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FOTD 12-07-13 (Outside-In Fractal [A-7.5,M-7])
by Jim Muth 13 Jul '13

13 Jul '13

FOTD -- July 12, 2013 (Rating A-7.5,M-8) Fractal visionaries and enthusiasts: Today's image shows what happens when an everyday Mandelbrot set is infected with Z^(9) energies in its depths. The quadratic part of the image is totally obliterated by the Z^(9) stuff, yet it is the quadratic part that prevents the image from being just another Z^(9) moth-eaten spider-network image. Today's scene lies in the debris filling the main bay of a small minibrot just east of the large minibrot on the main spike of the parent M-set. I named the image "Outside-In Fractal" because in some areas it shows what I call anti-bifurcation. The art rating of 7-1/2 makes the carnival-like scene worth seeing. The math rating of 8 will be of interest chiefly to those familiar with the math aspect of fractals. The calculation time of one minute will make everyone happy, though happiness can be further increased by checking one of the web sites. For maximum convenience, view the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Check it in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Immerse yourself in the full glory of the FOTD back images at: <http://www.Nahee.com/FOTD/> The weather was cloudy but otherwise pleasant here at Fractal Central today, with reasonable humidity and a temperature of 79F 26C. The fractal cat had his excitement when two strange cats began courting on the back porch. The next FOTD will be posted within the average time. Until whenever, take care, and God makes sure that right always prevails. The problems arise when people don't know right from wrong. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Outside-In_Fractal { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.743339171285614/+0.00000064472093323\ /9.6376e+011/1/-92.5/0 params=9/1e+020/0/0 float=y maxiter=2250 inside=0 logmap=41 periodicity=6 mathtolerance=0.05/1 colors=000zzzzzzzzzzzzzzzzzqzzhzz_zzSzz0yz0uz0zz0x\ s0uq0rp0po0pm0pk0mi0hf0dd0`d0Xd0Ub0Pb2Mb5Ha9DaDA_G\ 6_J6_O6ZR6YV6YY6V_6P_6L_AG_DCaH7aM7aP7aU7cZ7ca7ce7\ cg7Yi7Tk7OgEWeVcafjmzzmzzmzzmzzePzk7zp7ym7ji7_e7Pa\ 9EZI2VQ0R_0Of0Xf0cf5`V0XK0V90R70O70M7069_67c67i67o\ 67sXy_VuWUrTRoPRlLPiIOfEOdDMb9Ka5K_2JY0HW0HV0Jj7Kw\ LMwYPwWJ7cH7cF7cF7aD7aD7aB7_A7_A7_87Y87Y67Y67W67W6\ 7W67V67V67V67T67T67R67T67T67V67V67V67W67W67W67Y67Y\ 67_67_67_67a67a67a67c67c67c67e67e67g67g67z67z67z67\ z67z67z67z67z67z67z67z67z67z67z67z67z67z67z67z67z6\ 7z67z67z67z67z87z87zA7zA7zB7zB7zD7zA7aA7aA7aA7_A7_\ A7_A7_A7YA7YA7YA7YA7YA7WA7WA7WA7WA7WA7VA7VA7VA7VA7\ VA7TA7TA7TA7TA7RA7RA7RA7RA7RA7PA7PA7PA7PA7PA7OA7OA\ 7OA7OA7LA7LA7LA7LA7LA7JA7JA7JA7JA7JA7IA7IA7IA7IA7D\ A7GA7IA7LA7OA7PA7TA7VA9WAE_AIaALcAQgAViAYjAboAfqAj\ sAblAWgAQaAKWACRA7LA9JACI } 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 11-07-13 (The 33rd Degree [A-7,M-7])
by Jim Muth 11 Jul '13

11 Jul '13

FOTD -- July 11, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: Today's image shows some Z^(33) hi-jinks. The scene of the action is the remnant East Valley area of a prominent minibrot on the filament extending from the northwest shore of the large period-2 bud of the parent Mandelbrot set, which is quadratic only on the surface. The order-33 corruption is visible in the circular features, which contain 32 lobes. The underlying quadratic framework is obvious in the arrangement of the circles, which resembles a familiar Z^2+C Julia set. The art and math values are both 7, meaning the image is a bit above average, but nothing to get over-excited about. The name "The 33rd Degree" has nothing to do with Freemasonry. It refers to the order-33 corruption that infests the depths of the Parent M-set. The calculation time is a speedy 40 seconds. It will waste the time of no one. But viewing the image will be easier on one of the web sites. Relief from labor may be found at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The library of back images is online at: <http://www.Nahee.com/FOTD/> Quite pleasant weather was enjoyed by all here at Fractal Central today, with blue sky, cotton-candy clouds, lower humidity and a temperature of 84F 29C. The next FOTD will be posted in the proper time. Until whenever that might be, take care, and would the group really responsible for all our problems please stand up. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_33rd_Degree { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-1.254742878629916/+0.3786539363043855/\ 2.474522e+010/1/32.5/0 params=33/1e+050/0/0 float=y maxiter=1600 inside=0 logmap=64 periodicity=6 colors=0003Of4Pf5Qg6Rh7Si8Uj9VkAXlBZmC`nDanEcoFepG\ gqHhrIjsJltKnuLouOnsRmrUmqXlp_loakndjlgjkjijmiiphh\ rhgmfehdddbc_`bWZ`RY_MWZIUYDSW9QV4OU0NT3LR5JQ7HP9F\ NCDMEBLG9JI7IK6HN9IPBJRDKTGKVILXKM`FJ_JLZMMYQNYTOz\ XPz_QzcRzfSzjTzmUzqVztWzl7zwXzqYzlZzg_zb`zYazTbzOc\ zJdzEdzFezGezGezHfzIfzIfzJfzKgzKgzLgzMhzMhzNhzzkzz\ hzzezzbzzQzzQzzRzzRzzRzzRzzRzzRzzRzzRzzRzzRzdRzeRz\ fSzgSzhSziSzjSzkSzlSzmSznSzoSzpSzqSzpTzqSzzSzzSzzS\ zzSzzSzzRzzRzzRzzRzzRzzRzzRzzQzzQzzQzzQzzQzzQzzQzz\ PzzPzzPzzPzzPzzPzzOzzOzzOzzOzzOzzOzzOmtmmtmmtmmtmm\ ummummummummummummummummummvmmvmmvmmvmmvmmvmmvmmvm\ mvmmwmmwmmwmmwmmwmmwmmwmmwmmwmmxmJxzJxzJxzJxzJxzJx\ zJxzJxzGyzIxzJxzKxzLxzMxzNxzOxzPxzQxzRxzSxzTxzUxzV\ xzWxzXxzYxzZxz_xzawzbwzcwzdwzewzfwzgwzhwziwzjwzkwz\ lwzmwznwzowzpwzqwzrwzswzvyzuxztwztvzsuzstzrszrrzqq\ zqpzpozpnzomzolznkznjzmiz } 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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video card
by JackOfTradeZ＠comcast.net 11 Jul '13

11 Jul '13

""Would someone please confirm (or refute) my understanding that the video card and its driver supporting (or not supporting) VESA video modes is the thing that makes Fractint not run on some machines -- rather than the version of Windows? I've run Fractint on both Windows 98 and WinXP successfully. - Hal Lane"" I believe you are correct. I run FractInt on an Alienware Area-51 system, bought in 2006. It has a GeForce 8600 and Athlon64 dual core chip. Fractint SCREAMS! Even when run in a default command shell under WinXP Media edition. Although with some complex fractals it slows down and chokes up, but not often. Booting with a Win98-DOS-7 CD it runs just a little better. Also, under windows, there is a free app called "game booster" (google for it) which shuts down all "unnecessary" services; it is meant to optimize the system for game play. It gives a significant performance improvement. One other thing - I have confirmed that Athlon64 chips are far superior to Intel for Fractint in WinXP. But this is for systems 6-12 years old, that may not apply to current systems.

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Fractint & VESA - Would someone please confirm (or refute)...
by Hal Lane 11 Jul '13

11 Jul '13

Tim said: > Running on older > Windows versions or DOS itself has the problem that you have to take some > additional steps to get very many video modes working. I'm not even very > sure how to do that any more. My understanding is that the video cards and their drivers are the problem, rather than Windows or DOS. If the video card and its driver doesn't support the VESA modes that Fractint uses, *that* is the problem. I got relief from a video chip which only supported DOS VESA 640 x 480 -- built onto a mother board in the inexpensive machine I'm using under WinXP -- by taking Albrecht Niekamp's advice and getting an old (used) nVidia GeForce 6800 video card. Its drivers do *lots* of VESA modes -- and as a bonus, my particular model of their 6800 series has a 2nd video out port that I put another display on. I haven't yet bought and connected a 2nd power cable to the nVidia card. But I don't play any heavy duty 3D video games, so I haven't needed the extra power the 2nd cable provides yet. Would someone please confirm (or refute) my understanding that the video card and its driver supporting (or not supporting) VESA video modes is the thing that makes Fractint not run on some machines -- rather than the version of Windows? I've run Fractint on both Windows 98 and WinXP successfully. - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Hi
by Ram Peloquin 11 Jul '13

11 Jul '13

No longer have a DOS/Win 95 computer. Fractint may have been the program I thoroughly enjoyed. I just booted up an XP desktop and probably have a Win 98. What program will run and 'cycle' fractal creations in either system? Thanks, Richard

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FOTD 09-07-13 (The 101 Ways [A-6,M-8])
by Jim Muth 09 Jul '13

09 Jul '13

FOTD -- July 09, 2013 (Rating A-6,M-8) Fractal visionaries and enthusiasts: Today's image shows what happens when an everyday Mandelbrot set is infested in its depths by Z^101 energies. The parent M-set looks like your everyday, fractals-101, M-set, but this is only on the surface. Today's image lies rather deep in a moth-eaten elephant trunk in East Valley of the large main-spike minibrot of its parent, where the quadratic and order-101 energies interact in most unusual ways. The incredibly thin overlapping order-101 rings are arranged in a quadratic pattern, with interesting variations of both shape and thickness. This math interest raises the math value to a very respectful 8, while the art value remains a questionable 6. The name "The 101 Ways" has nothing to do with an old song. (Are there any such things as new songs?) It refers to the infecting power of Z. The calculation time of 1-1/3 minutes will pass fast after the skeletal nature of the rings becomes apparent. Visiting the web sites will let satisfaction come even faster. Save over a minute by checking the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Scads of FOTD back images are online at: <http://www.Nahee.com/FOTD/> Lots of clouds, occasional showers and a temperature of 84F 29C made today one to be forgotten here at Fractal Central. The fractal cat did forget the day. He forgot it before it began. The fractal humans never remembered the day in the first place, so how could they forget it? The next FOTD will be posted. The only question is when. Until that great moment arrives, take care, and is a star a tiny point of light in the night sky, or is it a blazing nuclear furnace. Or is it both of the above, or is it neither of the above, or does the question have any real meaning at all? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_101_Ways { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=t center-mag=-1.747272931689331/-0.00241119913400097\ /2.128e+008/1/130/0 params=101/1e+150/0/0 float=y maxiter=2500 inside=0 logmap=38 periodicity=6 colors=0003`U3ZW3XY3V_3Ta3Rc3Pe3Ng3Li3Jk3Hm7FgBCbF\ 9XJ6SM6NK8LIAJGCHFEFDGDBIB9K98L7AM5CN4EO3GP2HQ1JR8\ KSFMULNWSKXZKYdKYkKWoKVjXTdgHcm7_p0Vo0Rm0Mk0Ih0Dc0\ 9Z07U06O05Q54QA3NF6LK9IPBVUEUUGTTJSSLRROTQNUROTTQS\ URRWSOWSQXTRYTSZTU_TV_TW`TYaTZbT_cT`cTbdTceTdfUfgU\ ggUhhUiiUkjUlkUmkUolUpmUqnUumSrnUonWlnXinZfn`cnaan\ cZoeWofTohQojNokKomGppIonJnmKmlLmkMljF7iF3iIBjLDkO\ GlRImULnXNo_PpbSqeUrhXskZtnauqcvsewdQZQABRCGSDKTEO\ TFSUGWVH_WJcWKgXLkYMoZNsZOwHFzNRzTazZmzcxzZrzUmzPm\ zKmzFmzAmz5mz1mz8mzEmzKqzHpzFozDnzBmz8lz6kz4jz2jz3\ kz3kz4kz4kz5kz5kz6kz6kz7kz7kz7kz9gzAmzCmzDmzEmzGmz\ HmzJmzKmzLmzNmzOmzPmzPmzPmzPmzPmzPmzTmzXmzWmzWmzWm\ zVmzVmzVmzUmzUmzUmzUmzXmzYmzZmz_mz_mz`mzamzamz`mz_\ mzZmzZmzRmzKmzRmzYmzdmzkmzomzVmzAmzFmzJmzNmzRmzVmz\ gmztmzhmz_mzSmzJmzBmz5mzmmznmznmzomzpmzqmzrmzsmztm\ ztmzsmzsmzrmzrmzqmzqmzpmz } 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 08-07-13 (Linearity [A-7,M-7])
by Jim Muth 08 Jul '13

