMQAHO3CNEDGOD9YD3K6DX\ EOWMPUUQTaRRiSQqTPxTRj9NWTJIkSDi`8hi4ge4Za4QY4IU49\ Q41UGVYRwV5mTSrRSwPTwNTwLTwB`c1gL0`I0VF0PC0I90C640\ 6063xRgkLZ_GQOAHC58xUGobcgXY`RSTMMMGHEBB755xUs9FT7\ CO6AK58G36C248124K0nU9EM6AF47723VX8FG4yvfVTL8SO6OK\ 5KH4GD3CA286143LJWFEOA9G548surgigXYXMNMBBBIUyFPpCL\ gAHZ7CQ58H248esmXgcPXUGMK8BAzoze7rS4_E2I_o7Ug6P`5K\ T4FM3AE2571sVf`KSIAE5Oz4Kq3Hh2D_2AR16I039QJcD9KuEq\ iBfY8WN5LB2AEoRBfM9YI7QD4H9284ngDaX9PM6CB3gmMZcHQU\ DHK88A4mhpeahZW`SPULJMECF767`G0I80BBq99i77a66U44N3\ 3F117tMmaEXJ7G1JV6Ls5Hi4E`3AS27I139HDSEBOC9LA8H86E\ 64A4372138d36W24O13G1180`YrRPdIHR98D2Ar16_03IhJ0XE\ 0M90B406Zb5UY4QT3LO3HJ2DE } END PARAMETER FILE=========================================

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Cat Owl
by Mike Frazier 09 Aug '11

09 Aug '11

It kind of looks like cat eyes on an owl face. The eye was duplicated by zooming in on a dead end arm in an outer oval. Here is a link to an image: http://dl.dropbox.com/u/33642054/image/cat_owl_640_5.jpg The parameter file used to make the image: Cat_Owl { ; Exported from Fracton. ; time = 16 min 24 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=-0.637200976593501474305583909687372908\ 30227891481784063632604796741094157599155163508087\ 42304787770826763730022536123600894299/-0.49499504\ 32196933461151370819730504957834722284332283559435\ 47904232277233494036263419341207160436966026740508\ 8485608901318991/8.333333437499999e+114/1/-68/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=20000 inside=0 proximity=0 colors=qaHtcGwfGziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDT\ GDQDCNBCK8C413000443775BB8EFAIIDLMFPQISUKWXNZ`PbdS\ egUikXloZprasvcsvcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZ\ P`XO_UMYRKWPJUMHSJFQIJOHMMFQKETIDWGB_EAbDCeCEgBGjA\ Hm9Jp8Lr7Nu5Px5Nu6Kr7Ho8El8Bi98fA5cB6`D6ZE7WF8UG8S\ H9QJANKBLMCIOFKQHNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljl\ olornrulprkmnikkgihffdddabbZa`W_YSYWPWUMVRITPFRNCQ\ K8OI5RK7TN9WPBYRD`TFbWHeYJg_LiaNkcPneRpgTsiVulYxn_\ zpawn`tk_piYmfXjdWgaVcZT`WSYURVRQROPOLOKJNHGMDDLAA\ KADMAGNAIPALQAOSARUBUWBXYB__CbaCecChfCkhDnjDqlDtnC\ qlBmjBjiAfg9cf8_d8Xc6SY5NS4IM3EH29B145000311632943\ D54G75J87MA8QB9TCAWEBZFCbHEfHBjH9nH7pH6rH5vH3zH0vH\ 2rG3mE2hD2cB2ZA2U81P71K51F41A30510000330760BA1ED1I\ G1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3ql4tq3wu1zz0ww1tt2pp3\ mm5jj6gg7cc8``9YYAXVBURBROBOKBLHBJDBGABD6CA3C80CC4\ CH8DMCDRGEWKE`OFeSFkWInZH } -- Mike Frazier www.fracton.org

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FOTD 08-08-11 (Wast-Eest [9])
by Jim Muth 08 Aug '11

08 Aug '11

FOTD -- August 08, 2011 (Rating 9) Fractal visionaries and enthusiasts: Today's image is named "Wast-Eest". This is not a scrambled form of a German expression; it's a combination of the compass directions 'West' and 'East'. I gave the image this name because it shares attributes of minibrots on both the West and East sides of the Mandelbrot set. The outer turquoise area of the 'shield' around the invisible minibrot at the center has obvious East Valley characteristics, while the brilliant yellow star within shows obvious features of minibrots on the West side of larger minibrots on the main stem of the Mandelbrot set. All this craziness is explained by the location of the scene. Today's image lies on the main stem of the Mandelbrot set, deep in the East Valley of the large minibrot at -1.75, just beyond the tip of the main spike of a much smaller minibrot. The rating of a 9 is justified, at least IMO. The intense coloring, which I spent some extra time on, adds to the value. But we need to break some new ground if we hope to keep the 9-rated FOTD's coming. The calculation time of 22+ minutes is slow, but the image may be viewed already calculated on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition 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/> Monday brought continued mugginess and passing showers to the Fractal Central area. The temperature of 84F 29C was within reason, but would have been much more pleasant without the humidity. The fractal cats ignored the humidity as they dredged up an old toy ball and batted it up and down the long hallway. The humans had an acceptable day. I busied myself by finding fractals and watching the showers pass by. FL had a slow day also. Her garden is at its mature stage, and needs less maintenance. Actually, now that we have lost our biggest customer, we have a lot more time to take it easy. The next FOTD will be posted in 24 hours. It will be another deep one. Until then, take care, and the world situation is getting bleak indeed. Sunday evening while we were watching TV, we became annoyed at the constant flood of financial doomsday stuff on one channel and switched to another channel, just in time to see some noted scientists (rational-thinking Atheists) state that everything is an accident. There is no God watching over us, there is no afterlife waiting for us, and that is that, . . . period. Hearing the great news, all I could say was, "have a happy day!" Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Wast-Eest { ; time=0:22:14.08-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.7494\ 33457574382940859478434/0/5.774687e+023 params=0/0 float=y maxiter=6000 bailout=16 inside=0 logmap=2075 symmetry=xaxis periodicity=6 colors=0002Je8LcDNbIQaNT`SW_YZZbb_gg`llaqqbvvbzxYz\ ymzzzzzzS3FOBCLIAIP7EW5Bb28i0Ae3Ca5DY8FUAGQDINFJJI\ LFKMBNO7PP4RK3MG2I002C2D819404EcMCYIASF8MC6H94B625\ 3s`LlWIfSG`OEVKBOG9IkgCje6hc4fa3dZ3aW3ZT2WR2SO2PL2\ MJ1JG1GD1CA0980650321DI0BG0AE09D08B079058046034023\ 0117k`6gY6dV5`T5YQ4UN4RL3OI3KF2HD2DA1A7165032EHhCF\ cBD_ACW8AS79O67K56G34C238114YHF5Eb4BV38NzY_vWYrTVm\ NOhHIcBCK56jMlbIcVEWNBOF7G738iNkaJcUFWNBOF7G7387Q_\ 6NW5KS4HO3EK3BG28C1580241G30E20C20B209108106104003\ 0010WYQ8yk7sf6mb5hY5bU4XQ3SL2Uz2Gm1BU054yFmrDgkBad\ AXY8RR6MTKUD3B615iUxdRq_OkWLeL8KNFUICOD9I96C436JSy\ CId69KRYTOUQMRNJOLHLIEIFCFD9CA797465232bkJmkHXcGU_\ EzzDOTBLPAzzzFI7CE59B467z331CZzBWQAUO9SM9zz8OJ7LH6\ JF6zE5FC4DA3A838z2cz1cz0czYczVz5Tz5Qz4Oz4Lz3Jz3Hz3\ Ez2Czz9z17z14z02z0MzcIzzFzzCzM9zH6zB3z53zJ2zF2zC1z\ 91z60z3zzVozUezUWzUMzUCzU } END PARAMETER FILE=========================================

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FOTD 07-08-11 (Shield of Chaos [9])
by Jim Muth 08 Aug '11

08 Aug '11

FOTD -- August 07, 2011 (Rating 9) Fractal visionaries and enthusiasts: Today's image once again takes us rather deep into the Mandelbrot set. I use the qualifier 'rather' because a magnitude of only 8*(10^19), such as today's, can hardly be considered deep by current standards. The scene is located in the Seahorse Valley area of a minibrot on a filament extending from the northwest shore line of the second bud out the main spike of the Mandelbrot set -- the bud just beyond Scepter Valley. The rating of a 9 is an honest one that includes a hefty bonus for the extra effort I put into finding the colors. The rating was also helped by the unusually chaotic yet well-defined 'shield' surrounding the nearly invisible minibrot at the center. The name "Shield of Chaos" refers to this feature. Since the image is of relatively modest magnitude, the calculation time is a relatively reasonable 12 minutes, a span of time that few but the most impatient fractalists will miss. For the convenience of the impatient or those with DOSaphobia- stricken computers, the finished image is posted for instant viewing at: <http://www.crosscanpuzzles.com/Archives.html> The image 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/> Partly cloudy skies with a muggy high temperature of 88F 31C made for a lazy day today here at Fractal Central. The laziness was briefly interrupted in the afternoon by a drenching thunder- shower, but within 1/2 hour the sun was again shining and the laziness returned. The fractal cats, in keeping with the spirit of the day, passed the time being lazy. At one point, Cassie tried to get fresh with Nico, but the big guy has better sense than to get involved in such activity on such a lazy day. The humans did mostly nothing, which is what they are best at, though FL was still recovering from Saturday's wet kayak trip down the river. The next FOTD, another scene deep in the Mandelbrot set, will be posted in 24 hours. Another rating of a 9 is not guaranteed however. Until then, take care, and if you believe that the five physical senses give a true and total picture of reality, then use your common sense and become a materialistic, scientific rationalist. (Whatever one of them is!) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Shield_of_Chaos { ; time=0:12:12.26-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.2560793137735\ 0679724147/0.382892246842947145144187/8.49528e+019\ /1/17.5/0 params=0/0 float=y maxiter=3000 bailout=16 inside=0 logmap=588 periodicity=6 colors=0006FJ7FJ7FI7FI8FH8FH8FG9FG9FF9FFAFEAFEAFDA\ FDBFCBFCCFCCFCDFCDFCEFCEFCFFCFFCGFCGFCHGCHGCIGCIHC\ JHCJGCKGCKFCLECLDCLCCJCCIBCGACF8CD6CC4CD7BE9BFBAGE\ AIG9LI9OK8RN8UP7XR7_T6bW6eY5i_5la4od4sf3wh3zj3zl6z\ m8znBzpDzqGzy_zYVzeMzmD1QWKUOaYGsa8qNVp8pYNpXOfWPX\ SDOO2FMcHBK8POqCCRmrDX_8GI4hysiZ9UN6FB3uStrkO_WGIG\ 8901JR79D3xwwhhhUUUFFFGMpCGb8BQ45D1Co09b06Q03Dtbae\ TSSJJE991p90Q4Fkkdv1Rb0DJ0IbUCQK6DAoDEQ67BeZ7SN3EB\ oDdZ3RH1DlBmO5PxH6U839VITQOJHG988LlkAOOL7AF57A3551\ 2V_ZNRQFIH798r3pd2bR1QD0DMjkEVW7FGL3nA1PJRN9DB3wD2\ h91U60F3T_Q`xzRhmIUM9FBzBzV5D5gJ3kE2T91B4SCoimZKsY\ ASHHG`cyoUibKVQAFDmKUPAFVYTggMmiLrjLjdScZZWTePNkTM\ hWLfZKdaJadI_gHYjGWWPOHXH2dA8`IEYPKVWQSbWPiaMpgJwb\ RvZYuVdtYcs`crccqfcpicolcnocmrmmhmXZmGPm0VzC`zOfz_\ lzjpz_szPvzEyz3szAmzGhzMbzSXzYSzcMziHzoLzfPzYTzPXz\ G_z8azBbzEczGdzJezLXzObzN } END PARAMETER FILE=========================================

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<Mike Frazier> Re: Shut Eye; Spike Star images
by Hal Lane 07 Aug '11

07 Aug '11

Mike, Thanks for posting the links to your nice images: Shut_Eye and Spike Star. I verified that DOS Fractint can read and run the parameter files written by Fracton that you provided. And I appreciate your web page with the clear explanation of the "Line Method". When I had previously read an explanation given at: http://stardust4ever.deviantart.com/art/Making-X-Fractals-155341193 I felt it wasn't clear enough to immediately know how to go about using it. Nice images! - Hal Lane ######################## # hallane(a)earthlink.net ######################## ============================================================= Author: Mike Frazier Date: 2011-08-05 14:38 -400 To: Fractint and General Fractals Discussion Subject: [Fractint] Shut Eye Kind of looks like a closed eyelid or a sideways cat's eye. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/shut_eye.html Here is a link to a page with a step by step method for making line fractals: http://www.fracton.org/fmlposts/line_method.html The parameter file used to make the image: Shut_Eye { ; Exported from Fracton. ; time = 5 min 36 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=-0.637200976593501474305583909687372908\ 30227891481784063632604796741094157599156902438932\ 939287497/-0.4949950432196933461151370819730504957\ 83472228433228355943547904232277233494056237054403\ 58652795/5.3333334e+76/1/42/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=10000 inside=0 proximity=0 colors=qaHtcGwfGziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDT\ GDQDCNBCK8C413000443775BB8EFAIIDLMFPQISUKWXNZ`PbdS\ egUikXloZprasvcsvcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZ\ P`XO_UMYRKWPJUMHSJFQIJOHMMFQKETIDWGB_EAbDCeCEgBGjA\ Hm9Jp8Lr7Nu5Px5Nu6Kr7Ho8El8Bi98fA5cB6`D6ZE7WF8UG8S\ H9QJANKBLMCIOFKQHNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljl\ olornrulprkmnikkgihffdddabbZa`W_YSYWPWUMVRITPFRNCQ\ K8OI5RK7TN9WPBYRD`TFbWHeYJg_LiaNkcPneRpgTsiVulYxn_\ zpawn`tk_piYmfXjdWgaVcZT`WSYURVRQROPOLOKJNHGMDDLAA\ KADMAGNAIPALQAOSARUBUWBXYB__CbaCecChfCkhDnjDqlDtnC\ qlBmjBjiAfg9cf8_d8Xc6SY5NS4IM3EH29B145000311632943\ D54G75J87MA8QB9TCAWEBZFCbHEfHBjH9nH7pH6rH5vH3zH0vH\ 2rG3mE2hD2cB2ZA2U81P71K51F41A30510000330760BA1ED1I\ G1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3ql4tq3wu1zz0ww1tt2pp3\ mm5jj6gg7cc8``9YYAXVBURBROBOKBLHBJDBGABD6CA3C80CC4\ CH8DMCDRGEWKE`OFeSFkWInZH } ============================================================= Author: Mike Frazier Date: 2011-08-06 09:52 -400 To: Fractint and General Fractals Discussion Subject: [Fractint] Spike Star Zooming deeper into the center of yesterdays post Shut Eye doubles the number of arms. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/spike_star.html The parameter file used to make the image: Spike_Star { ; Exported from Fracton. ; time = 10 min 52 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=-0.637200976593501474305583909687372908\ 30227891481784063632604796741094157599156894004533\ 254891959565453745/-0.4949950432196933461151370819\ 73050495783472228433228355943547904232277233494056\ 06774192000330176229172915/2.150537661290323e+90/1\ /-10/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=10000 inside=0 proximity=0 colors=siVulYxn_zpawn`tk_piYmfXjdWgaVcZT`WSYURVRQR\ OPOLOKJNHGMDDLAAKADMAGNAIPALQAOSARUBUWBXYB__CbaCec\ ChfCkhDnjDqlDtnCqlBmjBjiAfg9cf8_d8Xc6SY5NS4IM3EH29\ B145000311632943D54G75J87MA8QB9TCAWEBZFCbHEfHBjH9n\ H7pH6rH5vH3zH0vH2rG3mE2hD2cB2ZA2U81P71K51F41A30510\ 000330760BA1ED1IG1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3ql4tq\ 3wu1zz0ww1tt2pp3mm5jj6gg7cc8``9YYAXVBURBROBOKBLHBJ\ DBGABD6CA3C80CC4CH8DMCDRGEWKE`OFeSFkWInZHqaHtcGwfG\ ziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDTGDQDCNBCK8C41300\ 0443775BB8EFAIIDLMFPQISUKWXNZ`PbdSegUikXloZprasvcs\ vcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZP`XO_UMYRKWPJUMH\ SJFQIJOHMMFQKETIDWGB_EAbDCeCEgBGjAHm9Jp8Lr7Nu5Px5N\ u6Kr7Ho8El8Bi98fA5cB6`D6ZE7WF8UG8SH9QJANKBLMCIOFKQ\ HNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljlolornrulprkmnikk\ gihffdddabbZa`W_YSYWPWUMVRITPFRNCQK8OI5RK7TN9WPBYR\ D`TFbWHeYJg_LiaNkcPneRpgT } ============================================================= ----

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FOTD 06-08-11 (Revisited Venue [9])
by Jim Muth 07 Aug '11

07 Aug '11

FOTD -- August 06, 2011 (Rating 9) Fractal visionaries and enthusiasts: Today's image is a dive into the FOTD image of August 2, which explains the name "Revisited Venue". Considering the wealth of detail and the effort I put into the coloring, the rating of 9 is fully justified despite the revisit, at least in my own opinion. My first impression of the image was surprise that a simple minibrot on a filament could be surrounded by such detail. But maybe it should not be so surprising, considering the magnitude of almost 10^25, a magnitude at which the entire Mandelbrot set rivals the size of the visible universe. (The present estimates are that the visible universe is about 27,000,000,000 light years in diameter.) Unfortunately, with great magnitude comes great calculation time. The one-hour calculation time of today's image should therefore come as no shock. But the hour may be saved by viewing the completed image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The same image is available in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The venerable FOTD web site, where the FOTD images have been posted since April 1997, may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds and heavy rain spoiled today here at Fractal Central. Despite the bad weather, FL spent the day paddling down the Susquehanna River in a kayak, while I stayed dry inside FC, where the recently installed sump pump did its job in the basement. The fractal cats, who are almost always dry, became a little concerned about FL's absence, but forgot their concern when they caught the scent of tuna. The next FOTD will be posted in 24 hours. Until then, take care, and be alert to the tiny changes around you. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Revisited_Venue { ; time=0:58:12.88-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4163\ 228057479504343786651367/5.86616949859403407792674\ 69e-4/6.844241e+024/1/-10/0 params=0/0 float=y maxiter=6000 bailout=16 inside=0 logmap=2540 colors=000BCPBCPBCPBCPBDOBDOCDOCDOCEOCEOCEOCEOCFNC\ FNCFOCFPDGQDGRDGSDGTDHUDHVDHWDHXDIYDIZEI_EI`EJaEJb\ EJcEKdELeFMfGNgHOhIPiJQjKRkLSlMTmNSnPToQTnSUmTUlVU\ kWVjYViZVh_WgaWfbXedXdeXcgYbhYaiYaj__k`ZlbYmcXneWo\ fUphTpiSqkRrlQsnOtoNuqMvrLvsKwsJwsIwsLwsPwsUwsZwsc\ wshwsmwsrwsvwszwszwszwsvrnrnimjdhf`cbWZZRUVMPRIMND\ JJ8KH4KF3IA2G51E00C00A00A00A00A00A00Amm`ru4qq5pn5o\ j6ng6md6l`7kY7jU8iR8iO8kN7lN7mN7nM7oM7pM7qL6rL6sL6\ tK6uK6vK6wK6iR9JMmJIjKFfKBcL7_L4XJA_IGaHMdGSfFXiDb\ kChnGnpKtsPyuUssZnqciphdnm_lrVkvQizLhz8oj8cWB4PD0K\ D2G83B8578B000rONmVScXOUZKI`GCaC6PO0DZWSdzej4fI3WD\ 2L91A4by3Qd2DK1VhtFMSvH2T81Iv8Dg69T44E2nu7Ya4HJ21Y\ k0HOz0lV0OlX5`O3OG2B712Sg1IT09EhduXUfMcTBcEFcO7cCm\ cdXmRGmDemmVm`LmPAmCFz_BzR7zI3z9Pz7Gz4zz2zz6zz4zz3\ zz1zzizzYzzNzzBzzOzzEzzAzz72z3LznEzY7zHtz_nzlczPUz\ IKzCAz69z`4zIlzRXzNaz2Jz1 } END PARAMETER FILE=========================================

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Spike Star
by Mike Frazier 06 Aug '11

06 Aug '11

Zooming deeper into the center of yesterdays post Shut Eye doubles the number of arms. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/spike_star.html The parameter file used to make the image: Spike_Star { ; Exported from Fracton. ; time = 10 min 52 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=-0.637200976593501474305583909687372908\ 30227891481784063632604796741094157599156894004533\ 254891959565453745/-0.4949950432196933461151370819\ 73050495783472228433228355943547904232277233494056\ 06774192000330176229172915/2.150537661290323e+90/1\ /-10/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=10000 inside=0 proximity=0 colors=siVulYxn_zpawn`tk_piYmfXjdWgaVcZT`WSYURVRQR\ OPOLOKJNHGMDDLAAKADMAGNAIPALQAOSARUBUWBXYB__CbaCec\ ChfCkhDnjDqlDtnCqlBmjBjiAfg9cf8_d8Xc6SY5NS4IM3EH29\ B145000311632943D54G75J87MA8QB9TCAWEBZFCbHEfHBjH9n\ H7pH6rH5vH3zH0vH2rG3mE2hD2cB2ZA2U81P71K51F41A30510\ 000330760BA1ED1IG1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3ql4tq\ 3wu1zz0ww1tt2pp3mm5jj6gg7cc8``9YYAXVBURBROBOKBLHBJ\ DBGABD6CA3C80CC4CH8DMCDRGEWKE`OFeSFkWInZHqaHtcGwfG\ ziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDTGDQDCNBCK8C41300\ 0443775BB8EFAIIDLMFPQISUKWXNZ`PbdSegUikXloZprasvcs\ vcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZP`XO_UMYRKWPJUMH\ SJFQIJOHMMFQKETIDWGB_EAbDCeCEgBGjAHm9Jp8Lr7Nu5Px5N\ u6Kr7Ho8El8Bi98fA5cB6`D6ZE7WF8UG8SH9QJANKBLMCIOFKQ\ HNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljlolornrulprkmnikk\ gihffdddabbZa`W_YSYWPWUMVRITPFRNCQK8OI5RK7TN9WPBYR\ D`TFbWHeYJg_LiaNkcPneRpgT } -- Mike Frazier www.fracton.org

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FOTD 05-08-11 (Long Time Coming [7])
by Jim Muth 06 Aug '11

06 Aug '11

FOTD -- August 05, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Long Time Coming". When you start running the parameter file, you'll know the reason for the name. But as always, relief for the slowness is at hand. The finished image is posted in glorious 640x480x256 GIF format at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version may be accessed at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> though it might take a short time for Hal to calculate it. The original, now classic, FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The slowness of the image is due to its magnitude, which is a whopping 7*(10^34). With such a great magnitude comes great slowness, and it certainly is evident in today's image. Today's image is what I found on a dive into the image of two days ago, with much the same colors and features. Since the image is kind of a repeat, I could rate it no higher than a 7, which is actually not all that bad. I have not done the math, but I would guess that at the scale of today's image, the entire Mandelbrot set exceeds the size of the visible universe many times. The M-set is a great example of one-way infinity. Just like the time we are supposed to enjoy life in heaven, it is limited in only one direction. It has an infinite depth, but is limited to a value of 2 at its upper extremity. The clouds continued here at Fractal Central all morning, but around noon time the clouds broke, leading to a relatively pleasant afternoon, with a near normal temperature of 82F 29C. The fractal cats paid little attention to the outside conditions as they slept through most of the day. The humans spent the day preparing for tomorrow, when the next FOTD will be posted. Until then, take care, and if those aliens from Sirius-C are really running things here on earth from behind the scene, they had better take a few lessons on how to run a world. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Long_Time_Coming { ; time=2:16:13.91-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.9405\ 241488044005398444157863951936232/4.90100508596080\ 5102535300737409795e-6/7.654e+034/1/112.5/0 float=y params=0/0 maxiter=32767 bailout=16 inside=0 colors=000QcrUcqTcrTcrScsScsRcsRctQctQ`tPYuPVuPSuV\ Pt_NseKsjIrpFruDqzBquGnpKlkPjfThaXfXadSebOi`NibNic\ MidMieLifLigKihKiiJijMikPilUfmZdhccchcZmcUrcPvcKzh\ Azm9zmGzmEzmDzmCzlAzk9wk8vj7ti8rg8oe9ia9cWAZOAUJBQ\ GBMCCK7CI4DG5D9A8EDDIGIMFMQDRUBVYA_a8ce6hi5lh8jgAi\ fCheEgdHfcJebLdaNcbRc`PbZObXNbVLbTKaSJaQHaOGaMF`KD\ `JC`HB`F9_D8_B7_97bA6_A6YA6WA6TA6RA6PB5MB5KB5IB5FB\ 5D864B5BE5HG5OJ5UM5`N1gO5fP9fQDfRHeSLeTPeUTdVWdW_d\ XdcYhcZmc_qb`tb`vb_w_YxYWwWUuUTsSRqQPoONlMLkKKiIIg\ GGeEEcCCaA8Y0B`8DbGFdNHfVJhbJjeLjiKghJdgHafGZeFThF\ WdFZ`FaXFcTFfPFiLFlHFnDFq9Ft5Fv2ikrcmsYotSquMsuGuv\ Aww5xwqhpnfokeoicnfbndama_m_ZlXYlUWkVWjWXiXXhYYgZY\ f_Ze_Zd`_c`_ba`aa``aa_baZb`Yb_XaZY`X__UbYSdXPgWNiU\ KlTInSFqSEsRDsRCpQBkQAgQAdO9`N8XL7TJ6PF6MA5I54E03A\ 526A2AF1FI1KL0PL0UO1XQ1_S1bV1eX1gZ1iY6kXAmXFmWJmWP\ jJUjGZmCcp9cs6cvBcuGctLcs } END PARAMETER FILE=========================================

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Shut Eye
by Mike Frazier 05 Aug '11

05 Aug '11

Kind of looks like a closed eyelid or a sideways cat's eye. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/shut_eye.html Here is a link to a page with a step by step method for making line fractals: http://www.fracton.org/fmlposts/line_method.html The parameter file used to make the image: Shut_Eye { ; Exported from Fracton. ; time = 5 min 36 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=-0.637200976593501474305583909687372908\ 30227891481784063632604796741094157599156902438932\ 939287497/-0.4949950432196933461151370819730504957\ 83472228433228355943547904232277233494056237054403\ 58652795/5.3333334e+76/1/42/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=10000 inside=0 proximity=0 colors=qaHtcGwfGziFwfFtdFqaEnZEkWEhUEeREaODZMDWJDT\ GDQDCNBCK8C413000443775BB8EFAIIDLMFPQISUKWXNZ`PbdS\ egUikXloZprasvcsvcsvcsvcqsaoq`mnZlkXjiWhfUfdTdaRbZ\ P`XO_UMYRKWPJUMHSJFQIJOHMMFQKETIDWGB_EAbDCeCEgBGjA\ Hm9Jp8Lr7Nu5Px5Nu6Kr7Ho8El8Bi98fA5cB6`D6ZE7WF8UG8S\ H9QJANKBLMCIOFKQHNSKPUNSWQUYSX_VZ`Y`b`cdcfffihiljl\ olornrulprkmnikkgihffdddabbZa`W_YSYWPWUMVRITPFRNCQ\ K8OI5RK7TN9WPBYRD`TFbWHeYJg_LiaNkcPneRpgTsiVulYxn_\ zpawn`tk_piYmfXjdWgaVcZT`WSYURVRQROPOLOKJNHGMDDLAA\ KADMAGNAIPALQAOSARUBUWBXYB__CbaCecChfCkhDnjDqlDtnC\ qlBmjBjiAfg9cf8_d8Xc6SY5NS4IM3EH29B145000311632943\ D54G75J87MA8QB9TCAWEBZFCbHEfHBjH9nH7pH6rH5vH3zH0vH\ 2rG3mE2hD2cB2ZA2U81P71K51F41A30510000330760BA1ED1I\ G1LJ1PN2SQ2WT2_W2b_3fb3ie3mh3ql4tq3wu1zz0ww1tt2pp3\ mm5jj6gg7cc8``9YYAXVBURBROBOKBLHBJDBGABD6CA3C80CC4\ CH8DMCDRGEWKE`OFeSFkWInZH } -- Mike Frazier www.fracton.org

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FOTD 04-08-11 (Rainbow Bound [8.5])
by Jim Muth 05 Aug '11

05 Aug '11

FOTD -- August 04, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image continues the August theme of scenes very deep in the Mandelbrot set. The scene is located at the tip of a filament network extending from a bud on the southwest shore line of the large period-3 bud on the north side of the main bay of the Mandelbrot set. The magnitude of the image is over 5*(10^30), quite deep, but nowhere near as deep as we might venture before the month ends. The rating of an 8-1/2 indicates that the image is the best of the past couple weeks. The 1/2 point is a reward for the extra effort I put into the coloring. The name "Rainbow Bound" refers to the coloring, which, if anything, goes beyond the limits of what is considered artistically proper in conservative fractal art circles. The calculation time of 20 minutes is surprisingly fast for an image of such magnitude. The image may be seen in all its finished glory on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> without the need of running a clumsy parameter file. It may be seen in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The traditional FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The clouds hung around most all day here at Fractal Central, spitting out occasional sprinkles of rain, holding the temperature to 79F 26C, and keeping the fractal cats alert. The humans made it through another in an endless string of similar days, with little to remember for the effort. The next FOTD will be posted in 24 hours. Until then, take care, and is it possible for absolutely nothing to actually exist? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Rainbow_Bound { ; time=0:20:38.02-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.2165\ 70560414920318282567460174879624/0.678702032923820\ 83041952706034004063/5.4e+030/1/-40/0 params=0/0 float=y maxiter=12000 bailout=16 inside=255 colors=000sRHqXHpbHo`Ln_OnZSmYVlXYlWakVdkUg601dP`Y\ LVRHPKCID8C646qUNiPJaLGUHDNC9F86743l0Be09_08U06O05\ I04C02601qNKkKIfIG`GEWDCRBAL98G66A44522WP7RL6MH5IE\ 4DA3972431NzLFeE7L7nU3eP2YK2UN1cg1ms0zzUsuFin1_j0K\ e0Fb0DZ0CW0BT0AQ08M07J06G05D0390260130cC7`B6ZA6W95\ U95R84P74M63K63H53F42C32A317215102001ku0ck0Wa0OT0G\ J089CSPBQNAOL9MK8KI8IG7GF6ED5DB4BA4983762551330119\ b78Z67V56S55O44L34H33E22A1171030OPvLMpiZOiZOgYMeWK\ cTIaRGZPEWNCTLAQK8NJ7KJ6LI5OH4UH3cI2mK1tKUpKSlKQiK\ OeKMbKKZKIWKGSKFOKDLKBHH9EE7AA5773331FPcDLZBIU9FP7\ CK59F36A1359du6Uf4KT2AE`J0YH0VG0TE0QD0NC0LA0I90F80\ D60A507405202101BC09A089078067056044033022011NznKr\ gHjaEbVBVP8NJ5FC276`XWYUTVSRTPPQNMNLKLIIIGGFEDDBBA\ 99776544222lDjhCfeBcaA_Z9XV8US7QO6NL5KH4GE3DA2A716\ 3035PX3GM18BAS69P58N57L46J46H35F34C23A238126114002\ 0s5lo4hk4eg3ac3Z_3VW2Szzz } END PARAMETER FILE=========================================

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FOTD 03-08-11 (Fractal Marmalade [7])
by Jim Muth 04 Aug '11

04 Aug '11

FOTD -- August 03, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's scene lies in Seahorse Valley of a minibrot that lies in the East Valley of a larger but still tiny minibrot far out on the main spike of the Mandelbrot set. The image shares both Seahorse Valley and Elephant Valley characteristics. I named the image "Fractal Marmalade" because of the original coloring, which has been changed toward the green side since I coined the name. The rating of a 7 is about average for these deep images, but the necessary slowness holds things down a bit. The calculation time of just under 1/2 hour is admittedly slow. Time may be saved by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> or in high-definition 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/> Heavy clouds and occasional rain spoiled Wednesday here at Fractal Central. The temperature of 75F 24C was comfortable enough, but with the rain falling, who cared. The fractal cats grabbed a couple quick glances of the outside conditions before settling to sleep for most of the day, while the humans made it through the day with only a few minor hangups. The next FOTD will be posted in 24 hours. It will be another scene deep in the Mandelbrot set. Until then, take care, and do you ever get the feeling that things are not exactly as they appear? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fractal_Marmalade { ; time=0:29:32.17-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.9405\ 2414880440053986394/4.901005085960791676e-6/2.8572\ 34e+019/1/32.5/0 params=0/0 float=y maxiter=15000 bailout=16 inside=0 mathtolerance=0.05/0 colors=000QcrUcqTcrTcrScsScsRcsRctQctQ`tPYuPVuPSuV\ Pt_NseKsjIrpFruDqzBquGnpKlkPjfThaXfXadSebOi`NibNic\ MidMieLifLigKihKiiJijJikIilIimzinziozipziqz`bzTOz2\ 3zL9zaGzcEzeDzhCzjAzk9wk8vj7ti8rg8oe9ia9cWAZOAUJBQ\ GBMCCK7CI4DG5D9A8EDDIGIMFMQDRUBVYA_a8ce6hi5lh8jgAi\ fCheEgdHfcJebLdaNcbRc`PbZObXNbVLbTKaSJaQHaOGaMF`KD\ `JC`HB`F9_D8_B7_97bA6_A6YA6WA6TA6RA6PB5MB5KB5IB5FB\ 5D864B5BE5HG5OJ5UM5`N1gO5fP9fQDfRHeSLeTPeUTdVWdW_d\ XdcYhcZmc_pb`rb`sb_s_YsYWrWUqUTpSRoQPnONlMLkKKjIIi\ GGhEEgCCfA8c0Be8DfGFgNHhVJibNnjLjiKghJdgHafGZeFThF\ WdFZ`FaXFcTFfPFiLFlHFnDFq9Ft5Fv2ikrcmsYotSquMsuGuv\ Aww5xwqhpnfokeoicnfbndama_m_ZlXYlUWkVWjWXiXXhYYgZY\ f_Ze_Zd`_c`_ba`aa``aa_baZb`Yb_XaZY`X__UbYSdXPgWNiU\ KlTInSFqSEsRDsRCpQBkQAgQAdO9`N8XL7TJ6PF6MA5I54E03A\ 526A2AF1FI1KL0PL0UO1XQ1_S1bV1eX1gZ1iY6kXAmXFmWJmWP\ jJUjGZmCcp9cs6cvBcuGctLcs } END PARAMETER FILE=========================================