08 Jul '13

FOTD -- July 08, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: Today's scene lies on the main spike of an oversized and very distorted Mandelbrot set corrupted in its depths by Z^1 energies. Since Z^1 equals straight Z and straight Z is a linear expression, the deeper minibrots remain quadratic shaped. The image's chief interest, (as is almost always the case), lies in the patterns surrounding the minibrots. I named the image "Linearity" since any number raised to the power of unity remains unchanged and therefore is linear. This does not mean that today's image consists of only straight lines however. The overall effect is a curvilinear one. The art and math parts of the image both rate an above average 7, which makes the image worth the 1-1/3 minutes required to calculate it. The web sites can eliminate the calculation task. The finished GIF image is posted at: <http://www.crosscanpuzzles.com/Archives.html> with a hi-def rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Typical summer weather prevailed here at Fractal Central today, as the temperature reached a muggy 84F 29C under a partly cloudy sky, while an early afternoon shower made things interesting. The fractal cat spent most of the afternoon in the laundry basket. The fractal humans had a day notable for having nothing happen that was worth noting. The next FOTD will be posted when it is found and ready. Until whenever that might be, take care, and if everyone who thinks he has seen a real ghost is merely hallucinating, then maybe we should consider hallucinations to be a different kind of reality. And perhaps those who do not see ghosts are having anti-hallucinations of being unable to see what really exists. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Linearity { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip symmetry=xaxis center-mag=-9.926077323446844/0/2.4055e+007 float=y params=1/10 maxiter=2400 inside=0 periodicity=6 colors=000J5pJ4tJ3wH8tGCqEHnDLkBQhAUf9Zc7b`6gY4kV3\ pS2tQ8gLEWHKJDA09hX8rzzssosp`onUlkGiiIefLbdN_aPWZR\ TXTPUWMSYJP_FNaCKc9IeBLcCOaDR_EUYFXWGZUIaSJdQKgOLj\ MMmKNoJOmMPlOQkRRjTSiVTgYUf_VeaWddXcfYaiZ`k__m`Zpa\ YrbXtT_gJaW9cK0e82gC4hG6iJ8jNAkRClUDmYFoaHpbJqcLrh\ NsmPtrQuzPszOrzNpzMozLmzKlvJkrIimHhhGfcFeZFdVGeTGe\ TGeTGfTGfTGfTGgTGgTGgTGhTGhTGhTGiTGiTGiTGiTHiZIicJ\ ihKimLirMiwLgkLe`KcQKbFM`EO_DPZCRXBSWAUV9VU8XS7ZR6\ _Q5aO4bN3dM2eL1_R4UW6O`8IfACkC7pEPmGfjIHECxgKreJmc\ IhaHb_HYYGTWFPXBOVFNTIMRMLPPKNSJLWIJZHHbGFeEAjFEhF\ HgGKeGNdGQcHTaHW`HZ_IaYIdXPcWUbSTaOrmmqmmpmmommqkm\ timvgmxemwcmxamy_mzYmzWmzUmzSmzQmzOmvMmrKmmKhhKccI\ ZYFUSCRK8PE4KA0F82B51A007zKYtQXqVXnWWkWWgWWcXV_XVW\ XVSYUO`UKcZQfcWihZkl`mmZimXemWamUZmSVmRRmPNmNKmMGm\ KCmI8mH5mGAiFEeFJbENZDRWDWSC_PBcLBhIAlE8r2ApBBoKCn\ SDm`Eli9tuFkqKBbK9fJ8iJ7m } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 05-07-13 (Seven and One-Half [A-6,M-5])
by Jim Muth 08 Jul '13

08 Jul '13

FOTD -- July 07, 2013 (Rating A-6,M-5) Fractal visionaries and enthusiasts: The name of today's image, "Seven And One Half", says it all. The oversized parent Mandelbrot set is corrupted in its depths by Z^(7.5) energies, and today's scene lies in the remnants of the East Valley area of the largest main-spike minibrot beyond the great minibrot. Unlike the situation that existed in the recent half-power images, the one large discontinuity in today's image is quite obvious. It lies on the left side of the minibrot, though it is still quite hard to determine exactly what is going on in the arrangement of the spiral arms. The artistic rating of 6 and math rating of 5 also says it all. The image is, well, interesting, while the math theme is pretty well worn out. But not being one to give up quickly, I will stick with the power-and-a-half theme for at least one or two more images. Today's image is a rather slow one, making a trip to one of the web sites a wise choice if impatience is to be avoided. The official FOTD web site, with the finished image, is at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def renderings are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The blast-from-the-past FOTD images are at: <http://www.Nahee.com/FOTD/> A hot sultry day here at Fractal Central, with a temperature of 93F 34C and humidity to match, suddenly became quite pleasant at 5pm when a thunder storm struck with heavy rain and 60mph, 100kph, winds. When the storm moved out 20 minutes later, the street was littered with fallen tree limbs and the temperature was a far more reasonable 73F 23C. The fractal cat noticed the change by switching from stretched-out mode to curled-up mode. The humans simply enjoyed the refreshing change, though FL spent time propping up flowers that had flopped over in the tempest. The next FOTD will be posted in something near 24 hours. Until then, take care, and the next time you're abducted by aliens, be sure to take along a camera. Such pictures would certainly go viral on the internet. Many people still don't believe in the aliens. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Seven_And_One_Half { ; time=0:03:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip periodicity=6 center-mag=-186.0480820482014/-0.00853079612278277\ /7.871e+010/1/-90/0 params=7.5/100 float=y inside=0 maxiter=3200 logmap=394 mathtolerance=0.05/1 colors=00000E10E20F30F40G50G60H70H80I91IA2JA3JA4KA\ 5KA6LA2MA3NA3OA3PA3QA4RA4SA4TA4UA4VA4WA4XA4YA4ZA4_\ A4`A4aA4bA4cA4dA4eA4fA4gA4hA5iA7jA9kABlADmEFmJHlOJ\ lTOkYSjbXjgailchmfinijojjpjhpggpcfp`epYdoUcoRboNao\ K`oIXoGYoEZoC_oA`n7am0el3bl5`l7Zl9XlBVlDTlFRm2TlKP\ nPMpUIrZCtcFuhHumKuqMyrOxsMwrLvpJuoItnHslFrjEqgCpe\ Bpc4o`7mZAkXDiVGeTJaQMYNUVKSUIQUGPUENUDMUCKQBIOAHM\ 9FI8EJ7CE68959A5AA6BA8CFADKDEPEFUFG_HHaIIcKJeLKgML\ iOMkPNmIZmLVmNSmQOmSLmVImXEm_BxXAtZ9p_9ma8ib8fd8be\ 7_g7Wh6Tj6Pk6Mm5In5Hw2Gs4Fo5Ek7Dg8Cd9B`BAXC9TE8PF7\ MG8NL9OQ9PVAQ_ARdFQgKRhPRhURhZSicSicSicTjhTjmTjrUk\ vUkzVjvUksUkpUlmUlkUmiTmgTnfTneTocToZSpUSpPSlKSlFQ\ pAOm8MkAKgBIfDGjCEgCCeBAcBAaAA_FFbKKePPiUUfZWccY`c\ _YcaVccSheQmgNriKwkHwmEwmBrm8qm6qm7qm8qm8qm9qoAqqA\ qsBquBlwFhxIcyM_zPWzTRzWNz_JzbEzfAzi3zm6zl8zlAzlCz\ kFzkHzkJzjLzjOzjQziSzizzz } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 05-07-13 (Five and One-Half [A-7,M-6])
by Jim Muth 05 Jul '13

05 Jul '13

FOTD -- July 5, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image is a scene in an oversized Mandelbrot set corrupted in its depths by Z^(5.5) energies. Once again the number of outer elements is twice the order number of the inner minibrot. Also, the discontinuities are again almost invisible. The most obvious streaks out from the minibrot toward the northwest, but vanishes before it interrupts the near-perfect symmetry of the 11 outer elements. To find today's scene, travel out the main spike of the parent M-set until you reach the largest minibrot between the set itself and the main minibrot. Then go to the large minibrot on the west branch of the filament extending from the period-3 northern bud of this main-stem minibrot. This sub-minibrot is well on the way to becoming an order 5.5 one. Today's scene lies somewhere in the area that once was its East Valley. The name "Five and One-Half" refers to the order of the corruption infecting the parent M-set. The art rating of 7 indicates that I consider the art aspect of the image to be a little better than the math aspect, which is now becoming a bit stale. Despite the staleness however, I will continue this math course until it becomes boring. The calculation time of 1-5/6 minutes is slow enough to give boredom a chance to raise its head. The web sites are there to relieve boredom. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> with a hi-def rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the FOTD back images at: <http://www.Nahee.com/FOTD/> Typical midsummer weather prevailed here at Fractal Central today, as the temperature reached a high of 91F 33C under a sky filled with billowing cumulus clouds, and the humidity made things appropriately uncomfortable. The fractal cat passed the day stretched on the bathroom tile floor, while the fractal humans spent the day working. All in all, the day makes very dull reporting, not at all like the days of twelve years ago, when the original fractal cats, Thomas and Tippy, spent the summer days prowling the area around old Fractal Central, lurking in the holly thicket, chasing birds, driving away intruding cats and getting into other assorted mischief. The next FOTD will be posted when the time is right. Until whenever, take care, and I have yet to see someone who thinks the world is real actually prove that it is real. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Five_and_One-Half { ; time=0:01:50.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip periodicity=6 center-mag=-162.6076103993194/+0.4162767713201903/\ 5.974896e+008/1/-90/0 params=5.5/100 maxiter=1600 float=y inside=0 logmap=290 mathtolerance=0.05/1 colors=000QB8QB8PA7OA7N97M96L96K86J86I75H75H75G64F\ 64E64D54C53B43A43943832832732621433521411311210100\ 0003Kz2Fo2Ac15U10K00A0008X_7VX6TV6RS5PQ5OO4ML4KJ3I\ G3GE2EC2B9187154022bf`_cZYaXW_VUXTSVRQTPORNMOLKMJI\ KHGIFEFDCDBAB9897665443221uD8sC7oB6nA6j95f85b74c64\ Z53U42U32U216113000GBTA7E53ODXLBUJARH9OF8LD7IA5F84\ C639426213QykOuhNreLocKk`JhZHeWGbUFZRDWPCTMAQK9MH8\ JF6GC5DA497265132WX8VV7UU7TT7SS7RR6QQ6PP6OO6NN5MM5\ LL5KK5JJ4II4HH4GG4FF3EE3DD3CC3BB2AA299288277166155\ 1000000zzczzdzzWyzNtsEopIknMflQbjUYiYUgaPfdLegGdjC\ cm7bp3as4`n5`j6_f7_b8ZY8ZU9ZQAYMBYHCXDDX9DX5FW6HW7\ JW8LV8NV9PVAQVAQTAQRAQPAQNAQLAQJAQHAQFAQDAQC9o_7q_\ Cs_Ht_Mv_Rw_Wy_`z_ehYkRXp9Wu8Xm8Yf7`b7bZ6eVPgRWjN_\ lJchFhjBlcDnUElPCkOBiNAhM9fL7eK6cK5cU4ccVccuccUIm3\ SmPamijmzrmzzmzqmzimzamzTmzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 04-07-13 (Sandy Hectares [A-6,M-6])
by Jim Muth 05 Jul '13

05 Jul '13

FOTD -- July 04, 2013 (Rating A-6,M-6) Fractal visionaries and enthusiasts: Today's image shows some of the craziness that can erupt in an oversized Mandelbrot set corrupted in its depths by Z^(4.5) energies. The central minibrot is clearly of order 4.5, while the orangish disk surrounding it holds 9 lobes. The image is located in the half-morphed East Valley of a small minibrot on the main stem of the oversized parent M-set; the art and math ratings are both an average 6. The image is notable for its lack of obvious discontinuities. One discontinuity does extend northeast from the minibrot, but vanishes by the time it reaches the edge of the sandy orangish area. The name "Sandy Hectares" is a spin-off of 'Sandy Acres'. A hectare, as most of the world knows, is a measure of area in the metric system. It is equal to about 2-1/2 U.S. acres. The calculation time of 1-1/4 minutes is reasonably fast. Viewing the image on the web sites is not much faster, but it certainly is more convenient. Patience will be preserved by checking the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And will be rewarded in hi-def at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images, numbering in the thousands, are online at: <http://www.Nahee.com/FOTD/> Today brought partly cloudy skies, high humidity and a temperature of 90F 32C to Fractal Central. The fractal cat's activities were stifled by the heat early in the morning, leaving him with nothing to do but sleep. The humans made it through the day unstifled. The next FOTD will be posted in a couple days. Until then, take care, and if at first you don't succeed, try and try again. Then give up. Don't waste energy trying to succeed at a hopeless task. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Sandy_Hectares { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip passes=1 center-mag=-180.9984843250203/-0.0007606639992212/\ 1.776399e+011/1/167.76/0 params=4.5/100 float=y maxiter=2250 inside=0 logmap=104 periodicity=6 mathtolerance=0.05/1 colors=00000h00e00c01`02Z03X04U05S06Q07O07M17K27I3\ 8G48E58D68B78989999AA9CBADCCEDEFEGGGKHINIKRJMUKOXL\ Q`MRcOSeRTgUUiXVk_WmbYoe_qh`rkbsndtqeutgvwiwzjwzhw\ ziwzmwzmwzmwzmwzmwzmwzowzqwztzzvzzzzzzzzzzzzzkrwcm\ w6ew3Uw01n62fB2YG3QL3HU40c40U50K60A7008IM8MJ9RGAVC\ BZ9Cb6Cf3Fd7HcBKaFM`JOZNRYRTWUWVYYTa_SebQidPmfOpeO\ neOldOkdOicOgcOfbOdbOcaOaaO_`OZ`OX_OV_OUZOSZORzYzm\ Zzz_zm`zzazmbzzczmczzdzmezzfzmgzzhzmizzizmczzYzmSz\ dNzhHvkBxn6zm8um9qmAmmBhmCdlD`lEWlFSlGOlHKnVcpgvmh\ tkisijqgjpeknblm`mkZmjXnhVogSpeQpdOqbzrazs_zmZzmNz\ mCzm1zmFzmTzmfzmszmrzmqzmpzmozmnzmmzhgzhbzgXzgSzeT\ zcUzaVz`WzZXzXXzVYzcZzc_zm`zmazmazcZzcXzcVzcTzcQzc\ OzcMzcKzcIzcHzcHzcHzcGzcGzcGzcGzhHzhIzhIzhHzhGzhFz\ hEzhDzhCzhBzhAzh9zh8zh8zhCzhFzzIzzLzzOzzRzzUzzXzz_\ zzbzzHzzDzzAzzYzzTzzOzzRzzKzzNzzPzzRzzTzzVzzXzzZzz\ `zzbzzdzzQzzTzzWzz_zzbzze } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 01-07-13 (Primed for Action [A-7,M-7])
by Jim Muth 02 Jul '13

02 Jul '13

FOTD -- July 01, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: Today's image combines Z^(37) elements and Z^(2) elements, with the higher order elements dominating the center of the image and the quadratic elements dominating the outer parts. All this action lies in the East Valley area of the parent fractal, which is another oversized Mandelbrot set. The name "Primed for Action" came to mind when I realized that the number 37 is probably the first number a person thinks of when he is asked to name a prime number between one and fifty. The art and math ratings are both 7 -- FOTD average. The calculation time of 2-1/3 minutes is a bit on the slow side. Luckily, the web sites are there to rescue one from wasted time. The official web site is at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Lots of clouds and occasional showers marked the day here at Fractal Central, while the temperature of 82F 28C and high humidity made it feel quite tropical. The fractal cat and semi- fractal humans took it in stride. The next FOTD will be posted, that much is sure. The question is exactly when. Until whenever, take care, and with so many high-profile trials on TV, a person needs a score card to know who they should consider guilty or innocent. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Primed_for_Action { ; time=0:02:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip maxiter=1750 center-mag=+27.53334264330222/-0.6710880924736258/\ 2.59e+011/1/-115/0 params=37/100 float=y inside=0 logmap=340 periodicity=6 mathtolerance=0.05/1 colors=000NSrLUqKVqMTpOSoPQnRPmTOlUMkWLjXKiZIh`Hga\ GfcEedDdfCchAbi9ak8`l6_n5Zp4Yq2Xs1Wt0Vs2Xs3Ys4Zr6_\ r7`r8aqAcqBdqCeqDfpFgpGhpHjoJkoKloLmoMnnOonPqnQrmS\ smTtmUumVvkTsiSqgRoeQmcPkaOh`MfZLdXKbVJ`TIYRHWPGUO\ ESMDQ097KCOIBLGAJE9HC8FB6D95A748536324112yZ7uW6qU6\ mS5iQ5eO4aL4YJ3VH3RF3ND2JA2F81B61740320cD6aC5_B5YB\ 5XA4VA4T94R94Q83O73M73K63J62H52F52D42C31A318216215\ 10310100aogWg`R`VLTPGMIAEC576S9_P8WM7SJ6PG5LE4IB3E\ 82A517203iATf9Rc8Pa8OZ7MX7KU6JS6HP5GN5EK4CH3BF39C2\ 8A26714513201wNHtMGrLFpKFmJEkIDiHDfGCdFBbFB_EAYD9W\ C9UB8RA7P97N86K75I75G64D53B43932621411200sIKoGIlFH\ hEGeDFaCDZBCVABS9AO78L67H56E45A33722311tuzqrvnoskl\ phimefjbcg``cYY`VVYSTVPQSMNPJKMHHIEEFBBC889556223f\ mBag9Xa8SX7NR6JM4EG39B2451FYtEWzDVzDUzCTzCRzBQzBPz\ AOzAUz9Uz9Uz8Zz8Zz7Zz6Zz6Zz5hz5hz4hz4hz3hz3hz2mz2m\ z1mz1mz0mz0mz0mz0mz0mz0mz } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 29-06-13 (Cubuc Conundrum [A-7,M-7])
by Jim Muth 02 Jul '13

02 Jul '13

FOTD -- June 29, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: Here's a quick fractal to calculate quickly then gaze at in awe and wonder. The parent fractal is an oversized Mandelbrot set corrupted in its depths by cubic energies. Today's scene lies on the main spike of the parent, in the largest minibrot beyond the main minibrot. This parent minibrot is about half way morphed from quadratic to cubic, with today's scene located in the debris between the two main buds. The name "Cubic Conundrum" sounds interesting, but means nothing special. Both the artistic and math values are a bit above average, making it worth the effort to spend 30 seconds or so calculating the scene. Non-calculating fractal fans may find relief at the web sites. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> with a hi-def rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> A rather pleasant partly cloudy day with a temperature of 86F 30C ended with a brief but heavy shower here at Fractal Central today. Both the fractal cat and fractal humans approved. The next FOTD will be the one for July 1. Until then, take care, and don't look here for a clever closing remark. I'm not feeling very clever today. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Cubic_Conundrum { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip center-mag=-18.56267776521526/+0.00000010142410\ 922/4.227709e+008/1/116.25/0 params=3/10 float=y maxiter=900 inside=0 logmap=46 periodicity=6 colors=0000600810A20C30E40G50I60K73MB7OFBQJGSNLURQ\ WVVYY__acbegeikhmokqsnuwqxuosslorjjpgfodamaYkZUjWP\ hTLgQGeNCdL8aI9ZG9XF9UDARCAPAAM9BJ7BH6BI8AIB9IE9IH\ 8JK7JN7JR6JW5J`5Ia6H_6HX6GV6GT6FS7ER7ER7DQ7DP7CO8B\ O8BN8AM8AM8DN9GO9JO9MPAOQARQAURBXSB_SBaTCdUCgUCjVD\ mWDoWDmVElVEkVFiVFhVFgUGeUGdUHcUHaUH`TI_TIYTJXTJWT\ JYWL_ZNa`PccQefSghUikWjmXljVmgUoeSpbRr_PsYOuVNvSLx\ QKyNIyKHyIGvHKpHOjGSeGWcF_cFccEgcEjcMhcMhc`Rc`RcaR\ caRcaScaScaScaScbScbScbTcbTcbTcbTccTccTAczBczBczBd\ zBdzBdzBdzBdzBdzBezBezBezBezBezBezBfzBkWBkWBkWBkWB\ kXBlXBlXBlXBlXBlXBlYBmYBmYBmYBmYBmY9wZBwYDwYFwYHwY\ JwYLwYNwYPwXRwXTwXUwXWwXYwX_wXawWcwWewWgwWiwWkwWlw\ Whw_dwb`weXwhTwkPwnLwqHwtFwyEwwEwvEwuEwtEwsEwrEwqE\ wpEwoDwnDwmDwlDwkDwjDwiDwhDwgDzfDzeCzdCzcCzbCzaCz`\ Cz_CzZCzYCzXCzWBzVBzUBzTBzSBzRBzQBzPBzOBzNBzMEzNGz\ OJzPLzQNzRQzSSzTUzUXzVZzV } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 25-06-13 (Ground Base [A-7,M-6])
by Jim Muth 25 Jun '13

25 Jun '13

FOTD -- June 25, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image is named "Ground Base". The name has nothing to do with a mountain climbing expedition, it is simply a name I grabbed out of the air and gave to the image. The generating expression is rather unusual. It adds 6.1 parts of Z^(0.1) to a whopping 6100 parts of Z^(100) on each iteration to make a fractal resembling a heart lying on its side. Today's scene lies near the bottom (east) point of the heart-shaped bay. The artistic worth is a 7, the math value, a 6. The calculation time of 1-1/4 minutes will pass in a flash. But the flash may be avoided by checking the web sites. The rendered image is posted at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def rendering is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back fractals are at: <http://www.Nahee.com/FOTD/> The heat and humidity here at Fractal Central today was broken in the afternoon by a light thunder-shower, which dropped the temperature from 90F 32C to 77F 25C. Both the fractal cat and fractal humans approved. The next FOTD will possibly be posted soon. It is also possible that the next fractal could be many months away. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Ground_Base { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-5.126410111140562/+0.02644449329121534\ /1.132883e+009/1/32.5/0 params=6100/100/6.1/0.1/0/\ 0/0/0 maxiter=5000 inside=0 logmap=59 periodicity=6 colors=00005F05F05F05G05H05I05J05K05L06M29R4DV5H_A\ LcKPg_WggbZphczmiwkfsfdpbamY_hUXcPUbOSgGPzZ_zUjzKk\ oPmkVnf_oadzXmzTtzQkzqHmZK28QsNaramrLKc`dkmVPnjc8U\ jJalUindqphiMkoXmtgCd8MiKWoWetg08QIgXRlbZpggum0oII\ sVZvfzmttsskDilPkmannmpUmHds_IXBUfQdpd7kBIoMUrXdvg\ MO6VamempuUqsdrqorFnY9PBKObAbQOj_ari8nlNrnavpKTE1C\ 06T3IaG_v1eMt`SsWYrQbpLhoaPaq6OmENiMNdTM``LkTXuMhX\ aY9qO`b`OtZawhlrkmunnwpG8oPMpYZqflrZYHdgUjpfZevcju\ gotktsnZ8YXTcfaipjNpDo9IoRVohfsXkrdmqkopz0uz0rz0vz\ 0rz0gz0jz0mz0jz0Qz0Zz0bz0gz0kz0Qz0gz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz2zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zzhzz9zzWzzQzzozz\ pzzqzzrzzfzzizzlzzozzUzzbzzjzzOzzczzazzezzjzznzz0z\ zXzzozzYzzbzzhzzmzzqzzrzz_zzizzOzzWzzczzkzzbzz8zzO\ zzczzazzjzzxzzuzz1zzSzzMzzUzzbzzjzzBzzQzzdzzRzz`zz\ izzwzzuzzszzZzzLzzazzezzi } 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 24-06-13 (Salad is Served [A-7,M-7])
by Jim Muth 24 Jun '13

24 Jun '13

FOTD -- June 24, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: The parent fractal of today's image is a Mandelbrot set corrupted in its depths by cubic energies. The image is located between the two East Valleys of a larger minibrot that lies in an elephant trunk on the south shore line of the single East Valley of the parent Mandelbrot set. The name "Salad is Served" came about when I was reminded of one of the light feminine salads FL always orders when we eat out. Of course, since I am not a rabbit, I do not eat leafy weeds. I order masculine foods heavy in meat and starch such as meat loaf and sweet potatoes. Today's image rates a slightly above average 7 for both the artistic and mathematical aspects. I have already explained the art part -- the image looks like a salad. But the math part is a bit more subtle. The six strawberry clusters surrounding the cubic minibrot at the center are arranged in three groups of two -- a perfect blending of the quadratic and cubic elements. And the strawberry rings increase in complexity as they approach the minibrot. The calculation takes 45 seconds to complete on the average SOTA desktop machine, and far longer if it will run at all on a 'smart phone', 'tablet' or 'I-pad'. Regardless, the finished image is available for instant viewing on the FOTD web sites. The official FOTD web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Typical sultry midsummer weather prevailed here at Fractal Central today with partly cloudy skies, a temperature of 90F 31C, and rumblings of thunder in the area. Only a few drops of rain fell at FC however. The fractal cat spent the afternoon sleeping in a laundry basket, while the humans did the real work. The next FOTD will be posted soon. Until soon arrives, take care, and sometimes we may fool others quite easily. It is not always so easy to fool ourselves however. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Salad_is_Served { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=+0.3319162826083197/-0.0407134040528868\ /1.885573e+011/1/113.75/0 params=3/300/0/0 float=y maxiter=2400 inside=0 logmap=79 periodicity=6 colors=000A0CA0DA0EA0FA0GA0HA0IA0JA0KA0LA0MA1NA2OA\ 3PA4QA5RA6SA7TB8UC9VDAWEBXFCYGDZHE_IF`JGaKHbLIcMJd\ NKePMfROgSQhTSiUUjWWkXYlY_mZapbcseevfgxghzhizhizgh\ vfgregmdfhbec_dZYdVWcRUbOSaKQaHP`IP_JPZKPYLUXMZWNc\ VOhUPmTPr_LveIzkFvhEreDmbCh_BcYBZVAWS9SP8RM7QK7SNE\ TQLUTRTRQSPPRNOQMNPKMOILNGKMFKLDJKBIJ9HI8GH6FG4EF3\ EG7GHAIIEKJHMKKOLOQLRSMUUNYWO`YPc_QgaRjcRmdXkgaiif\ hklfmqdovcqt`osZnqWmpUloSkmPjlNikLgiIfhGezEdzBcz9b\ z7az8Zz8Xz9Vz9Sz9QzAOzALzBJzBHzBEzCCzCAzD7zD5zD3zG\ GzJSzMdzOpzSrzWsm_umcvmgxmkymozmpympxrcwrcvrcurcur\ ctrcsrcrrcqrcqrcprcorcnrcmrcmrcmrcmkrmmqmoqmqpmspm\ tpmsokrniqmgpleokcnjbmi`lhZkhXjgVifTheSgdQfcOebMda\ KdaJfeVhifhjhijjijkijmjkojkqjksjktkmoknjkpekq`krWl\ tSluNlvIlxDly8lz4ks9kmEjgJjaOjWSiPXiJahDfh7kh1oi2l\ j2jk3hk3fl4cm4am5_n5Yo6Wp6Tp7Rq7Pr8Nr8Ln7Rj7Xg6bc6\ h_5nX5tZ7p`9maBjcDghEHfFI } 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 23-06-13 (Mathematic Mystery [A-6,M-9])
by Jim Muth 24 Jun '13