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FOTD 02-08-11 (Mandelbrot Affair [7.5])
by Jim Muth 02 Aug '11

02 Aug '11

FOTD -- August 02, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: FOTD themes have been few and far between lately, so I have decided that August will be a theme month. The theme for the August FOTD images is scenes deep in the Mandelbrot set. Today's image lies not all that deep however, just deep enough to make arbitrary precision math the better choice. The image, which requires 12-1/2 minutes to finish when arbitrary precision math is used, will calculate in only 2 seconds when standard math is used, but with a slight degradation in quality. I have included two parameter files -- one slow with high quality, and one fast with compromised quality. The scene is located on a filament extending from the northeast shore line of the main bay of the first large minibrot on the main stem of the Mandelbrot set. (the minibrot centered around -1.417) The name "Mandelbrot Affair" seems fair enough. After all, had it not been for Mr. Mandelbrot, we might never have discovered fractals. (Well, that does seem a bit unlikely, but the discovery might have been postponed quite a while.) The rating of a 7-1/2 includes a bit of a reward for the coloring, to which I gave a modicum of extra effort. The calculation time can be either fast or slow, depending on the image quality desired. The slow, high-quality version of the finished image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The traditional FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Tuesday brought sun filtered by high cirrus clouds, comfortable humidity and a temperature of 86F 30C to Fractal Central. The day also brought joy to the hearts of the fractal cats, who got into a friendly tussle that grew a little out of control. The humans had a typical day, which leaves next to nothing to remember the day by. The next FOTD will be posted in 24 hours. Until then, take care, and when will the next crisis erupt? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mandelbrot_Affair { ; time=0:12:38.52-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4163\ 2280574795804/5.86616949871998e-004/1.184349e+013/\ 1/67.5/0 params=0/0 float=y maxiter=5000 bailout=16 inside=0 logmap=554 mathtolerance=0.05/0 colors=000BCPBCPBCPBCPBDOBDOCDOCDOCEOCEOCEOCEOCFNC\ FNCFOCFPDGQDGRDGSDGTDHUDHVDHWDHXDIYDIZEI_EI`EJaEJb\ EJcEKdELeFMfGNgHOhIPiJQjKRkLSlMTmNSnPToQTnSUmTUlVU\ kWVjYViZVh_WgaWfbXedXdeXcgYbhYaiYaj__k`ZlbYmcXneWo\ fUphTpiSqkRrlQsnOtoNuqMvrLvsKwsJwsIwsLwsPwsUwsZwsc\ wshwsmwsrwsvwszwszwszwsvrnrnimjdhf`cbWZZRUVMPRIMND\ JJ8KF4KI6MK8OM9POBRQDSTEUVGVXIXZJY`L_mm`ru4qq5pn5o\ j6ng6md6l`7kY7jU8iR8iO8kN7lN7mN7nM7oM7pM7qL6rL6sL6\ tK6uK6vK6wK6iR9JMmJIjKFfKBcL7_L4XJA_IGaHMdGSfFXiDb\ kChnGnpKtsPyuUssZnqciphdnm_lrVkvQizLhz8ocN8WQ4PS0K\ N2GI3BD578BHGHRON_VSUXOOZKI`GCaC6PO0DZWSdzej4fI3WD\ 2L91A4by3Qd2DK1VhtFMSvH2T81Iv8Dg69T44E2nu7Ya4HJ21Y\ k0HOz0lV0OgT5XL3ME2B712Sg1IT09EhduXUfMcTBcEFcO7cCm\ cdXmRGmDemmVm`LmPAmCFz_BzR7zI3z9Pz7Gz4zz2zz6zz4zz3\ zz1zzizzYzzNzzBzzOzzEzzAzz72z3LznEzY7zHtz_nzlczPUz\ IKzCAz69z`4zIlzRXzNaz2Jz1 } Mandelbrot_Affair { ; time=0:00:02.12-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4163\ 2280574795804/5.86616949871998e-004/1.184349e+013/\ 1/67.5/0 params=0/0 float=y maxiter=5000 bailout=16 inside=0 logmap=554 mathtolerance=0.05/1 colors=000BCPBCPBCPBCPBDOBDOCDOCDOCEOCEOCEOCEOCFNC\ FNCFOCFPDGQDGRDGSDGTDHUDHVDHWDHXDIYDIZEI_EI`EJaEJb\ EJcEKdELeFMfGNgHOhIPiJQjKRkLSlMTmNSnPToQTnSUmTUlVU\ kWVjYViZVh_WgaWfbXedXdeXcgYbhYaiYaj__k`ZlbYmcXneWo\ fUphTpiSqkRrlQsnOtoNuqMvrLvsKwsJwsIwsLwsPwsUwsZwsc\ wshwsmwsrwsvwszwszwszwsvrnrnimjdhf`cbWZZRUVMPRIMND\ JJ8KF4KI6MK8OM9POBRQDSTEUVGVXIXZJY`L_mm`ru4qq5pn5o\ j6ng6md6l`7kY7jU8iR8iO8kN7lN7mN7nM7oM7pM7qL6rL6sL6\ tK6uK6vK6wK6iR9JMmJIjKFfKBcL7_L4XJA_IGaHMdGSfFXiDb\ kChnGnpKtsPyuUssZnqciphdnm_lrVkvQizLhz8ocN8WQ4PS0K\ N2GI3BD578BHGHRON_VSUXOOZKI`GCaC6PO0DZWSdzej4fI3WD\ 2L91A4by3Qd2DK1VhtFMSvH2T81Iv8Dg69T44E2nu7Ya4HJ21Y\ k0HOz0lV0OgT5XL3ME2B712Sg1IT09EhduXUfMcTBcEFcO7cCm\ cdXmRGmDemmVm`LmPAmCFz_BzR7zI3z9Pz7Gz4zz2zz6zz4zz3\ zz1zzizzYzzNzzBzzOzzEzzAzz72z3LznEzY7zHtz_nzlczPUz\ IKzCAz69z`4zIlzRXzNaz2Jz1 } END PARAMETER FILE=========================================

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FOTD 01-08-11 (Little Lost Child [8])
by Jim Muth 01 Aug '11

01 Aug '11

FOTD -- August 01, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "Little Lost Child". The reason for the name is that the parameters were lost when I saved the image in the wrong GIF format. But do not despair. The image, which rates an 8, may be viewed on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Unfortunately, since the parameters are lost, there is no high- definition version available on Hal's site. The lost parameters are not that big a drawback because the calculation time is over an hour, and it is unlikely that many fractalists would actually have run the parameter file even if it had been available. The image is a scene deep in the East Valley of a minor minibrot on the main stem of the Mandelbrot set. It is definitely not the large minibrot, but without the parameters I have no way to determine exactly which minibrot. Even though the parameters are gone, I have chosen this image to be FOTD for August 01 because of the unusually rich, almost too rich, colors. Monday was sultry here at Fractal Central, with a mix of clouds and sun. Thunder threatened several times but nothing ever developed. The fractal cats would have preferred a temperature a little below the 90F 32C, but they made the most of it. The humans accomplished what needed to be done, without incident. The next FOTD, complete with parameter file, will be posted in 24 hours. Until then, take care, and one sure way to be misinformed is to watch all those popular science shows on the cable channels. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= NO PARAMETER FILE AVAILABLE -- SORRY! END PARAMETER FILE=========================================

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FOTD 31-07-11 (Spider Test [6.5])
by Jim Muth 01 Aug '11

01 Aug '11

FOTD -- July 31, 2011 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is one in a series of tests, which is what I named it. I originally calculated the image with the passes set to 1. The resulting image took near 16 minutes to calculate, but was pictorially perfect. The passes=g option was fast enough but left too many holes in the web. Passes=b finished in 5 minutes, but totally missed the web. This left me with passes=t, which finishes in just under 10 minutes, and misses only a few minor bits of the spider web. The image lies in the parent fractal that results when 10 negative parts of Z^(-1.1) are combined with Z^(-11.1) before (1/C) is added on each iteration. This parent fractal is another of those indescribable ones that appear when double negative powers of Z are calculated. And since the powers are negative, the fractal is subject to evaporation. Today's image is an evaporated one, though instead of setting the bailout to one-googol, I set it to 10^40, which is still large enough to evaporate the scene. The rating of a 6-1/2 is an improvement over recent images, though still far short of traditional FOTD quality standards. The image may be thoroughly enjoyed by running the parameter file, or by viewing it on the FOTD web site 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/> Saturday and Sunday here at Fractal central were near perfect days, with tons of sun, lower humidity and a near perfect temperature of 88F 31C. The fractal cats enjoyed the conditions as much as is possible for cats to enjoy a thing, while the humans had a pleasant two days. The next FOTD will be posted in 24 hours. Until then, take care, and let your mind soar to the stars. Your body is stuck to the ground. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Spider_Test { ; time=0:09:55.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+4.8057119805/+1.925110761/48177/1/\ -172.5/0 params=-10/-1.1/1/-11.1/0/1e+040/0/0 float=y maxiter=1500 inside=bof61 periodicity=0 colors=000DcbFc`GcZIcYJcWLcUMcTJcRKcSLcSLcSMcSMcSN\ cSNcSOcSOcSPcSPcSQcSQcSVcTZcUbdVgYVkRWoKXsDXoCVlCU\ `nSalVajYbh`cfcdcfeaif_lA0FtdvgWqWOlJFg54`77b89cAC\ eBEfDHgEJiFLjHOkIQmKTnLVoNYqO_rOdvPasQ_qRYnSWlSUiT\ SgUQdVObWM_WKYXIVYGTZEQ_CO_AMXDPVFRSHTQJVOLYLN_JPa\ HScEUeA0FAYjP8dP8eP7fP7gP6iP6jP5kP5lP4mP4nP3oP3pP2\ qP2rP1sP1tO2sN2sM2sM2rL2rK2rK2qJ2qI2qI3pH3pG3pG3oF\ 3oE3oE3nD3nC3nC3nE2kG2hI2eJ2bL2`N2YO2VVPXS1PU1NV1K\ X1HZ1E_1C`2Ea2Fb2Hc2Id2Ke2Lf2Ng3Oh3Qi3Rj3Tk3Ul3Wm3\ Xn4Zo4_p4aq4br4ds4et4gt4hq7fo9emCdkEciGagJ`eL_cNZe\ RagUciYfk`hmckogmqjpidhuquwcwxo1zo3hc4mc5US6NM7QO6\ TP6WQ6YR6`S6cT6fU6hV6kW6nX6pY6qW9qUCrTFrRIsQLsOOsN\ RtLUtJXuI_uGbvFevDhvCjqBkmAki9ld9l`8mX7mS6nO6nK5oF\ 4oB3p73p84n95l96jA7iB8gB9eCAdDBbDC`ED_FEYFFWGGVGHT\ HIRIJQIKOJLMKMLKNJLOHMOGMQENRCNSBLUEKWHJYKIZMH`PFb\ SEcUPCYPBZPB_PA`PAaP9bP9c } 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 29-07-11 (Retrogression Track [6])
by Jim Muth 30 Jul '11

30 Jul '11

FOTD -- July 29, 2011 (Rating 6) Fractal visionaries and enthusiasts: Sometimes the names of the FOTD images almost take on a life of their own. For some strange reason, the name "Retrogression Track", which came to mind out of nowhere, seems so right that I had no choice but to give this name to the image, even though the name has no logical connection with the image. The image is an evaporated one, which lies in the parent fractal that results when 2.8 negative parts of Z^(-1.8) are combined with 0.2 negative part of Z^(-5.5) and (1/C) is added on each iteration. This parent fractal consists of three large, nearly circular bays surrounded by three even larger irregularly shaped bays. Today's scene lies in an irregular circular ring that terminates a fairly normal filament extending from the southern irregular bay. The rating of a 6 is another in a string of July disappoint- ments. We all enjoy those images that rate an 8 or a 9. Such images are sometimes hard to find however. If they could be found at will, they would no longer be worth a high rating. The calculation time of 5-3/4 minutes is a bit slow for an image that rates merely a 6. The finished image is available online at: <http://www.crosscanpuzzles.com/Archives.html> and in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> At this point I am tempted to write a paragraph or two about the stupidity of politicians on the left as well as the right, but in the name of brevity and to avoid offending, I will count to ten and hold my peace. Typical lazy midsummer weather continues here at Fractal Cen- tral, with daytime temperatures around 90 tempered by occasional showers. The fractal cats enjoy such lazy conditions. They pass the days doing nothing, which is more than the humans can do. The next FOTD will be posted in 48 hours on July 31, and after that, the images will be posted every day, as has been the usual FOTD schedule for 14-1/2 years. Until then, take care, and before the answer can be found, the problem must be fully understood. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= RetrogressionTrack { ; time=0:05:47.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=b center-mag=+1.825872109106356/-2.055248499489045/\ 7.675226e+009/1/-100/0 params=-2.8/-1.8/-0.2/-5.5/\ 0/10000000000000000.0/0/0 float=y maxiter=1200 inside=bof61 periodicity=0 colors=000Y00K0H60b00x00z00z00z00z00z00000_00M0YM0\ zM0z_0zj0zu0zz0zz0xz0pz0jz0mz0mz0000mK0m00m00m00e0\ 0_00U00M00H00C004000000000000000000000000000000000\ 000000600C00000M00S00Y00b00g00v00r00k00zzYSzjmzzzz\ pxzz1zzzEgz0zz0bz0_z0Yz0rz0Sz0Sz0Pu0Mm0Ke0HY0EP0gH\ 0ME0SC0_C0e9cz90r6cz6cr9mm91g91bC1YC4zC4ME4HE4CE46\ Hz1Hm0H60K60Kz0K60KK0CY04g40uC0zM0zU0zb0zp0rz0bz0K\ z01z00z06z0SzHjzeezb_z_Ux_PrYMmYHgUCbU6YS1SS0MP0HP\ 0CM06M01K00K00P00S00Y00_00b00g00j00m00r10u40z60z90\ zC0zE0zE0zC0zC0zC0x90r96m9Hg6S_6bU6mP4xK4zE4z90zU0\ zp0zz0zz0zz0zz0zz6zzEzzMzzUzzezzmzzuzzzzzzzzzzzzxz\ zxzzzzzzzzzzzzzzzzzzrzzjzzbzzUzzMzzEzz6zz0zzCmzPPg\ b1Pp06z04r04j01e01Y00P00H00C004000000z0xz0pz0gz0br\ 0Ug0MY0HM09901000000zu9HzzCzzpzzmzzmzzjzzjxzgrzgmz\ egzeezb_zbUz_Pz_MzpSuzYbzbKzg1zm0zp0zr0zu4zuCuxHjz\ M_zSPz_Eze6zj0zrpH0z00m00 } 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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FYI fotd RSS feed brief hiatus
by Richard 29 Jul '11

29 Jul '11

I'm doing some work on migrating the image computation to a secondary machine that XMission has graciously provided me just for this purpose. During that time, the FOTD RSS feed won't be updated as the image computation is moved. I expect it will be back up and producing new images in a week or so. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>

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FOTD 27-07-11 (Bad Moon on the Rise [No Rating])
by Jim Muth 27 Jul '11

27 Jul '11

FOTD -- July 27, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image gets no rating because it is not of my own creation. I picked it up quite a few years ago, probably from somewhere on the internet, and found it in my storage bin a couple days ago. The reset=1730 in the parameter file shows that it was created with an older version of Fractint. I named the image "Bad Moon on the Rise". Well, it does show a circle that easily could be a moon rising behind a landscape of who-knows-what. The image was created by the fn(z)+fn(pix) formula, one I almost never even think of using. But since images like today's are possible with this formula, maybe I should think about it a little more. The calculation time of 24 seconds is fast by any standards. The finished image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Tuesday here at Fractal Central brought a temperature of 90F 32C and a few light passing showers. The fractal cats slept away most of the day, while the humans kept the mundane things going. The next FOTD will be posted in 48 hours. Until then, take care, and don't believe all those doomsday forecasts you hear about. So far they have been 100-percent wrong. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BadMoon_on_theRise { ; time=0:00:24.06-SF5 on P4-2000 reset=1730 type=fn(z)+fn(pix) function=sin/cosh center-mag=-2.00749/0.409275/15/1/-82.5/0 params=0.7/0.333/0.5/0.5 float=y bailout=50 inside=bof60 decomp=256 sound=off colors=bosboscpsdptdpteqtfqtgruhruiruisujsvksvltvm\ tvnuwnuwouwpvwqvwrvxswxswxtwxuxyuxyuyyuyyuzz000000\ 00000000000100100100100200200400400500500500500600\ 600800800900900900B00C00D00D00D00E00E00E00E00E00F0\ 0F00F00F00F00F00F00G00G00G00G00G01H01H01H01I01I01J\ 01J01J01K01K01L01L01M01N01O01O01O01P01P01P01U01G01\ G01G01G01H01H01H01H01I01I01I01I01J01J01J01J01K01K0\ 1K01K01L01L01L01M01M02M02M02N02N03O03O04O04O04P05P\ 05P05P06Q06Q07Q07Q07R08R08R08R09S09S0AS0AS0AT0BT0B\ T0BT0CU0CU0DU0DU0DV0EV0EV0EV0FW0FW0GW0GW0GX0HX0HX0\ HX0IY0IY0JY0JY0JZ0KZ0KZ0KZ0L_0L_0M_0M_0M`0N`0N`0N`\ 0Oa0Oa0Pa0Pa0Pb0Qb0Qb0Qb0Rc0Rc0Sc0Sc0Sd0Td0Td0Td0U\ e0Ue0Ve0Ve0Vf0Wf0Wf0Wf0Xg0Xg0Yg0Yg0Yh0Zh0Zh0_h1_h2\ `h3`h4ai5ai5ai6bi7bj8cj9cjAcjBdkBdkCdkDekEelFelGfl\ HfmHgmIgmJgmKhnLhnMhnMinNioOjoPjoQjpRkpSkpSkpTlqUl\ qVlqWmqXmrYnrYnrZnr_os`os } END PARAMETER FILE=========================================

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FOTD 26-07-11 (Way-Out and Deep [7])
by Jim Muth 27 Jul '11

27 Jul '11

FOTD -- July 26, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a very deep one. It lies on a filament that extends from a larger minibrot that in turn lies on a filament that extends from the fourth bud out the main negative spike of the Mandelbrot set. Even though the M-set has been so thoroughly explored, I still feel that today's image, due mostly to its coloring, is worth a rating of a 7. The name "Way Out and Deep" describes the location of the scene in its parent fractal, the Mandelbrot set, which BTW is pretty much the parent of all fractals. The calculation time of 16-1/2 minutes is within reason, considering the image's magnitude of almost 10^29. But setting up and running DOS parameter files can be quite a chore, so relief has been prepared at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image is posted for instant satisfaction. The image is posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Sunday brought more heat and humidity to Fractal Central. The temperature of 95F 35C caused the fractal cats to glue them- selves to the coolest things they could find. Monday brought a mixture of sun and clouds, with a torrential shower in the aft- ernoon. The clouds and rain held the temperature to a more pleasant 86F 30C. The fractal cats must have approved of the cooler conditions -- they became active. The humans took things in stride. The next FOTD will be posted in 48 hours, but in August we will return to the (almost) daily schedule of FOTD images. Until next time, take care, and what can be done about __________ ? (Fill in the blank with your favorite plight.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Way_Out_and_Deep { ; time=0:16:33.99-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.4207\ 01558907537367341920538201323/0.048266941411681502\ 6997120975273168/7.701659e+028/1/35/0 params=0/0 float=y maxiter=3600 bailout=16 inside=0 logmap=670 colors=000scVpdTmeRjfPghNdiL`jJYkHVmFSnDPoBMp9Jq8M\ mDOiIZfEQeMHkQHrTJyYHoWFeUDWSD0fCMR7ezBfzFfzJfvNfr\ RfmUfrTfrSerRerQdsPcsOcsMbsLbsKasJ`sI`sH_s2TsF_sEZ\ sDYsCYsBXsAXs8Ws7Vs6Vs5Us4Us3TsF7DAFS6MewU4vUDqUGz\ _JzYMzXPzWTzUWzTZzSazQdzPgzOhzOjyEkwChuBetAbr8`p7Y\ o6Vm5Sk3Qj2Nh1Kg0Id4Gb8EZADUABPAAKA8E05zz7ut8gs8_p\ 8Sl8Ji8Bf82f63d84b94`A5ZB6XD6VE7TF8RG8PI9NJALK9IDA\ KLAMSBNZBPeBQlEPiHPfJOcMOaOOZRNWTNTWNRYMO`MLdIIbMJ\ aPK`SL_VLZZMYaNXdOLoWWgOf_GpT8hPS`MkXJhUHfQFdNDbKG\ cHJdEMdBPe5Qi9SeCUaFVYJXUMZQP_MSaIWcEZdAaf6dg2fb4g\ Y5hTBiOFkJKlEPm9Un5Zm6cm7hmDmmKrlQvlWzl_zkczjezicz\ gaze_zcYzZWzUWzPWzKVvKUrKWmPYhO_eNaeMceLeeKgeJieIl\ eHoeGreFteGp_GmVGjQHgLHdGHaBI`FJ_JJ_MKZQLYULYXMX`N\ cdNcgOckPcoPcrQcvQcyScxTcwUcvVzzWzzXzzYzz_zz`zzazz\ bzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 23-07-11 (Shimmering Outflow [6])
by Jim Muth 23 Jul '11

23 Jul '11

FOTD -- July 23, 2011 (Rating 6) Fractal visionaries and enthusiasts: The parent of today's image is an oversized north-south oriented string of large bays, with the largest bay on the south end of the string. This south bay is also the one that at first glance appears to be critical. Today's scene is located in the debris on the northeast shore line of this southern bay. I named the image "Shimmering Outflow". I can see nothing in the image that might justify such a name, but the words have a kind of poetic feeling that gives them validity. The image's rating of a 6 is perhaps a bit conservative, but with a calculation time of a fast 2 minutes, the parameter file will take little time to calculate the image. The task of running a DOS parameter file may be avoided entirely by going to the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and viewing the finished image there. The high definition version may be seen at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may always be accessed at: <http://www.Nahee.com/FOTD/> Friday was a real scorcher here at Fractal Central, with blazing sun, oppressive humidity and a record high temperature of 106F 41C that made any outdoor activity a misery and life in the air- conditioned indoors too sultry for absolute comfort. The fractal cats did what cats do in hot weather -- they stretched out in the coolest places they could find. The humans simply took it easy. With more clouds, Saturday was a little more bearable, but the high temperature of 95F 35C was still much too warm for comfort, and the humidity was even higher. The next FOTD will be posted in 48 hours. Until then, take care, and did you hear about the squatter who was unhappy with his lot. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Shimmering_Outflow { ; time=0:02:01.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.51084599010437/-1.333502283883086/\ 2.016719e+008/1/147.5/0 params=-5/-1.4142/-0.7/-5/\ 0/525/0/0 float=y maxiter=2000 inside=0 logmap=223 periodicity=6 colors=0000AF0AF0AF1AJ2AJ3AI4AN5AM6AN7AM8AN9AMAANB\ 8MCCNDDMEEMFCLGGKHFJGFIFGHEGGEGFDFFCEECDEBCEBBDABD\ 9AC9AC89C79B7AB6BA6CA5D94D94E93E82F82F71G71G72I92J\ B2KC2LE2MG2NH2OJ2QK2RM2SO2TP2UR2VT2WU2YW2ZX2_Z2``2\ aa2b_2cY2aW4_U5YS8WQAUOCSMEQKGOIIMGKKEMICOI8QI6TH6\ PH6QG6MG6NG6JF6JF6ME6PE6PE6KENKEbKI`UM_cQZaUX_YWXa\ VVeTTiSRmRPpQRnPSmOTlOVkNWiMXhMYgL_fL`dKacJcbJdaIe\ _HfZHhYGiXGjVFlUEmTEnSDnQEoRDpRDqRDqRDrRCsRCsRCtRC\ uRBvRBvRBwRBxRAxRAyRAzRAzRAxSBwSBvTBuTBsTBrUCqUCpV\ CnVCmVClWDkWDiXDhXDgWDfWEdVEcVEbUEaTEbRDcPDdODdMDe\ MCfLCfKCgKChJCiJBiIBjKBkLBkMBlNAmNAnOKnOUoNcpNmzUz\ zUzzUzzUzzMzkNcjNUhOKhOCgPCfPCeQDiQDhREhREgSEfTFeT\ FdUGcUGcVGcVHhWHmVImVImUImUGmUFmUDmVCmWAmW9mX7mY6z\ Y4z`3zb1zc0zmdzmbzmazm_zmZzmXzmWzmUzmTzmRzmQzmOzmJ\ zmNzmRzmUzwYzw`zwdzwgzwkzwnzzrzzuzz9zzBzzDzzFzzHzz\ JzzLzzNzzPzzRzzTzzVzzXzzZ } 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 21-07-11 (Reference Standard [6])
by Jim Muth 21 Jul '11

21 Jul '11

FOTD -- July 21, 2011 (Rating 6) Fractal visionaries and enthusiasts: I named today's image "Reference Standard" because it illustrates a standard object. Objects resembling the one that fills the frame appear very often in fractals with features of both the Mandelbrot set and the Mandeloids created by a higher power of Z. The higher power in today's image is 31. Objects similar to the one in today's image exist in immense numbers on the filaments extending from the half-morphed large minibrot on the main stem of the parent, which closely resembles a normal Mandelbrot set. Today's image lies on one of these filaments. The rating of a 6 is disappointing, even for me. I guess my excuse is the hot weather here at FC, which makes one think of nothing but taking it easy with a cold drink. But after all, it is midsummer, and laziness is the order of the day. I could probably beat the heat by moving to Patagonia for the summers, but the twice yearly trips could prove quite costly. Relief in the form of fractals is far more cost effective. The calculation time is a fireball 17 seconds -- fast by any standard. And the image is posted in finished form at: <http://www.crosscanpuzzles.com/Archives.html> and in high-definition 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/> Unrelieved heat, haze and humidity prevailed here at Fractal Central on Wednesday and Thursday, with a high of 95F 35C on Wednesday and 100F 38C on Thursday. It should hardly be necessary to say that the fractal cats spent both days in the coolest spots they could find. The humans also sought the coolest places. The next FOTD, which should be a very cool one indeed, will be posted in 48 hours. In the near future, we will return to the daily posting schedule, and I'll hopefully get out of the fractal doldrums. Until next time, take care, and believe the things you want to be true. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Reference_Standard { ; time=0:00:16.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-1.758898341086305/+0.01826569421574188\ /3.4381e+010/1/-32.5/0 params=31/1e+030/0/0 float=y maxiter=1000 inside=0 logmap=37 colors=000FemKhlPkkUnjZqicsheuhfxgduabrXamR_hMZcGX\ ZBWU6SP7PL7MH8JG8FE9CD99CA6BAe2ed7hdBkdGnzzqzttzqv\ zommndmhdmbdcXdcRdbLdbFda9da4dzFMzFLzFKzFJzFJzFIzF\ HzFGzFGzDMzBSzAXz8bz7gz5mz4rzAnzFjzEkzEkzDkzDkzDkz\ HizLgzPezTczXaz__zPSzFLz5Ez8PzB_zEjz0yz5kzAYzELzIO\ zMRzQUzUXzY_zabzdezBuzIvzOwzUxz_yzezzkzzmszolzqezs\ ZzuSzvLztNzrPzpRznTzhRzcPzZNzULzPKzUNzZPzbRzgTzlWz\ pYzu_zyazpbzhbz`bzWXzRSzNMzIHzDBz96z_hzdbzhYzmTzqO\ zvJzzEzkKzgIzcHz_GzWFzSDzOCzKBzHAzFFzDKBzOEzSHzVKz\ ZNzaQzdTzhWzkZznwzcuzXtzQszJrzCkz9dz7Yz4Sz2Pz9MzGJ\ zNGzUDz`BzfAzd9zc8za7z`7z_8z_9z_9z_Az_Bz_Bz_Cz_Cz_\ FzaIzbLzdOzeRzgUzhXzj_zkYziXzgWzeVzcUzaTz_SzYRzWPz\ _NzbMzfKziJzmHzpGzsCzc8zOIzUSzZazdjziozVtzGyz1fzyV\ zcJzJKzIKzHLzHLzGMzFMzFUzCazAiz8qz6xz4tzPqzipzeoza\ nzYnzVpzVqzVrzVszVtzVrzRpzNozJjzKfzLazLYzMUzNPzNLz\ OHzOSzPazPkzQWz7Qz4Kz1Oz8 } 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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FOTD 19-07-11 (Mandelbrot's Pride [8])
by Jim Muth 20 Jul '11

20 Jul '11

FOTD -- July 19, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is merely an everyday scene in the conventional math range of the overworked Mandelbrot set, yet it rates a lofty 8. This rating is justified because I awarded myself 1-1/2 extra points for the coloring, which occupied a full hour of my limited time. Without the fancy coloring the image would have rated no more than a humdrum 6-1/2. The scene lies in the spiral seahorse-like tail of a tiny period-38 bud on the northwest shore line of the main period-2 bud of the Mandelbrot set. The maxiter of 15000 is a bit too low to fully resolve the large, unusually spectacular minibrot at the center of the image, but it results in the best coloring, so I posted the image slightly under-resolved. The name "Mandelbrot's Pride" is likely true. Mr. Mandelbrot was surely proud of his accomplishment of bringing fractals to the public attention (around the year 1980). But fractals, at least in their Julia aspect, were actually discovered many years earlier by Mr. Julia, who unfortunately had no computers to show the world what he had found. The calculation time of 9 seconds is insignificant when compared to a lengthy human life span of about 3,000,000,000 seconds, so go ahead, run the included parameter file and enjoy the image. You'll never notice the lost time. Another way to enjoy the image is to view it on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> or in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and don't forget the original web site at: <http://www.Nahee.com/FOTD/> Monday here at Fractal Central was hazy and hot, with a tempera- ture of 95F 35C that kept the fractal cats stretched on the coolest floor they could find. But at 6pm a noisy thunder-storm moved in, which dropped about 2.5cm of rain and lowered the temperature to 73F 23C. The thunder caused the fractal cats to grow alert, though they did not become alarmed enough to dash for cover. Tuesday began hot and muggy. By midday the temperature reached 90F 32C, which sent the cats once again into hot-weather mode. But a cooling thunder-shower arose around 5pm, which brought them back to life. The humans had reasonably uneventful days, which is the kind of day we enjoy. The sick computer is once again in full health, though with all the viruses out there, no guarantee of continued health can be given. The next FOTD will be posted in 48 hours. Until then, take care, and we'll never reach the stars until we find a way to leave our bodies behind. But when we do this, the universe will be ours. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mandelbrot's_Pride { ; time=0:00:09.66-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.1375835316682\ 11/+0.2095148760940262/7.282211e+011/1/137.5/0 params=0/0 float=y maxiter=15000 bailout=9 inside=0 logmap=-2227 periodicity=6 mathtolerance=0.05/1 colors=0008LV8NV8OV8PV8RV8SV8TV8TV8SV8ST8QS8PQ7NO5\ MN4KL0LK1MQ7NWDObIPcOQcVRcVTcVScVRcVQcVPWVOQVNLV83\ V01T01Q01O01N01K01I11H31V4Dg4O_ATMENDCM00A05B3BD8H\ DENEKTFQ_FVozYzzjLzlLzxNzcNxWNtOWzINmBNj4Ng0Nc0N`0\ LW0NY0OY0OY0QY0S_0S_0T_0T_0V`0W`0W`0Y`0_b0_b0`b0Yg\ 0`b0bY0eV0gQ4hN8lIDmFHoBNs7St4Wx0`z0ez0jz0oz0xz0tz\ 0sz0ox0ms0ll0hg0gb0eY0bS3`N5_I7WEAV8DT4EQ0HO0KN0LQ\ 0KS0KT0KV1KW3KY5K_8K`AKbDKeEKgHKhIKjLKlOKmQKoTKqVK\ sYKveIt_KtVKtQKsLKsHKsDKs8Kq4Kq0Kq0Kq0Ks0Ls0Ls0Lt0\ Lt0Lt0Lt0Nv1Nv3Nv4Nx4Nx5Nx7Ox8OzAOzAOzBOzDOzEOzFQz\ HQzHbzIbzKbzLbzNbzNbzOszQszSszTszTsvSzvQzzVzzVzzVz\ zEzzHzzLzzKzzKzzKzzIzsIzsIzsIzsHzsHzsHzsHzsFzsFzsF\ zsFzsEzsEzsEzhEzhDzhDzhDzhDzhBzhBshBshBsjAsjAslAsl\ AsmAsmAso8so8sq8sq8ss8ss8st7st7sv7sv7sx7sx7sz7sz5s\ z5sz5sz5sz5sz5sz4sz4sz4sz4sz4sz4sz4sz5sz5jz5bz5Wz5\ Wz5Wz5Wz5Yz5Yz5YzD3zK3zS4 } END PARAMETER FILE=========================================

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<Alex Dukay> Re: FOTD 09-07-11 (Wheel of Misfortune [8])
by Hal Lane 19 Jul '11

19 Jul '11

Alex, > I've just checked your new 'July' section and the links only > work after July 13th. Thanks for letting me know that those images had gone missing . Apparently, when my hosting provider moved my site to a new server they failed to move those files. I'd previously fixed a couple of other problems I'd discovered, but I hadn't realized that all those images had not been moved to my new server. I've uploaded the images again and checked the July page (and the end of June) and verified that they all load OK again. Again, thanks for letting me know so I could fix the problem! - Hal Lane ######################## # hallane(a)earthlink.net ######################## ------ Alex Dukay wrote: ---------------- Date: 2011-07-17 21:07 -400 To: Fractint and General Fractals Discussion Subject: Re: [Fractint] <Lee Skinner, all> Re: FOTD 09-07-11 (Wheel of Misfortune [8]) I've just checked your new 'July' section and the links only work after July 13th. All links prior to that date return the infamous '404' message. Alex Dukay ---