24 Jun '13

FOTD -- June 23, 2013 (Rating A-6,M-9) Fractal visionaries and enthusiasts: Today's image has a math rating of 9, which is an exceptional rating for the mathematical aspect of an image. The rating is based on the lack of discontinuities. All images that have a fractal exponent of Z in their generating expression must contain discontinuities. There is no way around it. Well, maybe there is! Today's image takes us into a area of debris polluting the large northern bud of the large minibrot on the main stem of the parent Mandelbrot set, which is corrupted in its depths by Z^(3.5) energies. The minibrot at the center is purely of order 3.5, but checking the elements beyond the minibrot, I see a ring of seven, arranged nearly perfectly, with no discontinuities in sight. It's impossible, but there it is, for all the fractal world to stare at in awe and wonder. But don't be too shocked. Discontinuities actually *are* in the image, but I have arranged the colors so that the breaks are invisible. Despite the exceptional math interest, the artistic aspect of the scene is boringly average. The rating of a 6 will win neither praise nor trophies, but the image is still worth the 50 seconds required to calculate it, if only to see a symmetrical Z^(3.5) fractal not filled with breaks. Checking the web sites will eliminate the calculation nuisance. Feel pleasant! View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Be Happy! View the hi-def rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Be in total bliss! View the thousands of back images at: <http://www.Nahee.com/FOTD/> Typical midsummer conditions prevailed here at Fractal Central today, with mostly clear blue skies, a hot sun, and a sweltering temperature of 90F 32C. Early in the afternoon the fractal cat found a cool spot to stretch out in, and stayed there until evening when the sun went down. (Sunset was at 8:43pm EDT today here at FC.) The fractal humans took it easy most of the day, avoiding distractions such as cook-outs. The next FOTD will be posted shortly. Those who can see time as an illusion might be able to view the next image at once. The rest will have to wait. Until whenever, take care, and as I see it, time is not an illusion. It is the fourth dimension of space, viewed edge-on. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mathematic_Mystery { ; time=0:00:50.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-1.759072351009887/+0.01430659715177246\ /4.875516e+009/1/42.5/0 params=3.5/1000/0/0 float=y maxiter=2000 inside=0 logmap=52 periodicity=6 colors=00043S54T65U76V87W98XAAYCCZFF_II`LLaOObSRcV\ UdYXe`_gcbigekjhmmkoonqrqsutuwvzzwmzxczyUzzKvwArt0\ mq0hoIclHZiGUfFQcEP`DPYCOVBNSANP9MM8MK7LI6LH5WF8eE\ BoCEyBGvCFtCFrCEoCEmCDkCDiCCfDCdDBbDB_DAYDAWD9UD9R\ E8PE8NE7KE7IE6GE6DD4EE6EE8EEAEFCEFEEFFEGHEGJEGLEGN\ EHPEHQEHSEIUEIWEIYEIZPMTZQOhUIrXDqWCqVBqVBqUApUApT\ 9pT8pS8oS7oR7oQ6oQ5nP5nP4nO4nO3mN2mN2mM1mM1qUGtaUw\ igzpuwmtujtshtqetnbsl`sjYshWsfTscQraOr_LrYJrVGqTDq\ RBqP8qN6qM6rM6rM6rL6sL6sL6sK4uL6sL8qMApMBnNDlNFkNG\ iOIgOKfPLdPNcQPaQQ_QSZRUXRVVSXUSZSS_ROfSKlSGsTCyTE\ vVFtWGqYIoZJl`KjaLgcNedObeP`gRYhSWjTTkURmWOnXMpYJq\ ZHr_Jo_Lm_Nk_Pi`Qg`Se`Uc`WaaY_aZYa`WabUbdSbfQbgObi\ MckKcmIcoGcpEdrCdtAdv8dw6at7_r7Yp7Wn7Ul7Sj7Qh7Of7M\ d7Kb7I`7GZ7DV4EX7FYAGZDH_GI`JJbMKcPLdSMeV4p7MfYPhZ\ Rj_Tl`VmaXobZqcaub`rc`oc`mc`jc`hc`ed`cd``d`Zd`Wd`U\ d_Re_Oe_Me_JecYjdXjeXj`Vk } 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 20-06-13 (In Search of Reality [A-7,M-6])
by Jim Muth 21 Jun '13

21 Jun '13

FOTD -- June 20.2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image is evaporated, which means that all the 'outside' stuff, from which the points eventually will escape, has vanished and been replaced by a screen consisting of totally 'inside' stuff, from which no points will ever escape. This bit of mayhem is a result of the ridiculous bailout radius of 10^100, better known as one-googol, which has been set by the imag(p3) parameter. A flat screenfull of all-inside stuff can be quite boring, but the active inside fills can often bring these 'dead' images to life. In today's image the 'bof61' fill does the job. The formula behind the madness subtracts 2.72 parts of Z^(-2.7) from 8.5 parts of Z^(-1.6) then adds (1/C) on each iteration. This creates a parent fractal with X-axis symmetry, which resembles a Mandelbrot set rotated 180 degrees with its west end facing east and its normal east end replaced by a large open bay. A kind of double crescent moon lies in this open area, and today's scene lies in one of these crescents. The name "In Search of Reality" does not refer to one of the current crop of contrived 'reality' TV shows. It refers to the questionable reality of things like fractals, sub-atomic particles, and of course ghosts. The calculation time of 2-3/4 minutes is slow enough to make the calculation a bother. But the web sites can bring a miracle cure. Forget about calculating the image on that DOS-challenged machine. Let me be the one who does the work. Check the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images without limit are online at: <http://www.Nahee.com/FOTD/> The weather was near perfect here at Fractal Central today, with a temperature of 82F 28C and a Photoshop-blue sky decorated with the kind of clouds that have faces in them. The fractal cat slept all afternoon while the humans went on a short trip in the surrounding countryside. The next FOTD will be posted before too long, most likely within 24 hours. Until then, take care, and skeptics know that truly paranormal things such as ghosts are all in the mind. At the same time, some people have already experienced the paranormal. But it's a trick of their minds, and they must be shown their understandable mistakes. To hear scientific claims that make ghosts and hauntings seem like everyday normality, they should talk with a cosmologist or a physicist. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= InSearch_OfReality { ; time=0:02:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.49734043483/+0.60763443273/197902/1/\ -60/0 params=8.5/-1.6/-2.72/-2.7/0/1e+100/0/0 maxiter=1400 inside=bof61 logmap=yes periodicity=10 colors=00084N64L45K25I05H3AJ5EL7IM9MOCQPEURGYTIaUL\ eWNiXPmZRq_QtaPwcPzdOyeNxeNwfMwfMvgLugLthKthJsiJri\ IqjIqjHpkHokGnlFnlFmmElmEknDknDjoCioCioAbc8XT6QH4K\ 68O8CSAFWCJZEMbGQfIUiKXmM`qOctQaqR`oS_mTZjUXhUWfVV\ cWUaXS_XRXYQVZPT_OQ`MO`LMaKJbJHcHFcGCdFAeE8fD6fH5e\ K5eN5eR5dU5dX5d`5cc5cf5cj5bm5bp5bs5bV8e7BgEHjLNmST\ pZZreduljxspzrmwrktrhrrfordlrajr_gqXdqVbqT_qQXqOVq\ LSqJPqHNnIOlIPiIQgIRdISbITfbZpUzgJzTJXRJYOZZML_YVo\ `_uEKbCZc9Kd7YeTQfccchhh9OiHgiQWiYcjTYjnmzvoztijrh\ jqhjogjY_johqkmwiejgdjfdjdcjbbjlcj`ijZajYajY`kY`lZ\ aniYlY`kY`jY`iY_hY_gY_fdVeY_dXZbXZaXZ`XZ_XYZ`TYXYX\ XYW50A50A50A50A50A00A50A50A51F52E`I0dK0hP0jU0lY0n_\ 0pa0rc0te0um0vj0wn0xr0zv0zz0sv0mr0cmQUhVLe`Ffe9gj3\ ho7`l8OiADfC3cE4dF5dG6eI7eJ8fK9fMmgNBgOBhQChRDiSEi\ UFjVGjWHkYIkZJl_Jl`LhaNebPbcQ_dSXdUUeWRfXOgZLh`Iia\ EhaFgaGfaHeaIdaJcaKcaLbaM } 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 21-06-13 (Four Alarm Minibrot [A-8,M-6])
by Jim Muth 21 Jun '13

21 Jun '13

FOTD -- June 21, 2013 (Rating A-8,M-6) Fractal visionaries and enthusiasts: Today's image is one of the fieriest of all time. And for good reason. The generating expression adds 666 parts of Z^(666) to (1/Z) before adding straight C on each iteration, and we know what happens to those who dabble with the number 666. They become ensnared by the beast and then spend all eternity with him in the fiery pit down below, which I hear is hotter than a nuclear furnace. Today's image gives us just a glimpse of that pit. (Good gosh, I hope I don't end up down there!) The name "Four Alarm Minibrot" refers to the fires in the fiery furnace. I have no idea if a minibrot might lie in the midst of the actual inferno, but I do see one at the center of today's image. The image's artistic rating of an 8 reflects the extra effort expended creating the effect of a nuclear fiery pit. The math rating of a modest 6 indicates that nothing very unusual is going on in the math aspect of the image. The calculation time of a mere 30 seconds will pass virtually un-noticed. But the annoyance of setting up and runnind a DOS parameter file may be eliminated by checking the image on one of the web sites. Calculation may be avoided by checking the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def rendering is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> The first official day of summer brought typical summer weather to Fractal Central. The temperature reached a moderately hot 84F 29C under a hazy sun. The fractal cat wanted the cool air turned on, but we humans are putting it off as long as possible. A lot of the winter chill is still trapped in the heavy brick walls of FC. The next FOTD will be posted within a reasonable time, which is most often but not always 24 hours. Until whenever, take care, and the world certainly has changed since I was a kid, but I have yet to decide if the change is for the better or worse. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= FourAlarm_Minibrot { ; time=0:00:30.00 SF5 at 2000MHZ reset=2000 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-0.18405946781423/+0.12052312284457\ /8.71e+008/1/-117/0 params=1/-1/666/666/0/0/0/0 maxiter=2500 inside=0 logmap=77 periodicity=10 colors=000D00A00F00H00H10K10K20O20N30R40Q50U60U70X\ 80X90ZA0_B0aC1bD2dE3dF4fG5hH6iI7kJ8lK9mLAnMBoMCpND\ qOErQDsSDtUDuVDvWDwXCxYCyZBz_Bz`BzaBzbAzcAzdAze9zf\ 9zg9ziAzkKznUzqcztmzwzzzzvwzsumpscmqUjoQimQhkQgiPf\ jPekPdlPcmPbnOanO`nO_nOZnO`nOanObpSbnQbmObkMbiKbgI\ bfGbfEbeCbdA`e8ae8bd8cd8dd8ed8fc8gd8he8ie8jf8km8lm\ 8mm8nm8om8pm8qm8rm8sm8tm8um8vm8wm8xm8ym8ym8zm8zm8z\ m8zm8zm8zm8zmAzmCzmEzmGzmIzmKzmMzmOzmQzmSzzUzzWzzY\ zz`zz_yzZyzYxzXxzWwzVwzUvzTuzSuzRtzQtzPzmPzmOzmNzm\ MzmLzmKzmJzmIzmHzmGzmFzmEzmDzmCzmBzmAim9im8hm7jm6k\ m4jm5im6gm8fm9emAdmBbmDamE`mF_mGYmImmJmmKmmLmmNmmO\ mmPmmQmmRmmSmmUmmVmnWmoYmpYmqYmrYzsYztYzuYzvYzwYzx\ YzyXzzXzzXzzXzzXzzXzzXzzXzzXzzXzzXzzXzzXzzXzzXzzXz\ zXzzXzzXzzXzzUzzLzzDzzEzzGzzHzzJzzKzzMzzNzzPzzQzzR\ zzTzzUzzWzzXzzYzz_zzZzzZzzYzzYzzXzzXzzWzzWzzVzzVzz\ JzzIzzGzzFzzDzzCzzAzz9zz7 } 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 19-06-13 (An Old Friend [No Rating])
by Jim Muth 19 Jun '13

19 Jun '13

FOTD -- June 19, 2013 (No Rating) Fractal visionaries and enthusiasts: Today's image shows an old friend in a new light. The old friend is the curious Julia Z^(2.003)+C rectangle, which in today's image is located at the point where the arms branch out from the main trunk of the vaguely human figure. Actually there are an infinity of rectangles in the image, so don't try to count the extras. The new light is the fact that the image is not a pure Julia scene. It is double rotated 0.03,0.03 degrees, or 1.8,1.8 minutes, from the true Julia orientation. (Double rotation is a strange motion that is possible only in space of more than three dimensions.) 1.8 minutes of rotation does not seem to be much of a change, but when it is done very close to the Julia orientation it makes a big difference. In today's image it has totally obliterated the left half of the humanish figure. This rectangle is one of the first things I found when Fractint gained the ability to calculate fractional exponents, which I think was in 1992. The rectangle struck me at once. It has no right to be there. It just doesn't make sense. But there it is anyway, for all the world to see. Since the rectangle as well as the human-like figure has appeared so often as a FOTD, I could give the image no rating. It's still kind of pleasant to look at however, and with a calculation time of 25 seconds, it will cause no impatient fidgeting. An alternative way to view the image is to check it online at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the back images are posted at: <http://www.Nahee.com/FOTD/> Near perfect weather made everyone happy here at Fractal Central today. The sky was a clear Photoshop (or old Kodachrome) blue with only a few small puffy white clouds, while the temperature reached a comfortable high of 77F 25C. The fractal cat made it through the day in true feline fashion, alternating between playing, eating and sleeping. The fractal humans had an average day, with nothing out of the ordinary to report, which is boring to report but was pleasant. The next FOTD is coming, and will be posted in a day or two. Until whenever that great moment arrives, take care, and what happened to the squatter who was dis-satisfied with his lot? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= An_Old_Friend { ; time=0:00:25.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/-0.0248852\ /9.655172 params=89.97/0/89.97/0/-1.7435/0/\ 0.000175/0.073883/2.003/0 float=y maxiter=2400 inside=0 logmap=yes periodicity=6 colors=00070R70Q60Q60P60P60O60N50N50M50L50L50K40K4\ 0J40I40I40H40G30G30F30F30E30D20D20C20B20B21A12A139\ 1481581670761862973A85B96CA7DB9ECAFDBGEDIFEKGFMHHO\ HIPIJQJLRKMSKNTIOUGQVETWDWXCZYBaZAd_9g`8ja7mb6pc5p\ e4sgAwiKzkUtmcsomqqzkszkqziomgmcekUcjKajM_jQYjUVgV\ TeVRcVPaVN_VLYVIWWGUWESWCQWAOW8MWBOXEQYHSZJU_MW`PX\ `SZaU`bXbc_ddbeddgegifjkgmmhonhhfjb_lXSnQLpKDrE6tJ\ CnNIiSOcWUZ`_TdeOadRZcTWbVTaXQ`ZN_`L_bIZddYOaVSZSW\ WP`UNdRKhOHlLEpJCtOFuTIvXKvaNwfQxjSxoVysXyfTtUPpHL\ k5Hg8JfBKfELfHNfKOfNPfQQfTSeWTeZUeaWedXegYeiZeZL_`\ UdbXidZneVsgQl_LeaJZcZSeULgPEiK7kG0mL5kPAiTFfXKb`P\ YeUUiZPmcLqhHulGpiFkgEfeEcbDa`C_ZCYWBWUAUSASQIUNPW\ KWYHb`EicBpi8wn5sl9okCkiFhhIdfL`eOXiSUgVQfYMd`IccF\ bfCah9cj6cl4cn7clAhkDhjGhiJhgMmfPmeSmdVmbYma`m`bm_\ amZarZarY`rY`rY`rX`rX_rX_rW_zW_zWczXfzYiz_lz`ozarz\ bQzi4zt3zp3zl3zi2ze2za2zZ } 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 18-06-13 (Strawberry Circle [A-7,M-6])
by Jim Muth 18 Jun '13

18 Jun '13

FOTD -- June 18, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image came about when I mixed 1.11 parts of Z^(-11.1) with 11.1 parts of Z^(-1.11) before adding (1/C) on each iteration. These parameters are entirely whimsical, with no special significance. The unusually large bailout radius is needed to avoid cutting off the oversized parent created by the parameters. This parent fractal is immense, but when all of it is squeezed onto the screen, it appears as a typical double-negative exponent thing with many odd-shaped bays and satellite rings. Today's image lies, as do so many FOTD fractal images, in a valley in one of the many bays of the parent. The name "Strawberry Circle" might seem to refer to a springtime festival, but it actually refers to the pinkish ring on the teal background surrounding the central minibrot. The artistic value of 7 and math value of 6 (all values strictly IMO) are near average, meaning the image is at least worth a look, but don't expect to be knocked over. The calculation time of 6-1/4 minutes is slow, but remember the old saying -- 'anything worth having is worth waiting for'. Of course, this wait may be avoided by checking the image on one of the web sites. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are at: <http://www.Nahee.com/FOTD/> The day began with a notice of computer CMOS battery failure here at Fractal Central. At least I know how to correct this problem, and I'll correct it as soon as I get around to it. The day's weather featured lots of clouds and humidity, with a temperature of 81F 27C. Rain threatened, but as of post time never appeared. The fractal cat passed the day checking for unwanted cats. When he was not checking, he took it easy eating and sleeping. The humans kept busy doing human activities. The next FOTD will be posted in the proper time, which usually means 24 hours. Until whenever, take care, and how will we ever find the resources to get men on Mars? We will be far too busy fighting climate change. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Strawberry_Circle { ; time=0:06:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.964592534819971/-0.8471298936440086/\ 3.663697e+012/1/-70/0 params=1.11/-11.1/11.1/-1.11\ /0/1000 float=y maxiter=2250 inside=0 logmap=446 periodicity=6 mathtolerance=0.05/1 colors=0000KZ0KZ0KZ0KZ0KY0KX0KW1KV1KU1KT1KS0JQ0IP0\ HO0GN0FL0EL0BK0CJ09H09OF3F06KR0D30RX0JK0Kc0NX1Pl1R\ i3TpEeuKXzMmzUzzZzzczzhzzmzxgzzmzyczvUztOzsPzpSuoU\ vlXyjYzi`zfbzedzg_qjWclRRoNDqSDtWDv`DydDziDzlDzqDz\ uDzuDzuDzuHuuKouNiuRbuTXuWRu_KuaDwd6te7peDlfHifLeg\ RagUYiYUibRjfNjjJjkHkkGlkFllDnlCnlAol9pn9pn7qn6qn4\ so3to1to0uo0uk4vi9vgDvdHvbKv_OvXSvUUwSYwPawNewKgwH\ kwFowCqwbjsdajfUaNKP0IJ4FK9JRCNXGRbJUiNWkQXnUXpXYs\ _Yua_ud_ufYuiXukXuoYup_uv`uz`oz`izaczaXzaRzYKzWDzS\ 6zP1zL1zJ1zG1zC3z93z43z14z04z04z13z13zA1zJ0zS0z_0z\ f0zg0zi1zi3yj4vk6uk7sl9qnAonCnoDloFipHfqKbsN`tPcuR\ hvTmwWryYvz_zzavzdrzfmzghzkcloZbrXUvbXui_soaptdnzf\ kzgizffzddzaazY_zWXzSUzRUzOWzLWzIXzGZzD_zA`z9`zDYz\ HVzLRzPOwTLuXHs`FpdCng7kk4in1bozYpzSrzNuzHwzKzzNzz\ PzzSzzUzzXzzYzz`zzbzzezzgzzjzzlzznzzpzzszzuzzvzzpz\ zkzzezz_zzUzzUzzTzzTzz0zz } 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 17-06-13 (The Lost Monument [A-9,M-6])
by Jim Muth 17 Jun '13

17 Jun '13

FOTD -- June 17, 2013 (Rating A-9,M-6) Fractal visionaries and enthusiasts: Today's image has an art rating of a 9. This is because I went out of my way to find a coloring that would make the image resemble a real 3-D monolith. The rating shows that I consider my efforts pretty successful. The math rating is a humdrum 6. After all, how interesting can the expression Z^(1.009)+C be regardless of how far up the hyperladder it is calculated. As a matter of interest, today's image was calculated 120 levels up the ladder. The parent fractal is a grossly oversized thing resembling a primitive stone arrowhead plunging back to earth. Today's scene lies in the chaos on the eastern edge of the arrowhead. The name "The Lost Monument" implies that regardless of how far one might search, he would never find the scene depicted in the image, since it exists only in the world of fractals as well as in the mind. I leave it to the individual fractalist to decide if mathematical fractals and human thoughts are to be considered in any way real. The calculation time of 6-1/2 minutes is slow enough to bring impatience to the more restless fractalists, so hooray for the web sites, which can bring relief. Find relief from mathematical anxiety by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Extra happiness may be found by viewing the hi-def rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Total bliss lies on the web site at: <http://www.Nahee.com/FOTD/> where the FOTD back images are posted. Rather sultry conditions prevailed here at Fractal Central today, with partly cloudy skies, some humidity and a temperature of 86F 30C. The fractal cat felt playful in the morning, but calmed just after noon to enjoy a quiet afternoon sleeping. The humans had a busy day, with FL working in her garden while I supervised. The next FOTD will be posted in a period of time that will seem to pass in a flash. Until then, take care, and before a problem can be solved, the nature of the problem must first be recognized. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Lost_Monument { ; time=0:06:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.652403251/+1.25954557/386/0.9057/\ -45/0 params=1.009/0/120/2400 float=y maxiter=1800 inside=255 logmap=645 periodicity=6 colors=000W_zW_zX_zY_zV_zW_za_zZ_zb_zb_zX_zX_z`_z`\ _zW_zUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdz\ UdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUd\ zW_zU_zS_zR_zP_zF_zK_zO_zS_zU_zU_zU_zU_zU_zU_zU_zU\ dzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzUdzP_z\ P_zP_zP_zP_zP_zP_zP_zP_zP_zP_zP_zP_zP_zP_zP_zU_zT_\ zS_zR_zQ_zQ_zP_zO_zN_zM_zM_zN_zO_zP_zP_zQ_zU_zU_zU\ _zU_zU_zU_zU_zU_zU_zU_zU_zU_zU_zU_zU_zU_zU_zU_zU_z\ U_zU_zU_zU_zU_zU_zU_zU_zU_zU_zT_zQ_zO_zL_zI_zF_z8_\ zD_zI_zN_zR_zW_zU_zU_zU_zU_zU_zW_zU_zU_zU_zu_zt_zt\ _zs_zr_zq_zq_zp_zo_zo_zn_zm_zl_zl_zk_zj_zi_zi_zh_z\ g_zt_ym_xg_wa_vV_uPdtKisKnrUsqcsvzxtzvtrtsmrmhllci\ lZgkUdjPZdMWcJUcJQbIPXIIWILWIJV8FKDDJ8BID9ID3HD6G8\ 4F83FDDE3DDD8U88CD1CI1BI1B81B810010D1AD10D1A010D1A\ D10D1A01081A81A31081A81A010010D1C810D1BD1A010C1AD1\ 0D1AE1A510F1A510G10C1AB1A } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 16-06-13 (East to Freedom [A-7,M-6])
by Jim Muth 17 Jun '13

17 Jun '13

FOTD -- June 16, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image is named "East to Freedom". The only reason I can give for the strange name is that the image lies on the east edge of one of those fractal fans that are so common in parent fractals created with two negative exponents of Z. The rating of a 7 is only slightly above FOTD average. Despite the brilliant colors, there have been so many similar images in the past that the theme has become hackneyed, holding down the rating a point or so. The calculation time of 3-3/4 minutes will drag a bit, but the drag may be avoided by visiting the web sites. Be at peace with the abstract realm of numbers. Check the finished lo-def image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> If hi-def is your thing, check the rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the past images, which are posted at: <http://www.Nahee.com/FOTD/> Morning clouds gave way to afternoon sun here at Fractal Central today. The fractal cat stretched out on the hardwood floor as the temperature reached a pleasant 81F 27C. The humans simply had a pleasant day, though I have noticed how much less active our pleasant days have become since I launched the FOTD in April of 1997. The fractal cat's pleasant days are slowing down also, especially now that he has no lady playmate to keep him on the run. The next FOTD will be posted in a day or two. Until then, take care, and don't agitate yourself by playing violent video games. Create a peaceful aura by enjoying a good murder mystery. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= East_to_Freedom { ; time=0:03:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+5.011007493465/-0.127916407873/460360\ /1/130/0 params=-10/-1.1/-0.1/-11/0/800 float=y maxiter=2400 inside=0 logmap=221 periodicity=6 colors=00002U02U02S02R02O02O02K02K02I12I22G42G53E6\ 4B7576456215105004004004001000500B60HC0NJ0VR0a_0ig\ 0su0qo0ol0ni0le0kb1kY4iW6hT8fP9dNCcJEcGHaDI_BLZ8OY\ 6RW4UW0WV0YU0aS0dQ0eQ0gP0iN0jM0lL0nJ0oI0qH0sG1zF4v\ D5zG9xD6vC4vB1mA0m90m50m70hA0ZC0cD0cF06F02F00F00D0\ 0D00F00D00C00D00F10F60G92FE4FI6GN8GT9GXCGbDFgGDnID\ sJCzNBzOBzNGzNJuLNnLQnLQnJQnJQnJQnIQnIQnIQnHQnHQnH\ QnEQnCQn9Qn8Qn6Qn4Ql0Pj2Ni6Mg8NeCNdEPbIPaLQaPQbTUb\ XUb_ZbdZdgcdlcdohduhexmezmezhezhYucTocNjZHeZJaURXU\ YTPeUQnWQnXQnYQnYQnYQnYNnYNnYLnYLnYInYHnbHneHniGnn\ GnlGnjGniFegFeeFYdFYbDYaFY_IYYMYYP_YUbAieAjiKklKqo\ UqsUtvcznczg9d_DQUGFOJ7HN2CP07N19N4CO7DOBGOFIPIJOM\ NNQPNSRNVRLPJJLEIG8HC4TJ0dS0sW0oc0nc0lm0jm0gm0ez0d\ z0bz0az0Yz0Xz0Wz0Uz0Tz0Pz0Oz0zz0zz0zz0zz0zzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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 14-06-13 (Tree Time [A-7,M-6])
by Jim Muth 14 Jun '13

14 Jun '13

FOTD -- June 14, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: I have used today's formula very rarely, so it is almost like a new one. It might be wise for newer fractal fans (if any) to include it in one of their formula files. There have been many fractal trees in FOTD history, and today's image is another tree. Most FOTD trees have been shaped like apple trees, but today's tree resembles a pine tree, or more specifically a Christmas tree, since it appears to be decorated with lights. The image is also the entire parent fractal, which was generated by calculating the expression Z^(1.1)+Z^(-1.1)+C in the Oblate direction and rotating the scene 90 degrees. This parent fractal is actually a sideways view of the Seahorse Valley of the critical Mandeloid slice of the parent Julibrot. The name "Tree Time" is a simple comment on the image and the frequency of fractal trees in FOTD history. The artistic value of 7 and mathematical value of 6 are close to average, which makes the calculation time of 45 seconds kind of a bargain. Make life even easier by checking the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of FOTD back images are at: <http://www.Nahee.com/FOTD/> A very pleasant though slightly chilly day was enjoyed by all here at Fractal Central today. I enjoyed the interesting clouds in the sky; FL enjoys the near perfect mix of sun and rain that has her garden in top shape; the fractal cat Nicholas enjoyed his extra treat of turkey and cheddar. For the record, the sky was partly cloudy and the temperature reached a high of 75F 24C. The next FOTD will be posted within a matter of hours. Exactly how many hours remains to be seen. Until whenever, take care, and why stop halfway with only *gun* control? Let's pass a law to control everything that could be used to hurt anyone. No, that wouldn't work. We would have to ban fists, which certainly can cause injury, and that would mean removing everyone's hands. And what about mouths, which sometimes utter words that can cause more harm than fists and guns combined? It appears that banning things would not work. We'll just have to pass a law to control human behavior. But then who would write the laws describing which type of human behavior would be banned -- idealistic young liberals striving for social equality or greedy old capitalists striving for more profit . . . or maybe Big Brother, or even the aliens from Sirius-C. Too bad -- I guess nothing is going to change. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Tree_Time { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=dec-97.par formulaname=OblateMix center-mag=3.20558/0/0.3299/\ 9.2497/90/0 params=1/1.1/1/-1.1/0/-1.36989 float=y maxiter=5000 inside=253 logmap=yes periodicity=6 colors=00000b00a00`00_01X02Y03Y04Z05_06_07`08a09a0\ Aa0Ba0Ca0Da0Ea0E`0F`0G`0I`0J`0K`0L`0L_0M_0N_0O_0OZ\ 0PZ0RZ0TZ0WZAYYK`YUcYceYmgYsiXtkXumXvnXwpcxumzzzzz\ zyzmxwcwtYvqZunZtmZskZriZqg_pe_oc_nb`mb`laakaaj`ai\ `ah_bg_bfZbeZbdYccYcbXcaXc`Wd_WdZVdYVdXUeWUeVTeTSf\ TSfTRfTReTQeTPeTPdTOdTOcTNcUMcUMbULbUKbUKaUJaUIaUI\ `UH`UH_UG_UF_UFZUEZUDZUDYVCYVBYVBXVAXVAWV9WV8WV8VV\ 7VV7VU7UT7TT7TS7SS6SR6RR6QQ6QQ6PP6OO6OO5NN5NN5MM5L\ M5LL5KL5KK4JJ4IJ4II4HI4GH4GH3FG3FF3EF3DE3DE3CD3BD2\ BC2AC2AB29A28C29D29E39F39G49H59I69J69K79ZAcZAcZBdZ\ BdZCdYCeYDeYDeYEfYEfYEfYFfYFgXGgXGgXHhXHhXHhXIiXIi\ XJiWJjWKjWKjWLkWLkWLkWMlWMlVNlVNmVOmVOmVOmVPnVPnVQ\ nUQoURoURoUSpUSpUSpUTqUUqUWqUXrTYrT`rTdsTgsTjsTotT\ mtTltSjuSguSeuSduSdvScvScwSbwRawR_vQZuQYtPXsOWrNVq\ NUpMToLSnKRmKQlJPkIOjHNiHMhGLgFKfGLgHLgHKgIKgIJgJJ\ gJJfKIfKIfLHfLHfHAKMHfNGf } frm:OblateMix {; Jim Muth z=real(pixel)+flip(real(p3)), c=flip(imag(pixel))+imag(p3), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2): z=(a*(z^b))+(d*(z^f))+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 13-06-13 (Superfractal [A-7,M-5])
by Jim Muth 13 Jun '13