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<Lee Skinner, all> Re: FOTD 09-07-11 (Wheel of Misfortune [8])
by Hal Lane 18 Jul '11

18 Jul '11

> The link to July, 2011 seems to have disappeared from your FOTD page. Lee, Thanks a lot for letting me know. It's fixed now. I was temporarily mystified as to how I overwrote(?) the correct version on the server, as the only version I have on my hard drive is the correct one. I just now uploaded it again to put the July link on the Home page. I also found that the June page of FOTD's had lost its July link. That's fixed also. My best guess as to what happened is that when my hosting service recently moved me to a new server, the backup they restored to the new server didn't have the July link that I put onto my "Home" FOTD page (or the most recent changes in the June page). All, Can anyone tell me whether my "home" page: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html *ever* had the July link on it? Please let me know if anyone spots any other irregularities, untruths, errors, etc. -- or has any recommendations -- for my "stopgap" site for Jim's FOTDs. - Hal Lane ################################# # hallane A T earthlink D O T net ################################# --------- Lee Skinner wrote: -------------- Date: 2011-07-17 13:56 -400 To: Fractint and General Fractals Discussion Subject: Re: <Mike Frazier> Re: FOTD 09-07-11 (Wheel of Misfortune [8]) Hal, The link to July, 2011 seems to have disappeared from your FOTD page. Lee Skinner ---

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FOTD 17-07-11 (7-armed Heptafractal [7.5])
by Jim Muth 17 Jul '11

17 Jul '11

FOTD -- July 17, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image lies in an everyday Mandelbrot set that has taken on order-7 characteristics in its deeper depths. To find the scene we start at the period-4 bud on the northeast shore line of the parent M-set then go to the largest minibrot on this bud's filament network. This minibrot is still a reasonably normal one, but when we check the minibrot on this minibrot's main stem, we find that it is well along the way of morphing into an order-7 minibrot. Zooming in even farther, we check the area where the larger minibrot's main stem joins the smaller morphing minibrot, an area we might call the East Valley area of the smaller minibrot. We notice that the main stem branches into a series of shallow spirals before it enters the actual bay. We check one of these spirals. By the time we have gone deep enough to find an even smaller minibrot in the spiral, the minibrots have all totally morphed into order-7 shapes. Today's image shows one of these order-7 minibrots. The curved arms radiating from the minibrot indicate that the scene lies on a shallow spiral network. But all this confusing verbal description totally fails to give a visual impression of today's image. To enjoy the image, it will be necessary to run the included parameter file, which runs in 5-2/3 minutes, or to surf to the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> to view the finished image there. A high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic web site may be accessed at: <http://www.Nahee.com/FOTD/> The name "7-armed Heptafractal" was of my own invention. Anyone who knows exactly what it means also knows where the Tropic of Sir Galahad is located and what the song 'Stairway to Heaven' is all about. The rating of 7-1/2 indicates that I consider the image a little better than normal, but nothing to write home about. Heat returned to Fractal Central on July 16 as the temperature reached 88F 31C. The day was saved however by the humidity, which remained on the dry side all day. The fractal cats passed the day lounging on the living room floor, avoiding the sunlight that occasionally filtered through the trees. At post time on the 17th, the weather was looking like a repeat of the 16th. The day of the humans on the 16th was acceptable, as are most days here at FC. The next FOTD will be posted in 24 hours, but hopefully, by the end of the week, we'll have the FOTD back on its traditional every-day schedule. Until next time, take care and have fun dreaming of trips into interstellar space. You're surely never getting there in person. But isn't it curious that we have evolved the ability to dream dreams and feel desires that have no chance of being realized. One would wonder what the evolutionary advantage of such a frustrating ability might be. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 7armedHeptafractal { ; time=0:05:38.74-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip inside=0 center-mag=+0.355833037442585/+0.6498625194640629/\ 5e+012/1/-25/0 params=7/1000000000000.0/0/0 float=y maxiter=3200 logmap=-714 mathtolerance=0.05/1 colors=000SAUTBUUBUUBUUBUUBUUBUUBUUBUUCUUCUUCUUCVU\ DWUDXUDVUEUUEUUEUUFUUFUUFTUGTUGTUHTUHSUISUISUJRVJR\ VJRVKSVKTVKTUKUUKVUKVUKWUKXSK_UMXWOVYQT_SQ`UObWMdY\ Jf_HgaFicCkeKkgPkiUkkZkmckohkqlkomkmnkkokipkgqkerk\ cskatl_ulYvlWwmUxmSymQzjPwhOtfOqdNnaNk_LiYKhWIfTHd\ RFbPE`AEAADAADABCA9CA6BA6BA4AA5AF9BJCBHFBGICFLDEOF\ ERGDUHDXHB_H9cI8hI6mI4rI3vI1zI0vH3rG6mF8hEBfDDdCGb\ BJ`ALc9OX8Qc7TT6Wc5YP4`c5cN4bc4bP4bc4bQ4bc4bS4bc4b\ U4bm3aV3am3aX3am3aY3am3a_3am3a`3am6`Y8`mA`WC`mE_UH\ _zJ_SL_zNZQPZzSZOUZzWYMYYz_YKbYzdXIfXzhXGjXziYJiYz\ iYMiYziYOiYziYRjYzkYTlYzmYWnYzoYZqYztY`wYzzWzzY_z_\ zzaWzczzeRzgzziLzjzzjPzjzzjSzjzzjWzzzzjYzzzzfzzzzz\ czzzzz_zzzzzXzzzzzTzzzzzQzzzzzMzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzEzzAzzBzzBzzAzzAzzAzzCzzEzzGzzIzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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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<Mike Frazier> Re: FOTD 09-07-11 (Wheel of Misfortune [8])
by Hal Lane 17 Jul '11

17 Jul '11

> Here is a deeper zoom into one of the ovals of this fractal: Thanks for the nice image - and the antialiasing. I believe that there are 512 gray stripes in the blue ring, and 1024 gold "candelabra fingers" with a gold background, just centerward from the blue ring. Also, the identical counts are repeated on the larger rings -- with the 1024 pattern being the gray "candelabra fingers" with the red background. I don't believe that I've been able to clearly see period doubling taken to 1024 before. Thanks again for the anti-aliasing that made seeing this possible. - Hal Lane ######################## # hallane(a)earthlink.net ######################## ------- Mike Frazier wrote: ---------------- Author: Mike Frazier Date: 2011-07-16 14:44 -400 To: Fractint and General Fractals Discussion Subject: Re: [Fractint] FOTD 09-07-11 (Wheel of Misfortune [8]) Here is a deeper zoom into one of the ovals of this fractal: http://dl.dropbox.com/u/33642054/image/woma41_1200_5.jpg -- Mike Frazier www.fracton.org

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FOTD 09-07-11 (Wheel of Misfortune [8])
by Jim Muth 16 Jul '11

16 Jul '11

FOTD -- July 09, 2011 (Rating 8) Fractal visionaries and enthusiasts: Problems mount here at Fractal Central. The machine that was doing the work on the FOTD web site has come down with a rather nasty virus of the 'fake alert' variety, which left it unable to do anything but give fake warnings that it was infected with a virus. The stated cure was to go to a web site and download a certain program, which was certainly useless and would require that we give a credit card number, which would certainly be stolen. The machine is now in the shop, where the technician will try to clear out the fake alert virus, which is certainly no fake. Today's image is a scene quite deep in the period-26 radical on the north-by-west shore line of the main bay of the Mandelbrot set. The name "Wheel of Misfortune" refers to the out-of-action computer that is hopefully on the road to recovery. After careful consideration, I rated the image at an honorable 8. Since the image is a very deep one, the calculation time is a slow 18 minutes. And to make things worse, the finished image will NOT be posted to the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> until hopefully some time next week. But salvation is at hand, for the image will soon be posted in high definition on Hal Lane's web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the traditional web site at: <http://www.Nahee.com/FOTD/> Rain fell most all day Friday here at Fractal Central, with a temperature of a cool but very humid 73F 23C. The conditions were perfect on Saturday however, when the clouds of Friday gave way to Kodachrome blue skies, with cottonpuff white clouds, much lower humidity and a temperature of 86F 30C. The fractal cats were cat-like all day. The humans waxed angry when the computer got sick on Friday, but things settled down on Saturday. The next FOTD will be posted in 48 hours. Until then, take care, and let me know when (if ever) man reaches out toward the stars. The harsh fact is that, as long as we need to take our cumbersome bodies along, with all the necessary life-support equipment, we'll probably never get beyond the moon. It's just too damn expensive and the financial problems here on earth are too damn serious for us to waste money on such childish space-cowboy stuff. Too bad it was all a dream. So suck up, stop crying, and take it like a man. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= WheelOf_Misfortune { ; time=0:18:13.46-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y params=0/0 center-mag=-0.1937408443716777257397830313851/0.65\ 43465677029328435966803440113/4.3905e+026/1/-19.5/0 maxiter=6000 bailout=6 inside=0 logmap=780 colors=00000A01B02C02D03E03F14G24H35I45J56K67L78M8\ 9N9AOAAPBAQCARBCSAEV9GY8I`7Kc6MhCOmIQrOSvUUzZVzcZz\ cczchzcmzcrzcvzeHUbGX`FZYEaWEcTDfRChOBkMBmPGkRLiTP\ gVUeXYcZba`f_bkYdoXamYZkZXi_Ug`SeaPcd_`hccmkhntmow\ rpzsqzurzwszxtzyuzzvzzwzzzP77N43M10WK0db0ea4fa7g`B\ h`Ei`Ii_Lj_Pk_SlZWmZZmZajYZgXXdWVbVT_URXUOVTMSRKPP\ INNGKMDHKBFI9CF79C57C39A9B9FC8KE6QF5VH4`I2eKBkLApJ\ IqIPqGWqFbrDirCprBwrIrpPmnWhlbdji_hpVfvResPcpOamN_\ jLYgKWdJUaISZGQWFOTEMQDKNBIKAGH9EE8CFHIFQOFYUFf_Fo\ eFwjPvknvktvtwvwzzzwrwuowslrpionfpldpjaqgZreWscTta\ Rt_SnZShYTbWTYVUSNHI0CI3LQ6UY9bsCqzIgeclYUcQ_aIWUF\ TNCQF9N87XPhYMYQ9BZKNgjldbcbWV`PM4YlCUcKQVSMM_76ZD\ A3IPBVvNc_Lc3WcONc`TcPRcoVcWmcFimEemEamDvmypmljm`d\ mPLmoSmWTm5Vm8XzBdztUzGWzFYzEzzIzzGzzEzztzzZzzSzzK\ zzIzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 15-07-11 (A Simple Diversion [4])
by Jim Muth 15 Jul '11

15 Jul '11

FOTD -- July 15, 2011 (Rating 4) Fractal visionaries and enthusiasts: Today's image earns a rating of a mere 4, which I admit is below average. It is simply another everyday scene in East Valley of the Mandelbrot set. The actual location is in the Seahorse Valley of the large minibrot on the shoulder of the period-18 elephant on the south side of East Valley. I did put a small extra effort into the coloring, though not enough to earn the standard half-point bonus. The name "A Simple Diversion" describes the image, which came about almost accidentally as I noodled at the fractal keyboard. The calculation time of an even 10 seconds will put no time pressure on even the busiest fractalist. But running parameter files is still a nuisance. To make things as simple as possible, check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> or the high-definition version 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/> Thursday and Friday here at Fractal Central were virtually identical, with lots of sun, wispy clouds, low humidity and a temperature of a comfortable 84F 29C. Conditions were so pleasant that the fractal cats passed the chilly morning hours curled in their cold weather positions. Little of note happened in the human world, but not so with fractals, which always have existed and always will exist. If fractals are merely an invention of the human mind however, they have no reality at all, and will cease to exist with the demise of the last person who knows about them. The next FOTD, for better or worse, will be posted in 48 hours. And it should not be too long before we return to the every-day schedule. Until next time, take care, and maybe fractals are not the only semi-real things that are creations of the human mind. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Simple_Diversion { ; time=0:00:10.00-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.2799927583330\ 883/-0.00863883735311807/2.073768e+011/1/-137.5/0 params=0/0 float=y maxiter=15000 inside=0 logmap=2910 mathtolerance=0.05/1 colors=000gM_gM_gOaeOaePadPbdQbbQbbTaaTbaWbaXbbY_b\ __baYbbY_dYXeXUeXQeXPeWMgWJhWGjUDlUAmU9lT6jT3hT0gP\ 0eP0dP0bQ0_Q0XO0UL0PI1LG2GF2DD39A559618805903A02A0\ 1D02F02I03J33L83OC5PG5TL5UP6WT6YX6_a8be8dj8eo9ht9j\ y9mzAozAqzAozCmzClyDjvDhqFgmFehFdeGbaGaYI_UIYQJXFJ\ XCJYDIYDIYDI_DI_DI_DIaDGaDGaDGbDGbDGbDGbGJbILWLMWM\ OWOPWQQWTTWUUWQWWQXWTYWW_WPaWFbUJaTJ_TEYQJXXeWXdUW\ dTUbQUaPT_OQXMQTLPQJOPIOOGMMFLLDLJCJLAIJ9II8GI6FI5\ FI5JF6MC8I99J9AL8CO6DI6FL5GM3IO3IO3JM5JA5JA5JA5JA3\ JA3JA3JA2LA2LA2LA1LA1LA1LA0LA8YA9YA9Y0Ad0Ab0CW0DO0\ FG0G90I20M00T00Y09d3LjAYoIltPyyWezaPze8zj0zo1zq9zr\ IztQzv_zwhzyzmzzzmmzzaqzPgzDXz2Mz0DzDUzLQzQOzXLzbI\ zhGzeMzbTz_XzYbzWgzTmzQrzLjzGIzCYr8TmDWhJYePaaUdY_\ gUejQdlOzoQtrU_vXXw_IP00Pq0PT0P5zdj_dO8d2ydPJd3ody\ XdbFdJ0d1ldmzdy0t80t10t00t0PzDPz5Pz0dz0dz0tz0tzztz\ OtzDzz0zzLzzAzz1zz0zzzzzd } END PARAMETER FILE=========================================

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FOTD 11-07-11 (Glorious Celebration [7.5])
by Jim Muth 14 Jul '11

14 Jul '11

FOTD -- July 13, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image lies deep, but not all that deep, in a filament extending from the large north period-3 bud of a minibrot that lies on a minor branch of the filament network extending from the period-4 bud on the northeast shore line of the Mandelbrot set. And now that we (hopefully) know exactly where the scene is located, the thing to do is rush to enjoy its glories. Perhaps a bit over-enthusiastically, I named the image "Glorious Celebration". I leave it to the viewer to invent a reason for the celebration. The rating of a 7.5 means that the result will be worth the effort of spending the 17 minutes required to calculate the image. But sometimes the worth of an object is in the mind of the individual. Those who feel that no fractal is worth a 17-minute wait may find eventual relief on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image will be posted in a day or so. Immediate relief may be obtained by viewing the finished image in high definition on Hal's web site 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/> Tuesday proved to be a hot sunny day here at Fractal Central, with a temperature of 93F 34C that kept the fractal cats stretched out in hot weather mode most of the day. The people passed the day in waiting mode -- waiting for word from the computer shop that the sick machine has been restored to health. The word never came, but things are looking up. Wednesday began with light rain, but cleared off by midday, leading to a very pleasant afternoon with lots of sun and a temperature of 84F 29C. Late in the day we got word from the computer shop that they have isolated the problem and should have the machine up and running by Thursday. (Damn virus!) The next FOTD will be posted in 48 hours. Until then, take care, and visiting other worlds by ingesting LSD seems a workable way to play space-cowboy. But, forgetting about legality, there is always that little problem of reality. How would the LSD trippers get the world to take them seriously? How would they demonstrate that the things they observe on their trips are really out there and not just a lot of unreal drug-induced hallucinations? Jim (I never inhale) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= GloriusCelebration { ; time=0:17:40.56-SF5 on P4-2000 reset=2004 type=mandel passes=1 bailout=16 center-mag=0.3810124098623526005883449162/0.685148\ 192066715948738221395/1e+023/1/-150/0 params=0/0 float=y maxiter=5000 inside=0 periodicity=6 colors=000o00r03t0Av0Gx0Oz0Wz1cz2lA2KA3KA3KA4KA4KA\ 5KA5KA6KA7KA7KA8KA8LA9MA9NAAOABPACPADPAEPAEPAFPAFQ\ AGRAGSAHTAHUAIVAIWAJXAJYAKZ8K_7K`7Ka5Kb5Kc3Kd3Ke3K\ f1Kg1Kh0Ki0Kj0Kk0Kl0Ln0Mp0Nr0Ov0Pz0Qz0Rv0Sr0Tm0Uh0\ Uc0UZ0UU0WP0WK0WF0WA0U50U10S00S00Q00Q00Q00O00O00M0\ 0M00M01O0AQ0KS0UU7aWAcUEeSIgQMgOQiMSlKWnI_nGcoEerC\ irAnt8rv7vx5xx3zz1zz0zz0zz0zt3zl7zcCzWGzOMzGSz8Wx1\ av0ct0ev0ev0ev0ex0ex0ex0ez0ez0ez0ez0ez0ez0ez0ez0ez\ 0lz0ez0_v0Un0Og0I_0ES08K03E007000100500733AA7CIAEQ\ EIYIKeMMnQQvUSzYUzcUzaUz_Uz_UzYUvYUtWUoWUlUUiUUeSU\ aSU_QUWQUSOUQOUMMUKM_CIc7Eg1Cl08r05v03zh0ze0zb1z_3\ zX5zU7zP8zKAzFCzAEz5Gz1Iz3Kz7Mz8OzCQzESzIUzKWzO_zQ\ czShzUmzUrzWtzWwzWwzYzzYzzYwz_mz_hz_hzaczaczaQxcQx\ cOvcOteMreMoeMngKlgKlgKocGv_EzWAzS7zO3zK1zCCz7Mz1W\ z0ez0oz0zz0zvGnctSevUexUgxUgzWizWizWlzYlzYnzYnz_oz\ _oz_a10c00g00g00i00l00n00 } END PARAMETER FILE=========================================

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FOTD 11-07-11 (The Pale Fractal is Alive [8])
by Jim Muth 11 Jul '11

11 Jul '11

FOTD -- July 11, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a simple recoloring of a non-FOTD image I posted several weeks ago. The coordinates show that the scene lies on the north-northwest shore line of the main bay of the Mandelbrot set, though I have forgotten the exact location. The name "The Pale Fractal is Alive" is a comment on the pale colors. Such paleness may be considered a fault, but at least in my opinion, the paleness in today's image is a virtue. The rating of an 8 is true 'in my opinion' also. Those who enjoy their fractals with intense colors may consider the rating overblown. I consider it only a little if any exaggerated. The calculation time of 28 minutes is no exaggeration. The magnitude of over 2*(10^31) requires arbitrary precision math with all its slowness. But all is not quite as bleak as it seems, for the finished image will sooner or later, more likely later, be posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version will be posted notably earlier at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> while the original web site may be accessed at: <http://www.Nahee.com/FOTD/> Sunday turned into another perfect day here at Fractal Central. The digital blue skies were made all the bluer by the cottonball white cumulus clouds, while the temperature hung around a pleas- antly warm 86F 30C and the humidity remained at a reasonable level. The fractal cats spent most of the day sleeping, Nicholas on the top of the secretary and Cassie on a chair. The humans spent the day trying to enjoy the day, which is a sure way to not enjoy it. The next FOTD will be posted in 48 hours. It might be another very deep one in the Mandelbrot set. Until then, take care, and if anyone knows how we might bring about the kind of outer-space adventures we see on sci-fi TV, please let me know. (I guess I should note the word 'fiction' in the phrase 'Science Fiction'.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ThePaleFracIsAlive { ; time=0:28:47.51-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.1544\ 30158076852307578200573930148812/1.028184051437829\ 95934904475562903725/2.386084e+031/1/-15/0 params=0/0 float=y maxiter=2800 bailout=9 colors=000HHHGGGGGGFFFFFFEEEEEEDDDDDDCCCCCCBBBBBBA\ AAAAA999999888888777777666666555555444444333333222\ 22211111100000000000000011111122222233333344444455\ 5555666666777777888888999999AAAAAABBBBBBCCCCCCDDDD\ DDEEEEEEFFFFFFGGGGGGHHHHHHIIIIIIJJJJJJKKKKKKLLLLLL\ MMMMMMNNNNNNOOOOOOPPPPPPQQQQQQRRRRRRSSSSSSTTTTTTUU\ UUUUVVVVVVVVVWWWXWWYXXZXX_YY`YYaZZbZZc__d__d``e``e\ aafaafbbgbbgcchcchddiddieejeejffkffkgglgglhhmhhmii\ miimjjmjjmkkmkkmllmllmmmmmmmnnmnnmoomoomppmppmqqmq\ qmrrmrrmssmssmttmttmuunuuovvpvvqwwrwwsxxuxxwyyyyyz\ zzyyywxxuxxswwrwwqvvpvvouunuumttmttmssmssmrrmrrmqq\ mqqmppmppmoomoomnnmnnmmmmmmllllllkkkkkkjjjjjjiiiii\ ihhhhhhggggggffffffeeeeeeddddddccccccbbbbbbaaaaaa`\ `````______ZZZZZZYYYYYYXXXXXXWWWWWWVVVVVVVVVUUUUUU\ TTTTTTSSSSSSRRRRRRQQQQQQPPPPPPOOOOOONNNNNNMMMMMMLL\ LLLLKKKKKKJJJJJJIIIIIIHHH } END PARAMETER FILE=========================================

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FOTD 05-07-11 (Challenger Fractal [7])
by Jim Muth 10 Jul '11

10 Jul '11

FOTD -- July 05, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image is a scene deep in East Valley of the large minibrot on the negative spike of the Mandelbrot set. And when I say deep, I mean deep. With a magnitude of over 10^96, the image is one of the deepest I have ever found. It is so deep in fact that the features are unfamiliar, though the typical East Valley goofy eyes are apparent. Yes, there is a minibrot at the center. I have not yet been down there, and due to the time factor might never go there, but if someone with a super-fast machine feels tempted to see what lies much deeper in today's image, you have my blessings. Unfortunately, the extreme depth also makes the image one of the slowest. The calculation time of over 2-3/4 hours will try the patience of even the most patient fractalist. This is where the FOTD web site comes to the rescue however. The finished image is posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is, or soon will be posted in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the original FOTD web site at: <http://www.Nahee.com/FOTD/> Monday proved to be a rather pleasant and typical Independence Day here at Fractal Central in central Pennsylvania. The koda- chrome blue skies and cottonpuff clouds simply begged to be photographed. (Even though the old Kodachrome film is gone, the sky is still blue.) The temperature of 84F 29C was warm enough for swimming, while the humidity was low enough for comfortable outside activities, and the dry weather was perfect for the evening fireworks. The fractal cats do not like independence day. The bangs of exploding firecrackers had them on edge most all day, and when dusk came and the explosions picked up, the dynamic duo took shelter in the bedroom until the noise settled down. Meanwhile, FL and myself had an uneventful day. Unless something unex- pected turns up, the next FOTD will be posted in 48 hours. Until then, take care, and with civilization on the brink of collapse, I wonder whether its replacement will be worse or better. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Challenger_Fractal { ; time=2:46:45.77-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.749879763723303625053154128808566087\ 33087068131509407390221609977764152792206339038580\ 35532704313692/3.711275390023365538060136900393279\ 23739521658716180513365112109254521643684694156138\ 251e-15/1.208835e+096/1/-112.5/0 params=0/0 float=y maxiter=10000 bailout=25 inside=0 colors=000QDXPCWOBWNAVNAVM9UL8UK7TJ7SJ6SI5RH5RG4QF\ 3PF2PE2OD1OC0NC0NE1PF1RH1TI1VJ1XL1YM1_N1aP2cQ2eR2g\ T2hU2jV2lX2nY2p_1rZ2qZ3pY4oY5nX6mX7lW8kW8jV9iVAhVB\ gUCfUDeTEdTEcSFbSGaRH`RI_QJZQKYQKXPLWPMVONUOOTNPSN\ QRMRQMRPMSOLTNLUMKVLKWKJXJJXIIYHIZGH_FH`EHaDGbCGbB\ FcAFd9Ee8Ef7Dg6Dh5Dh4Ei5Fi6Gi7Hj8Ij9JjAKkBLkCMlDNl\ EOmFPmGPmHQmIRmJSmKTmLUmMVm`Um_TmZSmZRmYRmYIzPKzPM\ zONzOSzNXzNazNfzNkzMpzMuzMzzMvzNrzOnzPjzQfQRcSS_UT\ WWUSYVO_WLaXHcYDeZ9g_5i`2k`3gX3dU4`R4YN5UK5RH6ND6K\ A7G77D4CGAGJFKLKOOQSRVXT_`WddZjh`olctoeymeykfxifxg\ gwegwchvahuZitYjsWjrViqVfpVcoV`mVYkVViVSgVPeVMdVJb\ VG`VDZVAXV7VV5UW6TX6SY6SZ6R_7R_7Q`7Qa7Pb8Pc8Oc8Od8\ Ne8Mf9Mg9Lh9Lh9KiAKjAJkAJlAIlAIlcCi_EfXGcTH`QJYMLV\ JMSFOPCQM8RJ5TG2UF6TE9TDDTCGTCKTBNTART9US8YS8`S7dS\ 6gS5kS5nSBmUHmWNlYTl_Zkadkcjjepjgvjhplgjmgdof_pfUr\ eOsegYTgZUh_WiaYjb_kc`leb } END PARAMETER FILE=========================================

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FOTD 07-07-11 (Way-Out Deep-East [7])
by Jim Muth 07 Jul '11

07 Jul '11

FOTD -- July 07, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's rather striking image lies in the East Valley area of a larger minibrot near the tip of the negative stem of the Mandelbrot set. The name "Way-Out Deep-East" refers to the location of the scene. The converging arms show that the scene lies very close to the escape radius, which in today's image lies very close, at -2. The rating of a 7 indicates that the image is good enough to be worth a look, though maybe not quite worth the 22 minutes required to run the included parameter file. Those 22 lost minutes may be saved by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version may be viewed at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The honorable classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Midsmmer heat prevailed here at Fractal Central on Wednesday, with blazing sun and a temperature of 93F 34C. The fractal cats weathered the heat in the coolest places they could find. The humans did what humans do when it gets hot. They took it easy. The next FOTD, another very deep one, will be posted in 48 hours. Until then, take care, and I hear that someone has theorized that a second dimension of time might exist in the sub-atomic realm. If so, motion in time down there would be as free as motion in space is for us up here, but I would hate to have to work out the math. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Way-Out_Deep-East { ; time=0:22:05.90-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y center-mag=-1.999996470333724681839775166903411/3.\ 0909517916650017312333e-13/3.950279e+030/1/-160/0 params=0/0 maxiter=6000 inside=0 periodicity=6 colors=000WfZXdVYcQZbM_aHfYAa_EXbHUfLQiPNlTJoWEs_J\ gjEofAubek60x25z_PlRxQXf_Jlw9zq8zn8zk8Kf6Gb6CZ63Z8\ 8V6DT4HQ3MD1iS4_K3TH1LE0D6052021000004000000000000\ 0000000000022568AAEGEJLGPNDKPGPQKUTSZUVcWYicVpZXnW\ _lRakOdjKfiGigDlf9ofZJZUVjUQcVLYYGS_COb7Id3Ec6Ib8L\ aBQ_DT_FW0FW3HY9LZFOZLS_QW_KWWGZUB_R6bN2cLDTNOKR_C\ WgIanNeuSlzYpPMO0C007927M86ZC3kG0wS9s`JojQkjSejUbj\ VYjXVjXQjYMjZHlVMoRPpNUsJWuF_wAcy5fz0jw0Xs0Ko06l00\ d30Y86REBJHFGMJBTQ0Wz0Yk6YVDZJJa6Ob0LN1JCBJ0IM6INB\ HPGHRMHTQGVWGYnSXgLWbFWW9YQ0WS3VTAVUGUVNVWUVYZW_fX\ UcWOaVHZj9`aBYUBWOCVIDVCEU5ET0FR0GREBZZ6fw0os3ao6Q\ k9FQ5C50260888EAGLBORBYYCfcDoknyoWxoExpAoX7kF8gE8c\ D8aE9YC9VBARC9PBHMJOMQXM_dRzeOrgNzhKwkHckFkkGkpEls\ Dk000r97o72l40k30j30f80cA0aE0ZH0WL0UO0RR0Oc0QV0RN0\ UG0W80P5M0_kbbk0_kYCOYHHWMNWQSWWWRVaVYbY`baabcccff\ djiezzjorfhjddib_g`lj6bgL } END PARAMETER FILE=========================================

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FOTD 03-07-11 (Bubbles on the Rocks [?])
by Jim Muth 06 Jul '11

06 Jul '11

FOTD -- July 03, 2011 (Rating ?) Fractal visionaries and enthusiasts: Today's image rates a question mark because I'm not even sure that it's a true fractal. It looks more like a 'painting' by one of those 'modern' artists who have more showmanship than skill and make up for their lack of ability by manipulating the gullible public into paying good money to see their awkward efforts. But then again, beauty is in the eye of the beholder, so who can say for sure that something like today's FOTD image, with its awkward colors and shapes, is not real art. Certainly not myself! I named the image "Bubbles on the Rocks" for some reason that I have long since forgotten. It came into being when I started fumbling with the Mystic2 formula, which draws nothing but empty circles unless the inside is set to an active fill, such as the 'bof60' fill that creates the action in today's image. The bottom edge of the image is 'outside' stuff. The crazy detail that fills most of the frame is actually 'inside' stuff made manifest by the 'bof60' fill. This is chaos carried to the extreme, with no signs of a unifying theme either in the shape or coloring. The image calculates in only 55 seconds, so why not go ahead and calculate it despite my less-than-favorable comments? After all, one person's junk is another person's treasure. For the convenience of those who do not calculate parameter files, the image is posted, already calculated, at: <http://www.crosscanpuzzles.com/Archives.html> The hi-def version is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the venerable FOTD web site at: <http://www.Nahee.com/FOTD/> A typical summer day passed uneventfully here at Fractal Central on Saturday, with sunny but rather hazy skies and a temperature of 88F 31C. The fractal cats also lived the day uneventfully, not realizing the exciting life they might have had if we had decided to let them be indoor-outdoor cats. The day of the humans was routine, as life tends to become in its third stage. The present plans are to post the next FOTD in 12 hours, but even the best laid plans sometimes go awry, so check to see what happens. The next image is already safely on disk and ready to fly. Until whenever, take care, and life comes in three stages -- early, middle and late. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BubblesOnTheRocks { ; time=0:00:55.42-SF5 on P4-2000 reset=1950 type=formula formulafile=basicer.frm formulaname=Mystic2 function=cos passes=1 center-mag=+0.71234614/-0.70069042/830/1/-45.5/0 params=1/1/1/1/1/1 float=y maxiter=90 bailout=100 inside=bof60 logmap=yes periodicity=0 colors=000muzktzirzgpzenzclybjwahu`fs_dqZboY`mXZkW\ XiUUgTSeSQcRO`PMYNKVLISKGPJEMICJGAGE8DC6AB08E16G26\ I36K46M57N67O77Q87S98TA8UB8VC8WD9XE9YF9_G9`G9aHAbI\ AcIAdJAeJBfJBhJBiKBjLCkMDlNEmOEnOGoNHoNJoMLoMNoMQo\ LVpLVpLVpKVpKVpJVpJQqJLqIGqIBqIBqHBqHBrHBrGBrGBrFB\ rFBrFBsEBsEBsEBsDBsDBsDBrECqEDqFDpFEoFEoGFnGGmGGmH\ HlHHlIIkIJjIJjJKiJKhJLhKMgKMfKNfLNeLOeMPdMPcMQcNQb\ NRaNSaOS`OT`OT_PUZPUZPVYQVXQVXQWWQWWRXVRXURXUSYTSY\ SSYSSZRTZRT_QT_PU_PU`OU`OU`fGiy0sx2rx4rw6rw8qvAqvC\ quEpuGpuIptKptMosOosQorSnrUnqWnqYmq_mpampcmoelogln\ ilnkkmmkmokprnmpkkniimfgkdejach_agX_eVYdSWbQUaNS_L\ QZJU`HYbGacFbdEbdEbdDbdDbdCbeCbeBbeBceAceAcf9cf9cf\ 8cf8cf7cg7dg6dg6dg5dg5dh4dh4dh3dh3bl1cj2dh3eg4fe5g\ c6hb7i`8jZ9kYAlWBmUCnTDoREpPFqOGrMHsKItJJuHKvFLwEM\ xCNyBNtDPoFRjHSeJUaLVXNXSPYNR_JT`IU_HVZGWYGXXFYXEZ\ WE_VD`UCaTCaTBbSfsvguwhwx } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END PARAMETER FILE=========================================

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Binary Disarmament
by Mike Frazier 05 Jul '11

05 Jul '11

This fractal started with a deep zoom into elephant valley. After taking some side paths and seeing what changed, that information was used to customize the image. A notable find in this fractal was a side path that reduces the number of arms by any chosen binary number. This particular fractal reduces the number of arms from 256 to 8. Choose a similar feature on a ring closer to the minibrot at a magnification of 1.8E+37 to get a larger reduction of arms or zoom out more from this area and pick a similar feature at the next ring to get less. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/binary_disarmament.html The parameter file used to make the image is below: BinaryDisarmament { ; Exported from Fracton. ; time = 1 min 57 sec at 640 x 480 with no aa ; on a Mac Pro 2 x 2.8 Ghz Quad-Core Xeon reset=2004 type=mandel passes=1 float=y center-mag=0.3621521493849173225653015936229961154\ 020303874746001572686474146939631186233564272156/0\ .7697027186599243781549340712467568527349109424266\ 821242302855761785090545156785712693e-1/1.61616163\ 6363636e+71/1/-10/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=10000 inside=1 proximity=0 colors=000fTDeSDdRDcQDbPD`OE_NEZMEYMEXLEVKEUJETIES\ HERGEPFFQFFRGFSHFTIFUJFVJFWKFXLFYMFZNF_NF`OFaPFbQF\ cRFeSFdSFcRFbQFaPF`OF_OFZNFYMFXLFWKFVKFUJFTIFSHFRG\ FPFFPFFQGFRGFSHFTIFUIFVJFWKFXKFYLFZLF_MF`NFaNFbOFc\ PFcPFbOFaOF`NF_MFZMFYLFXKFWKFVJFUJFTIFSHFRHFPFFSNC\ <2>UODVPEWQFXRGYSHZTH`UIaVJbWKcXLdYMeZMf_Ng`OiaPjb\ QkcRldRmeSnfTogUphVriWsjWtkXulYvmZwn_xo`zpaypaxo`w\ n_vm_ulZtkYsjXriXqhWphVogUnfU<5>g`P<5>aWL<2>WQG000\ <5>888<7>III<7>RRR<7>```<9>jjj<9>lll<9>bbb<9>TTT<9\ >JJJ<9>999<10>000PFF<2>`OF<2>lXE<2>xeD<2>p_CgTD } -- Mike Frazier www.fracton.org

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A Fractal?
by juanw＠shaw.ca 04 Jul '11

04 Jul '11

Don't know if this is fractal-based. Certainly looks that way, and I find it remarkable! http://inoyan.narod.ru/kaleidoskop.swf John W.

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Re: [Fractint] A Fractal?
by Hal Lane 04 Jul '11

04 Jul '11

------- John W. said: ------- > Don't know if this is fractal-based. Certainly looks that way, > and I find it remarkable! > http://inoyan.narod.ru/kaleidoskop.swf ------- Alex Dukay said: -------- > I wonder how it was done? Here's a guess as to what's going on in the kaleidoscope algorithm: There's: - a precalculated unseen fractal - real-time copying of a pie wedge-shaped area from the fractal - real-time translating and rotating of the pie-shaped mask that decides what part of the source fractal to copy from. - These translation and rotation matrices are controlled both by a built-in timer and in response to cursor movement. - real-time pasting of the copied pie-shaped area 12 times -- each of the 12 instances rotated 1/12 of the way further around a circle. So, we have lots of pixel copying, but no fractal calculations going on while the kaleidoscope is being displayed. Btw, I'm pretty sure that Shock Wave Flash has built-in capabilities for translating and rotating sprites. If your sprite happens to be a big wedge from a fractal instead of an icon (like in Hamster Dance) the software doesn't care. Anyone else have any ideas about the kaleidoscope at the link above of methods that could easily produce what's going on? - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Scale of the universe
by Lee H. Skinner 04 Jul '11

04 Jul '11

Although not a fractal, I thought many here who enjoy zooming in and out of fractals would enjoy this interactive presentation: http://primaxstudio.com/stuff/scale_of_universe/ Lee Skinner

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FOTD 01-07-11 (Squared Octagon [7])
by Jim Muth 02 Jul '11

02 Jul '11

FOTD -- July 01, 2011 (Rating 7) Fractal visionaries and enthusiasts: Without the FOTD to keep it active, the grand old Fractint list seems to be slipping into a torpor. So I have decided to resume the FOTD on an every-other-day basis, alternating the daily FOTD's with a day of working on the FOTD web page. Things were still rushed here at F.C. on Friday, meaning the discussion will be terse. Today's image is a scene deep in a filament on the northeast shore line of the main bay of the Mandelbrot set. It actually lies on a filament in the image of June 24, at a magnitude about twice as great. Many of the same themes appear in today's image, though the large outer square and the smaller inner octagon are totally missing from the previous scene. Perhaps a bit liberally, I rated today's image at a 7. The name "Squared Octagon" refers to the geometric shapes in the image. The calculation time of 17 minutes is slow, but given the magnitude of the image, the slowness is unavoidable. The finished image is available 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/> Total sun, low humidity and a temperature of 82F 28C made Friday an ideal day here at Fractal Central. The fractal cats spent the day sleeping, perhaps showing signs that they are no longer kittens. The humans' day was acceptable, with little problems but no big disasters to speak of. The next FOTD will be posted in 48 hours -- but then again, maybe it will be delayed. Until whenever, take care, and as the owl said, it's 'too hot to hoot', which spelled backward is 'too hot to hoot'. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Squared_Octagon { ; time=0:17:21.84-SF5 on P4-2000 reset=2004 type=mandel center-mag=0.44658826674909\ 358559395849/0.37152108221226800868923596/3.8e+020\ /1/62.5/0 params=0/0 float=y maxiter=6400 inside=0 colors=000FabCbdAde7fg4hk5hh5de5_b4YZ5V_5S`5Pa5Mb5\ Lc5Jd5He5Ff5Eg5Ch5Ai58j57j48g49d4Aa4B_4CX4BU4AR4AP\ 4AM4AJ3AI4AH4AG5AF5AF6AE6AD7AC7AC8AB8AA9A99A9AA8AA\ 7AB7EA9H9AL8BO7CR6DV5EY4F`3G_5JZ6LY8OX9QWATVCVVDYU\ F_TGbSHdRJgQKiTHnQLkOOhLReJVbGY_E`XBcU9gR6jO4mL2pI\ 7mJBjKGgKKeLPbMT_MYXNaVOfSOjPPoMQsKQpNRmPSjSSgUTdW\ UaZUZ`VWbWTeWQgXLlVOiXQfYSd_Va`X_aZXc`UdcSfePggNhi\ KjlHknFmpCnrAoqDmpFkoHioJgnLemNcmPalR`kTZjVXjXViZT\ haRhcPgeNfgMeiKekIdmGcoEcqCbsAau8aw7fsBkoFqkLogJmc\ Ik_GiWFhVDfUCdTAbU9aV7_W6YY4W_3V`2UY6UVATTETQITNMS\ LQSIUSGXQFYPEYNEYMDZKCZJCZIB_GA_FA_D9`C9`A8`97a87a\ 66a57b39b2Cb1Fb1Ib2Ld2Oe2Rf2Ug2Xh2_i2bj3el3hm3kn3n\ o3qp3tq3wr2zv3ws4uq5so6pl6nj7lh8ie9gc9eaBd_CcZEbXF\ aWH`UI_TKZRLYQNXOOWNPVLRUKSTIUSHVRFXQEYPC_OB`N9bM8\ cL6dK5cJ8cJAcJCbJEbJGbJIbJKaJMaJOaJQaJS`IV`IX`IZ`I\ `_IbXWSUXTSXVPYXMZYKZ_H_` } END PARAMETER FILE=========================================

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An unscheduled fractal
by Jim Muth 29 Jun '11

29 Jun '11

Fractal visionaries: To give assurance that I am still doing fractals, here is a scene I recently found deep in the Mandelbrot set. It is not an FOTD. The FOTD will be resumed when my FOTD web site is in respectable condition. The parameter file is rather slow, which will give lots of time to ponder the mysteries of fractals. Until next time, stay tuned and enjoy the occasional fractals from Fractal Central. JIM START PARAMETER FILE======================================= Ellipse_of_the_Day { ; time=0:28:47.51-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.154430158076852307578200573930148812\ /1.02818405143782995934904475562903725/2.386084e+0\ 31/1/-15/0 params=0/0 float=y maxiter=2800 bailout=9 inside=0 symmetry=none periodicity=6 colors=000F`UF`UE_UD_VCaVCcVBeWAgWAiWBkVClVDkUEiUF\ gUGeVGcVHaVH_VIYVIWVJUVJSVKQVKPVKOVLNVLMVMLVMKVNJW\ NIWOHWOGWPFWPEWPDWQCWQBWRAWR9WS8WS7WT6WT5WT4WU6VU8\ UUATVBSVDRVFQWGPWIOWKNWMMXNLXPKXRJYSIYUHYWGYYFZZEZ\ `DZbC_cB_eA_g9_i8`j7`l67pU8nTAmTBkSCjRDhRFgQGePHdO\ JbOKaNL_MMZMLWLLUKLSJLQILOHLMGKJFKHEKFDKDCKBBK9AJ1\ 8K79KDAKIAKOBKUCLZCLdDLjELoELuFKzFUzZcvYjrYgmXdhXa\ cXZcWWcWTcVUcVXcOZcVYcabehcclmWnkXoiYpfZqd_rbas`ct\ _ep_gm_ijZkgZmdZo`ZqYYrVYsSYtPWuJYtM_tPasRbsUdrWfr\ Zhq`iqckpemphnpjnoXnpUnqWnrYns`ntcnufnvmnwfnxRny7n\ x9oxBqxDswFuwHwwOxwZyvezwmzxpzyvzzzzzzzzzzzzzzzzzz\ zvzzrzzmzzhzutVrqUpoTmmSkkRiiQfgPdeOacN_aMY_LVXKTV\ JRTIORHMPGJNFHLEFJDCHCAFB0634A78DBCHFGKJKONORQSVUW\ YY_aacdeghioopmmnkkljijhhhffgedecbcaaa`__ZYZXWXWVV\ UTTSRRTNUSOSRPRRQQQRPPSNPTMOULNVKNWJMWHMXGLYFKZEK_\ DJ`BIaAIb9Hc8Hc7Id6Ie6If6 } END PARAMETER FILE=========================================

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Multifractal_10 (War - Zoom into "Islands in the Sun")
by Albrecht Niekamp 26 Jun '11

26 Jun '11

Hi, I´m not sure about your reactions to this one. It´s not a pretty one, can´t be with that title, but very unusual indeed. Please tell me what you think. Thanks. Albrecht -------------------------start par------------------------- 20105az2 { ; War ; Time 0.52.39 ; Mandel-secant-mmods ; Zoom into "Islands in the Sun" ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-1.13058642478997200/+0.28449817625896450/693\ .8962/1.1228/101.291651332089913/-2.44095331583978226 params=-0.05825983458967864/0.3785210730307932/20105.035\ 64960102/25234.2207090221/151024.0204808192/384.32768524\ 288/384.00482000595/128.1007683001/256.1007683001/256.20\ 07683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=n0B00z<78>vv4ww3ww2<2>zz0zz0zy0<77>z40z30z20z20z1\ 0z00<9>s07r08q08<3>n0Cm0Dl0E<59>50u40v30w<3>00z000 }

3 3

The missing FOTD's explained
by Jim Muth 26 Jun '11

26 Jun '11

Fractal visionaries and enthusiasts: I have been trying to get my FOTD web site up to date for several months, with little success. There is simply not enough time in one day to write a new FOTD and work on the 125 or so months that still need to be put up on the web site. Regret- fully, I will need to stop posting the daily FOTD until the web site is in better shape. How long this will take is anybody's guess, but with the good stuff that has been posted on the Fractint list recently, I doubt that a fractal drought is on the way. Meanwhile, keep checking the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> where things will still be happening, and keep your eye on the new multifractal images being posted on the Fractint list. They could lead to an entirely new world of fractals. JIM

1 0

Lee Skinner MFR Zooms _(019ba3)
by Albrecht Niekamp 26 Jun '11

26 Jun '11

Hi, this is a new zoom into one of Lee´s MFR Images. Another way of displaying the dualism shown in the "Islands in the Sun" image. Tension: Dark colours Released Tension: Light colours. Although this is a relatively deep zoom it has many more zooming spots especially where the two come together. Albrecht --------------------start par------------------------------ 019ba3 { ; Expander ; Time 0.20.04 ; fractal training device ; source Lee Skinner ; Image Albrecht Niekamp ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_ni ismand=y function=exp/exp/exp passes=t center-mag=-1.57088265758921400/+0.15471848579516250/143\ 399.1/1/95.0000000000226237/3.88578058618804789e-016 params=-0.8940855128635518/0.8105868709372235/384.00001/\ 256.1133/4094.00016/768.0003400000001/768.0076800000001/\ 256.01024/18937.52/5 float=y maxiter=3072 inside=maxiter outside=tdis logmap=yes symmetry=none periodicity=0 rseed=-2436 colors=000000Aaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<\ 2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6\ ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS\ 5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3D\ N2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1\ or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7\ c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rwz\ ovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1Q\ A1NA1<3>D92<6>UXAW`BYcC<3>hrI<6>JkgFfp } -----------------------start frm--------------------------- FRM:multifractal_ni { ; Albrecht Niekamp 24.3.03 ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect by S.Gallet d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave 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)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

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Two Left Turns
by Mike Frazier 25 Jun '11

25 Jun '11

I did some more exploring in the Bristling Energy fractal. The name Two Left Turns came from the process I used to find the image. I made two left turns when I chose the path to zoom into. The two left turns added the two octagons to the fractal. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/two_left_turns.html The parameter file used to make the image is below: Two_Left_Turns { ; Exported from Fracton. ; time = 5 min 42 sec at 640 x 480 with no aa ; on a Mac Pro 2 x 2.8 Ghz Quad-Core Xeon reset=2004 type=mandel passes=1 float=y center-mag=-0.126245138931413858672422416646500180\ 6066151164938915275145862382678838012749e1/0.40833\ 58177658692924030543625981883443850512333421119460\ 012321903238149605257/7.58518528e+65/1/0/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=12000 inside=135 logmap=6951 proximity=0 colors=80G80G80G80G80H80H80I81I71I71J71J72J72J72K6\ 2K63K63L63L63L63M54M54M54M54N55N55N45O45O46O46P46P\ 46P37P37Q37Q37Q37R38R28R28S28S29S29S29T19T1AT1AU1A\ U0BV1CV2DW4EW5FX6GX7HY9IYAJZBKZCL_EM_FN`GO`HPaJQaK\ SbLTbNUcOVcPWdQXdSYeTZeU_fV`fXagYbgZch_dhaeibfibfi\ cgjdhkfikgjlhkljlmkmmlnnnpnoqoprorspqropqnopmnnllm\ kkljjkiiighhffgeefdddcccbaba`a`__ZZZYYYXWXWVVVUUUT\ TTRRRSSSUUUVVVXXXYYY___aaabbbdddeeeggghhhjjjkkkmmm\ <9>zzx<9>wrg<2>ujS<4>q`9<5>lT0<5>fM1<4>`F2<3>U83<1\ >O13ujS<1>q_9<2>lT0<2>fM1<2>_F2<2>U83O13ujSq_9<1>k\ T0<1>fM1<1>_F2<1>U83O13ujS<1>q_9<1>lT0<1>fM1<1>_F2\ <1>U83<1>O13<3>ujS<6>q_9<3>kT0<3>fM1<3>_F2<3>U83<3\ >O13<2>zzz } -- Mike Frazier www.fracton.org

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Multifractal_10 (Islands in the Sun)
by Albrecht Niekamp 25 Jun '11

25 Jun '11

Hi, another new and original image, unique shapes and "pseudo 24bit" colours. Lots of zooming spots. Have fun! Albrecht -------------------------start par------------------------- 20105a { ; Islands in the Sun ; Time 0.52.39 ; Mandel-secant-mmods ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-1.24239/0.0032193/2.971136/1.1324/90/-1.2337\ 3533611470521e-014 params=-0.05825983458967864/0.3785210730307932/20105.035\ 64960102/25234.2207090221/151024.0204808192/384.32768524\ 288/384.00482000595/128.1007683001/256.1007683001/256.20\ 07683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=n0B00z<78>vv4ww3ww2<2>zz0zz0zy0<77>z40z30z20z20z1\ 0z00<9>s07r08q08<3>n0Cm0Dl0E<59>50u40v30w<3>00z000 }

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Re: [Fractint] FOTD 14-06-11 (Tsunami-Plus [8])
by Brian Prentice 24 Jun '11

24 Jun '11

Here are four more details from this amazing fractal: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20e.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20f.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20g.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20h.png Brian Prentice

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FOTD 24-06-11 (Everyday Mandelbrot [6])
by Jim Muth 24 Jun '11

24 Jun '11

FOTD -- June 24, 2011 (Rating 6) Fractal visionaries and enthusiasts: The FOTD image for today lies on a filament moderately deep in the northeast period-5 radical of the classic Mandelbrot set. It is an everyday scene in the set, which is why I named it "Everyday Mandelbrot". The rating of a 6 is modest, and in fact it could even be excessive for such an everyday scene. I did put some extra effort into the coloring, though not enough to add the usual half-point reward to the rating. The top feature of the image is its lightning-fast calculation time of 1+ second. This incredible speed is a result of the super-fast type=mandel algorithm, with the exact time probably being determined mostly by factors other than pure processor speed. There is not much more to be said about today's FOTD except to remind those who do not run parameter files that the finished image is available 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/> Thursday began with a light shower here at Fractal Central. The rain ended by 10am but the clouds and humidity hung on for the rest of the day. The fractal cats languished in the temperature of 86F 30C, but found enough energy to ask for food. The humans had another typically uneventful day. The next FOTD image will be posted in 24 hours. Until then, take care, and never forget that the golden rule works both ways. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= EverydayMandelbrot { ; time=0:00:01.21-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.4465882667194\ 553/+0.3715210822167352/3.768528e+010/1/-175/0 params=0/0 float=y maxiter=3200 inside=0 logmap=224 periodicity=6 mathtolerance=0.05/1 colors=000HAKIAKJAKKAKLAKMAKNAKOAKPAKQAKRAKSAKTAKU\ AKVAKWAKXAKYALZAM_AN`AOaBPbCQcDRdESeFTfGUfHVeIWdJX\ cKYUPSKKNABH000BE68FFAIGCLHEOIFRJHVKJZLLbMNfNRjOWn\ PaoQdsRhvSmxTmzUmvXhrZcm`ZhbVcdS_fRWhQSjPOlOKnNGpM\ CrM9tPCnSEiVIcYLZaOTeSOiVIkXDhUFeRHbOJZLLXINVGPSER\ QCTOAVM8XK6ZO4`U2bc3Zm4Vz5Rz6Nz7Jz8GiMSX_cLlnLdpKa\ nJ_mIYkHWjGTiFRgFPfENeDLcCIbBGaAE_9CZ9AY8CX8EW8GV8\ HU7JT7LS7NR7OQ6QP6SO6UN6VNE_KMcIThF`lDbpBcnDdmFelH\ fkJgjLhiNigOjfQkeSldUmcWnbYoaZpb`qbbrccwcewdgwdhwe\ jvelvfmvfovfpuenteltejsehsdfrddqdbqd`pcZpcXocVocTl\ eRjfQhhOeiNckMalKZnJXoHVqGSrFPtDSuCUvBWwFYwI_wLawO\ cwRewUgwXiw`kwcmwfnwiowlpwoqwrrw`svJtuOutSvsWwr`wq\ dwphwogwnfwmewldwkcwjbwiawhawg`wc_wb_waZw`Zw`Ww`Tw\ `Qw`Nw`Lw`Iw`Fw`Cw`9w`7xa9yaAzaBzaCzbDzbEzbFzbGzcH\ zcIzcJzcKz`LzZMzWNzUOzSPzWDzZ1zX3zV4zT5zS6zQ7zO8zN\ 9zLAzJBzICzHFzTLzYNzbPzfR } END PARAMETER FILE=========================================

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Re: [Fractint] minibrotz
by JackOfTradeZ＠comcast.net 23 Jun '11

23 Jun '11

. "Is it possible to determine from looking at the image where the minibrots are located?" I dont know if there is a rigorous scientific method, but after staring at these things for years you tend to get an "intuitive feel" for it. .

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Multifractal_10 (Necklace)
by Albrecht Niekamp 23 Jun '11

23 Jun '11

Hi, a new image today, created with only 3 of possible 5 formulas. Multifractal_10 is already available. Note: Dont shut off, generation is visible after some minutes! Albrecht --------------------------------start par----------------- 20705a { ; Necklace ; Time 39.15.00 ; Mandel-newton-mmods ; Image-frm-colours Albrecht Niekamp ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=cos/exp/exp/sin passes=t center-mag=-0.413195/0.0032193/8.572457/1.1324/-90/-1.23\ 373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/20705.035\ 64960102/25234.2207090221/151024.0204808192/384.32768524\ 288/384.00482000595/128.1007683001/256.1007683001/256.20\ 07683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=00040C<3>50G50H00E<2>A8TEHaIQj3Yqbe_FYI0L0<3>yrB<\ 3>yB3z00t60<3>UY0Nd0Gk0<2>ns1zz0<3>zI4z66w67<3>h3Fe2Ha1J\ Y0L<3>t8qzAzuAv<3>ZEdTE`OFX<2>6IJ<3>YcMdiMknNrtOzzP<3>`_\ QVTQOMRIFRB8S<3>8Yk7dp6ku5rz<6>7_g7Xd7Ub<3>9IR<10>7fA7i8\ 6k7<3>5u0<3>5c05Z05U0<3>5B0<3>UY0`b0fh0<2>zz0<9>jU1iR2gO\ 2<3>`A3<16>q8Ar8As8At8Bu8Bw7Cw8Cv8Dv9E<7>xA_xBayBd<2>zCm\ zCmzCmzzzYXc<3>JhnFkqBnt7qw<15>KGaLE`MBZ<3>Q1T<4>bGZdK_g\ N`<3>r_f<3>ggPeiKbkF<2>Uq1Xq2_q4<8>40B40B }

2 1

FOTD 23-06-11 (Crack in Ringworld [8])
by Jim Muth 22 Jun '11

22 Jun '11

FOTD -- June 23, 2011 (Rating 8) Fractal visionaries and enthusiasts: When I wrote the description of the 'On the Wrong Track' image of June 21, I assumed that when the sequence of elements switches to order-7, the series increases in powers of 7. But when I checked, I found that the series actually grows by doubling the 7 elements, making a 7,14,28... sequence. My hasty error, which was first noticed by Hal, is made obviously clear in today's image, where the continued doubling of 7 is quite apparent. The scene is the area immediately surrounding the central minibrot of the June 21 image. I have intensified the colors to bring out the background pattern, where smaller order-7 minibrots fill the scene to infinity. Unfortunately, the magnitude of the image is at the limit of resolution, and these smaller minibrots are mostly beyond reach. The rating of an 8 includes a generous full-point reward for my coloring work, which I admit did make use of another program, but also manages to bring out some otherwise almost invisible inner detail and fills the screen with rarely seen shades of intense blue. The name "Crack in Ringworld" gives recognition to one of my favorite sci-fi series. It also refers to the crack in the expected smooth 'powers of two' sequence. The calculation time of just under 5 minutes is a bit on the slow side. Boredom may be held at bay however by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and by viewing it in high-definition 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/> A typical summertime day passed uneventfully here at Fractal Central on Wednesday. The temperature of 88F 31C was a little too warm for total comfort, while the clouds were a little too prevalent for sun lovers. The forecast of numerous showers proved to be a scare tactic, as not a single drop of rain fell. The fractal cats alternated between taking it easy and chasing each other up and down the hallway. The humans had a typical uneventful day. The next FOTD will be posted in 24 hours. Until then, take care, and Atheism is doomed to forever remain an unconfirmed philosophy. (Just like Theism?) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Crack_in_Ringworld { ; time=0:04:54.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.1962128361703373/+0.6526484177635142\ /6.174367e+012/1/-51/0 params=7/1e+017/0/0 float=y maxiter=7200 inside=0 logmap=415 periodicity=6 mathtolerance=0.05/1 colors=000zz05Nb5Nb5Ne5Ne5Ng5Ng5Ng5Nj5Nj5Nl5Nl5Nl5\ No5No5jo5jqzzzzzzzzzzzzzzyzzxvzwpzvhzubztPzsKzoFzj\ GzeSxGNuEIsCGoCCg99`75X73S50N30I30E109005001000000\ 00000000000000000000000000100300500710910C10E30G30\ I50I50L50N70N70P90P90SC0VC0VC0XE0XE0ZG0`G0`G0bI0eI\ 0eL0gL0gL0jN0lN0lP0oP0oP0sS0sV0uX0uZ1x`3x`5zb7ze9z\ gCzjGzjLzlPzoXzq`zsezsjzuoxxsuzxszzqzzqzzqzzqzzqzz\ qzslzjgz`bzPZzGVz7Sz0Nz0Iz0Ez09z09z07z07z0Xz0hz0Xz\ 0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0hz0Xz0h\ z0Xz0hz0Xz0hz0Xz0oz0Xz0hz0Xz0hz0Qz0Qz01k01k01a00z0\ 0k00a00k00k00a00a00z00k10a10k10a10a10X10k10k10a10k\ 10i10f10d10d10b10`10Y10T10W10T10T10e10b10`10`10Z10\ X10X10V10S10S10P10P10N10N10L10LN0zN0GN0zN0Ej0zj0Cj\ 0zz09z0zz07zjzz05z0zzj3z0zzj1z0zzj0z0zzj5z0zz0Izjz\ z0Xz0zzjjz0zz0uz0zzjxz0zzjxz0xzjxz0xzjxz0xzjxz0zzj\ zz0zzjzz0zzjzz0zzjzzS`zjb } 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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Lee Skinner MFR zooms
by Albrecht Niekamp 22 Jun '11

22 Jun '11

Hi, I love this one because it keeps you watching. Albrecht -------------------------start par------------------------- Jrula2 { ; Jrula2 ; structures+overlays+partial symmetry ; frm+image Albrecht Niekamp ; source+colours Lee Skinner ; time 11.29.00 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal ismand=n function=exp/exp/exp passes=t center-mag=+1.09441249371272300/+0.21759644730115380/76.\ 36852/1/-102.499999999999915/-3.17669501814776822e-013 params=-0.1740997192297128/-0.2996141087069308/384.00004\ /256.1106/2048.00016/768.00009/768.01536/256.01025/28424\ .5/12 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000t2tv2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>\ zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA\ 0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfp\ Aaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<2>zzz<3>jqdfo\ _blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBi\ ODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6\ <10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G\ 0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<5>s1or2qs2r } ----------------------------start frm---------------------- Frm:multifractal { ; Albrecht Niekamp 24.3.03 ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave 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)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

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FOTD 22-06-11 (In-Depth Examination [7.5])
by Jim Muth 22 Jun '11

22 Jun '11

FOTD -- June 22, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a scene lying very deep in the north shore line of the main bay of the Mandelbrot set, just west of the large northern bud. Yes, I realize that it is a spiral, and I'm not supposed to like spirals, but the image is worth at least one quick glance. The name "In-Depth Examination" refers to the image's magnitude of 6*(10^28). That same magnitude makes the image a slow one however, so don't expect instant gratification if you decide to run the parameter file. I could rate the image no higher than a 7-1/2, since it lies in the Mandelbrot set, the most over-explored of all fractals. The rating of a 7-1/2 includes 1/2 point for my coloring effort. Perhaps I should have rewarded myself only 1/4 point. On second glance the coloring appears to be not all that great. To avoid spending the better part of an hour running the included parameter file, check the finished image posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is posted in high definition 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/> Heat, haze and humidity made Tuesday rather stifling here at Fractal Central. When the temperature reached a high of 88F 31C the fractal cats shifted into summer mode and stretched out on the cool tile floor. The humans took things pretty much in stride. The next FOTD will be posted in 24 hours. Until then, take care, and may the guardians of the universe rush to your aid whenever you need it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= InDepthExamination { ; time=0:50:47.98-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.1956331366108\ 86566268009760456792/0.653501797677887321513464499\ 778281/6.236299e+028/1/77.5/0 params=0/0 float=y maxiter=12500 inside=0 logmap=3025 periodicity=6 colors=0002273374475676887A99CAAEBBHCDLDEOEFRFHVGI\ YHJ`ILdJMgKNjLNhMNgMNfNNeNNcONbONaPN`PNZQNYQNXRNWR\ NUSNUSOWTPYTQ_SRaRScQTeQUfLVgHWhJXiLYkNZlP_nR`oS`p\ U`oW`mY`k_`ia`gb_edadjcdmeamgZmiXmkUmlSmmPmnMmnKmo\ HmpFmqCmq9mr7ms4ms2mr4mq6mp8moAmnCmmEmlFmfGi`GeVGb\ PGZJHVDHS7HO2HL7GMBGMFGNKGNOGNSFOWFO`FOdFPhFPlFPmH\ UmIZmKcmLhmNmmOqnSpoVppZpqaprdpshptkpunpvrpwupwxpt\ uqqsqopqlnrjkrgiregrbds_bsY_sVYtTVqQTnOUkYVhZVe_Wb\ _T_XQXVNUTKRQHONEMKCLF9KE7KO5KZ4KhzcfncugEtaJtXOzm\ csMYmHb`CQK7KP8Sc8`i8_o8WzUSvJXn8Vh8Tb8RY8UU8XTEQT\ JUTOYTTXTYRTgLcpFms9zzCmmEccGUXIKTKAPM7LO4IQKDKT3H\ ZAEZHBZO8ZV5ZamVemSimOmmLqmHumEwmAkW6Z28QG9HUA8g8A\ h7Ci6Ej4Gk3Il2Kl9MmGOmNQmTSm_UmzWmzYmz_mzc9zfDziGz\ lJzoMzqPzmEzmCzmAzm9zm7zm6zm4mz3mz4mz4mz5mz5mzAmzF\ mzKmzzmzzmzzmzzmzzmzzmzzmzzEzzEzzEzzFzzFzzFzzOzzSz\ zVzzYzz`zzPzzOzzOzzNzzNzz } END PARAMETER FILE=========================================

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Lee Skinner MFR Images
by Albrecht Niekamp 21 Jun '11

21 Jun '11

Hi, this is the second zoom into one of Lee´s images - and....judge yourself! Albrecht ------------------------------start par-------------------- galla2 { ; galla2 ; time 19.07.00 - be amazed! ; frm+zoom albrecht niekamp ; source+colours lee skinner ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_1 ismand=y function=exp/exp/exp/exp passes=t center-mag=+1.02131581270836200/+0.00006507034526879/217\ .751/1/-90/-1.23373533611470521e-014 params=-0.1738944669942329/-0.3000579851680044/384.00004\ /2048.1133/768.00008/768.00128/1024.00256/1536.01024/189\ 22.01/0.32 float=y maxiter=2048 inside=maxiter outside=tdis logmap=yes symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000uxxwyyzzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8\ CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>hr\ I<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>z\ z1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>\ TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY\ 4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H\ <3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1\ mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7\ `c7aa7c_7eY<3>FcgHciJbl<3>S_v<5>invlqvotvsww } -------------------------------start frm------------------- Frm:multifractal_1 { ; Albrecht Niekamp 270503 ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif ba=trunc(d) d=round((d-ba)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) mi2=trunc(d) b2=(d-mi2)*100000 ; d=imag(p3) fac2=trunc(d) ob2=(d-fac2)*100000 ; d=real(p4) mi3=trunc(d) b3=(d-mi3)*100000 ; d=imag(p4) fac3=trunc(d) ob3=(d-fac3)*100000 ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) dd=dd-d*1000 or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) d=trunc(dd/100) dd=dd-d*100 or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) d=trunc(dd/10) dd=dd-d*10 inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) inr2=dd>5 dd=dd-inr2*5 v3=(dd==3) v4=(dd==4) d2=(dd==2)+(dd==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) mm=round((d-dd)*100) da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) ; if (ismand) z=0 if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else c=p1 z=pixel endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn4(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if (bo>b1) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2&&bo<ob2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3&&bo<ob3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

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FOTD 21-06-11 (On the Wrong Track [8])
by Jim Muth 21 Jun '11

21 Jun '11

FOTD -- June 21, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is definitely on the wrong track. It lies in the western branch of North Valley of its parent fractal, which on the surface is an un-notable Mandelbrot set. When we start at the surface of this parent, all is as it should be, with the spirals like seahorse tails that would be expected in this area. But by the time we reach the depth of the first minibrot, we find that something has gone wrong. The minibrot has become a disorganized mess rather than the well-defined quadratic midget that would be expected. The inside of this fractal mess is filled with piles of debris however, and in this debris some strange things are happening. Checking one of these debris piles, we find it is an area of anti-bifurcation filled with more seahorse tails. Today's scene lies in one of these tails. Around its edges, today's image presents no problems. It consists of everyday quadratic stuff with the expected 4,8,16... series of elements. But about halfway in, things go terribly awry, and the sequence resets itself to the order-7 series of 7,49,343... When we reach the central minibrot the surprises continue. Instead of a quadratic minibrot we find a full-blown order-7 one, with 6 lobes, surrounded by an area holding a legion of smaller similar minibrots. The reason for all this craziness is known only by the gods of numbers, and they are not revealing their secrets. As for myself, I see simply another fractal surprise in a world where there are so many surprises that the surprises are in danger of losing their ability to surprise. The rating of an 8 includes a half point or so of optimism. The name "On the Wrong Track" describes the 'wrong' minibrots cluttering the center of the image. The calculation time is an eminently reasonable 2-4/5 minutes. The finished image is posted for maximum convenience 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 original classic FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Monday brought too many clouds for perfection, but it remained dry, and the temperature of 82F 28C was near perfect. The fractal cats had a reasonably peaceful day, though at one point I heard Cassie cussing at Nicholas. The humans had an equally peaceful, but dull day. The next FOTD will be posted in 24 hours. Until then, take care, and if we didn't have all those fantastic wireless internet devices, how would we communicate? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= On_the_Wrong_Track { ; time=0:02:49.16-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.1962128361703378/+0.6526484177635086\ /8.891464e+011/1/-7.5/0 params=7/1e+017/0/0 float=y maxiter=3600 inside=0 logmap=339 periodicity=6 mathtolerance=0.05/1 colors=000qBkqElqHmqKnqNoqQpqTqrWrrZsratrdurgvrjwr\ lxrlxpktmhqjdng`keXhbTd_PaYLZVHWTETUDOVCKWCGXBCYA8\ ZC4`D6aG8cH9dKBfMCgOEhQGjSHkVJmXKnZMo_NkZQhWTeTVaR\ YZO_WMbTJePHgMEjJClG9oC7r94t62w30y25t29p2Dl2Ih2Mc2\ Q_2UW1ZS1cO1gJ1lF1pB1s71t3BsFLoRVlbdhnmeyjfveksapp\ dpogpnkolnokonjpllpjmognoeonbqn`smYumWwkXxiXygXzfX\ zdXzbXzaXz`Wz_VzZUzYTzXSzWRzVQzUQzTPzSOzRNzQMzPLzO\ KzNKzMIzMHzMGzMFzMEzMDwMCtMBqL9nL8kL7hL6eL5bL4_L3X\ L2UK3RJ3OI3LH3IG3FF4EE4CD4BC4AC49G6CJ7EN8GQ9IUAKXB\ M`CPcDRgETjFVnGXqHZlQ_hY_de``j`Xl_UnYRmWPjTMfRKcPH\ _MFXKCTHAPF7KD5GA2B80761982BA3DB4FD5HF6JG7KI8LK9ML\ ANNBOOAQQ9RR9SS8TT8UU7VV7WW6XX6YYKZZK__U``Uaacbbcc\ cmecmgcziczkbzmazo`zq_zsZzuYzwXzx_zgWzSTzNUzIVzDWz\ 8Xz9YQAZSB_UC_VD`XEaZFa`GbbHccIdeJdgKeiLfjLfhMggNg\ fOgePhdQhcRhbSiaTi`Ui_VjZWjYXjXYkWZkV_kWaiWchWegXg\ fXheXjcYlbYnaYp`Yq_p5idVj } 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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Bristling Energy
by Mike Frazier 20 Jun '11