13 Jun '13

FOTD -- June 13, 2013 (Rating A-7,M-5) Fractal visionaries and enthusiasts: Look up in the sky! It's a bird, it's a plane, it's Superfractal, complete with its superinsignia on its chest. Well, actually, it's an Oblate view of one of the strange rectangles in the East Valley of the split main minibrot on the negative X-axis of the Z^(2.003)+C Mandeloid. Today's image might not be faster than a bullet, more powerful than a locomotive, or able to leap tall buildings in a single bound, but if it had appeared in the 1930's, around the time the other superhero did, it would have been considered super indeed. My opinion of the image's artistic worth is in the range of a 7, while the math worth rates a humdrum 5. The math aspect might have rated a point or two higher if so many similar rectangles had not appeared so many times before. The name "Superfractal" came to mind when I saw a stylized letter 'S' in the image. The 'S' consists of what remains of the open area of the curious Julia rectangle. Requiring a wait of 8-1/2 minutes, the calculation time is slow, there is no doubt of that. But the wait can be eliminated by checking the web sites. The image has been rendered and posted to the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def versions are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> The day began with a bang as a heavy thunder-storm broke out here at Fractal Central. When the storm ended, the rest of the day brought lots of clouds and a few light showers. With a little sun mixed in and a temperature of 79F 26C, it was still a pleasant day however. The fractal cat, who did not like the thunder, braved the storm nevertheless in his favorite chair. The humans noted that the additional 1.15 inches, 3cm, of rain was too much of a good thing for the fractal garden, which is becoming rather waterlogged. The next FOTD will be posted when the bull cows come home. Until whenever these apparent hermaphrodites arrive, take care, and keep affirming that there are no aliens from space secretly running the mess we've worked ourselves into here on earth. After a while, you might actually start to believe yourself. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Superfractal { ; time=0:08:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.000000295\ 34029771/-0.00001939834553309/8925.013/0.03549/\ -89.0561575137423063/88.6599571880745998 float=y params=0/90/0/90/-1.7435/0/0.00019/0.07682/2.003/0 maxiter=64000 inside=0 logmap=80 periodicity=6 colors=000bMjaLj_KkZJkYIkXIkWHmVGoUFqQGrTHsVItXJu_\ KvaLwQMwQNwROwRPwSQvSRvTSuTSuURtUQtUPsUOsSNrUOrVPq\ WPqXQoYRl_Rj`ShaTfbTccUadU_fVYgWWhWTiXRjYPlYNmZKn_\ Io_Gp`Epb8q`CqZGrXKrWOrUSsSWsQ_sPctNgtLktKnsJorIor\ HoqHoqGopFooFooEonDomDpmCpmBplBpkApk9pj9pj8pi7pj4q\ i7pi9piBpiEphGohIohKohNohPogRngTngWngYng_nfamfdmff\ mfhmfjmehkdgicfgbdeacc`ba_`_Z_YYZWXXUWWSVVQUTOTSMS\ RKRPIQOGPNERI1OMDLQPJU_IV`HW`GX`FY`FZ`E_`D``Ca`Cb`\ Bc`Ad`9e`9f`8g`7h`6i`2ja6i`Ah_Dh_HgZLfYOfYSeXWfUVe\ XUeZUe`TdbTddSdfRciRckQcmQboPbqUgtPbsLYrGTqCOp8KpB\ MlDOhFQeHSaKVYJUZIUZIUZHU_GU_GU_FU_EU`EU`DU`CU`CTa\ BTaATaATa9Tb8Tb8Tb7Tb6Tc6Tc5Tc5Tc8UbAUbCVaEVaHWaJW\ `LW`NX_Qc_Sc_UcZWcZZcZ`cYbcYdcXgmXimXkmWmmWqmYomWn\ mVlmUkmTimRhmQfmPemOcmMbmL`mKcmJcmIcmGcmFcmEcmDcmB\ cmAmm9mm8mm4mm7mmAmzCmzFmzHzzKzzMzzzzzzzzzzzzzzzzz\ 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 12-06-13 (Two Plus Two Equals Five [A-6,M-6])
by Jim Muth 13 Jun '13

13 Jun '13

FOTD -- June 12, 2013 (Rating A-6,M-6) Fractal visionaries and enthusiasts: Today's moth-eaten image lies in the same parent fractal as yesterday's image. But instead of lying on the southern edge of the 'fan', it lies in a tiny valley in a small hole along the X-axis at the eastern edge of the fan. Because of the current phone and e-mail spying flap, I am currently reading the novel '1984' for the third time. The name of today's image, "Two Plus Two Equals Five", came about when I remembered what poor Winston had not only to say but also to know was true. The image's ratings show that I truthfully believe that both the artistic and mathematical values are near average. The greatest drawback of the image is its annoyingly slow calculation time of 25 minutes on the typical SOTA PC machine, though I hear it will run faster on a SOTA MAC. But don't be alarmed by the slowness. Remember the FOTD web sites, which can always save the day. Calculate the image for yourself with frustration, or view it with much less frustration already rendered on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and enjoy the hi-def versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and all the FOTD back images at: <http://www.Nahee.com/FOTD/> A mix of clouds and sun with a high temperature of 81F 27C made today quite pleasant here at Fractal Central. The fractal cat displayed his fractal nature by sleeping most of the afternoon, while the humans tended to more human things such as work and gardening. The next FOTD will most likely be posted in one day, two at the most. Until whenever, take care, and keep an open mind. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 2_Plus_2_Equals_5 { ; time=0:25:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+4.704917286396/-0.000960883653/1811176\ /1/132.5/0 params=-11.1/-1.11/-1.11/-11.1/0/100/0/0 float=y maxiter=6400 inside=0 logmap=757 periodicity=6 colors=000ekWcl_bmd`nh_omYpqXpuYntZms_kr_jr`iqagpb\ fobeoccndbmeale_lfZkgYjgWjhViiUhjSgjRgkQflOemNdmMd\ nKcoJboIbnJanJanKamKamLamLalMalM`lN`kN`kO`kO`jP`jP\ `jQ`iQ_iQ_iR_hR_hS_hS_gT_gT_gUZgUZfVZfVZfWZeWZeXZe\ XZdXYdYYdYYcZYcZYc_YKOWTHkKMZBRN3VB5UB7TB8SBARBIIH\ BRB3a35_67Y98WBAUEBSGDRJEPLGNOILRJJTLIWMGYOE`PCbRA\ eX3kS9gOFcKL`FRXBXT1hU7aQCWMHQIMJERDAX32W77WBBWFGW\ JKWNOWRTWVXWZ`WbeWfiWjmZkjalgdmdfmadi_bfZ`cYZ`XXYV\ VVUURTSOSQLQOIPMFOKCNI8NJ9MJ9LK9LK9KL9KLAJMAIMAINA\ HL7GNAHPCIREJTGKVIKXKLZMM`PNbROdTOfVPhXQjZRk`RgXhd\ UygZijbUzAAzAKzAUzAczAmzAzzAmz9cz9Uz9Fz8Ez8Dz7Cz7B\ z7Ay89x88w88v87u87t86s85s95r94q94p93o92n92m91m91lB\ 3kD5jE6iG8hI9gJBfLCeNEdOFcQHbRI_QMYQQVPTTPXQO`OOcc\ NgcNkcMncMrcLvmLmmPmmTmmWmm_mmcmmcmmcmmhmmhmmhmmhm\ mhmzmmzmmzmmzmozmrzmuzmrzmpzzzzzzzzzzzzzzzzzzzzzzz\ 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 11-06-13 (Holes in the Story [A-6,M-6])
by Jim Muth 11 Jun '13

11 Jun '13

FOTD -- June 11, 2013 (Rating A-6,M-6) Fractal visionaries and enthusiasts: Today's image is filled with tiny holes -- thousands of them -- and each hole holds an entire fractal universe. Noticing the abundance of universes, I named the image "Holes in the Story". Of course, the name has nothing to do with one of those trendy watered-down 'light' murder mysteries made for the ladies. The large minibrot filling the center of the frame is under- resolved. Raising the maxiter to around 3000 would eliminate this flaw, but it would also change the coloring, which is not all that great to begin. (I am a constant critic of my own frequently flawed work.) The formula behind all the madness is totally whimsical. For no particular reason I combined 11.1 negative parts of Z^(-1.11) with 1.11 negative parts of Z^(-11.1), and then added (1/C) on each iteration. The resulting parent fractal is an oversized thing with a prominent 'fan' with the blade pointing east along the X-axis. Today's scene is located on the southern edge of the fan blade. The artistic and mathematical worth both rate an everyday 6. The image is not great, but those who do not check it will never know what they have missed. Unfortunately, the calculation time of 5-3/4 minutes will drag, even for the most ardent fractal fan. Here is where the time- saving web sites rush to the rescue. For instant serenity. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> If hi-rez is your thing, check the image at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Armchair archaeologists may check the ancient FOTD images at: <http://www.Nahee.com/FOTD/> The day turned out not so bad here at Fractal Central. A brief shower in the morning cleared out in time for a partly cloudy afternoon, with a temperature of 77F 25C. The fractal cat gave approval by sleeping through most of it. The humans had an average day of getting the things that needed to be done out of the way. FL spent time admiring her roses, which are giving the best performance in years. The next FOTD will be posted when the time is right. Until the right time arrives, take care, and Big Brother is surely already among us. All we need to do is recognize him? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Holes_in_the_Story { ; time=0:05:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.42737934414/-2.347260171984/1984005/\ 1/60/0 params=-11.1/-1.11/-1.11/-11.1/0/100/0/0 float=y maxiter=2000 inside=0 logmap=-282 periodicity=6 colors=000IgoJieMdaOZYRUVRRRRPQVKPZFMbAKe8Ig9Gi9Ck\ D9kH9mMAcHAUF6O83H33J44N49P5ET6LV6QZ7V`7`d9gfAmkBs\ nCxfEo`MeVUXSXTOeOIoGExCCzCCzCCzCCzCCzCKzCPuBUmA_d\ 8eY8oVEvQKzMOzPMzQMxRMvSKuTKsWJqXJoYGmZGk_Gi`FdXI`\ ULVRORPPOMPMJTJGXFE`BAd99g99kAAoBBsCCvCCxH333G84LF\ 5PK6TQ6XV7`b9dgAjmBnsCszCuzCyzCzzCzzCyzCrvFiiJbYOV\ PNNBRJ5XP6bU8gZDmdGshLxnOzrSzvUzyXzzZzz`zzrxxxnxzZ\ szfuzlwzquuvvvuvmxxdzyWzzMzzCzuCzqCznCziCzfCxaCvZC\ uUBqOAoLAkG9iC9g99d88b77a77T6FO5RL8eJBuECzCCzHCzK8\ dN4IP5KR5LTENTNPVUR`dVbmXgx`hz`hz`CQzCMzCJzCEzCCzC\ CzCCzCCzCCzTF6VK6VO6VTCXXK_bTbgafmhhqmjvrjzxjzzlxu\ kqoiiicdbde`dg_dg_fiYfiYfkXhmVhmVhoUjoUjqSjsRlsRlu\ PluPvmCznCznCznCznCznC`zzZyzXwzWuzUszSrzcozcmzckzc\ izcfxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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 10-06-13 (The Mandy in Space [A-7,M-6])
by Jim Muth 10 Jun '13