20 Jun '11

I was doing some deep zoom exploring in the Mandelbrot set and stumbled across an area that had a minibrot with straight meandering arms and electric looking tendrils. Out of curiosity, I zoomed into some of the deeper minibrots near the original minibrot and compared the image to the original. Is it possible to determine from looking at the image where the minibrots are located? Is there any way to know how each minibrot will differ from the original? Here is a link to a web page with the original image and links to more pages of what I found: http://www.fracton.org/fmlposts/bristling_energy_p1.html The parameter file used to make the original image is below: Bristling_Energy { ; Exported from Fracton. ; time = 32.2 sec at 640 x 480 with no aa ; on a Mac Pro 2 x 2.8 GHZ Quad-Core Xeon reset=2004 type=mandel passes=1 float=y center-mag=-0.126245138931413858672422416646502888\ 500881791e1/0.408335817765869292403054362598174616\ 49786835564/2.22222225e+31/1/0/0 params=0/0/0/0/0/0/0/0/0/0 maxiter=4000 inside=1 logmap=1034 proximity=0 colors=80G80G80G80G80H80H80I81I71I71J71J72J72J72K6\ 2K63K63L63L63L63M54M54M54M54N55N55N45O45O46O46P46P\ 46P37P37Q37Q37Q37R38R28R28S28S29S29S29T19T1AT1AU1A\ U0BV1CV2DW4EW5FX6GX7HY9IYAJZBKZCL_EM_FN`GO`HPaJQaK\ SbLTbNUcOVcPWdQXdSYeTZeU_fV`fXagYbgZch_dhaeibfibfi\ cgjdhkfikgjlhkljlmkmmlnnnpnoqoprorspqropqnopmnnllm\ kkljjkiiighhffgeefdddcccbaba`a`__ZZZYYYXWXWVVVUUUT\ TTRRRSSSUUUVVVXXXYYY___aaabbbdddeeeggghhhjjjkkkmmm\ oooppprrrsssuuuvvvxxxzzzzzyzzxzzwzyuzxsywryvpyunxt\ lxskxsiwrgwqewpdvobvn`vmZulYukWukUujStiRthPtgNsfLs\ eKsdIrcGrcErbDqaBq`9q_7pZ6pY4pX2oW0oW0nV0nU0mU0lT0\ lS0kS0jR0jQ0iQ0iP0hO1gN1gN1fM1eL1eL1dK1dJ1cJ1bI1bH\ 1aH1`G2`F2_E2ZE2ZD2YC2YC2XB2WA2WA2V92U83U73T73T63S\ 53R53R43Q33P33P23O13N04N04M05M05L05L06L06K06K07J07\ J07I08I08I08H09H09G09G0AF0AF0AF0BE0BE0BD0CD0CC0DC0\ DB0DB0EB0EA0EA0F90F90F80G } -- Mike Frazier www.fracton.org

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Lee Skinner MFR Images
by Albrecht Niekamp 20 Jun '11

20 Jun '11

Hi, after some weeks on the mail I finally received Lee´s Multifractal DVD and it´s definetely worth waiting for. All images were created using the preliminary stages of my multifractal formula as it developed in 2003. The smaller part are zooms into images I posted that year but using Lee´s colours. The bigger part he created zooming out into total view and then zooming in again. I will post some own zooms mostly using Lee´s colours and some own new images. The images are posted together with the frm used; as it is not compatible with the final stage it should be used only for calculation of that image and therefore has no input possibilities. Only images created using multifractal_10 are compatible with the frm you have downloaded, there were no changes in the code. Albrecht ---------------------Start par---------------------------- Ascp14a1 { ; Ascp014a1 ; colours and image ; by Lee Skinner ; zoom and frm ; Albrecht Niekamp ; Time 21.03.00 ; Fractint Version 2004 Patchlevel 11 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal ismand=y function=exp/sin/exp passes=t center-mag=-1.36397552835101600/-0.74493857542845080/916\ 23.65/1/130.000000000123777/4.68308725132260406e-011 params=-0.1740997192297128/-0.2996141087069308/384.00004\ /256.1106/4096.00016/768.00009/768.01536/128.01025/28984\ .5/0 float=y maxiter=2048 inside=maxiter outside=tdis logmap=10 symmetry=none periodicity=0 rseed=-2436 cyclerange=2/255 colors=000000Aaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<\ 2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6\ ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<8>zY4zV5zS\ 5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3D\ N2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1\ or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7\ c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rwz\ ovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1Q\ A1NA1<3>D92<6>UXAW`BYcC<3>hrI<6>JkgFfp } --------------------start frm------------------------------ Frm:multifractal { ; Albrecht Niekamp 24.3.03 ; d=real(p2) fac1=trunc(d) b1=(d-fac1)*100000 ; d=imag(p2) da=d<0 if (da) d=-d endif mi1=trunc(d) d=round((d-mi1)*10000) p6=trunc(d/100)/10 d=d-1000*p6 if (da) p6=-p6 endif p7=d/10 ; d=real(p3) ba=trunc(d) mm=round((d-ba)*100000) ; d=imag(p3) fac2=trunc(d) b2=(d-fac2)*100000 ; d=real(p4) mi2=trunc(d) fac3=round((d-mi2)*100000) ; d=imag(p4) b3=trunc(d) mi3=round((d-b3)*100000) ; da=real(p5) t=da<0 if (t) da=-da endif start=2-t dd=trunc(da) da=round((da-dd)*100) if (dd<5) start=0 vb=(dd==3)+(dd==4) else d=trunc(dd/10000) vb=(d==3)+(d==4) dd=dd-d*10000 d=trunc(dd/1000) or1=d>5 d=d-5*or1 vv1=(d==3) vv2=(d==4) dd1=(d==2)+(d==4) dd=dd-d*1000 d=trunc(dd/100) or2=d>5 d=d-5*or2 vv3=(d==3) vv4=(d==4) dd2=(d==2)+(d==4) dd=dd-d*100 d=trunc(dd/10) inr1=d>5 d=d-5*inr1 v1=(d==3) v2=(d==4) d1=(d==2)+(d==4) dd=dd-10*d d=trunc(dd) inr2=d>5 d=d-5*inr2 v3=(d==3) v4=(d==4) d2=(d==2)+(d==4) endif ; d=trunc(da/10) da=da-10*d ab=d>=5 d=d-5*ab bb1=(d==1) bb2=(d==2) dd=da>=5 da=da-5*dd ab=ab+dd ab1=(da==1) ab2=(da==2) ; d=imag(p5) dd=trunc(d) d=round((d-dd)*1000000) le=d>10000 da=trunc(dd/10) so1=((da==1)+(da==3)==0) so2=((da==2)+(da==3)==0) dd=dd-10*da wo=dd>=5 dd=dd-5*wo ir1=(dd==1)+(dd==3) ir2=(dd==2)+(dd==3) if (le) freq=round((trunc(d/10000))*10) ;frequency_lake effect d=d-freq*1000 level=(trunc(d/100))/100 ;water level d=d-level*10000 ampl=d/100 ;amplitude of the wave 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)) d3=2*q*t rs=2*bo*(dd+flip(1))*t z2=center+(-q-bo*dd-flip(bo))*t z=pixel-z2 d=imag(conj(d3)*z)/imag(conj(d3)*rs) if (d<=level) da=level-d z=z+2*da*(1+ampl*sin(freq*da^0.2))*rs endif z=z+z2 endif if (ismand) if (vb) c=0.4*log(sqr(pixel^mm)) z=z*le else c=z*le+pixel*(le==0) z=0 endif else c=p1 z=z*le+pixel*(le==0) endif t=0 d3=(ismand==0) u=d3 : if (vb) if (d3) z=(z*z-real(c))^(z*u+imag(c)) else z2=fn1(z)+c ;Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (ab) z=z*z+c+c*c-p7 ;Pusk s Istv n elseif (d3) z2=z*z z=z2*z2+(p6+u)*z2+c else z2=z*z ;Pusk s Istv n z=z2*z2+(p6+u)*z2+c-p1 endif bo=|z| If (wo) t=t+1 if ((t<mi1)+(bo>b1)) u=2*(fn1(t/fac1)) if (ismand) z=z*u if (vb) c=0.4*log(sqr(pixel^mm)) else c=z*le+pixel*(le==0) endif else z=z*le+pixel*(le==0) c=p1*u endif wo=0 if (ir1) t=0 endif endif elseif (start) t=t+1 if (start==2) if (bo>b2) u=2*(fn2(t/fac2)) rs=or1 ab=bb1 if (dd1) if (rs) z=pixel endif c=p1*u vb=vv2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=1 endif elseif (t>mi2) u=2*(fn2(t/fac2)) rs=inr1 ab=ab1 if (d1) if (rs) z=pixel endif c=p1*u vb=v2 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v1 if (vb) if (so1) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=1 if (ir2) t=0 endif endif elseif (bo>b3) u=2*(fn3(t/fac3)) ab=bb2 rs=or2 if (dd2) if (rs) z=pixel endif c=p1*u vb=vv4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=vv3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif start=0 endif elseif (t>mi3) u=2*(fn3(t/fac3)) ab=ab2 rs=inr2 if (d2) if (rs) z=pixel endif c=p1*u vb=v4 d3=vb else d3=0 z=z*u c=z if (rs) z=0 endif vb=v3 if (vb) if (so2) mm=mm+mm endif c=0.4*log(sqr(pixel^mm)) endif endif start=0 endif endif bo<=ba }

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FOTD 20-06-11 (Pulverized Petals [8])
by Jim Muth 20 Jun '11

20 Jun '11

FOTD -- June 20, 2011 (Rating 8) Fractal visionaries and enthusiasts: I might have been a bit liberal when I rated today's image at an 8, but I do rather enjoy the colors, even though they were created more by the Fractint program than the fractal artist. The image is a scene in the main stem area of a Mandelbrot set caught about 2/3 of the way morphed into an order-9 Mandeloid. I named the image "Pulverized Petals" because that's what came to mind when I first saw the colors. Despite the brevity of this discussion, the image is actually a rather pleasing one, and with its calculation time of just over 1 minute, quite a bargain. Those who do not run parameter files may find the finished image posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Check for the high definition version of the image at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And check the original FOTD web site at: <http://www.Nahee.com/FOTD/> Near perfect weather conditions prevailed here at Fractal Central on Sunday, making life pleasant for cat and human alike. The cats spent much of the day sleeping and the rest of the time watching the world pass by, while the humans took it easy in the typical human way. Otherwise, nothing of note happened. The next FOTD will be posted in 24 hours. Until that glorious moment arrives, take care, and what a freak of nature is we. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Pulverized_Petals { ; time=0:01:06.57-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=-1.625965108406691/+0.00200616428920929\ /1.931447e+009/1/-130/0 params=9/100000000000.0/0/0 maxiter=1800 inside=0 logmap=75 periodicity=6 colors=000zzrzzmzzhzzczzZzyUzxPzwKzvFzuFztEzsEyrCy\ qCypCyo9yn7ym5yl2xk1wi1wg0xe0yc0xa0x_0xY0wW0wU0wS0\ sQ2oO4kN6gM8cLB`KDYJFVIGSHIPGJMFKJEIGDGECDCADA9D98\ D96D85D84D72D72D79D9DBAGACL9DV8Eb7GiGHqPIxZJtPJpFJ\ lMKhMKdNKaOLYOLUPLQQMMQMJRMFSNBSN7TN3UN0UL0SK0QJ0O\ I0NH0LG0JE0HD0G000C0EB0CA0A90980760550340230020010\ 0zP0sM0mK0gH0`F0VC0PA0I70C50620xaYsZVoWSjTPfRMbOKY\ LHUJEQGBLD8HA6D83850420V2lT1iR1fP1cO1`M1YK1VI1SH1P\ F1MD0JC0GA0D80A607504301100xDKU679K1Q0WN0SL0PJ0MH0\ JF0GD0DA0A807604401200wKFqIDlGBfE9aC7WA5R94L72G50A\ 305109R58O47M36J25H14E04C0390270140020hLNcIK_GHVEE\ RCBMA9I86D63940420CuzBrzAozAlz9iz9zz8zz8zz7zz6zz6z\ z5zz5zz4zz4zz3zz2zz2zz1zz1zz0zzlzzhzzezzbzz_zzXzzU\ zzRzzOzzLzzIzzFzzCzz9zz6zz3zzqzznzzlzzjzzhzzezzczz\ azz_zzXzzVzzTzzRzzOzzMzzKzzIzzFzzDzzBzz9zz6zz4zz2z\ zOzzJzzEzz9zz4zzPzzMzzJzz } 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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FOTD 19-06-11 (Zero Equals Infinity [6])
by Jim Muth 19 Jun '11

19 Jun '11

FOTD -- June 19, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a quickie, a scene I found after only a 5-minute search in the parent fractal that comes about when 1.5 negative parts of Z^(-5.8) are combined with 3.6 negative parts of Z^(-1.6) before (1/C) is added on each iteration. This parent fractal is basically indescribable, though it may easily be seen by backing out of today's image. The name "Zero Equals Infinity" resulted when I felt a bit of disappointment over today's creation. When a zero or an infinity appears in a theorists math, it's usually a sign his theory is in trouble, just as my fractal for today was in trouble from the moment I found it. As a result of the image's shortcomings, I could rate it no higher than a humble but not disgraceful 6. The 'tdis' I applied to the 'outside' parts of the image helped a little, but not enough to raise the rating to the 7 that I strive for in all FOTD images. The dragging 42 minutes required to run the parameter file helps not at all, but salvation is at hand on the FOTD web site, where the image is posted, already calculated. The web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> To see the image in high definition, go to: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, with a temperature of 84F 29C and reasonable humidity, made Saturday quite a pleasant day here at Fractal Central. The fractal cats took things easy; the humans did the same. The next FOTD will be posted in 24 hours. Until then, take care, and the theory of (almost) everything may turn out to be nothing at all like we expect. (I will remove the mocking 'almost' from my description when the theory includes the conscious minds that are seeking the theory.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ZeroEqualsInfinity { ; time=0:42:11.38-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.4270338604367973/+1.228832738472935/\ 2.76106e+007/1/-77.5/0 params=-1.5/-5.8/-3.6/-1.6/\ 0/0/0/0 float=y maxiter=18000 inside=0 outside=tdis logmap=2939 periodicity=6 colors=000mzUTYRRbOOfLMkIJoFHsCLqEPpFToGXnH_mIYnMW\ nQUnUSnYQnaOndSgaWaZZWWbQTfJQiDNm7Kp1Hq5Fr9DsDBsH9\ tL7uP5vT3vX2pS1kO1eK1`F1VB1Q71L31K3AK3IK3RJ3ZJ3gJ3\ oZuyUwtPxoKyjFzeXuMnp3oj6pe9q`CrWFsRIsMKeQRTTYGXd3\ _kDUWNPGWK1XRDXXOYbZYhiYnttH_rhykjzdlzZnzSpzLrzFtz\ obCo_KoYRoWYoUdoSkoQrik3PpA5tG9nJCiMGdPJ_RMVUQQXTL\ _WGaZSU`cMbnEYcGTTIOIKJ7MNDJQJGUODXUA_Z7bXDeVJgUPj\ SVmQ`oPfmNalMYkKTiJPhHKgGG9_38`78`A8`E8`H7aK7aO7aR\ 7aU9cWBeYDg_FhaHjcJleLngMohTnV_mHfm4bj3_g2reaqfbqg\ bqgbphcphcpicpicimVbpNWsFQv7RoEShKSbQTWWTQaUJgUDmX\ Z6JNW6BtBAmGAfLA_PAUUANZAGcA9gA3aD5XF7SI9NKBIMCHVN\ GbYFjgKgdPdaUbZZ_XcXUhVRmSOrQMmOPhNScMV_LXVJ_QIbLH\ eHGgNFdSFbYF`bEZhEXmEVYcC_`A`Y9aV8bT7dQ6ihqihqgfoe\ dmVYaLRRAKG0E559CA4IHAHOFHUKH`QHgVHm_HPhb0pw2fm4Yc\ 5PVDRUKSUSTUZVUfWUmXUtYUuWRvVOvTMwSJwQHxPExOCbahWi\ YPrNKsCKt`KuVKvQKwLUxRczX } 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 18-06-11 (Harlequin Corner [7])
by Jim Muth 18 Jun '11

18 Jun '11

FOTD -- June 18, 2011 (Rating 7) Fractal visionaries and enthusiasts: With today's image we return to the warhorse MandAutoCritInZ formula and one of the near-infinite variety of fractals it creates. The image came about when I combined 1.5 negative parts of Z^(-5.8) with 3.6 negative parts of Z^(-1.6) and added (1/C) on each iteration to produce one of those indescribable double- negative parent fractals with multiple stacked bays and filaments terminating in rings. The image is located at the tip of a filament extending from a bud along the shore line of one of the bays. The excessive colors held the rating to a 7, but also inspired the name "Harlequin Corner". The 'corner' part of the name is a meaningless afterthought. The color palette is a random one created with one casual strike of the <enter> key. It needed no tweaking. After all, how can a random palette be tweaked to make it more random? The image is a very fast one, finishing in a lightning-fast 43 seconds on my P4-2000mhz unit. With the image being so fast, no one should have a reason not to run the included parameter file and enjoy the resulting happiness. For the convenience of those who do not run parameter files, the finished image appears on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version is posted 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/> A mix of sun and clouds, with more clouds than sun, made Friday a day that left room for improvement here at Fractal Central. The temperature of 81F 27C was close to ideal however. The fractal cats had a typical cat day. They awoke at daybreak, meowed for their breakfast, meowed for their dinner, and meowed for their evening treat. The humans, who sometimes feel like the cats' servants, had an otherwise uneventful day. The next FOTD will be posted in 24 hours, without a guarantee of prompt- ness of course. Until then, take care, and go out to protest actively or stay home and complain quietly. Regardless of what you do, nothing will change. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Harlequin_Corner { ; time=0:00:43.11-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.183710624218/+1.343487367273/1426025\ /1/-107.5/0 params=-1.5/-5.8/-3.6/-1.6/0/0/0/0 maxiter=1700 inside=0 logmap=119 periodicity=0 colors=000JBT95EYi8HN4mMJxIDU96BcakZO_QIOHCC861Pe0\ KZ0GS0CL08E047b28T16J14902NtLIhGDYC9M84B4wu8euzLTV\ ZZWzUzQQOLLKHHG`ZC888mm4pQ_CIk69OzLIeECL76ZAFH57tQ\ 2jL1aH1SD1J80940ywNnmJdcFVUBKK7AA3rEGR78l7Oc5KW4GO\ 3CG28814UNbPJWKFQFBJAFV5366Oz4A_3Fd25I129haBaz5Um4\ M`3FP27C1vQEnMCgJA_G8TD7M95E63731Wy4Pl3J`2Cc16C0JL\ nX2QQ1KJ1FD0A605wifnb_eWUYQOPJIHDC866Czz9jj6VV3FFf\ VDLF60_G0SC0L90E6073Ou_IfRCTI6E93FO17C1kiMN8DL78E4\ hSKlXOpaSsfWwk_zpcsqblrbesbZtbSubMvbXDxQAk465J7_D5\ O62CqQ1fK0WF0LA0A50L6VE4K72AG5e82LnEKKTxGNkCH_8BO4\ 5CH3UE2QC2MA1I81F61B4072034iE3bC2WA2Q81J61D40628aS\ ElxBcm9Wc7OU4GK28ATQIPMFLJDIGBED9Am67m43m26mo4mY2m\ HMmTEmJ7m9NmEFm97m4pmCmm8mm4mmXmzOmzGmz8mzYmzTmzOm\ zJmzEmz9mz4mzvmzjmzZmzNmzBmzzHzVTzsJz`9zIkzm_z`OzP\ CzCrzCgz9Xz7Mz4Bz2kzpezi_zbUzXOzQIzJCzD6z6UzlOzbIz\ TCzJ6z9Fz9Bz67z43z2bzuTzf } 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 17-06-11 (Three Strikes and In [8])
by Jim Muth 16 Jun '11

16 Jun '11

FOTD -- June 17, 2011 (Rating 8) Fractal visionaries and enthusiasts: With today's FOTD we take a brief break from the land of ultra- low exponents and check the land of mixed exponents. But have no fear, we'll soon return to the near-linear stuff. We check the parent fractal that comes about when a Mandelbrot set is caught about halfway through the process of morphing into a Z^(3.5) Mandeloid. This parent fractal resembles a Mandelbrot set with its head cut off and sprouting more buds and arms than an octopus. Today's scene lies in the area where Seahorse Valley of the Mandelbrot set once was located. The valley has long since been obliterated, but a bit of scattered debris remains in the vicinity. Today's image lies rather deep in some of this debris. I rated the image at an 8, and this time it *IS* because of the coloring, most of which came about serendipitously. (If I had created the colors myself, I would have awarded myself the standard half-point bonus and rated the image at an 8-1/2. The image is a fast one. To see it, run the included parameter file or visit the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Paul's original FOTD web site may be reached at: <http://www.Nahee.com/FOTD/> Thursday was spoiled by too many clouds here at Fractal Central, while occasional showers of rain made things even less pleasing. The fractal cats didn't worry about the clouds, though they seemed to approve of the temperature of 72F 22C, neither stretching out to keep cool nor curling up to keep warm. The humans had a typical mid-week day. The FOTD is now up to date, and unless an antiquing trip arises on Saturday, will remain up to date for the foreseeable future. The next one will be posted in 24 hours. Until then, take care, and did you hear about the Atheist who died and was surprised when he found out that he was right? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ThreeStrikesAndIn { ; time=0:00:57.95-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.7815581763978199/-0.0665776945443642\ /3.261242e+011/1/2.5/0 params=3.5/5/0/0 float=y maxiter=1800 inside=0 logmap=84 periodicity=0 colors=00010u10s10q30o40m50j60g70d80a90ZA1WA3TA5QA\ 7NA9KABHACCABDABD9AK6AK9FKBJUENUGRUJUcLZcOacQdmTgm\ VjmYkz_lzamzUSFUVGVXHW_IXaJYcKYfLYhM_jNamOcoPeqQgt\ RjvSmxTitReqPanNYjMUgKQdIM`HIYFEVDASC6RB4PA5N97L98\ J8AI7BI6DI6FI5GI4IJ3JI3LH2MG1OF0PF0RL5SRAUXEVbJXhN\ YnSZtWy1Ht4Kp7MlAOhDQdGS`JUXMWSPYOS_KVaGYcC`e8cg4f\ i0hk4jj8ljBmjFojJqjMrjQtjUvjXwj`yjczjfuliqnllpohrr\ ctu_ur`qp`mnaikaeibagbYecUbcQ`dMZdIXdEdSNlGWs4cs6d\ s7es9esAfsCgsDgsFhsGisHitJjtKjuMkuNkuPkvQlvSlvTlwV\ mwWmxYnxZnx`nyaoycoydozcczcSzYPzTMzNKzIHzCFz7Cw2Aw\ 39w49w58w58w67w77w86w86w95wA5wB4wB4wC3wD3wD3rEBmUJ\ cUQcUYcUdcUlcUzcczUczUczUczKczKczCmtCmuCmuDmuDmuDm\ uDmuDmuGmszmrzmqzmpzmozmmzmlzmkzzjzzizzgzzfzzezzdz\ zczz`zzZzzWzzUzzTzzTzzTzzSzzSzzSzzSzzRzzRzzRzzQzzQ\ zzQzzQzzTzzVzzYzz_zzbzzdzzgzzizzlzznzzqzzszzrzzqzz\ pzzpzzozznzzmzzmzzlzzkzzj } 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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FOTD 16-06-11 (Doomsday Descends [8?])
by Jim Muth 16 Jun '11

16 Jun '11

FOTD -- June 16, 2011 (Rating 8?) Fractal visionaries and enthusiasts: I'm still trying to get caught up, so today's discussion will be brief. The image is little more than a study, checking on the scenery that might actually lie down in these depths. Since the image is not actually a finished product, I needed to add the question mark to the rating of an 8. The rating is mainly for mathematical reasons. The artistic worth is merely average. The exponent of Z has once again been taken half-way to unity, all the way down to 1.0022, but at a level around 4.47 turns up the hyperladder, the parent fractal is anything but a featureless lopsided ellipse. In fact, the L-shaped parent fractal is more surprising than today's scene, which lies inside it. I named the image "Doomsday Descends". I would have added 'from the upper right' to the name, but there was no space to fit it in. Actually, the name is a comment about those ridiculous 'end of the world' and 'climate change' shows that fill the 'science' channels. Wow! They sure have me worried enough to bust out laughing. The drawback with today's image is its crawling slow calculation time of 1/2 hour. But to see the image already calculated and save a half hour or so, check the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> To see the image in high-definition try: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> Wednesday was a near repeat of Tuesday here at Fractal Central, with a few less clouds and a warmer temperature of 82F 28C. The fractal cats appreciated the added presence of the humans as well as the near-ideal outside conditions. At the same time, the humans had their own stuff to do, which was completed on schedule, making for an uneventful day. The next FOTD will be posted in about 8 hours. If it actually appears at that time, the FOTD will be caught up. Until whenever, take care, and if heaven isn't there when you get there, who would you accuse of false advertising? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Doomsday_Descends { ; time=0:30:27.15-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=+1.301632800620646/-3.838888125922276/\ 17269.51/1/70/0 params=1.0022/0/4.72765/800 float=y maxiter=5200 inside=0 logmap=-3360 periodicity=0 colors=0001R81M40H10C0080030040440B61G64M89R8CW9Gk\ MO`9JR0CS0ET0EV0GW1GY3H_6H`8Jb9JcBKeCKfEMhHMiJOkKO\ lMPnOPnPPkSTiVWfY_e`bbbe`chYckWWnTcqPOtPfwOGzKhzKS\ fMczOTnOcwOcteWWeWVeWShWRkWOlWMfWKfWHcWH`WGcWGcWEb\ WTcWScWPcWOc`KYYJ__JYYHWYHWWGVVGVTETTETSESSCSRCRPB\ ROBPO9PM9OK9MH8MG8KC6K96J64J44G14E03B0390160140040\ 040040010110100300400400600800811933B46B69C8CE9EEB\ GGEHHGJHGKJGMKGOKGPMGRO9_CGSOKKYRChV4r_0z`1zb3zc4z\ e6ze8zfBzhCziEziGzkHzlJznMxoOxoPxqRxrSxtVwtWwvYww_\ wx`wxbxiizWqzJxz4zz6zz6zzczzczzhzzmzzfzzczz9wz9wz9\ zzBvzBtzBrzCrzCqzCqzCozEozEnzElzElzGkzGkzGizGizHhz\ JfzJezKczMbxM`qO_lOYhPYeRWbRVcSTcSSeTReVPfVOfWMhWM\ hYOfYPeYRe_Sc_Tb_Vb_W``Y_`__``Y`bWbbVbbSbbPbbMc`Jc\ YGeSCeP9eM8cO9cOCbPEbPG`PJ`RK_RM_SOYSRYTSWTTWTWVVY\ VV_TWeTWiSWqSYxRYzR_zP_zP`zO`zO`zMbzMbzKczKczKhzKc\ zK`zKYzKTzKRzKOzKKzKGzKCz } 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 15-06-11 (Into the Depths [8])
by Jim Muth 16 Jun '11

16 Jun '11

FOTD -- June 15, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD image is late, but it's still worth the effort of a trip to the FOTD web site. In the image we venture ever closer to the point of total linearity. In fact, since yesterday's image we have gone half-way to unity. The value of the exponent in today's image is 1.0045, yet it still creates fractals with interesting detail. There must be something special about the point 4.45 levels up the log ladder when the 'recip' function is applied. Regardless of which mathematical quirk the image came from, it is worth a rating of an 8, much of it due to the mathematical factor. If I had had more time to work on the coloring, I might have raised the image to a rating of an 8-1/2. As it is, I devoted most of the color work to creating the 3-D effect in certain areas. The name "Into the Depths" describes the fall toward unity. Though today's image is quite close to the limit, I would not be surprised if tomorrow's is even closer. Check back to see. The image may be seen without the nuisance of calculating it by checking the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The hi-def version is posted 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/> Tuesday was a bit chilly but otherwise very pleasant here at Fractal Central, and the clouds were spectacular. The fractal cats thoroughly appreciated the temperature of 66F 19C, reverting to curl-up mode for their afternoon siestas. The humans, who were out of town all afternoon, let them sleep undisturbed. The next FOTD will be posted in just a few hours. Until then, take care, and what will those who base their world view on the reality of the material universe do, if it turns out that everything is an illusion? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Into_the_Depths { ; time=0:16:58.75-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-2.100288591283524/-1.442130840681714/\ 528.8877/1/115/0 params=1.0045/0/4.45/3600 float=y maxiter=5200 inside=255 logmap=966 periodicity=6 colors=000IpVKpTLpSMpRNnPPnNQnMSnLTnKUnJXnIYmGZmFa\ mEbmDcmCfmBgmAik9lk8nk7ok7rk6tk5zn4zm4uk4qj4lj4gh4\ cg5_g5Xe5Td5Qb5Nb5K`6H_6F_6DZ6BX69X6AT7BR8DNAELAGI\ CHGDJDELBGN9GP7JR5KT4MW2N_2NY2PX2QW1QU1RT1RR1SQ1TP\ 1TN0VN0VM0WK0XJ0XI0ZH0ZH0_F0`E0`E0bD0bC0dB0dD0`E0Z\ F0XG0VH0TI0RJ0PL0NM0LN1KP1IQ1GS1FT1DU1CT2DS3ES4ER5\ FR6FQ7GQ9GPAGPCGNDINFINGJNJJMLKMMKLPLLRLKTMKWMJXNJ\ _NIbPIePHhQnZTWdRHjQ9sW9pS9nP9mM9kJ9jG9gE9eC9dA9b8\ 9`69_49X39W29V19T09S09R0BQ0DQ1FQ2HQ3JQ5MQ7NQARQCUQ\ FQIGTMIXQI_TIcXIgbJlgJqkJupJzwKzuJzuJzuIyuIysGysGw\ sGwsGwrFurFurEurEtpDtpDupCvpCxuCzuBztBzsAzqAzpAznA\ wl9uk9sk8qk8oj7ni7mh7lh7kg7jd7ib7nZ7pW7gT7VQ7SN7PK\ 7MA7BA3EA5GA7HU9KUKN_KPUKS_KUUKSKMRKMQKMPKMNKMMKNL\ KNKKNIKNHKNHKNGKPEKPEKPDKPCKKBKLBKKBKKCKICKIDKHDKH\ EKGEKGEKFEJFFKEFKEGLDGMDHMBHNGHPGHQGIQFIRFJSEJTEKT\ DKVDLUCFU3IU7LUCNMKMMKLMK } 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 14-06-11 (Tsunami-Plus [8])
by Brian Prentice 14 Jun '11

14 Jun '11

Jim's near linear fractal for today is full of interesting detail. Here are some examples: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20a.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20b.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20c.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_20d.png Brian Prentice

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FOTD 14-06-11 (Tsunami-Plus [8])
by Jim Muth 14 Jun '11

14 Jun '11

FOTD -- June 14, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us ever deeper into the world of near- linearity. The exponent of Z in today's image is 1.009. Both common sense and instinct tell us that a fractal with an exponent so close to unity can only be a lopsided circle or a featureless ellipse at best. But as is the case with so many things that are known to be true in the world of science, common sense and instinct are wrong. The parent fractal of today's scene is an ellipse, that's for sure, but when calculated at the particular height of 4.45 levels up the logarithmic ladder, the ellipse becomes irregular along its edges. Today's image shows a close-up of some of this irregularity. I named the image "Tsunami-Plus". The reason for the 'tsunami' part of the name is obvious. The 'plus' refers to the shaft of total chaos shooting down and disappearing behind the wave. The rating of an 8 expresses my opinion of the mathematical worth of the image. If I had put more effort into the coloring, I might have given the image more artistic value and worked the rating up to an 8-1/2. The calculation time of 4-1/2 minutes will pass in a flash once the peak of the mighty wave appears, decorated almost like the wave in the famous Japanese drawing. The image is posted, fully calculated, on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition with possible variations 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/> Sun, clouds and a temperature of 75F 24C made Monday a refreshingly pleasant day here at Fractal Central. At least the fractal cats thought so. They reverted to their winter curl-up modes. The humans spent the day doing routine things such as gardening and serious work. The next FOTD, likely another in the how-low-can-you-go series, will be posted in 24 hours. Until then, take care, and all good things must come to an end, but so must all bad things. In fact, everything with a beginning in time must come to an end in time. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Tsunami-Plus { ; time=0:04:31.27-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=t center-mag=0.787447/-1.99784/1.8675/1/-77.5/0 params=1.009/0/4.45/2400 float=y maxiter=5000 inside=255 logmap=205 periodicity=6 colors=000U7AV8BW9CW9DXAEXBFYCGZDHZEI_FJ_FK`GLaHMa\ INbJObKPcLQcLRdNQeOQfQPfRPgTOhUOhVNiXNjYMj_Mk`LlbL\ lcKmdKnfJngJoiIpjIslGpkInkKlkMjjOhjQfjSdjUaiW_iYYi\ _WiaUhcSheQhgOhiLgkJgmHgoFgqDfsBfu9fw7fxAcwDawFZwI\ XwKUwNSvPPvSNvUKvXIvXEzZGv_HsaIobJldLheMegNahOZjQV\ kRSmSOnTLpVHqWEsXAuZ4tY7tX9sWBsVDrUFrUHqTJqSMpROpQ\ QoQSoPUnOWnNYmM`mLblLdlKfkJhkIjjHlkEpjHnjJljLkjNii\ PgiRfiUdiWciYah__haZhcXhfWghUgjSglRgnPdvPgpOikNkfM\ maLpWKrRJtMIxGIvHHtHGrHGpHFnHFlHEjHEhHDfHDdHCbIC`I\ BZHBXGAWFAXE9OE9MDAMDDMCFMBJNFIPJHPNGQRGSVJUZLVbNX\ gPZjR`mUapWcsYev_fyagr_hkYhdWiZVjSTjLRkEPk8OgETdJY\ aPbZUgW_lTdqRkwQiuPhsOgqNfpMenLdlKcjJbiIagH`eH_dGZ\ bFY`EXZDWYCVWBUUATS9SR8RP7QNpgQ7PM6SL6VK6XK6_J6aI6\ dI6fH6iH6kG6nF6pF6sE6aG6uE8tD9sDAsCBrCCrBEqBFqAGpA\ Hp9Io9Cr4Jo9QlDWjIbgMheRobVu`ZucSufLuiEul7IjaJk_Jk\ YL_QNPJPDCR25S36T47T58F0F } 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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Fractint version 20.04 patch 11 released
by Jonathan Osuch 14 Jun '11

14 Jun '11

Folks, Fractint version 20.04 patch 11 was released today. The executables can be found at: www.fractint.net or www.fractint.org Here is what's new: Fixed creation of sound PARs so that the sound= parameter appears after any other sound related parameters. Fixed sound related PARs in fract200.par. Fixed turning off sound when an image with sound is completed. Marcus Pallinger provided changes to allow compiling Xfractint on an Intel Mac. Fixed Xfractint version DivideBrot5 fractal type broken with patch 10. Fixed Xfractint ncurses interface broken with patch 10. Added a pause to the sound options via the use of the scalemap feature. Allowed scalemap value of 0 in PAR entries. Jonathan

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FOTD 13-06-11 (Quarter Something [No Rating])
by Jim Muth 13 Jun '11

13 Jun '11

FOTD -- June 13, 2011 (No Rating) Fractal visionaries and enthusiasts: My fractal energies were at an absolute minimum on Sunday. Nothing I tried worked out. I finally settled on the Julia set of the Seahorse Valley area of the Quaternion Mandelbrot set, where the two arms have just begun to merge. I put almost no effort into the coloring. (They say a fractal artist is judged by the effort he puts into the coloring. If this is so, today's image must be considered a total flop.) But the angular aspects of the scene are just notable enough to make the image worth the minute required to calculate it. I gave the image no rating because I did not want to embarrass myself with a rating of something like a 3. The name "Quarter Something" means nothing. It might have meant a little more if I had named it "Quat Something." The finished image is available at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is posted 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 mix of sun and clouds, with a few light showers and a temperature of 81F 27C, made Sunday an acceptable day here at Fractal Central. The fractal cats spent the day lounging, while the humans found more productive things to keep them occupied. The next FOTD will be posted in 24 hours. Until then, take care, and the world seems real, but how do we know that it is really real? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Quarter-Something { ; time=0:00:59.27-SF5 on P4-2000 reset=2004 type=quatjul passes=1 periodicity=0 center-mag=0/0/8/1/-90/0 params=-1.74925/0/0.01/0/\ 0/0 float=y maxiter=2400 inside=0 logmap=8 colors=000BCC7EC4GC8IACK9GM8KQ7OU6SX5W`4_d3cg2gk1j\ n0mg4o`8qUCsNGuGKw9Oy3St4So5Sk6Sf7Sb7Se9GhA4iD6iG8\ jJAjLCkOEkRGlTIlWJmZLm`NncPnfRohTokVpnXppYqm_rj`rg\ asdbsactZdtWeuTfvQgvNhwKiwHjxEkxBltClpDllDlhEldFl`\ FlXGlTHlPHlLIlHJlEJlLSeR__XhUbpOhxIdtMapQZlUWiYTea\ PadMYhJVlGRpDNtAKwEOsISoMWkQZhUbdYf`ajXemUiqQmuMqx\ JotGmqEkmBij9jbDjVGkOJkGMk9PlESmIUmMWnQZnU`oYbpaep\ egqiiqmlrqnruplskfqf`pbVnYPlTJkPDiK7hGTa9mV3nT8nSC\ nRGoQKoPPoOTpNXpM`pLeqKiqJmqIqqHunFslEriDpgBodAnb9\ l_7kY6iV5hT4gQ9bOEZMIVKNQISMGWIE`DCe9Ai5Bf4Bd4Ba3B\ _3BX2CV2CS1CQ1CN0CL0CJ0GN6KQBNUGRXLV`QYcVag_ejdhmi\ `nXTnLLn9UbIaSQiGZq5fcDkQLoDTsBbh9kZ7tP6rQ5pQ5nQ4m\ Q4kQ3iQ3gQ2fQ2dQ1bQ1aQ7`UD`YJ`aP`eV_i`_mf_qk_tkapk\ cmkeikffkhbkj_kkWkmTkoPkpMkmMljMlgMmdMmaMnZMnWLoTL\ oQLpNLpKLqHLqFLpJLoMLnPLmTLlWLkZLjbLieLihLgWNeJPc7\ RaAQ_CPYFOWHNUJMSMLROLPQK } END PARAMETER FILE=========================================

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FOTD 12-06-11 (Take Your Choice [6])
by Jim Muth 12 Jun '11

12 Jun '11

FOTD -- June 12, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image is in two parts, the lower left half and the upper right half. The viewer may choose which half he prefers. The lower left half is intact, while the upper right half is partially evaporated, with the evaporation front running diagonally through the central minibrot. The strange bailout value assigned the imag(p3) parameter controls the position of the evaporation front. The coloring is quite different in the opposing halves. I have worked on the coloring to emphasize the difference, but the result still rates no higher than a 6. The coloring effect in the upper right half was achieved by rendering the image with the inside set to 'zmag'. The other inside fills have varying effects. Actually, the image holds an error. I had intended to enter 8.8 as the value of the imag(p2) parameter, but somehow the decimal point never showed up, and I didn't notice the value of 88 until the image was completed. It was another of those serendipitous accidents that happen so often in fractals. The name "Take Your Choice" implies that the viewer can have it both ways. Those who prefer the lower left half of the image may reduce the bailout a bit and get an entire image like the lower left half. Those who prefer the upper right half may simply increase the bailout. (Setting the inside fill to 'bof61' has the same effect as lowering the bailout.) The calculation time of 4-3/4 minutes is slightly tiresome, but calculation may be eliminated by viewing the completed image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def version of the image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, which was started in 1997, may be accessed at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, with a few sprinkles of rain and a temperature of 86F 30C, made Saturday a routine weather day here at Fractal Central. The fractal cats forgot the day even before it began. I took things as easy as possible, aided by FL, who came to the rescue when I showed signs of doing some useful work. In reply, I gave her some morale support when she went to work in her garden. The next FOTD will be posted in 24 hours. My next fractal 'hot' spell is due soon, so check then to see it it has arrived yet. Until next time, take care, and if a physicist should prove that the world is not real. Would he really have proved it . . . Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Take_Your_Choice { ; time=0:04:45.38-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.433407804720116/+0.02731266503619226\ /1.578536e+008/1/-132.5/0 params=3/-1.8/0.6/-88/0\ /1.233827121e+027/0/0 float=y maxiter=1600 inside=zmag logmap=170 periodicity=6 colors=000rU2cY2a`1_c0Zf0Yc2Xa4W_6VX7UV9TTBSRDSOER\ MGQKIPIKOFLNDNMBPM9QOEPPJORONSTMUXLVYKXYJYYIZYHYYL\ XYPWQTVHcU9_J6I831A25B28D2BE2EG2HH2LJ2OK2RM2UN2XNE\ `NQcNafNmiNylMvkMtkLrkLpkLmjKkjKijJgjJdiJbiI`iIZiI\ Xi6A`5Ob4ad3neArOHu6MdFROOV8WYJc`TjR_lHfm7mn8qs9tx\ LsmXschrTtrJgoRVlZJieGfWDdMAbC7`3DZLIXbNVsawmQIMqu\ w`dtuy7hlNW`bNeDM_RLUdS_8QXKOUWMRgC13F9LIHa1ia8bgE\ WmgBMWIbFKiINny0an7fdDjUJn0XR7U`ERigxCWfYGXEHVPITZ\ JRhrap`VqppBgiM_bXSWgkk3YM3ROT1Gv8JtEMsEmUH`frPp`P\ q73OB9WEEcHKkPwO6zO2jU8bbEWjMsW74RBAYEFdHKktVlaSob\ VJNsBuOLbPawbdiYiXTnk7SYGeKq3QmtN`sro``aiif7``NSVb\ s80jDEaHSTLe_Edy`7kXNYTbqz6HdJI_VJUf_`UUXbPTj3bP8Z\ XCWcGSkZJ1RMSzG2oJGdLTUNe5My_cWUZcPUkN8mMEoLKqoPqd\ PrUPrkoJafVTYfHfJtuvgjtW_sGU6tU28gQBbYEYdHTknxPclZ\ U`homO_`c7hqJ2EKEZK1wK7uKDtKJsOUdMSiLQnlpsbfrTYrWP\ 9QPWY7URGfcVdMnCLeR000B00 } 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 10-06-11 (Two Times Seven [7.5])
by Jim Muth 11 Jun '11

11 Jun '11

FOTD -- June 10, 2011 (Rating 7.5) Fractal visionaries and enthusiasts: In today's image we return to the DivideBrot4 formula, one of the formulas I wrote while developing the FinDivBrot-2 formula, the one I now use most often for images with mixed characteris- tics. The FinDivBrot-2 is satisfactory enough, but the DivideBrot4 does a few things better than the FinDivBrot-2. Today's image shows one of these 'better' things. The scene is located rather deep in the East Valley of the oversized parent fractal, which on the surface resembles an everyday Mandelbrot set. Down at the depth of today's image however, things get out of control. The quadratic minibrots have transformed into order-7 minibrots, but these minibrots have lost all pretense of 7-part symmetry, and are surrounded by patterns that appear to be a combination of Z^2 and Z^7 features. The image shows an order-7 minibrot with every lobe doing something entirely different. Some lobes connect out to the surface, while other lobes quickly come to a dead end. Countless smaller minibrots fill the image, easily located by their brilliant orangish coloring. Though these smaller minibrots share a similarity, no two of them are exactly the same. The result of all this chaos is a rating of a 7-1/2, 1/2 point of which is due to the extra effort on the coloring. (If I had totally eliminated the color bands, the image could have rated an 8.) The calculation time of 3-1/4 minutes is not quite a bargain, but a fair price to pay. The name "Two Times Seven" refers to the mixture of quadratic and order-7 elements in the image. The fully calculated finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The image is posted in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The 14-year-old original classic FOTD web site with all the early images may be accessed at: <http://www.Nahee.com/FOTD/> Another hot, hazy, muggy day prevailed here at Fractal Central on Thursday, with a temperature of 95F 35C. Heavy storms threatened all afternoon, but at 6pm they had not moved in. The fractal cats took things slowly, even asking for their treats in subdued slow motion. The humans also had a slow day. FL was concerned with a rain gutter that overflows on her garden, but the repair is not yet in sight. The next FOTD will be posted in 24 hours. Until then, take care, and when we finally do work out a theory of (almost) everything, will we be able to understand it? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Two_Times_Seven { ; time=0:03:16.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 center-mag=+1.864192528962\ /-0.0236455806899/1.28447e+009 params=7/7/2400/0 float=y maxiter=6400 inside=0 logmap=696 colors=00059L5AM5BN5CO5DP5EQ5FR5GT5HU5HW5GX5GZ5G_5\ Ga5Gb5Gd5He9JdCLcFMbINaMO`PQ_SSZVVYZXXaZWd`YfcZhfc\ ikhipmhsreuvbxzXwzRuzMtvOrrPpmRmhSjcThZVeUWcPY`MZZ\ K_XMaUObSQcQSdTReWQfZQfaPgdOhgOijNilNgnQfpTdrWctYa\ v``xc_yeXxaUxZRxWVwTZwQcwNhvKmvHrvEvuBzu8zu5Qd9WT8\ aH8f68cABaEE_IGYMJWQLUUOSYQQaTOeVMiYKl_NmbQmeSnhVn\ kXom_opapsdpvfpxaqrXqmSrhQocOlZLiUJfRHcPE`QCYRAVS8\ SSCTR8_t4Ys6Xp8XmAXkCWhEWeGWcIW`JVYLVWNVTPVQRUOTUL\ VUIWUG_XJc_LgbNkdQogSsjUrlZqnblphhrnctt_vzYtwWruUp\ rSnpQlmOjkMihKgfIecGcaEaZC_XAYU9XSDURGSRJQQMOQQMPT\ KPWIPZGOaEOeCNhANk8Mn6Mq4Mq6Lq8KqAJqCIqEHqFGqHFqJE\ qLDqNCqOBqQAqS9qU8qW7qX6oZ5q`4sa4vd3zg2zi2zk5zl7zl\ AzmCzlFzkHzgGydGwaGv_GuYFtWFsUFrSFpRLnQRlQXj`bhchf\ cndctbczecjgcVicFjmKkmPkmUlmZmzcmzhnzmozrozwqzsszo\ uzlwzhyzeszcnzahz_czYZzWTzUOzSJzRIzQHzPHzOGzNGzMFz\ LFzKEzJEzIDzHDzGFzFGzEHzD } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 11-06-11 (Way to the Unknown [No Rating])
by Jim Muth 11 Jun '11

11 Jun '11

FOTD -- June 11, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image is a scene in the Z^101+C Julibrot. It is a simple diversion from the heavier things that the FOTD somteimes gets involved in. It's the type of thing I might have done 10 years ago, so I could give it no rating. But it's still a very fast 44-second image, well worth a glance. The image is not part of a Julia set, nor of a Mandelbrot set. It is sliced in a direction rotated 4-1/2 degrees from the Julia toward the Oblate orientation. This makes the image almost a Julia set, though one would never guess it from the appearance alone. The name "Way to the Unknown" sounds full of deep meaning. Actually, it has little if any connection to the image, and even less meaning. The most obvious features in the image are the 3 similar openings, though they failed to be mentioned in the name. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Check the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the original FOTD web site at: <http://www.Nahee.com/FOTD/> Friday brought a refreshing break to Fractal Central as a bit of cooler air slipped in from the north, dropping the temperature to 86F 30C and clearing away the haze and humidity. The fractal cats must have missed the change. They spent most of the day stretched in the coolest places they could find. The humans had a rather dull day, which appears to be typical of how things go in the summer here at FC. The next FOTD will see its moment of glory in 24 hours. Until then, take care, and if the answer is not what you had hoped for and expected, believe it anyway. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Way_to_the_Unknown { ; time=0:00:44.21-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.995001/0.963568/19.79345/0.7593/180 params=85.4/0/90/0/-0.9737/0/1.0066/0/101/0 float=y maxiter=1500 inside=255 periodicity=0 colors=000D07D08E0AF0CFAIEFOIJVMNWRQRVT7ZW7cVzmUzz\ zzzzzMaZBej1iuOd_j`FgaJdbzacQZdUzzzTf`QgdNhgKikHjn\ EkrBlv8my5nz2oz4kz6gz8czA_yCWwESvGPtILsKHqMDoO9nQ5\ lS2kR3mQ3nP3oO3qN4rN4sM4uL4vK5wJ5yJ5zI5zH6zzzzF6zF\ 6zEGwEPnDYeDfXDoOEjREeTE`VFWYFS_FNaGIdGDfG9hEFcCLZ\ ARU8XP6bK4hGKULZFPm0Tl1Wzzzj3`i4ch5eg6hf7je8me9ocC\ nbEmaGl`Ik_KjZMiYOhXQgWSfVUfSXcQ_aOa_MdYKgWIiUFlSD\ oQBqO9tM7wK5yI7uK8rLAnNBkODhPEdRGaSHZTFYVEYWCYYBYZ\ 9Y`8Ya6Yc5Yd6Wb7V`8U_8SY9RWAQVAPTFGIBNRCMQDLODJMEI\ LFHJWzzUvxTrtRnpQjlOfhNbdMZ`KVXJRTHNPGJLBeQjsmgojd\ kgahdZdaW`ZTYWQUTNQQKNNHJK71r83o94l95iA6fB7cB8`CAZ\ CBWDCTEDQEENFFKAXrBVoBUlCTiCRfCQcDP`DNZEMWELTEJQFI\ NFHKAOzDKdaMQ`LP`LP`LP_LP_LP_LPZLPZLPZLPYLOYLOYLOY\ KOXKOXKOXKOWKOWKOWKOVKNVKNVKNVKNUKNUKNUJNTJNTJNTJM\ SJMSJMSJMSJMRJMRJMRJMQJMQJMQILPILPILPILOILOILOILOI\ LNILNIKNIKMIKMHK7Gm6EfUsz } 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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FOTD 09-06-11 (A Great Sea-Change [7])
by Jim Muth 09 Jun '11

09 Jun '11

FOTD -- June 09, 2011 (Rating 7) Fractal visionaries and enthusiasts: I named today's image "A Great Sea-Change". It's kind of a redundant name, since a 'sea-change' implies a total transforma- tion, and a change cannot be any greater than total. What has changed in today's image is the surroundings of the tiny order-6 minibrot at the center, as well as the surroundings of the other minibrots scattered about the scene. Normally, the high-order minibrots are notably uninteresting, but when created by the FinDivBrot-2 formula, they leap to life, their surround- ings bursting forth with the most surprising kinds of widespread features. Enough said about today's image. The rating of an everyday 7 means that the calculation time of a measly 40 seconds will not have been spent in vain if the image proves to be a let-down. It also means that if I had worked harder, I might have improved the coloring. Avoid the calculation altogether by checking the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And check the original FOTD web site at: <http://www.Nahee.com/FOTD/> Heat, haze and humidity prevailed here at Fractal Central on Wednesday. The fractal cats escaped the heat by lying on the cool tile of the bathroom floor; the humans chose the artificial coolness of the air conditionier. With all this taken into account, the next FOTD will be posted in 24 hours. Until then, take care, and if someone tells you they know all the answers, ask them why there are still questions. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Great_Sea-Change { ; time=0:00:40.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.251911971871246/+0.342786793999404/\ 5.2845e+011/1/-20/0 params=6/6000000/0/0 float=y maxiter=1500 inside=0 logmap=69 periodicity=6 colors=000kmzjkyiixhgwgevfcueatd_sdYrbWqaUp`So_QnZ\ OmYNkXLiWJgUHeTFcSEaRC_QAYP8WN6UK5TG4VC3P72K11F10A\ 005cccmqzzzztqltlRthLtcFtZ9tV3sT5rR7rP8qNApLBpJDoH\ EnFGnDImBJl9Ll7Mk5Ok3PbEYUOfLYoCgxCeyCdyCcyCbyC`yC\ _yCZyCYyCWzCVzCUzCTzCRzCQzCPzCOzVa5Tc5Rd5Pf5Nh5Mi5\ zzzZLVWMTSNSPOQMPPJQOGRMDSLATKAPNAMQAJSAGVACXA9_A6\ aA3dA0fD3eF5eH8eJAdLDdNFdPIcRKcTMcUNaVN`WN_XNZYOYZ\ OW_OV`OUaPTbPScPQdPPeQOfQNgQMhQLeZZbgleikgkjiliknh\ mogoqfqrestduucrrdpodnldlidjfegcee`ecZeaWf_TfXQfVN\ fTKgRHgPEgNCgYDYhEOrFErGFrHGrIHrJIrKIrLJrMKrNLrOMr\ PMrQNrROrSPrTQrTQsURsUSsUSsUTtUTtUUtUUtUVuVWuVWuVX\ uVXvVYvVYvVZvVZvSTvPOvMJvJEvG9vE4sH9pKEnMJkPOiRSfU\ XcXaaZfZakXcoWakV`gU_cUZ`TXXSWTSVQRUMQSIQRFPQBOP7O\ O4MR6KU7IW8GZAE`BDcCBfE9hF7kG5mI3pJ2rKDiOO`SYSW`RZ\ cR`fRbiRdkQgnQiqQktQmvQommYlgUlbRlYOlTLlOHlJElEBl9\ 8l45g8FcCO_GYVKfRalQclQdl } 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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FOTD 08-06-11 (The Inhuman Brain [7])
by Jim Muth 08 Jun '11

08 Jun '11

FOTD -- June 08, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image, with its brain-like shape and complex networks, reminded me of a human brain. But it is not made of meat, it is made of numbers, so I named it "The Inhuman Brain". The image is part of a near-Julia view of the eastern extremity of the main bay of the (-Z)^(2.5)+C Mandeloid. It is not a Julia set, since it is rotated 45 minutes of arc away from the Julia orientation toward the Oblate orientation. Julia sets are 2-dimensional slices cut in a particular orientation through the 4-dimensional Julibrot figure. Today's image just misses the proper Julia direction. I rated the image at a 7, which is FOTD average. We have seen similar images several times in the past, so I could rate it no higher. The calculation time of 2-1/4 minutes is close to FOTD average also. As always, the completely calculated image is posted at: <http://www.crosscanpuzzles.com/Archives.html> along with the day's philosophizing. The hi-def version of the image is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Paul's FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Things were reasonably pleasant here at Fractal Central on Tuesday. The hazy sky and temperature of 86F 30C made things seem quite summer-like. But summer is expected to come in much stronger on Wednesday, so we'll see what happens then. The fractal cats had no complaints about the weather, though they did appear annoyed with each other at times. The humans had a typical day. The next FOTD will be posted in 24 hours. Until then, take care, and watch out for that conscious universe. It knows what you're doing even when you're asleep. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Inhuman_Brain { ; time=0:02:17.14-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 center-mag=0.621705/0/8.385427/1/90/0 params=89.25/0/90/0/0.3831/0/0/0/2.5/0 float=y maxiter=64000 inside=255 logmap=6 periodicity=6 colors=000cSobUmaWj_YgZ_dXaaWcZUeWTgTRiQQkNOkGPlKQ\ mNQnQRoTSpWSqWSpZYn_`k`chaffbidclceobgraiu`kw_luZi\ tXgrVdqSboP_nMYlKVkITiGQhEOfCLeAJf7Gd8Hb8Ia8J_8KZ8\ LX9MW9NU9OT9PR9QQAROASNATLAUL8Uzn6no2lk4kh6je8ibAh\ _CgXEfTFeQHdNJcKLbHNaEPcCR`BQZBPWAOUANR9MP9LM9LK8K\ H8JF7IC7HA6G76F25B46D56F66H76J86LA7MB7OC7QD7SE7VG8\ XH8_I8bJ8eK8gL8hL8hN9jOAlPAnQBpRCrSCsTDuUEwVEyWFzX\ GzYGzZHzZHwZHtZHpZIlZIhZIdZI`ZJYZJVZJSZJPZKzZKzZKz\ bLz`KzZKzXKzVKzUKzSKzQKzOKzNKzLKzJKzHKzAMzGKzMIzRH\ zXFzaEzgCzlBzr9zx5zw8zvBzuDztGzsJzwCzrLznUzjazfjza\ xzbuzbrzcpzcmzdjzdhzeezebzQmzYfze`zmUzpRztOzsPzrPz\ qPzpQzoQzoQzmRzlRzjRziRzgRzfRzdRzcRzaRz`RzZRzYRzVS\ zSTzPTzMUzKUzHVzEVzBWz9WzDXzGYzJYzNZzQZzT_zX`z_`zb\ azfazibzlczpczsdzvdzqezlfzggzbhz_lzZhzYezXbzW_zVXz\ UUzUQzTNzSKzRHzQEzPBzP8zRCzSFzUIzVMzXPzYSzfZzodzwj\ zmXzdKzW7zZDz`IzbNzgOzeQz } frm:SliceJulibrot5 {; 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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FOTD 07-06-11 (Deep Blue Fantasy [7])
by Jim Muth 07 Jun '11

07 Jun '11

FOTD -- June 07, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is another one found in haste, but thanks to the extra coloring effort, emphasizing grays and blues, it rates a respectful 8. The scene lies in the west "Elephant Valley" of the Z^(3.003)+C Mandeloid, which, due to the fractional exponent, has broadened into a kind of wedge. It is located in the chaos along the southern edge of this wedge. We have been to this area several times before, but I think today's visit, with its carry-over 'fishbone' theme from yesterday and somber blue coloring, is the most productive yet. The tiny minibrot at the center is rather poorly defined, a flaw that could be eliminated by raising the maxiter. But doing this messes up the colors, so I let the image go as it is. After all, everyone knows what a cubic minibrot looks like. The calculation time of 3 minutes is a fair price to pay for the finished product. The finished image may be seen on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> without the need to calculate it. The image may be seen in high definition 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 string of perfect days continued here at Fractal Central on Monday, with blue skies, low humidity, puffy white decorator clouds and a temperature of 81F 27C. The fractal cats enjoyed the outdoor conditions from indoors, where they stretched on the carpet in solid comfort. The humans' day was not quite as comfortable, but still a notch above average. The next FOTD will be posted in 24 hours. Until then, take care, and if a worrier lacks something to worry about, something will be provided. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Deep_Blue_Fantasy { ; time=0:03:26.85-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-0.386\ 8917576744657/-0.00190443108910178/1.911204e+010 params=3.003/0/0/0/0/0 float=y maxiter=3600 inside=255 logmap=471 periodicity=6 colors=000CHRDIREJTFKXGLXHMZIN_JOaKPbIQdHReFSgEShC\ TiATk9Ul7Un5Uo4Vq2Vr1Vs0PX0KBECOR5_T9XVCUXFRZIO`LL\ bPIdSFfVChY9j`7e`9a_BYcDUbFQaHM`IO`JP`KRWKSRLUSLVS\ MXSMYNNZJNaOScSXeWag_fidkkhpmlutuzjmvbeoWYgOR`GJTF\ IT9CN37IEFMONPPLOQKNRJMSILTHKUGJVFJWEIXDHYCGZBF_AE\ `9Da8DZCKWFQTIWYMWaQWkSEfXJb`NYeRUiVPmZLrbGvfCzjGx\ kKvlOulSsmWqn_pngN0jR7lVEnZLpbRrfYtjdvnkxrqqkpjdpc\ ZoXSoQLnJFnPNl_YrggynpzadeZ_aWUYTPUQJQOENMJQ`LvbOp\ m132HNgmgfgheaidWjDwXMkaV`fO`tSYqWVo_SmM7`VHfaOkbP\ kcQkwWtVaPby_ViOOVCKa9Gh7Co59v3IgBRTI_FPeIJjLDJO70\ Q_2dZC`bkbeLXeVThz89zEMfKZ1LAENNRP_sjNodUk__gVe0ci\ A_jDJRCIQBGPAFPIEd8DN7BN6AM59L47L36K25J24J36I47I58\ H69H6BG7CG8DG9EFAFFAHEBIECJDDKDDKDEKCFKCGKBHKBHKAI\ KAJKAKK9LA9LA8MA8NA7OA7OA7MAALADKAGIAJHAMGAPEASDAV\ C3YB0_C0ZD0ZE0ZE0ZF0ZG0ZH0YH0YI0YJ0YJ0YK0YL0XM0XM0\ XN0XO0XO0XO0WO0VO0UO0Uzzz } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 06-06-11 (Fishbone [7])
by Jim Muth 06 Jun '11

06 Jun '11

FOTD -- June 06, 2011 (Rating 7) Fractal visionaries and enthusiasts: Sometimes when I'm writing these FOTD discussions I feel like a merchant trying not to sell his goods. (It's not so unusual. After all, we hear electric power companies all the time telling us to use less of their product.) But I believe in honesty in fractal talk as well as in advertising, so I admit my fractal shortcomings. In today's image I'm playing catch-up fractaling, and the quality appears to have suffered. I managed to get the quality of today's image up from a rating of a lowly 5 to a rating of an average 7. It's an improvement over yesterday for sure, but still leaves us well below FOTD top quality. But an image is an image, and even though it's late, today we have an image. The parent fractal came about when I combined 0.001 part of Z^1001 with straight Z before adding straight C on every iteration. This uninspiring combination produces a parent fractal that is little more than a vague circle with a bit of action at its eastern extremity. Zooming in on this action reveals a tiny distorted Mandeloid and a section of the large circular arc, which in its entirety consists of 1000 lobes. Today's scene lies toward the rounded tip of the lobe closest to the Mandeloid. I named the image "Fishbone" because that's what came to mind as I studied it in search of a name. (The search was a short one.) The calculation time of 3-3/4 minutes will pass un-noticed. The finished image is available on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is available in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site with fractal images from as far back as April 1997 may be accessed at: <http://www.Nahee.com/FOTD/> The weather has been pretty pleasant for the past few days here at Fractal Central, with lots of sun and near normal tempera- tures around 79F 26C. I have been passing time trying to get the FOTD caught up. Maybe I should have simply skipped the FOTD for June 5. At least the fractal cats are sharing the work load, giving morale support when the fractaling gets rough. The next FOTD, the one for June 7, will likely be posted in a few hours. Until then, take care, and be ready for what may come. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fishbone { ; time=0:03:44.13-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.00857153940435359/-0.000026928341367\ 55/1.44275e+008/1/180 params=1/1/0.001/1001/0/0/0/0 maxiter=4800 inside=0 logmap=663 periodicity=6 colors=0006B`7CW8CQ9DLAEGBABDXsJToOQlTNiYJebGbgD__\ 4aX7_UAZSCYPFXNIVKKUHNTFQSCSQAVP7YO5_N8YMBXLDWKGVJ\ IUJLTINSHQRGTQFVPFYOE_NDbMCdLCfOAhR8jU6lX5n_3pb1re\ 0sd2sc3sb5ta6t`8t_9uZAuZCuYDvXFvWGvVHwUJwTKwTMxSNx\ ROxQQyPRyOTyNUyNVxLZxKbxIfxHjwGnwErwDvwCynDtfDpZDk\ RDgJDcHL_FSWD_SBfOCeNDdMEcMFbLGaKG`KH_JIZJJYIKXHLW\ HLVGMUGNTFOSEPREQQDQPDRJZSDtUMiWV_YcQZkGU6jU6kU6kV\ 6lV6mV6m_DgdJbiQYnWSsbNLRJRNCXI6bE049k5Aern6jmBclG\ XkLPjQIiVBh_4hd5fe5de6bf6af6_g7Yg7Wh7Vh8Yl9_oAbsBd\ vCfyKcySay__ygYynWybfuRpqSirScrTXrTRrUKsUEsV7sV1s_\ 5fd8VZKMjWDlg4jfDieLhdTfcaebidaqcayeYtfUohRkiNfkJa\ lGYnCTo9PnMRmYSljTqvmScyWQbZCHiV`sltpjnnihlgcjfYhe\ SfcNdbHbaCZ_GVZJSYMOXPKWSHVVDUYUTzDUbFVdHWfJWgLXiN\ YkPZmcZnMcmHglDkk8oj4siApbGmXLwRRmKXmEam8pmtomhomX\ omLomAKmmLmnMmnNmnOmnQmLVmfXzUYzH4zbKzL4zYFzOPzEfz\ abzLtzADz`LzQSzFmzLizGezC } 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 05-06-11 (Iterative Old One [5])
by Jim Muth 06 Jun '11

06 Jun '11

FOTD -- June 05, 2011 (Rating 5) Fractal visionaries and enthusiasts: Due to an antiquing expedition on Saturday, today's image is a super-quickie, both in calculation time and the time I spent creating it. It came about when I casually subtracted 0.67 part of (1/Z) from 0.67 part of Z^2, which resulted in a parent fractal consisting of a single large distorted Mandeloid with disconnected debris scattered around it. The north period-3 bud is the largest bud on the main bay of this parent Mandeloid. This bud has a prominent zig-zagging filament extending from it and terminating in a jagged string of connected holes. The string of holes is mirrored many times in today's image, which is located near the point where the filament joins the string. The image rates a 5, about as low as an image can go and still qualify for FOTD status. The name "Iterative Old One" does not refer to the fractalist. It refers to the image, which had potentially existed for all eternity before I stumbled upon it. The calculation time of 20 seconds is about as fast as an image can be, (unless the image is type=mandel or type=julia). 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 web site is at: <http://www.Nahee.com/FOTD/> Saturday here at Fractal central began sunny, but clouds moved in during the afternoon and built until a lively thunder-shower erupted at nightfall. The fractal cats had no complaints about the temperature of 77F 25C, but did not enjoy the noisy thunder. Meanwhile the humans had an acceptably pleasant day. The next FOTD will be posted within 24 hours. Until next time, take care, and if you hate those big greedy corporations that pollute the environment and take money from the people, punish them by no longer using their products. But if you need these products to maintain your life style, don't make yourself a hypocrite by speaking out and protesting. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Iterative_Old_One { ; time=0:00:20.60-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.5565691575516971/+0.5157652874537672\ /1.39e+009/1/-37.5/0 params=0.67/2/-0.67/-1/0/0/0/0 maxiter=312 inside=0 logmap=48 periodicity=6 colors=000hQCjTDlWEnZFpaGrdHthRtl`vqjwuszzz0AA4GF7\ NKAUPD_TGdYJiaMmfOojRmmTjhVbcDAKB8F96A655430210sbf\ q`do_cmZakX`iWZgVYeTWdSVbRU`QSgoChnEinFinHjnIjnKkn\ LknMlnOmnPmnRnnSnnUonVonWmkTkiRigOgeMecJcaHa_E_YCY\ W9WU7US4SQ2YMAbIHgEPlAWq6cv2jt1gs1dr1aq1Zp1Wz1Tz1Q\ z1Nz0Kz0Hz0Ez0Bz08z05z02z00z01z02z03z03z04zz5zz6zz\ 6zz5zz4zz3zz2zz1zzFzzDzzBzzAzz8zz6zz5zz3zz1zz9zz8z\ z7zz6zz5zz4zz4zz3zz2zz1zz0zzEzzDzzCzzCmzBkzBhzAfzA\ cz9az8_z8Xz7Vz7Sz6Qz6Oz5Lz5Jz4Gz3Ez3Cz29z27z14z12z\ 0Fz6Ez5Dz5Cz4Bz4Az49z38z37z36z25z24z13z12z11z00z0z\ zbwz`tzZrzYozWlzUjzTgzRezQbzO_zMYzLVzJSzHQzGNzELzD\ IzBFz9Dz8Az67z45z32z1AzW9zU8zS8zQ7zO7zN6zL6zJ5zH5z\ G4zE3zC3zA2z82z71z51z30z1pzymzujzrgzndzkazgZzdWz`T\ zYQzVNzRKzOHzKEzHBzD8zA5z62z37z16z06z05z05z04z04z0\ 4z03z03z02z02z02z01z01z00z0ez2gz2hz2iz2kz2lz2mz2oz\ 3pz3qz3sz3tz3uz3wz3xz3yi3 } 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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Re: [Fractint] AOTD 5_8_11
by JackOfTradeZ＠comcast.net 05 Jun '11

05 Jun '11

. Animation of FOTD 5/3/11 "Most Unexpected" is posted: http://www.fractal-animation.net/vid/ttlg.zip It is 34 Meg, running time 2 minutes. Strange. There are "windows" of complexity immersed in "seas" of relative simplicity. Almost look like 3D objects jumping out at you in the hi-rez 1024 AVI. <i>Through the Looking Glass</i> Enjoy. Comments welcome. JoTz .