10 Jun '13

FOTD -- June 10, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image lies in an easily missed parent fractal that comes into existence when Z^(100) is blended with 2 parts of Z^2 before straight C is added on each iteration. This parent is a lopsided series of circles, one inside the other, centered well west of the origin, with a tiny Mandelbrot set along the X-axis, rotated 180 degrees, with its west end facing east. Today's scene lies in an elephant-trunk spiral in the East Valley of this tiny M-set. If the formula function is changed from 'ident' to something else, the parent fractal loses its circular X-axis symmetry and changes into any number of grotesque shapes, but the inner details remain the same. The name "The Mandy in Space" has some connection to a futuristic scene in some old sci-fi movie. I forget exactly which movie was the inspiration. The artistic rating of a 7 indicates a little above average satisfaction; the math rating of a 6 indicates near average mathematical interest. The calculation time of 1-1/4 minutes will pass as swiftly as the time required to check the image on one of the web sites, but checking the web sites will eliminate the task of setting up and running the parameter file. Total relief from calculation pains may be found on the official lo-rez FOTD web site, which is online at: <http://www.crosscanpuzzles.com/Archives.html> The hi-rez image is online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Lots more FOTD fractals are online at: <http://www.Nahee.com/FOTD/> Today was rather unpleasant here at Fractal Central. Heavy clouds hung overhead all day, and rain fell constantly, varying from very light to rather heavy but never stopping entirely. To make things worse, the air was totally saturated, making the temperature of 70F 21C quite oppressive. The fractal cat took no notice of outdoor things, finding satisfaction instead in his treat of turkey and cheese. The fractal humans had an everyday day indoors. The next FOTD will be posted one day in the very near future. It could even be tomorrow. Until whenever, take care, and every time I see or read an official scientific explanation of how the neural network of the brain creates self-awareness, I just can't grasp the connection between the material neural network and the non-material conscious awareness of one's own existence. I guess I'm not as smart as I thought I was. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Mandy_in_Space { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-0.8662519660562518/-0.0868356105845902\ /6.607561e+011/1/67.5/0 params=1/100/2/2/0/0/0/0 maxiter=3000 inside=0 logmap=133 periodicity=6 colors=00000501702903B03D04F05G06H07I18J2AK3CK4EL5\ GL6IL7KK8MK9OKAQKBSJCUJDWJDYJE_JFaJGcMHePIgUJiZJkc\ KlhLmmLnrLovJpzJnvImrHkmHjhGhcGfZGdUGaQHZNHVMHSLHP\ KHJJIFIIAHI6GJ8JJFLKKOKPQLUTMZVMbYNg_NlbOpdOtgPxiO\ vjMtjLrkJplInlGlmFjnEhoCeoBcp9aq8_q6Yr5Ws3Us2St3Ts\ 3Uq4Wp5Xn6Ym6Zl7`j8ai8bh9cfAeeBfcBgbChaDj_DkZElYFm\ WGoVGpTHqSHrRGpSFnSEmSEkSDiSChSBfSBdSAcS9aS8`S8ZS7\ XS6WS5US5SS4RS3PS6QR8RQBSPDSPGTOIUNLVMOWLQXKTYJVYJ\ YZI__Hb`GeaFgbEjcDlcDmdCmeBmfAmeAmeAmdBmdBmcBmbBma\ Bm`Cm_CmZCmYCmbDmbDmcDmdDleDlfEkgEjhEjhEihEhhEghFm\ mFmmFmmOmmOmmUmmUmmcmmcmmmmmmmmzmmzmmzmmzmmzmmzmmz\ mmzmmzmmzmmzmczmczmczmczmczmczmczzczzczzczzczzczzc\ zzczzczzmzzmzzmzzmzzmzzmzzmzzmzzfzzfzzfzzgzzgzzgzz\ hzzhzzhzzhzzizzizzjzzjzzjzzjzzkzzkzzkzzkzzlzulzzlz\ zmzzmzzmzznzznzznzzozzozzpzzpzzqzzqzzrzzrzzrzzszzt\ zzuzzvzzwzzwzzxzzyzzyzzzz } 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 09-06-13 (Forbidden Universe [A-8,M-7])
by Jim Muth 09 Jun '13

09 Jun '13

FOTD -- June 09, 2013 (A-8,M-7) Fractal visionaries and enthusiasts: Some fractalists might be curious about the new rating system. In the new system 'A' refers to the image's artistic worth and 'M' refers to its mathematical interest. In today's ratings, I show that I consider the artistic worth of the image to be worth an 8, and somewhat better than the mathematical interest, which rates a 7. The image was created when I combined 1.3 parts of Z^2 with 10 parts of an unlikely Z^(-0.01) before adding straight (C) on each iteration. The parent fractal is most curious. It does not appear on the default screen, which is a total blank, but lies instead in the area around negative 10 on the X-axis. This parent resembles a Mandelbrot set being moth-eaten from the west. Today's scene is located in the East Valley area of a kind of jagged minibrot on the north edge of the moth-eaten area. Much of the image's effect is due to its rendering. To add some extra impact, I rendered it with the outside set to 'tdis' and the inside set to 'fmod'. The normal rendering, with the inside a flat black and the outside set to the iteration count, is rather boring. The name "Forbidden Universe" could be the name of a sci-fi adventure movie, but it is actually a reference to the infinity of equally real alternate universes that the erudite physicists are telling us most likely exist. (Of course, the physicists might be nuts! Some very rational skeptics already think so!) The calculation time of 2-3/4 minutes borders on slowness and might possibly turn away some potential new fractal fans. This is where the web sites do their time-saving work. The fractal calculation may be avoided by viewing the finished image in lo-rez at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and past images at: <http://www.Nahee.com/FOTD/> Uneventful weather prevailed here at Fractal Central today, with mostly sunny skies and a temperature of 79F 26C. The fractal cat, who is getting up in years and does not get to go outside like the past fractal cats Thomas and Tippy did, slept through the afternoon. The humans spent the day relaxing, which is getting ever more difficult to do in this ever-more-addictive culture we live in. The next FOTD fractal will be posted in the not-too-distant future. Until that ambiguous time arrives, take care, and we hear lots of talk about social 'change' and a fairer, more even distribution of wealth, but nothing ever changes. Poverty should be easy to eliminate. Since poverty is defined as a lack of the money needed to live a comfortable life, it could be eliminated by giving the underprivileged enough money to enable them to live comfortably. Why then do the world's governments refuse to distribute money to the underprivileged and end the unrest caused by the prevailing social injustice? Maybe the well-to-do need disposable scapegoats to blame for the problems brought about by their own misdeeds. Then again, maybe living an impoverished life is simply a part of the nature of some people, and poverty can never be permanently eliminated by giving money, which will soon be squandered. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Forbidden_Universe { ; time=0:02:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-10.38329737855416/+0.5276798594052841/\ 1892462/1/180 params=1.3/2/10/-0.01/0/0/0/0 float=y maxiter=1200 inside=fmod outside=tdis colors=000KIzIIzGIz9EzEIzJLzOPzTSzYVzbZzgazlezqhzy\ lzukzqjzmizihzegzafzYezUdzQczMbzIazE`zA_z6Zz2Zz3`z\ 4az5cz5dz6ez7gz8hz8jz9kzAlzBnzBozCqzDrzFtzDszCszAr\ z9rz7qz6qz4oz3pz2pzErzPsz`tzkuzlszlqzlozmmzmkzmizn\ gzneznczoazo_zoZzj`zfazbbzYczUdzQezMfzHgzDhz9iz4mP\ 5jN5gM6eL6bJ7`I7YH7WG8TE8RD9OC9MBAJ9AH8AE7BC6B90C7\ 3C42A20800600500300O0VQ5`SAfUFkWHlYLl_MmaJmjHnkFol\ DpmErkEngBnc5mW1eS3ZO4US6ZW7a_8daAfcBfeCeeEdcFcbGb\ aI`_J_ZLZYMXWNWVPVUQUSRSRTRQUQPVPQWNQXMQXLQYKQYJQZ\ IQZGQ_FQ_EQ`DQ`CQaBP`9QaARaBSaBTbCUbCVbDWcDXcEYcEZ\ dF_dF`dGaeHbeHceIdfIefJffJggKhgKigLjgLghJejIclHanG\ _pFYrEWtDUuCWnGYgJ_aNaVQcOTeIXgB_h5bmDcqLduTey_fb_\ RG_CHZJIYPJXVKW`LVfMUlNTrNTxMPrMMmMJhLGbLDYLATKCSJ\ DRIEQHFQGGPFIOEJODKNCLMCMMMUGW`Beg5on0ni4md8l_ClWG\ kRKjMOjISiDWh8_h4blQPpjCleHi`LeWQbRU_MYUPbPRfKTjFV\ nAXr5Zv8XtBVrSJMQIMOIMMIM } 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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AOTD 6_4_13
by JackOfTradeZ＠comcast.net 09 Jun '13

09 Jun '13

. The imagery is astounding; it seems like any real world phenomenon can be emulated by a fractal and a simple equation! You clearly see a large ship from a perspective just off the starboard bow. You see the hull, forward keel, deck, bow, air and water, with a distinct "3D" aspect right at the "water line"! This is the famous "burning ship" fractal, which I finally figured how to do in fractint (with a pointer from Michael Condron). There is a HUGE difference in render time from passes=1 to passes=g, and if iterations are more than a few hundred thousand it becomes impossible. A strange fractal. Looks like ships on fire, and a scene of the aftermath of a great sea battle - all burning. Alternatively, the "fire" takes on the appearance of ghostly castles and rising spires; St. Elmo's fire on steroids. The actual burning ship is not the parent fractal, it is the first largest "mini" along the spike, and you need to rotate the axis to get it in proper orientation. In a FractInt "*.frm" file, the classic Mandelbrot is: Mandelbrot (xaxis) { ; z = 0, c = pixel: z = z*z + c |z| < 4 } To make the burning ship, do this: ship1 { ; z = 0, c = pixel: z = abs(z)*abs(z )+ c |z| < 4 } Or this, which seems to render a bit faster: ship2 { ; z = 0, c = pixel: z = (abs(z))^2+ c |z| < 4 } 2 min 33 sec running time, 640x480 WMV, 45 MEG: http://www.fractal-animation.net/vid/ship.zip If you got the fractal stones for a 103 MEG download, this is a 1280x720 Hi-Res file: http://www.fractal-animation.net/vid/ship1280.zip Enjoy! JoTz .

5 4

Burning Ship
by JackOfTradeZ＠comcast.net 09 Jun '13

09 Jun '13

. My weblog says many download attempts, and most were incomplete. Is everyone having trouble downloading it? Is the file too big? Did anyone successfully play it? There have been no comments. I think it is one of my best, thats why I uploaded the big hi-res file. I can make a smaller file for download if anyone wants. . '

5 4

FOTD 07-06-13 (Bright Shadows [A-7,M-6])
by Jim Muth 07 Jun '13

07 Jun '13

FOTD -- June 07, 2013 (A-7,M-6) Fractal visionaries and enthusiasts: Today's intricate fractal came to life when I rendered a relatively ordinary fractal with the 'outside' set to 'fmod' and the proximity set at 0.25. This 'fmod' option all too often results in little more than a flat blank screen, but when it does work, as it does in today's image, the results can be well worth the effort. Today's generating expression combines Z^(2.05) with straight Z before adding straight C on each iteration. The resulting parent fractal resembles two partially merged Mandelbrot sets. Today's scene lies in the outer debris on the west shoreline of the main bay. The name "Bright Shadows" has nothing to do with an old TV soap opera. It refers to the brilliant patches spotted throughout the frame. With a rating of a 7, the image's artistic worth exceeds its math worth, which scores a rating of only a 6. The calculation time of 1-1/3 minutes will worry no one, especially those who choose to view the image on one of the web sites. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> with an enhanced rendering at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of past images may be checked and admired at: <http://www.Nahee.com/FOTD/> Today began cloudy here at Fractal Central and went downhill when the rain from T.S. Andrea arrived at noon. The chilly temperature of 66F 19C failed to bring cheer. The fractal cat gave up early and spent most of the day in my favorite chair; the fractal humans, who never give up, strongly disapproved of the weather conditions. I doubt that there will be time to produce a FOTD fractal tomorrow, so the next FOTD will be posted in two days. Until then, take care, and avoid becoming attached to any particular fractal. They have a way of vanishing without warning into the ether. (BTW, what is this 'ether' that things vanish into?) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Bright_Shadows { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-1.574988358385002/+0.01397662935983304\ /4.689995e+011/1/80/0 params=1/2.05/1/1/0/0/0/0 maxiter=1750 inside=0 proximity=0.25 outside=fmod logmap=yes periodicity=10 mathtolerance=0.05/1 colors=000260560A62E62H62K62P63T63W63`65c65g65j65o\ 67s67v77v78v98v98v6Av98vA8vC7sE7lG5eH5`J5UL3NO3HP2\ CR25T20U00W00Y00Z00`00Z50YA0WH0UL0TR0RX0Pa0Oh0Mm0M\ r0Om0Pj2PeARaJTXPTUCLf0Ct06t06t09t0Ct0Gt0Jt4Mt7PtA\ TtEWtHZtKbtNetRitUltYot`stcvtgytjztmztpzttztvztvzt\ vztvztvztvztvztvztvytvvtvstvotvltvitvjtvjtvjtmltel\ tYltPntHnt9nt9ntAotAotAotCqtCqtEqtEqtFstFstHstHttJ\ ttJttKyqJtkHqkFnkFjkEghCbeCZaAWZ9TW5OU9PSCPSERRHRR\ KRRMTPPTPTUPUUNYUN`WNbWLeYLhYLjbKmgKsoKvwcvzmvzzvz\ zvzmvzcvzCvz8mw5eo2Yg0PZ0HR09J04E00A34CA9GHEHNJLUN\ O`TPfYTmbUteYtiYtfWtcRtZMkUGcPBWK6PF6DC48A33903A33\ C42C67G67J67M68P68T6AW6AZ6Ab6Ce6Ch6Dl6Do6Ds6Fv6Fv6\ Hv6Hv6Hj7LPLP5YS9ZUAZUCZWE`WF`XH`XJ`XP`cWZhbZmhYto\ YtvWtvWtvbtvgrtnksscoyWmzPjzHhz8gz2`zAWzIRzPMzXHzc\ Czk7yrJOLT60Y60bP0gi0lz3pz7oerjbme`h`YeWW`RTWNRSJM\ NFHKCEH99D468065062060060 } 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=========================================