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FOTD 04-06-11 (A Minibrot in Heaven [8])
by Jim Muth 03 Jun '11

03 Jun '11

FOTD -- June 04, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "A Minibrot in Heaven". My concept of heaven is a place that everyone says is wonderful, but no one wants to go to. In my opinion, the reason for this contradic- tion is that we're not sure that heaven really exists. In a world built on science, faith does not carry the power it once did, and the world's religions appear helpless to do anything about it. What do I think of all this? Well, I spend time wondering whether there are fractals in heaven. Today's image offers a little hope of the beyond. It shows a minibrot floating through the etherial realm of heaven. This is the same minibrot that I mentioned in yesterday's discussion, and indeed, yesterday's scene lies within the brilliant white arc just southwest of the minibrot in today's scene. Just as in yesterday's image, the better part of today's image is inside stuff made visible by the 'bof60' inside fill. A good part of the outside stuff has evaporated away. The image rates an 8. It might have rated as high as a 9 if the muddy left-over 'outside' debris in the upper part had not been so intrusive. There could be a way to eliminate this stuff, but once again laziness overtook me and I decided to let the image go as is. The calculation time of under 1-1/2 minutes will test the patience of no one. The completed image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image may be accessed at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The 14-year-old classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Friday here at Fractal Central was another perfect early June day. The temperature of 77F 25C is right in the middle of the comfort range, and the humidity of 45 percent simply added to the comfort. The fractal cats spent most of the day being comfortable, doing what cats do when they are comfortable. They stretched out on the carpet. The day of the humans, (not to be confused with the day of the triffids), was slow. FL got caught up on some gardening, while I got caught up on some fractals. The next FOTD is due in 24 hours, but if one of those antiquing expeditions comes up, it might be late. Until whenever, take care, and what if we dis- cover that heaven is really not there? . . . Gulp!! Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Minibrot_in_Heaven { ; time=0:01:25.23-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=1.19207/-0.0303/5.911591/1/-110/0 params=-7/-1.7/-0.7/-7.7/0/2500/0/0 float=y maxiter=1500 inside=bof60 periodicity=6 colors=0007UA8UB8UC9VDIUfAWEAWFBLSBbhCRIRezDKKDZWE\ UMRfmK_NRboD`OPejC`OCacBaPBdiBbQBbQAcQAcRAdR9dR9dS\ 9eS8eS8fT8fT8fTDcSHaSMZSQXSUVS`SQzzzzzzzzzvwzrtzmq\ zhnwcltZjqVhnQfkOdhKbeH`dFZc00L20M40N80OC0SG0WK0_O\ 1cS2cW3d_4dc7eg9ekBeTEeWGeZIf`LfcNffPfhSfkUgnWgpZg\ s`gvbgxdgsednebif`efZ`fXWgVSgTNhRIhPEhNHjOKkONlOPm\ PSnPVoPXqQ_rQbsQdtRguRjvRlwRksPjoNilLhhJgdHfaGeYEd\ UCcRAbN8aJ6aG5cJ7eM9gPAiSCkVDmYFo`GqcIsfJuiLvlMrmN\ omOkmOhmPdmQamQYmRVmSRmSOmTKmUHmUDmVAmW7mWHfJQ_7SX\ BUVFVTIXRMYPP_NT`LWbJ_cHbaLd_PeZTfXXgW`hUdiThjRlkQ\ plOtmNxnLuhKrcJpZImUHkPLiTPgXTe_Xcc_agc_jgYnkWrnVu\ oWqoWmpWipXfqXbqXZqXWrYSrYOsYKsZHtZDtZ9tZ6fW5UU4GR\ 33P25Q47R58S6AT7CU8DV9FWBHXCIYDKZEM_FN`GP_FQZERYDS\ XDTWCUVBVUBWTAXS9YR9ZQ8_P7`O7`O7_O8_O8ZN8ZN8YN8YM9\ XM9XM9WM9WL9VL9VLAULAUKATKATKACBGSKASJBRJBRJBQIBQI\ BPICPICOHC4R55S66S76T87T9 } 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 03-06-11 (Random Mischief [6])
by Jim Muth 03 Jun '11

03 Jun '11

FOTD -- June 03, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image came to life when I combined 7 negative parts of Z^(-1.7) with 0.7 negative part of Z^(-7.7) before adding (1/C) on every iteration. The resulting parent fractal is one of those shapeless, pretty much indescribable things with lots of interesting detail. Today's scene is located in the southeast part of the parent, just beyond a ghostly pink Mandeloid that has pretty much evaporated into the fractal astral plane. The blue background was created by rendering the scene with the inside set to 'bof60'. The shredded, highly colored foreground stuff came about when I raised the bailout radius to 500. The overall effect is of a surrealist painting by one of the early 20th-Century artists, when surrealism was all the rage. It seems strange that artists were drawing fractal patterns well before we knew fractals existed. And unless I'm mistaken, women were quilting fractal patterns hundreds of years before the men discovered the patterns. When I stood back and carefully pondered the image on the screen, I decided it was worth a rating of a 6, which is above average, but nothing to get excited about. I have no idea where the name "Random Mischief" came from. It was simply on the screen when the time came to dream up a name. But with a little imagination, the image actually might be seen as getting into mischief. Mischief aside, the finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic web site can be found at: <http://www.Nahee.com/FOTD/> A stellar day prevailed here at Fractal Central on Thursday. The crystal clear sky and temperature of 75F 24C made outdoor activity a pleasure, while the breeze from the northwest cooled even the busiest outdoor worker. The fractal cats are never busy, but even they seemed pleased with the conditions. The humans had their own tasks to accomplish. FL is not quite satisfied with the progress of this year's garden, so she spent time gardening. I am never quite satisfied with anything, so I spent time pondering the unknown. The next thing to be pondered is the next FOTD, which will be posted in 24 hours. Until then, take care, and start every day with a fractal. If you're out of them, pick up a supply at the nearest fractal outlet store. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Random_Mischief { ; time=0:00:30.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=1.30834/-0.117586/67.48308/1/180 params=-7/-1.7/-0.7/-7.7/0/400/0/0 float=y maxiter=1500 inside=bof60 periodicity=6 colors=000PlVPiVPeUPbUPZUPWUPTTPPTPMTAATA0GA00A0LA\ 0GA0TAITggUztUhkTdcTmWSXOSA0RP8RzDQWIPZMOaROdVNh_M\ kcLnhLqlKtqJwuJtsKrrLopMmoNkmOhlTfjXdi_aabYbeXbgVb\ iTbmQaqO`tM_wKZzJYzHXzGWzEVzDUzITzMLzQMwVNtZOsbPqg\ QmkRloSjsTipUgmVejWchWaeX_bYY`YWaXYbX_cXadXbeXdfXf\ gXghXiiXkjXlkXnlXplXqgUobSmYPkTNiPKgKIeFFcADa6B_UZ\ wTXvSWvSVvRTvRSvQRuQPuPOuONuOLuNKtNJtMHtMGtLFtLEtS\ SfZdUeqH_lGVhFQcEL_DGVCBRB6MA1IA9GEGEINCMUAQ`8Ug6Y\ n4au2dt4et5ft6ft7gt8gs9hsAhsBisCisDjsEjpIknLllOmjR\ nhVnfYod`pbcq`fqWcnR`kUYfWWaYUY_STaPOcNKeLFgJBUNAG\ R92U83P63L42K82KC2JF2JJ2IM2IQ2HT2HX2G_2Gc2Ff2Fj2Em\ 2Eq2Et4Em6Ef8E_AETBEME8JGALIBOKDQMFSOHVQIXSKZUMaWO\ cYPeWMaUKZSIVQGSOEOMCLKAHI8EOELUJR_PYeUck_jqdpwivu\ jsskqqlopmmnnkloijpgiqegrcesact_buY`vWZwUXxSWyQUtP\ SoOQkNOfMMaLLYKJTJHOIBLWFKHDFG0KN1JM2IL3HL4HK5GK6F\ J7EI8EI9DHACHBBGmfTicRf`Q } 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 02-06-11 (FMOD to the Limit [5])
by Jim Muth 02 Jun '11

02 Jun '11

FOTD -- June 02, 2011 (Rating 5) Fractal visionaries and enthusiasts: Today's image is more a demonstration of the 'fmod' feature of Fractint than an actual fractal discovery. The scene of the action lies in a bit of satellite chaos circulating around the rather impressive fractal that results when 0.2 part of Z^3 is combined with Z^2 before C is added. When rendered in the normal equal-iteration manner, the image falls totally flat. Re-rendering it with the outside set to 'fmod' and the proximity set to 3 adds enough life to raise the rating to a humble 5, just enough to qualify it for FOTD status, at least on a fractalist's lazy day. The name "FMOD to the Limit" indicates that the FMOD outside is just about all there is to the image. The calculation time of 23 seconds means that little time will have wasted if the image falls flat even with the FMOD outside. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image may be accessed at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site is available at: <http://www.Nahee.com/FOTD/> I read in the morning paper of another cell-phone cancer scare, but I see no need for concern. All you wireless internet gadget addicts out there can take comfort knowing that the phone compa- nies would certainly warn us voluntarily if using their wireless gadgets is dangerous, just as the tobacco companies voluntarily warned us that using their tobacco products is dangerous. Another heat-wave type day prevailed here at Fractal central on Wednesday. The sun was scorching hot, while the temperature of 95F 35C made things uncomfortable even in the shade. The fractal cats, seeking comfort, found it on the cool bare floor, where they were happy all afternoon. The humans had an uneventful day. A similar day is expected tomorrow. The next FOTD will be posted in 24 hours. Until then, take care, and what do those scare-monger scientists have against wireless internet gadgets, which are so much fun? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= FMOD_to_the_Limit { ; time=0:00:22.94-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-5.135858728183282/+1.553327883652744/\ 1.560795e+012/1/40/0 params=1/2/0.2/3/0/0/0/0 float=y maxiter=1500 inside=0 proximity=3 outside=fmod periodicity=6 mathtolerance=0.05/1 colors=nYskYdlYfnXhmXilYhi_ge`gbbfZceVedSfdOhcLibH\ kaAk_Cl`ElaGlaImbKmcMmcOndQndSneUofWofYog_pgaphcpi\ eqigqjmyokuliqjhngfjedgccc`a`Z`XWZUUXQSWNPUJNSFJTG\ LTHMTHOTIPTJQTJSTKTTKUULWUMXUMZUN_UO`UObUPcUPdVQfV\ RgVRiVSjVTkVTmVUnUTpVUoVVnVWmVWlVXkVYjVYiWZiW_hW_g\ W`fWaeWadWbcWcbXdbXdaXe`Xf_XfZXgYXhXXhWYiWYjVYjUYk\ TYlSYmRYmQYnP_oPaoOcpNeqMgqLirKksJnrIqsJtsKwsLzsMw\ sMtsNqrNnqNkoNimNgjNehNcfNadN_bNY_NWYNUWOSUOQSOOPO\ MNOKLOJJOIHOHEOGCOFAOE8OF7ME6OE6PE6QE6RE6SD6TD5UD5\ VD5WD5XD5YC5_C5`C4aC4bC4cC4dB4eB4fB4gB3hB3iA3kA3lA\ 3mA3nA3oA2p92q92r92s92t92u92vA4uB6tC8sD9rEBqFDpGEo\ GGnHImIKlJLlKNkLPjMQiNShNUgOWfPXeQZdR`cSacTcbUeaUg\ `Vh_WjZXlYYmXWoWUpVSqUQrUOrUMpUKoTImSGlRFkQFjPFiOF\ hNFgMFfLFeKFdIFcGFbEFaCF`BF_BFZBFYCFXCFWCFUCFTCFSD\ FRDFQDFPDFOEFNEFMEFLEFKFFJFFIFFHFFGGFFGIEIJFKLGMOI\ ORKQUMSXOU_QWbSYeU_hWakYc } 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 01-06-11 (Rainy-Day Minibrot [No Rating])
by Jim Muth 01 Jun '11

01 Jun '11

FOTD -- June 01, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image is named "Rainy-Day Minibrot". I gave it this name because the image was resurrected from my 'reserve' files -- older images that I hold in reserve to recall when laziness attacks as it did on Tuesday. The image shows a minibrot of order 2.05 located near the negative X-axis of the parent fractal that results when the formula Z^2.05+C is iterated at a level of a measly 0.12 turn up the log spiral with the 'recip' function applied. This parent is shaped almost exactly like the minibrot. Since the image is an older one and I put almost no new coloring effort into it, I could give it no rating. But if I had rated it, I would have given it a rating around a 5.5. The calculation time is a very zippy 36 seconds. Calculation may be avoided however by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site is at: <http://www.Nahee.com/FOTD/> Total heat and humidity prevailed here at Fractal central on Tuesday. When the temperature reached a high of 95F 35C the fractal cats retired to the cool tile of the bathroom floor, where they spent the next several hours. Meanwhile the humans took things easy in their own way. FL checked to see that the garden was well watered, while I relaxed with a fractal. The next FOTD will be posted in 24 hours. Until then, take care, and the current issue of 'Time' magazine has an article about the tendency of people to look at the bright side of bad events instead of the realistic side. I have not yet had a chance to read the article, but it is proba- bly irrelevant. I am certainly not guilty of looking at the bright side of bad things. (I'll have more to say about this in an upcoming FOTD.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Rainy-Day_Minibrot { ; time=0:00:36.64-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=-1.372754717265681/+0.02681174574841239\ /4.650326e+011/1/7.5/0 params=2.05/0/0.12/0 float=y maxiter=1500 inside=0 logmap=67 periodicity=6 mathtolerance=0.05/1 colors=00080UC1UG2UK3UO4US7UWAU_DUcGSgJRzePzYOyRNs\ OLmLJhIHbFGYBES9CPEBRIAVP9ZZ8ea7ha5md3rg4zf4zd4d04\ d04e04f05f05g05g05h05i05i06h06c06Z06U06P06K07zU0zU\ 0zU0zU0zU0zS0vQ0sO0pN0oMBoLCoKDoJEoIFoHGoGHoFIoDJo\ BKoCLoCMoCNoCOoCPoCQoDRoDSoDToDUoDVoDWoDWnGVnIUmKU\ mMTmPSlRSlTRlVRhVWdV_`VdXVhTVmPVqLVvIVzHVvGVrFVnEV\ jDVfCVbGSaKPaNN`RK`UH_YF_`CZd9Zg7Yk4Yn2Ym3Xm4Wm5Wl\ 5Vl6Ul7Uk8Tk8Tk9SKgeKfcKebKd`Kc_KcZKbXKaWK`UK_TK_S\ KZQKYPKXNKWMKWLPXKTYJYZIa_Hf`GjaFnaFpcHqdJreLsfNtg\ OuiQvjSwkUxlWymXdg_LbbKcaJdaJeaIe`Hf`Hg`Gg_Fh_Fi_E\ iZEjZDkZCkYclYcmYcmXcnXcoXcoXcmWckWcmVcmVcmVcmUcmU\ cmTcmTcmTcmScmScmRcmRcmRcmQcmQcmQmzPmzPmzOmzOmzOjz\ NkzNmzMnzMpzMqzLszLtzLmzQmzUmzZzzbzzgzzkzzmzznzzoz\ zmzzlzzkzzjzzhzzgzzfzzezzdzzbzzazz`zz_zzZzzXzzWzzV\ zzUzzTzzRzzQzzPzzOzzNzzLzzKzzJzzIzzHzzKzzNzzQzzTzz\ VzzYzz`zzczzfzzhzzkzznzzq } 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 31-05-11 (Cave of the Ancients [7])
by Jim Muth 31 May '11

31 May '11

FOTD -- May 31, 2011 (Rating 7) Fractal visionaries and enthusiasts: I was surprised when yesterday's exponent of 1.009 actually produced a fractal; I was astounded when today's exponent of 1.0009 produced one also. In this range, all parent fractals are roughly egg-shaped, so I searched for parents with slight irregularities on their edges. In today's case, the parent fractal created by calculating the formula 8.98 levels doen the complex log ladder with the 'recip' function applied showed such an irregular area. When I zoomed into this area, I found today's scene. To me at least, the image resembles a view from deep in a cave, looking out toward a brilliant sky. When I switched on my thought processes, the name "Cave of the Ancients" soon came to mind. This name sounds as though some deep mystical truth lies in the depths of the image. Actually, nothing is implied but the near-mystical behavior of complex numbers. The basic color palette is a repeat of the black-and-white one from yesterday's image, though in today's scene I did tweak the colors a bit. The rating of an everyday 7 remains unchanged however. 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 classic web site is at: <http://www.Nahee.com/FOTD/> Lots of sun and a temperature of 90F 32C brought a feeling of midsummer once again to Fractal Central on Monday. The fractal cats shared the midsummer effect as they found cool places to stretch out and sleep. FL spent most of the afternoon working in the garden, while I got involved in a book about relativity (of all things). The next FOTD is due to be posted in 24 hours, but we suspect the day will be busy, so do not be surprised if it is late. Until whenever, take care, search for a full-metal poet, and realize that he or she might hold the key to the salvation of the earth. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= CaveOfTheAncients { ; time=0:26:24.87-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=-2.93440272/-3.75580389/693/1/123.5/0 params=1.0009/0/-8.98/3500 float=y maxiter=42000 inside=0 periodicity=0 colors=czz0000000000000000000000000000000000000000\ 00000000000000000000000000000000001001002002003003\ 00400400500500600601701712812823923934A34A45B45B56\ C56C67D67D78E78E89F89F9AG9AGABHABHBCIBCICDJCDJDEKD\ EKDEKEFLEFLFGMFGMGHNGHNHIOHIOIJPIJPJKQJKQKLRKLRLMS\ LMSMNTMNTNOUNOUOPVOPVPQWPQWQRXQRXRSYRSYNOUNOZTU_TU\ _UV`UV`VWaVWaWXbWXbXYcXYcYZdPP_QSWZ_e_`e_`e`ae`aea\ beabebcebcecdecdeQU`UW`efeefefgefgegheghecd`ghefge\ fgeefeWS`TUadeecdecdebcebceabeabe`ae`ae_`e_`eUV`RW\ `YZdYZdXYcXYcWXbWXbVWaVWaUV`UV`FDOTU_STZSTZRSYRSYQ\ RXQRXPQWPQWOPVOPVNOUNOUMNTMNTLMSLMSKLRKLRJKQJKQIJP\ IJPHIOHIOBAFBAJFGMFGMEFLEFLDEKDEKDEKCDJCDJBCIBCIAB\ HABH9AG9AG89F89F78E78E67D67D56C56C45B45B34A34A2392\ 39128128017017006006005005004004003003002002001001\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000 } 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 30-05-11 (Uncharted Territory [7])
by Jim Muth 30 May '11

30 May '11

FOTD -- May 30, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today we enter "Uncharted Territory", which is what I named the image. Never before have I checked a fractal with an exponent as close to unity as 1.009, making today's image uncharted for sure. The graph of Z^1.009 is virtually a straight line, so how is it possible that a fractal as rich and varied as today's could come about? The answer is the multi-valued nature of the complex logarithm. The complex log is multi-valued. This means that it has many, in fact an infinity of values, and all of them are 'correct'. When applied to fractals with fractional exponents, these different values create different fractals, all of which are correct. But curiously, when applied to exponents very close to unity, as is today's, these different values create some unexpectedly rich images, in effect turning a 'sow's ear' into a 'silk purse'. Today's image lies in one of these 'silk-purse' fractals. The parent fractal is an apparently featureless ellipse, but a close examination reveals a tiny bit of chaos on the southeast shore line. Today's image lies in this chaos. I used the built-in black-and-white color palette to create the 3-D effect. Other palettes might have worked better, but an attack of terminal laziness prevented me from trying to find one. This laziness held the rating to an everyday 7. The finished image may be seen on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition 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/> Typical midsummer weather made Sunday a typical midsummer day here at Fractal Central. The fractal cats spent the day doing what cats do when the temperature reaches 88F 31C -- they stretched out and went to sleep. The humans took it just as easy, though we did stay awake at least most of the time. The next FOTD is due to be posted in 24 hours. Until then, take care, and don't ask me what I think is wrong with the new world being brought about by the recent advances in technology. I just might start to answer. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= UnchartedTerritory { ; time=0:12:09.74-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.132209132/-1.699446787/4304/1/97.5/0 params=1.009/0/4.75/1500 float=y maxiter=4200 colors=000fffgggggghhhhhhiiiiiijjjjjjkkkkkkllllllm\ mmmmmnnnnnnooooooppppppqqqqqqrrrrrrssssssttttttuuu\ uuuvvvvvvwwwwwwxxxxxxyyyyyyzzzyyyxxxxxxwwwwwwvvvvv\ vuuuuuuttttttssssssrrrrrrqqqqqqppppppoooooonnnnnnm\ mmmmmllllllkkkkkkjjjjjjiiiiiihhhhhhggggggffffffeee\ eeeddddddccccccbbbbbbaaaaaa``````______ZZZZZZYYYYY\ YXXXXXXWWWWWWVVVVVVVVVUUUUUUTTTTTTSSSSSSRRRRRRQQQQ\ QQPPPPPPOOOOOONNNNNNMMMMMMLLLLLLKKKKKKJJJJJJIIIIII\ HHHHHHGGGGGGFFFFFFEEEEEEDDDDDDCCCCCCBBBBBBAAAAAA99\ 99998888887777776666665555554444443333332222221111\ 11000000000000000111111222222333333444444555555666\ 666777777888888999999AAAAAABBBBBBCCCCCCDDDDDDEEEEE\ EFFFFFFGGGGGGHHHHHHIIIIIIJJJJJJKKKKKKLLLLLLMMMMMMN\ NNNNNOOOOOOPPPPPPQQQQQQRRRRRRSSSSSSTTTTTTUUUUUUVVV\ VVVVVVWWWWWWXXXXXXYYYYYYZZZZZZ______``````aaaaaabb\ bbbbccccccddddddeeeeeefff } 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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The FOTD for May 30 will be late
by Jim Muth 30 May '11

30 May '11

Fractal fans: The FOTD for May 30 will be about 12 hours late, but it is on the way. Jim Muth

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Re: [Fractint] FOTD 28-05-11 (The Golden Mallard [5])
by Brian Prentice 29 May '11

29 May '11

This image prominently marks the position of five minibrots in Jim's fractal for 5/28/11. As you can see, several others are also marked although not so clearly. http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_08c.png Here are pictures of two such minibrots: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_08a.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_08b.png Brian Prentice

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FOTD 29-05-11 (Least Likely Spiral [No Rating])
by Jim Muth 28 May '11

28 May '11

FOTD -- May 29, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image is another super-quickie. I got lazy. Even the most ardent fractalists sometimes feel lazy when the weather is warm. To produce today's image I started with yesterday's mallard duck and gave him his proper plumage by rendering the fractal with the inside set to 'zmag'. (In my haste, I forgot to give the poor bird his plumage in yesterday's image.) Apparently, I also forgot to give him a bill. (A duck would have a hard time dabbling for food without its bill.) Today, feeling sorry for the bill-less bird, I went to the spot where the bill should have been attached, but nothing I tried came anywhere close to adding a workable duckbill. Finally, in frustration, I checked a small area of debris in the vicinity. After a brief search of the debris field, I found no bill, but the broken spiral that appears as today's image was enough for an FOTD. There is not much I might say about the image, which is best left to quack for itself. I gave the image no rating, though a rating of something like a 5-1/2 seems appropriate. The name "Least Likely Spiral" reflects the disconnected nature of the spiral, which I assume is endless. To see the image, set up and run the included parameter file. The image is posted already calculated on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> A very pleasant day prevailed here at Fractal Central on Saturday, with lots of sun and a temperature of 82F 28C. The humidity was rather high, but fractal cats do not worry about humidity, so the dynamic duo had a relaxed day, and even managed to avoid getting into trouble. The humans had a reasonably pleasant day also. I spent a good part of the time watching the clouds drift by, while FL busied herself working in the garden. The next FOTD will be posted in 24 hours. With the first holiday of summer coming up, the next fractal or two might be more quickies. Until then, take care, and I finally worked out the answer to the perplexing measurement problem, but as soon as I finished, my answer became uncertain. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= LeastLikely_Spiral { ; time=0:22:40.23-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.485482025/+1.43064256028/198250/1/\ 54.6/0 params=1.05/0/10.5/1500 float=y maxiter=3200 inside=zmag periodicity=6 colors=00012K22K32L42L52M62M73M73N83N93O93OA3PA4PA\ 4PA4Q54B54D54E55G55H55I65K85LA5NC6OE6QE6RE6SF6UF6V\ F7XG7XG7ZH7_I7`J7bK8cL8eN8fP8gR8iT8jU8lW9mX9oY9pZ9\ qJ9cJ9cAIQ9GV8FZ8Db7Cf7Aj69n68rGKfQWV_fJq53lBBgHIb\ MQZSXUYcPbkKhrGmyJooMpePqWRrMHv1Gq8FlEEgLEbRDYXCTc\ BOiBKo9Tk7`g6hc4p_3xX7wZAw_Dw`HvbKvcNvdQvePsaOpZNm\ VMjSLgOKdLJaHI_EFbLDdSAfZ8hdFfWMeNSdERZDQTCPOBOIAO\ D9UKCZREcXHicJniMspOxvQaicFYpAZg5_Z0`Q4aM7bIAcFDdB\ Ge8Jf4Mf1o1Cj8FeEH`KKWQMRWPMaRHgUCmWqrPqoMqmJqjGqh\ EelBVp8Ks6Np9PnBRkDTiFVgIXdKZbM``O_YPzVPzSPzPQzMQz\ JQzHQzKOzNNzQLzTKzWJz`LzdNzhPzlRzpTztVzgdzWmzgQzdO\ zbNz_LzYKzVIzTHzRGzLMzGRz3PzT1zS6zRBzQGzPLzOQzNUzK\ WzHYzRTz`PzjKzsGzqHzoIznJzlKzkLziMzhNzXRzLVzAZzJcz\ RgzZlzfpzntzfmz_gzS`zLVzPZzTazXez`hzdlzhozlszovzs_\ zvDzqMzlVzhczclz_tzcbzfMzgPzhRziTzjVzhSzfPzdMzbJz`\ GzZDzXAzV7zW8zX8zY9zZ9z_G } 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 27-05-11 (An Incredible Hole [8]) Type: Text
by Hal Lane 28 May '11

28 May '11

Brian, Nice variation on Jim's: FOTD 27-05-11 (An Incredible Hole [8]) - Hal Lane ######################### (\__/) # hallane(a)earthlink.net # (='.'=) ######################### (")_(") Author: Brian Prentice Date: To: Fractint and General Fractals Discussion Subject: Re: [Fractint] FOTD 27-05-11 (An Incredible Hole [8]) A very beautiful image Jim, I hope you spend more time with this fractal and devote future FOTD's to it. There are many more fascinating details to be found, for example my favorite so far is this spiral: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06d.png which can be found on the edge of the minibrot in the area closest to the hook. Brian Prentice

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FOTD 28-05-11 (The Golden Mallard [5])
by Jim Muth 28 May '11

28 May '11

FOTD -- May 28, 2011 (Rating 5) Fractal visionaries and enthusiasts: Due to an unexpectedly busy day on Friday, today's image is a quick and simple one, and the discussion is just as simple. The image is named "The Golden Mallard". On the surface it does resemble a duck floating serenely on an invisible body of water. (A lake transform might have been helpful in creating the water effect.) Actually, the image is the parent fractal that is created when the formula Z^(1.05)+C is iterated 10-1/2 levels up the complex logarithmic hyperspiral with the 'recip' function applied. (This function seems to work best with this formula, though I doubt that it is the most accurate.) The calculation time of 41 seconds will pass quicker than a car at the Daytona Speedway. But before this speed can be apprecia- ted, the included parameter file must be set up and run. The way to avoid this minor hassle is to view the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds and a temperature of 84F 29C made Friday a pleasant but rather warm day here at Fractal Central. The fractal cats spent the day taking it as easy as possible without giving up the activity that goes with asking for food. FL spent some of the time in the garden, caring for a sick rose bush. (I did not realize gardening was so emotional.) The next FOTD will be posted in 24 hours. Until then, take care, and the next time you think a deep thought, try to deter- mine how much the thought weighs. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Golden_Mallard { ; time=0:00:41.30-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=-1.58412/-0.336258/0.4444593/1/-20/0 params=1.05/0/10.5/1500 float=y maxiter=3200 inside=0 logmap=37 symmetry=none periodicity=6 colors=00012K22K32L42L52M62M73M73N83N93O93OA3PA4PA\ 4PA4QA4QA4RA4RA5SA5SA5SB5TC5TD5UD6UE6VE6VE6VF6WF6W\ F7XG7XG7YG7YG7YG7ZG8ZG8_G8_G8_G8`H8`H8aI9aI9bI9bI9\ bJ9cJ9cJAdKAdKAeKAeKAeKAfKBfKBgKBgLBhLBhLBhLCiLCiL\ CjLCjMCkMCkMDkMDlMDlMDmMDmNDnNEnNEnNEoNEoNEpNEpNEp\ OFoOFoPGoPGoQHoQHoRIoRIoSJoSJnTKnTKnULnULnVMnVMnWN\ nWNnXOmXOmYPmYPmZQmZQm_Rm_Rm`Sm`SmaTlaTlbUlbUlbUlc\ VlcVldWldWleXkeXkfYkfYkgZkgZkh_kh_ki`ki`kjajjajkbj\ kbjlcjlcjmdjmdjnejneiofiofipgipgiqhiqhiriiriiriiph\ gnhfmhekhdjgchgbfgaeg`cf_bfZ`fY_fX`gY`hZ`hZ`i_`j``\ ka`la`mb`nc`odbn_dmVelQfkRgjRhiRhiSihSjgSjgSkfTleT\ mdTmdUncUocUocUpcVpcVpcWpcWpcXpcXpcYpcYpcZpcZpc_Nm\ 7Mm8Mm9LmALmBKmCKmDJmEJmFImGImHcmIcmJcmKcmLcmMcmOc\ mNcmNmmNmmNmmNmmNmmNmmNmmNmmNmzMmzMmzMmzMmzMmzMmzM\ mzMzzMzzMzzMzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzKzzKzz\ KzzKzzKzzKzzKzzKzzKzzKzzz } 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 27-05-11 (An Incredible Hole [8]) Type: Text
by Brian Prentice 27 May '11

27 May '11

A very beautiful image Jim, I hope you spend more time with this fractal and devote future FOTD's to it. There are many more fascinating details to be found, for example my favorite so far is this spiral: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06d.png which can be found on the edge of the minibrot in the area closest to the hook. Brian Prentice

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FOTD 27-05-11 (An Incredible Hole [8])
by Jim Muth 27 May '11

27 May '11

FOTD -- May 27, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows one of the many holes that lie near the base of the hook in the image of May 23, when the exponent of the image is lowered from 1.08 to 1.078 and the minibrot tracked down. I named today's image "An Incredible Hole" because in some ways the attributes of the central hole are as unbelievable as some of the kooky claims now circulating among the credulous. (But remember that a claim is not necessarily false simply because rationalists disbelieve it.) To emphasize the hole's unusual qualities, I brought it to active life by rendering the scene with the inside set to 'bof61'. (When the hole appears as a flat black area, some of its impact is lost.) The bluish-pink coloring of the hole is unintentional. It came about by lucky accident. The hole is a true hole, and not simply an artifact of too low a maxiter. I tested the scene with a maxiter of 1,000,000 and found the hole unchanged. The amazing thing about this hole became obvious when I decided to count the number of large lobes around its edge. After several failed attempts to get an exact count, I realized that I would never get the count correct, for the large and small lobes with all their sub- and sub-sub-lobes, are of one and the same series. The total number of lobes is therefore infinite. The inside of the hole in today's image is actually an extension of the minibrot in the original 'minibrot for the ages' image. The original minibrot extends invisibly under the surface debris of the original image, well beyond the hook. The rating of an 8 seems justified. If I had put a bit more effort into the coloring, I might have rated it an 8-1/2. The finished image is available on the internet at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Thursday turned into a midsummer-like day here at Fractal Central, with enough heat, haze and humidity to satisfy the most ardent hot weather lover. The high temperature of 90F 32C totally satisfied the fractal cats, who stretched to their full cat lengths to show their pleasure. As of post time, a warning on the TV Weather Channel (I call it the Commercial Channel) of possible tornadoes in the area had proved to be a scare rather than a forecast. The humans had a relatively slow day, which was good in some ways, but not so good in others. If nothing goes wrong, which is usually the case, the next FOTD will be posted in 24 hours. Until then, take care, and yesterday's kookiness sometimes proves to be today's scientific fact, but before the question is settled scientifically, how does one tell the true kookiness from the kooky kookiness? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= An_Incredible_Hole { ; time=0:08:12.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.000750885846/+1.174041344618/144809\ /1/-47.5/0 params=1.078/0/16/525 float=y maxiter=4000 inside=bof61 logmap=-250 periodicity=6 colors=000zf0ze0ze0zc0yb0yb0wa0va0v_0tZ0tZ0sX0qX0q\ W0pW0pU0oT0mT0mR0lR0zhvjQ0iO0zaohN0hM0zUhfK0eI0vNU\ cH0oFNoF0h7F_E0a07ZC0Z07aB0W00W00U70U00T60R00R40Q2\ 0Q00O00N00N00L00J00H00G00F00F00C00A007009005005002\ 00300800A00H00H20N40N60O70Q90QB0RC0TC0TE0UF0UH0WI0\ XK0XM0ZN0_O0_Q0aR0aT0eU0hW0mX0rX0vZ0z_0za0zb0zd0zg\ 0zi0zl0zm0zm0zm0zm0zm0zm0zm0zl0zk0zj0zi0wh0wh0yh0y\ h0zh0zh0zh0zh0zh0zh0zh0zh0zh0zh2zh2yh4wh4ehZehZfh_\ fh_hh_hhaihaihaihajhbjhbjhblhblhblhcmhczUczUczUczU\ czUezUezUezUezUezUfzUfzUfzUfzUfzUfzUhzehzchzbhzahz\ _izZizXizWizUizTizRjzQjzOjzNjzMjzKlzIlzHlzFlzElzCl\ zBmz9mz7mz6mz4mz2oz0oz0oz0oz0zz0zzKzzKzzKzzKzzKzzK\ zzKzzKzzKzzKzzKzzKzzKzzKzzKzzKztKzvKzvKzvKzwKzwKzw\ KzyKzyKzzKzzKzzKzzKzzKzzKzzKzzUzzUzzUzzUzzUzzUzzUz\ zUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzUzzUzzUzzUzzUzzUzzUz } 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 26-05-11 (Cells of a Fractal Tree [7])
by Jim Muth 26 May '11

26 May '11

FOTD -- May 26, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us back to the original fractal tree that appeared as the FOTD for May 23, 2011. Today, instead of focusing on the entire tree, we venture deep into its fractal wood to check its internal cellular structure. What we find there is a field of strange flattened cells that look like they have been squashed in a press. But even more startling is that the field of cells appears to stretch into the distance toward a horizon, making a scene that could possibly exist on an alien planet circling another star. It's not so unexpected. After all, in the original discussion I did comment that these fractal trees also make good alien landscapes. To bring out the landscape effect, I gave the sky a shade of deep blue, which might be found on a planet with a thinner atmosphere than earth's. Luckily, unlike on Mars, there is no dust in this atmosphere to spoil the purity of the blue sky overhead. The name "Cells of a Fractal Tree" describes the coral-colored objects in the image. The rating of a 7 indicates that I consider the image to be above average but not exceptional. The finished image is available on the internet at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Total sunshine prevailed here at Fractal Central on Wednesday. The sun, along with the temperature of 82F 28C, made it one of the finest days of the belated spring. The fractal cats passed the day lazily watching the world go by, but snapped to full alertness when Cassie spotted a bedraggled long-haired white cat prowling in the back yard garden. The humans' day was acceptable. Other than working, I spent much of the day watching the tornado action on the Weather (and advertisement) Channel. FL spent some time working on her 'CrossScan' puzzles and hoping they become a big hit. I helped her hope. The next FOTD will be posted in 24 hours. Until then, take care, and if at first you don't succeed, try and try again -- and then give up. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fractal-Tree_Cells { ; time=0:01:00.06-SF5 on P4-2000 reset=2004 type=julzpower center-mag=+0.1591795970\ 85/+0.522912404175/5340717/1.4756/2.75/0 params=-0.1964/0/1.5/0 float=y maxiter=1500 bailout=25 inside=0 logmap=122 periodicity=6 colors=0002AU4AW6AY8A_AAaCAbEBdGDfIGhKKjMOlOSnQWpS\ _rUctXevYgxZizYkzYmzZoz_qzaqzdqzgrzjrzmrzmszmszmsz\ mtzmtzmuzmvzmwznxzoyzpzzqzzrzzszztzzcUOfWKdZNc`Qab\ T`eWZgYYi`WlcVnfTphSskQunPwqOysLsoImlFhiCbe9Yb6S_3\ NX9RZFU`LYaR`cXcdbgfhjhnnitqkytlwravqSuoHtn7rcIqTS\ pJaoHcnFemDglBik9kj7mi5oh3qg1sf0ue4vd7vdcdefcghahk\ `inZjpXksWlvUmxTnuUosUopUpnUqlUqiVrgVseVsbVt`VuZVu\ WWvUWwSWwPWxNWxLWvMVuMUtNUrNTqOSpOSnPRmPRlQQkQPiRP\ hROgRNeSNdSMcTMbTL`UK_UKZVJXVIWWIVWHUWHTXERYFQZGPZ\ HN_IM_IL`JJ`KIaLHaLFbMEbNDcOCcOBeSBfVAgYAi`9jc9kf8\ mi8nl7oo7prDjjIecN_XSVQQTPOSONRNLQNJPMIOLGNLEMKDLJ\ BKI9JI8IH6HG5GGAFJFFMKFPPESUEUZEXcD_hDbmDdjCagC_eC\ XbCV`BSYBQWBNTBLQAJOAGLAEJABG99E96B94992FE8KIEPMKU\ RQZVWcZahbfiZhiVjiRliNniKpiGriCti8vi5xayQcoXeecfXi\ eYfdYdcYbbZ`aZZ`ZX__VZ_TY_RWYUUWWSUYRS`PRbNPdLNfKL\ iIJkGImEGoDErBCtaWibZhc`f } END PARAMETER FILE=========================================

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FOTD 25-05-11 (Demystified Midget [6])
by Jim Muth 25 May '11

25 May '11

FOTD -- May 25, 2011 (Rating 6) Fractal visionaries and enthusiasts: In today's FOTD I have another go at the 'Minibrot for the Ages' that appeared as the FOTD for May 21. Well, actually it's not the same minibrot. The May 21 minibrot has an exponent of 1.08, while today's version has an exponent of 1.0745. As the exponent is reduced, the prominent hook changes into an arch, and the entire minibrot moves toward the main bay of the parent fractal, where it is quickly swallowed up. Today's image catches it as it plows through the fine grit on the shore line of its parent's main bay, shortly before it dives into the bay. To get top detail, it was necessary to render today's image at a maxiter of 32,000, which increases the calculation time to an annoying 40 minutes. The image was rendered with the outside set to 'fmod'. This is a mistake, since I wanted to try the scene in the normal outside=iter manner. But by the time I had realized the error, 40 minutes had passed, and the image was finished, and it even looked rather pleasing, so I let it go as FOTD for May 25. The name "Demystified Midget" indicates that all those strange holes around the base of the hook of the original version are actually parts of the second half of the minibrot peeping through. Today's image removes all doubt that half of the original minibrot is actually obscured from view. The rating of a 6 is for artistic value. The mathematical value is closer to a 9. To view the scene, either run the included parameter file or view the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-def version will soon be posted 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/> A mix of sun and clouds, and a summer like temperature of 81F 27C made Tuesday a near ideal day here at Fractal Central. The fractal cats must have agreed, for they spent an unusual amount of time watching the outside world, which is a cat's TV. The humans had an uneventful day. This is always a good thing, and if tomorrow is just as good, the next FOTD will be posted in 24 hours. Until then, take care, and never say never. If things keep going as they are, one of these days we may find that one plus one suddenly equals three. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Demystified_Midget { ; time=0:40:43.14-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-0.20382948/+1.15808753/112/1/-105/0 params=1.0745/0/16/525 float=y maxiter=32000 inside=255 outside=fmod periodicity=6 colors=000QDgQDgQEgPEgPEgPEgPFfPFfPFfOFfOGfOGfOGfO\ GfOHfNHfNHfNHfNIfNIfNIfMIfMJfMJfMJfMJfMKfMKfLKfLKf\ LLfLLfLLfLLfKMeKMeKMeKMeKNeKNeJNeJNeJOeJOeJOeJOeIP\ eIPeIPeIPeIQeIQeIQeHQeHReHReHReHReHSeGSeGSeGSeGTdG\ TdGTdFTdFUdFUdFUdFUdFVdEVdEVdEVdEWdEWdEWdEWdDXdDXd\ DXdDXdDYdDYdCYdCYdCZdCZdCZdCZdB_cB_cB_cB_cB`cB`cA`\ cA`cAacAacAacAacAbc9bc9bc9bc9cc9cc9cc8cc8dc8dc8dc8\ dc8ec7ec7ec7ec7fb7fb7fb6fb6gb6gb6gb6gb6hb6hb5hb5hb\ 5ib5ib5ib5ib4jb4jb4jb4jb4kb4kb3kb3kb3lb3lb3lb3lb4l\ c3hb2db2Xa1Pa1H`09K01K12K23K23K34K45L45M56N67O67P7\ 8Q79R89S9AT9BUABTBCTBDTCDUDEUDEUEFVEGWFGXGHXGIYHHY\ IIZIJZJJYKJYKKYLJYLKYMKYNKYNLYOLYPLYPMYQMYQNYRNYSN\ XSOXTOXUOXUPXVPXWPXWQXXQXXQXYRXZQXZRX_SX`SW`TWaUWb\ UWbVWcWWcWWdXWeYWeYWfZWg_Wg_Wh`Wh`WiaViaViaViaVjaU\ jaUjaUjaUkaTkaTkaTkaTlaSlbSlbSlbSmbSmbRmbRmbRnbRnb\ QnbQnbQobQobPobPocPpcPzzz } 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] MinibrotForTheAges
by JackOfTradeZ＠comcast.net 24 May '11

24 May '11

. ""If you change the real value of parameter 1 from 1.08 to 1.078, draw the midget corresponding to the one you posted today and then look at the south east side of the hook, you will find an area with an infinite number of midgets or holes. "" When I change from 1.08 to 1.078 I just get a pink background with a few jagged islands - no "hook" or main midget. What am I doing wrong? ""Here is a picture of that area: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06a.png and here is a detail of one of the midgets or holes: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06b.png"" Awesome pics - could you just post the 2 PARS for them? .

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Re: [Fractint] Fractint Digest, Vol 99, Issue 15
by JackOfTradeZ＠comcast.net 24 May '11

24 May '11

. ""If you change the real value of parameter 1 from 1.08 to 1.078, draw the midget corresponding to the one you posted today and then look at the south east side of the hook, you will find an area with an infinite number of midgets or holes. "" When I change from 1.08 to 1.078 I just get a pink background with a few jagged islands - no "hook" or main midget. What am I doing wrong? ""Here is a picture of that area: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06a.png and here is a detail of one of the midgets or holes: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06b.png"" Awesome pics - could you just post the 2 PARS for them? .

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FOTD 24-05-11 (Bubbles in Numbers [6])
by Jim Muth 24 May '11

24 May '11

FOTD -- May 24, 2011 (Rating 6) Fractal visionaries and enthusiasts: When certain people have trouble sleeping, they sometimes count sheep. When I can't sleep however, I begin mentally exploring an imaginary four-dimensional world. My imaginary world is truly four-dimensional; the problem is that I can mentally ex- plore it only one 3-D slice at a time. As our planet earth has a curved two-dimensional surface, my 4-D world has a curved three-dimensional hypersurface. On earth, two coordinates, latitude and longitude, are necessary to posi- tion a point; on my 4-D world, latitude, longitude and lithi- tude, (my own invention), are required. Moving in the lithi- tude direction does not take us into the sky or underground; it moves us in the third dimension, flat along the hypersurface. To reach a given location on this 4-D world, we start at the zero-zero-zero point on the equator, which is a great circle that circles the planet just as earth's equator does, and from there we travel until we reach the correct longitude. Now we find ourselves with a problem. Before we can set off toward the pole, we need to determine in which direction to go. On earth there are two directions, north and south, leading toward the two polar points; on my 4-D world there is a full 360- degree circle of directions extending from the equator, each direction leading to a distinct point on the polar circle. The direction in which we must travel away from the equator is the lithitude. Once we have chosen the lithitude, we need the lati- tude coordinate, which tells us how far to go toward the polar circle in the direction we are traveling before we reach our destination. But even stranger things than this happen on my planet. There is also the matter of rotation. On earth, rotation is a simple thing -- the planet rotates on its axis, a line that extends through the globe from pole to pole. But on my 4-D planet, the axis of rotation is a plane that cuts the hypersurface along the polar circle, a curiosity that causes complications. The problem arises because the polar plane exists in two dimen- sions that are stationary even as the planet rotates around it. The polar plane is therefore free to rotate on itself, with the equator as the axis of its rotation. And in a universe with 4-D gravity, it is unlikely in the extreme that the polar plane does not have at least some degree of rotation. The 4-D planet is subject to two independent rotations at the same time. Every point on the hypersurface as well as every point within the planet is tracing out what is known as a surface of double revol- ution, a kind of 4-D donut. Things on the surface of my planet move in paths resembling spirals, which curve back on themselves into closed loops. This means that the stars in the hypersky must move in helixes. What fun it must be to set up camp in some dark spot on the hypersur- face of my hyperplanet and point a hypertelescope at the hyper- stars and hyperplanets. The hypertelescopic clock-drive would be a complex device, but I'm sure that it could be made. If the two rotations are equal, things get even more complica- ted, but this is a story for another day. For now, we have a fractal to investigate. Today's image lies in the parent fractal that comes about when Z^(1.25) is subtracted from Z^(-1.75) before (1/C) is added on each iteration. This parent is more a field of debris with two large Mandeloids than a single object. Today's scene is located in some debris lying between the two largest Mandeloids. There is not much to be said about the fractal, so I'll let it speak for itself in visual terms. The name "Bubbles in Numbers" refers to the bubbly shapes in today's image and also to the fact that fractals are made of numbers. The rating of a 6 indicates that the image has room for improvement. To view the image, either run the included parameter file or go to the FOTD web site 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 web site may be accessed at: <http://www.Nahee.com/FOTD/> There were too many clouds at Fractal Central on Monday for the day to be considered a good one. The temperature of 75F 24C was fair enough however. The fractal cats spent the day plotting mischief, but fell asleep before they could put their plot into action. In the afternoon a tornado warning came over the radio, but the storm passed over with only a strong wind squall and a torrential rain. The day of the humans was one more in an unending series of similar days. But the older one grows, the more such uneventful days are appreciated. The next in the unending series of FOTD fractals will be posted in 24 hours. Until then, take care, and when do we get to see the all of fourth spatial dimension in one moment of time? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Bubbles_in_Numbers { ; time=0:00:30.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.03748573643483764/-0.655971033500649\ /1.5667e+010/1/-35/0 params=-1/1.25/1/-1.75/0/0/0/0 maxiter=500 inside=0 logmap=57 periodicity=6 colors=0000440650962C74F86I9AL7DO5HV4Kd2Nl1cu2tz2h\ ZPK35Q46X47b48h59n5AuKBzPBsKGk8Lc9QXAVjBnkGelKYmOQ\ nSIoWAp_2sWLvSbyOtv`atlJqfMnaOkXQhRTeMVbHXaMa`Qe_V\ iZZmYcqXguXky`lndmdgnVkoLnoBLCIF_J9wKLaUXHceMjmRqu\ WxrSppOimKbkGWhCPf8Id5Bc6Eb7Ha8K`9M_APZBSYBUdjo_il\ WijRigNieIicEi`9iZ5iXPVfgGpz1yy2xx3wx4wvAutGtsLrqR\ qpWonanmfmkiqjlthowgqzajpXdgRZYMTPHNGVVNgbUti`neai\ aacZaZVaTRaOOaIKaDHaDGbDFbDEcDDcHCdLCdPBdTBdXBdYAc\ Z9cZ9cSCaLF_EIY7LW0NV4TS8YQCbNFgLJlINqGQvEMbCIJAF0\ 8E62TGJXLL`QMcVOg_PkdRniSrnUurVqrUmrTksYitagueevic\ wmbxq`toZqnXnlWkkUgjSdhQagPZfPYeQXcQWbQW`QVZQUYRTW\ RTVRSTRRSRQQRQPTOQVMQXKRZIR`GSbESdCSfATh8Tj6Ul4Um2\ Uj5Vh8WfBWcEXaHY_KYXNZVQZTT_QW`OZ`MaaKdaUH0`IDVH2W\ H3XH5YH6ZH8_H9`HBDSaHQYKPVNNSQMPTLLWJIZIFRx_StYTqW\ UnUVkTVhRWePXbOYZMZWKZTI_QH`NFaKD5Qd8PaBO_ENXGNVJM\ SMLQPKORKLUJJUTeOWXJZNDaD } 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 23-05-11 (The Original Tree [No Rating])
by Jim Muth 23 May '11

23 May '11

FOTD -- May 23, 2011 (No Rating) Fractal visionaries and enthusiasts: Today, with time at a premium, it's back to fractals-101. When I booted the first version of Fractint that had the ability to calculate fractional powers of Z, the first formula I tried was the type=manzpower, and the second thing I did was check the Julia set of the point on the negative X-axis where the western shore line of the main bay lies. What I found was a fractal that rather resembles one of those extinct marine animals known as trilobites. But an animal that once oozed through prehistoric sea-floor slime makes a poor model for a fractal. Luckily however, the trilobite was surroun- ded by a ring of graceful though stylized fractal trees. One of these trees appeared as one of the very first FOTD images, though that image was calculated at a much lower maxiter than today's version. The original version cut off the deep spirals that engulf the sides of the crown of the tree. I could not give a rating to today's image. I put relatively little coloring effort into it, and it must be about the eighth fractal tree in FOTD history. The name "The Original Tree" simply reminds the viewer that such a tree was the first of the infinity of fractal trees that I stumbled upon. Actually, this fractal tree stuff is quite common in the fractals created with fractional exponents, and can be turned into several other rather convincing things such as fractal landscapes on alien planets. The finished image is posted, already calculated, at: <http://www.crosscanpuzzles.com/Archives.html> The hi-def version of the finished image is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic original FOTD web site is at: <http://www.Nahee.com/FOTD/> Saturday turned into the most pleasant day in over a week here at Fractal Central, with partly cloudy skies and a temperature of 81F 27C. A few showers were scattered around the area, but they all missed FC. Sunday was not so pleasant. The sky was totally cloudy and the temperature reached only 73F 23C. The fractal cats had two uneventful days, spent mostly sleeping. The next FOTD will be posted in 24 hours. Until then, take care, and do well in your endeavor. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Original_Tree { ; time=0:00:32.35-SF5 on P4-2000 reset=2004 type=julzpower center-mag=0.238352/0.49\ 311/6.45945/1/-1.5/0 params=-0.1964/0/1.5/0 float=y maxiter=1500 bailout=25 inside=0 periodicity=6 colors=000ci__haXgbTfcPecMdcIccEbcBac7`c4__0ZY0YZ3\ XZ3WY3VX3UX3TW2SV2RU2QT2PS2OR2OQ2OO4OQ6PS8QTARVBSX\ DTZFU`HVaIWcKXeMYfOZgR_dU``ZaTcbLgcDid6ie8ffAcgC`h\ EYhFZgH_eJ`cLaaNb_PcYRdVTeSVfPVfMVfJVbIUZHSVGQRFNN\ ELKDJGCHCBE8AC49A188397597797997B97DA7FA7HA7JA7LA7\ NB7PB7RB7TB7VB7XB7ZFC_IG`MKbPOcTSdWWf__gbchfgjikkm\ olpsmswXqkUmlRilPemMbmKZmHVnFSnCOoAKo7Ho5Dp29p06p3\ Bn6Fl9KjCOhFTfIXdHYaGY_GYYFYWFYUEYREYPDYNDYLCYJCYG\ BYEBYCAYAAY88TL9SOARRBQTCPWDOYEN`FMbGLeHKgIJjJJlKQ\ cLXWMcONjGOq8Px0Zj9gXIqJRz5_yIbyUexfhxrkvrhtrfsrdq\ rbor`nrZlrXjrUirSgrQerOdrMbrKarIarHbrGcqFdqEeqDepC\ fpBgoAho9io8in7jn6kn5lm4mm3mm3nl4nl4nl4nl4nk5nk5nk\ 5nk5nk6nj6nj6oj6oj7vRSoi7oi7oi7oi8oi8oh8oh8oh8oh9o\ g9pg9pg9pgApgApfApfApfBpfBpeBpeBpeCpeCqeCqdCqdDqdD\ qdDqdDqcDqcEqcEqcEqbErbFrbFrbFrbFraGraGraGraGr`Hr`\ HdZco_Wy_Ou`Qq`SnaUjaWfbY } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8])
by Hal Lane 22 May '11

22 May '11

Brian, Thanks for sharing these images. I like them a lot. Great images, and super coloring. The shrimp-like shapes in your "c" image below remind me of the extinct anomalocaris: http://bygonebeasts.wordpress.com/2010/10/26/anomalocaris/ - Hal Lane ######################### # hallane(a)earthlink.net # ######################### > -----Original Message----- > From: Brian Prentice [mailto:bprentice@webenet.net] > Sent: Sunday, May 22, 2011 1:26 PM > To: Hal Lane > Subject: Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8]) > > > Thanks Hal, I've just posted two more beautiful details: > > http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06c.png > http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06d.png > > Brian >

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Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8])
by Hal Lane 22 May '11

22 May '11

Brian, Nice images -- and coloring. - Hal Lane ######################### (\__/) # hallane(a)earthlink.net # (='.'=) ######################### (")_(") > I've been exploring your fascinating fractal for today. > If you change the real value of parameter 1 from 1.08 > to 1.078, draw the midget corresponding to the one you > posted today and then look at the south east side of > the hook, you will find an area with an infinite number > of midgets or holes. Here is a picture of that area: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06a.png > and here is a detail of one of the midgets or holes: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06b.png > Brian Prentice

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Re: [Fractint] FOTD 21-05-11 (Minibrot for the Ages [8])
by Brian Prentice 21 May '11

21 May '11

Jim, I've been exploring your fascinating fractal for today. If you change the real value of parameter 1 from 1.08 to 1.078, draw the midget corresponding to the one you posted today and then look at the south east side of the hook, you will find an area with an infinite number of midgets or holes. Here is a picture of that area: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06a.png and here is a detail of one of the midgets or holes: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_06b.png Brian Prentice

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Re: [Fractint] How do I plug screen coordinates into a julia type?
by Jim Muth 21 May '11

21 May '11

At 12:51 AM 5/19/2011 -0600, Jay Litwyn wrote: >MandelBroh { ; What can you do with this, Jim? > ; This is all I can figure for a parser formula >that does Julia types. > ; It requires plugging screen coordinates into >P4. >z=fn1(pixel) +P2, c=fn2(pixel) +P3: > >if(ismand) > z=z^real(P1) +c >else > z=z^real(P1) +P4 >endif > >|z| <= imag(P1) Jay: It looks to me as though you are trying to write a formula that will automatically switch between the Mandelbrot and Julia aspects of a fractal by toggling 'ismand' on and off. To get the formula to work as you intend, with the screen coordinates automatically entered into the P4 parameter, would probably require new parser code. But many of the formulas hard coded into Fractint already do just this. With a Mandelbrot image on the screen, (try the manzpower formula), strike the space bar. A marker will appear at the center of the screen. Move the marker to the area of the Mandelbrot scene that you would like to see the Julia set of, and strike the space bar again. The Julia set will instantly be calculated. Striking the space bar again will return to the Mandelbrot set. JIM

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FOTD 21-05-11 (Minibrot for the Ages [8])
by Jim Muth 21 May '11

21 May '11

FOTD -- May 21, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is titled "Minibrot for the Ages". This is admit- tedly an exaggeration, but the minibrot actually is the most impressive I have yet found in a Mandeloid with an exponent of Z less than sqrt(2). In today's image the exponent is a lowly 1.08. The parent fractal was calculated 16 levels up the complex- logarithmic hyperladder with the 'recip' function applied. Using this function probably defeats the original purpose of the formula, which was to create an animation of the different fractals that can be created from the different values of the multi-valued complex logarithm. This parent is shaped much like the minibrot in the image, though it lacks the prominent hook, and has a 'nose' on what would be the upper right side of its main bay. Today's minibrot is very large. In fact it is actually visible on the northeast shore line of its parent with only the slight- est magnification. The rating of an 8 might have been higher if I had devoted more effort to the coloring, which I admit is a bit haphazard. The image calculates is an unremarkable 3 minutes. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> and in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> Periods of sun interspersed with occasional thunder-showers made Friday an interesting day here at Fractal Central. The tempera- ture of 70F 14C was mild enough by winter standards, but rather chilly for late May in central Pennsylvania. The fractal cats had a typical day, though I think a bit of bad feelings arose between them in the afternoon. FL and I sometimes think of screening the back porch, adding shelves for the duo to leap onto, and making the entire porch into a catarium, where they can climb around and watch the world from their high, safe perches. The fractal cats appear to be ready for it. The humans had a frustrating day. We got word that one of our biggest customers will no longer be using our design services. This will leave more time for work on fractals, but less money for other things. Luckily, fractals are free and the supply of them is infinite. The next fractal will be posted in 24 hours. Until then, take care, and don't waste your energy worrying about things that have no chance of happening. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= MinibrotForTheAges { ; time=0:03:00.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=+0.106891367/+1.163747143/147.5/1/\ -178.25/0 params=1.08/0/16/525 float=y maxiter=12000 inside=0 logmap=158 periodicity=6 colors=000cKQaLPZMPWOOUPORRNOSNMTMJVMGWL6ZD9YGCYIE\ YLHZNK`PMaSPcUSdXUfZXh`_jcakedmhgojipljoijofjodkna\ kn_knXlmVlmSmlSmlRmlRlkQkjQiiQhhPfgPefXdeUcdSbcPbb\ N_YKYTIVOFSJDQEAG98A46mKzkFyj3ui5rh7ogDlWScLZUNdKP\ c4Rb9TaDVZIYWM_TRaQVcQXdPYePZfP`hQbkRdmSfoSgqRgsRg\ oTgkUegWccXb_Z`W_ZSaXObWKdUGeSAeS6eTDfRJgQPgPVhOai\ NgiMmjLskKykJubErV9nM4kE0gD5dDA`DFYDKUDPRCUNCZKCcG\ ChDCm93vACqALmAThAadAj_FyUDvVCtVArW9pW8nX6lX5jY2kX\ 3jY3iY4hY4gY5fZ5eZ5dZ6cZ6b_7a_7`_3Ep5MjATdK__UfUcm\ OmzEctJUpOQkSMgXQbaUZeYUjTPlaQniQopFqqLpqQprWor`os\ enskntpmyzzvwztuzqszoqzlovjmpgkceiVbgR`eOYcLWaIY_6\ U_FR_ON_WK_dH_lJZiLYgNYeOXcQXaSW_UWYVVWXVUZUSXQP_U\ QaXRc_SebTgfTiiUklVmoWorWkoXhmYzkzbhz_fzzezThzQkzz\ nzKqzHtzzwz4zz7zzzzzBzzCzzzzzDzzDzzEzzEzz0zzEzzRzz\ czzqzzpzzszzrzzqzzpzzozznzzmzzlzzkzzjzzizzhzzgzzfz\ zezzezzgzzizzkzzlzzizzfzz } 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 20-05-11 (Celestial Banquet [9.5])
by Jim Muth 20 May '11

20 May '11

FOTD -- May 20, 2011 (Rating 9.5) Fractal visionaries and enthusiasts: Today's image is not new. It is an updated version of a FOTD that I first posted over 10 years ago. For the image's second appearance, I did a slight outzoom and slightly intensified the colors. The result rates a 9.5, (at least IMO), with the extra half point honoring the coloring effort. The parent fractal is more a scattering of bits and pieces than a single large bay surrounded by interesting details. But there is one prominent element, and today's image lies in a valley of a bud in this large element. The name "Celestial Banquet" was inspired by the heavenly effect of the turquoise surroundings, where the angels are almost visible dancing on the gossamer clouds. I guess the saints are watching from the sidelines. The spiky arms shooting off in all directions give just enough impression of gateways to infinity to complete the transcendental experience. Actually, such a heaven, at least IMO, would be more of a hell than a reward. What could be worse than being stuck in a boring church service that would never end, lacking even the ability to escape into sleep. I have heard it said that when Casanova, having lived a life of sin, finally arrived at the golden gates, he was met by Saint Peter, who took no time in consigning him to the other place. Hearing the expected bad news, Casanova turned and saw before him two doors, one leading to a very solemn church service where the saved souls were forever praising God, singing unending hymns and listening to unending sermons; the other leading to a place of unending fun feast and sinful frolic, where the con- demned souls were wallowing in their own debauchery, eating and frolicking without the need to ever take a rest break. "It's not as bad as I feared," Casanova said as he turned toward the door leading to the place of debauchery. But before he could reach the door, Saint Peter called out and warned him that he had made a mistake and was going toward the wrong door. The 3-1/2 minute wait while the image cooks may be avoided by visiting the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and viewing the image, already calculated, there. The high-definition version is posted 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/> Heavy clouds and occasional rain prevailed here at Fractal Central on Thursday, with occasional rumbles of thunder thrown in for good measure. The temperature of 63F 17C kept thoughts of imminent summer far away. The fractal cats seemed not to notice the outdoor conditions. They were more concerned with being properly fed. The humans had an average day with the usual frustrations. The next FOTD will be posted in 24 hours. Until then, take care, and why look to the sky for the light when the light may lie at your feet? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Celestial_Banquet { ; time=0:03:31.68-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.par formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.1110932127946931/+0.0666019942450076\ /2.9199e+012/1/-52.5/0 params=1.1/-5/-1.1/1/0/0/0/0 float=y maxiter=3000 bailout=25 inside=0 logmap=405 periodicity=10 mathtolerance=0.05/1 colors=0009biAbhCckDdiEdlGfjHfjJhkKhkLilNjlOjmPjmR\ knSknTkoVloWlpYmpZmq_mqanrbnrdnrensfnshotiotjotkpt\ kptkptlptlptmptmptmptnqtnqtortortpstqstrttstttutuu\ tvvtwwtxxtyzzzzzzzzzzzzztzzzzzzzzzzzzzzzzzznlrgiq`\ epUbnNZmGVl7Rl8RlARkBRkDRjERjFSiHSiIShKShLSgNSgOSg\ PSfRSfSSeUSeVTdWTdYTcZTc`TbaTbbTbdUceTafTahTaiT`jT\ `hUZgWWeXUcYRa_P``MZaKYcHWdFUemTfURg8cu2Qh6SXAUKEa\ 5F_7GY9IXBJWEKVGLUINTKORMPQOQPRSNTTMVULXVKZXK`YJcZ\ Ie_HhaGjbFmdFoeErhDtmCwrByvAyzAyz6mV2cE4MG5NH6OI7P\ J9RLASMBTNCUODVPEWQFXRGYSI_UJ`VKaWLbXMcYOe_Pf`QgaR\ hbSicWncUkcSgcPddN`dLYdIUdGRdEOdCLmAHz8EzDDzHDYMCV\ QBRVBNZAKcAGm9Dz1AzmAzHA`PAYXAVdAWn0WmAXlKXkUYkcXj\ bWjaWi`Vi_Vi_UhZTiYTiXSiWRhVRhVQhUQgTPfSOeRNcQNbPM\ aOLbNLbNKaMJaLJaKIaJIbJHcKHdMGfNIhPLjQOlSRnTUoUXpW\ _qXbrZes_htakubnvdqwetxfwyhzzizzkzzlzzmzznzzczzUzz\ KzzHzzJzzKzzLzzMzzNzzOzzY } 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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How do I plug screen coordinates into a julia type?
by Jay Litwyn 19 May '11

19 May '11

MandelBroh { ; What can you do with this, Jim? ; This is all I can figure for a parser formula that does Julia types. ; It requires plugging screen coordinates into P4. z=fn1(pixel) +P2, c=fn2(pixel) +P3: if(ismand) z=z^real(P1) +c else z=z^real(P1) +P4 endif |z| <= imag(P1) }

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FOTD 19-05-11 (Twenty to the Clock [7])
by Jim Muth 19 May '11

19 May '11

FOTD -- May 19, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to the parent fractal that results when six parts of Z^(-2) are combined with ten parts of Z^(-10) on each iteration before (1/C) is added. This parent fractal resembles a 3-leaf clover with a prominent bud on the edge of the eastern leaf. Today's image is located on a minor filament extending inland from the shore of this bud. In an effort to make something of the original nothing image, I half evaporated it, then rendered the result with the remaining outside parts set to 'mult' and the newly-exposed inside set to 'bof60'. The result rates a 7. I named the image "Twenty to the Clock", partly for fun and partly because of the twenty converging arms inside each element. The image calculates in 2-1/3 minutes, but this time may be saved by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The venerable original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Lots of threatening clouds hung around Fractal Central all day Wednesday, but once again little rain fell. The temperature of 70F 21C was pleasant enough. Only the lack of sun could be complained about. The fractal cats passed the day wondering what life in the great forbidden outdoor world would be like. I passed the day thinking about cleaning out the spare room, and ending up doing nothing. FL spent the afternoon working in the garden, with me giving occasional moral support. The next FOTD will be posted in 24 hours. Until then, take care, and be of stout heart but lean body. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Twenty_to_theClock { ; time=0:02:20.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.10412374889474/-0.07981491857980604\ /1.116e+011/1/92.5/0 params=6/-2/10/-10/0/10000/0/0 float=y maxiter=1500 inside=bof60 outside=mult colors=000mczqttptootkotfntbntZkqeholelsbjzcmvcosc\ qoctlcvhcxeczbfyciyclycnycqxdtxdwxdyxduohqfknZnjQq\ fHtc9wWOxPaxIoxJnoJmfJlY6DsFUmNigPefQbfR_fTXeUUeVR\ eSW`Q`WOeRMiMKnHIsCGw7PqGXkOdeWai2_d5`_7ZV9XQBTLDR\ GFMBHF7D000ILODRQ8YS3cU8dTDeSIfSUWXdMaoBfz1kw5lu9m\ lsg000vsgusgttgstgrugqugpvgowfnwfmxflxfkyfjyfizfiz\ fjvcjr`jnYkjVkgTkcQl_NlWKlTImPFmLCmH9mE7nH6oK6oM6p\ P6pS6qU6qX6r_6ra6sd6sg6ti6tl6uo6uq6lk8ceAW_BNUDEOF\ 6IGBNEFRDKVCOZBTbAXf9aj8en7jr6nv5rz4rv6rr7ro8rkArh\ BrdCr`ErYFrUGrRHqQJpPLnNOmMQlLSkKUiIXhHZgG`fFbdDec\ CgbBiaAkYKnUUqQctMmwIwyRiu_WrgIogNjgRegWag_XgcTh`W\ iYZjV`jSckPflMhlJkmGmnDpnAso7up4xp2zk3xf4wa4vX5tT5\ sO6rJ6pE7oA7nBBdCFVDJLENBFQ2HR3IR4KS5LS6NT7OT8QT8R\ U9mmAUVzmcCXWDZWE_WEYmzXTJWSMVROUPRTOTSNWRMYQK`PJb\ OIeNHgMFjLElKDoJCqNFpQHpTKoWMoZPnaRndUmgWmbViYVeTV\ aOUYJUVEUR9TN4TJ0TGdfKbcK } 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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