1 0

FOTD 04-06-13 (Squiggly Pentagon [7])
by Jim Muth 06 Jun '13

06 Jun '13

FOTD -- June 04, 2013 (Rating 7) Fractal visionaries and enthusiasts: For today's awe-inspiring fractal diversion we venture into a parent fractal that is basically a HyperMandelbrot set, where we check the eastern edge of the north branch of Seahorse Valley. After a brief search we find today's scene, which appears to be a quintic corruption but is actually of another order entirely. I named the image "Squiggly Pentagon" because of the numerous squiggly armlets sprouting from the pentagon shaped ring. The rating of a 7 is an improvement over yesterday, though it still leaves much room for improvement. The calculation time of 6 minutes is no laughing matter. The image will take this long to finish on the average machine still able to run DOS, (if any still exist). To avoid impatience, I recommend viewing the image on one of the web sites. The official web site with the low-rez image is online at: <http://www.crosscanpuzzles.com/Archives.html> The hi-rez alternate renderings are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And scads of back images are available at: <http://www.Nahee.com/FOTD/> Perfect weather prevailed here at Fractal Central today as the temperature reached 75F 24C under a cloudless sky. The fractal cat, who is an indoor cat, passed the day sitting in the window, watching the fractal humans enjoy the day in the fractal garden. The next FOTD will be posted in the proper time. Until we find out how much time is to be considered proper, take care, and how can we be absolutely certain that reality is really real? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Squiggly_Pentagon { ; time=0:06:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot2 passes=t float=y center-mag=-0.749480813398176/+0.031703452082799/\ 5.498886e+010/1/89/0 params=0/0/0/0/0.2/0/1e-020/0 maxiter=4000 inside=0 logmap=981 periodicity=0 colors=000V4RQ8LLBGGFA8H2CI5GI8KIBNJERJHVJKZJNaKQe\ KTmL6lM9lNBlODlPFlQIlRKlSMlTOlURlVTlWVlXXk`_lYZmWY\ nUXnSXoQWpOVpMVqKUrITtCTrGTqJToMTnPTlSTkVTiYTh`Tfc\ TjcYecT`cPXcKScGNcBMc4Jc7HcAEcCCcF9cI7cK4dN2cQ0cSg\ caXcZKcVNcXQcZSc`VcbYcc_cebdgefigikjklmnnopzrszuuz\ zzzvtzvrzupvunrtkmtihsgcse`sbYr`VrZTqXQqUNpSLpQIpO\ GrJPsFYuBev7nt9Bw3vu4ss5pq6mo7jm8gk9di9agAZeBWcCTa\ DQ_ENa7GZEKWKOURSRXWzz_zzczzfzzbzzZzzVzzRzzOifKndG\ rcCva8z`5tb6oc7ie8df9ZhAUiBOkCJlDDnE8oEAnFCmFEmGGl\ GIlHKkHMkIOjIUiJZiJchKhhKmgLrgLvkMwkMwlRwqNwrJwwGw\ xCws8wt6vt5rp4mp3hq7cmAZmKUnUPmcKmmFlvAnz5oz3pz3qz\ 4lz4gm4bc5ZZ5UZ6UY6dY7dY7dY5sa7nY9jVBfRDaOFYKDUFGU\ HJUILUKOULQUNTUOVUQYUR_UTbUUdUWgUXiUYkRalOdnLgoJjl\ MeiOagRYdTUaWP_YLX`HUbDPb8Sd9VeAXgB_hCbiDdkEglFjmB\ imFijIhgLhcOg`RgYVfUYfR`eOceKfdHjdEmcApc7sc4va5r`5\ o_6kY6hX6dW7aV7YT7VS8RR8O } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 05-06-13 (Nothing in Nothing [M-7,A-8])
by Jim Muth 06 Jun '13

06 Jun '13

FOTD -- June 05, 2013 (Rating M-7,A-8) Fractal visionaries and enthusiasts: Today's image is a striking one, which earns it an artistic value of 8. It is also an evaporated one, which earns it a math value of 7. The name "Nothing in Nothing" is a comment on the fact that every point in the image consists of trapped inside stuff, supposedly eliminating the possibility of any fractal features. But just because all the stuff is trapped does not mean it just sits there. Like a tiger pacing in its cage, the inside stuff works itself into intricate patterns that can be revealed by the active inside fills. In today's image the bof61 fill does the job. The parent fractal consists almost entirely of a huge fractal 'fan' surrounded by a scattering of sun-bursts, with today's scene located near the eastern edge of the fan's blade. The appearance of this parent fractal changes greatly when the bailout radius is changed. As the bailout is increased, more and more points become ultimately trapped, and as far as creating 'outside' chaos goes, they simply vanish, or as I call it, they 'evaporate'. The calculation time of 5-1/2 minutes is slow by any SOTA standards, but the viewing delay may be eliminated by checking the finished image on one of the FOTD web sites. The official but lo-rez FOTD web site is online at: <http://www.crosscanpuzzles.com/Archives.html> Hi-rez variations are available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And kadoodles of back images are posted at: <http://www.Nahee.com/FOTD/> Absolutely perfect weather prevailed here at Fractal Central today. The temperature of 79F 26C was warm enough to keep the fractal cat in stretch-out mode, while the sun was warm enough and the wind light enough to make even outdoor water activities pleasurable. The fractal humans spent the day observing the 17-year cicadas that are currently singing and celebrating in the trees around the Central Pennsylvania area. The next FOTD will be posted. That much is virtually certain. What is in doubt is the exact time. Until whenever, take care, and if one assumes that what he observes is a real physical world, all he has to do is shut his eyes, hold his ears, and observe that the reality he had been observing no longer exists. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Nothing_in_Nothing { ; time=0:05:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+4.71691044048/-0.18503827863/5.57e+007\ /1/-110/006 params=-11/-1.1/-1.1/-11.1/0/1e+100/0/0 float=y maxiter=2100 inside=bof61 periodicity=10 colors=000R85_ABiBHrCMzERyIQyMPyPOySMyVKyYIybGyeFy\ iDwlBwpAwt8wz7xz7I8muz6I8muz60AXwz8ABcwzEI8myzLGBd\ yuSIAiyn_IGkykgNIlygmYKkyarcMzyWyhUzw`rg_ztdmgczrh\ iihfphbmh_mjWkkSkmRjpNjrJhtIhwEfyCgzAZr5Ri2J`1DV07\ O00G0090z6W040000000600I00E00B00700400100000000000\ 0000000000000000000000000000300600700B00E00G00K00M\ 03P26T49V4F_6I`6Md9QiBWkB_pDbrEgwGmzJrzJtzLzzJwzLt\ zLtzNozNmzOiyOgwPdtP`rP_pRWmRUiSRfRPdSLbRH`QF_RBXR\ 9VS5TS4RT1PT0VK0RP0OT3NX5J`9JdDHkFFpIEtMCyMCzNBzN9\ zM8wO6tN5rM4mM3kN2fN2dN2bP1_O1XO0VO0RP0PP0LP0KR0IR\ 0FR0DH0KR0C_16i22r44z66z66z55y65tB4rJ8mPDkYKfeRgm_\ iyigzmfzkdziazg_zfYzcWzaUy_SyWPwUOwSMwQKtOItMGrKEr\ GCpEApC9mB7m95k7209704D00I00O00T00_11d22k43r64d52T\ 40I307400100402606709B0DD0GE0KG0OK0RM0VO0_Q1dU2iW2\ mZ3rb4wd4zg5zi6zk6zm6zo6zq6zk6zi5pa4dY2VT0MO0DK04E\ 00B0090070070070270B70I60 } 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 03-06-13 (Patches and Spots [6])
by Jim Muth 04 Jun '13

04 Jun '13

FOTD -- June 03, 2013 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a venture into the fractal that results when the formula Z^(2.25)+C is iterated at a depth of one level down the hyperladder. The parent fractal appears as a large bay split along the X-axis, with prominent period-2 buds on the northwest and southeast sides. The image is located near the west edge of the main bay in some debris just north of the X-axis. The name "Patches and Spots" refers to the curious circular elements filling the frame. The rating of a 6 indicates only slight satisfaction. But the fireball fast calculation time of a mere 30 seconds will pass well before boredom has a chance to set in. The official FOTD web site is up and running at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations will soon be posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Scads of back images are online at: <http://www.Nahee.com/FOTD/> A pleasant partly cloudy day was fully appreciated by all those here at Fractal Central today. The temperature of 79F 26C was right in the middle of the comfort range, and was made all the better by the lower humidity. The next FOTD will be posted before long. Until then, take care, and don't be discouraged by the human condition. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Patches_and_Spots { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-0.7364825061/+0.0949250143/2823/1/\ -147.5/0 params=2.25/0/-1/0 float=y maxiter=1500 inside=0 logmap=31 periodicity=6 colors=000EY`EVaESaGUbIWcKYcL_dNadPceQeeSgfUigVkgX\ mhZoh_qiasjfupjwzmzzSbdFFY20R3BO3DL3GI6ELACPFFUKIU\ PLUUMUPNUKNPFOKAQK8SL9SP9UTAWXAX`BYdBZhCZlC_pD`tD`\ wKqsOoiRn_UmQXlGUcFSWEQNDOFDOJFOMHOQJOTLOWNO_PObRO\ fTOiVOlXOpZOs`OvbSr_VoXZlVaiSeePhbNl_KoXHrUFnXGjZG\ gaGccG_fGXhGTkGQmGMpGIrGFuGBwG8yGDvHHsHLqHPnITkIXi\ I`fJdcJhaJlZKpWKtUKsSLsRMsQNsOOsNOsMPsKQsJRsISsGSs\ FTsEUsCVsBWsAWrBUqCTqDSpERoFPoGOnHNnIMmJKlKJlLIkMH\ jNFjOEiPDiQCkUDlYEmaFoeGpiGqmHsqItuJuxJvizwVzxGzy2\ zw6zv9zuDzsGzrKzqNzpRznUzmYzl`zkdzigzhkzgnzfqzcjz`\ czYXzVQzSJzQCzREzRGzRIzSJzSLzSNzSPzTQzTSzTUzTVzTUz\ TTzTTzTSzTSzTRzTQzTQzTPzTPzXWz_azbgzemz`jzWhzSezNc\ zJazNZzQWzTTzWQz_NzbKzeHzhFzfDzeBzc9zb7z`5z_3zY1zX\ 0zY2zY4zY6zY8zYAzZCzZEzZGzZIzZKzZLzZJzZHzZGzZEzZCz\ ZBzZ9zZ7zZ6z`7za7zb7zd7ze7zf7zg7zi7zj7zk7zm7zn7zo7\ zp7znBzlFzjJzhNzfQzEdzEaz } 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 27-05-13 (Crab and Amoeba [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 27, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= Crab_and_Amoeba { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt01 center-mag=-76.8401/54.8944\ /0.006431008/1/22.501/0 params=-5.8/1.05/-3.4/-0.5\ /1.6/-0.3 float=y maxiter=90 inside=bof60 outside=tdis periodicity=0 colors=000000Zya_x_`wZ`uXatWbsUcrTdqRepQfnOdlLfiNg\ gPheRicSj`UkZWlWYmUZnR`oPbpMdqKerHgsFitCkx9nuAlrBj\ oBhlCfjCdgDbdD`aEZ_EXXFVUFURGSPGQMHOJHMGIKEIIBJG8J\ E5KC3KB4JD4IE4HG4GH4FI4EK4DL4CM5CO5BP5AQ59S58T57U5\ 6W55X34_55Y75X96WB6UD6TF7SH7RJ8PL8ON8NP9MR9KTAJVAI\ XAHd6Dk3Azq8z07w38s59r8AqAApDBoFCnICmKDlNEkPFjSFiU\ GhWHhZHg`IfcJeeKehKdjLcmMcoMbrNatOavO`uP_uPZtQYtQY\ sRXsRWrSVrSVqTUqTTpUSpURoVRoVQnWPnWOmXOmXPeSQYNRRJ\ SJEW77TCAQHCNLFKQHHVKEZMBcP8hR5lT7kU8kU9kVAkVBkWCk\ WDkWEkXFkXGkYIkYJkZKkZLkZMk_Nk_Ok`Pk`QkaRkaRjbSkaT\ kaUk`Vl`Wl_Xl_YlZZmZ_mY`mYanXbnXcnWdnWeoVfoVgoUinR\ goUfpXeq_drbcrdbsgatj`um_vp`ytZvrYtpXrnVplUmjTkhSi\ gQgePecObaM`_LZYKXWIXUJVVJTWKRWKPXKOXLMYLKZMIZMG_N\ BYMF_LJaLMbKQdJTeJXgI_hIcjHfkGjmGmnFqpFtqHrnJqlKoj\ MnhNlfPkcQiaSh_TfYVeWWcUYbR_`P`_NbYLcXJeVGfUEPAqQC\ pREnSFmTHkUJjULhVNgWOeXyd } frm:MandNewt01 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-(p1*c) b=3*z^2+(p2*c-1) z=z-p3*a/b 0.00005 <= |a| } END PARAMETER FILE=========================================

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FOTD 28-05-13 (The Ultimate Reality [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 28, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= TheUltimateReality { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=+0.01233031649858841/0/436.7201/1/-90/0 params=0.98/0.76/-0.23/0.45/1.00087/0/0/0 float=y maxiter=95 inside=bof61 logmap=yes periodicity=6 colors=00006600501802B03D03G04J05M06P07S08W09_09c0\ Af0Bj0Cl0Hf0c_zQU5mOzZHFzCzZIPzzUSzczzoLzqzjsFztzu\ vzzrCxnGwiKueOtaSrYWpT_oPcmQdjRegSfdTgbTh_UiXVjU21\ 5325435545655765875985A92BA5CB8DCCEEFEGJGHMGJQGLTH\ MUINWJOYKP_LQaMRcNSeOTgPUiQVkRWmSXoTYqUZsV_uW`wXaz\ YbzZcz_dz`ezagzbizckzcmzcmzcmzcmzcmzcmzcmzcmzcmwcm\ wcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwAjZHhVO\ gSVeOk0IhAJfLKcVLFmpLkhRh`XfTRDSxmkrjdlhYffRbmqah`\ P9DWPHduQMExSNjXWYGgyxOKlXLJ0cQEXWSRYi3Zh8_fC`eHY4\ 7_HC`THORLTWLY`Lc_LbaLacLpgnDT6JWAQZEWaIPOvUUiY_X2\ KsBPjKVaT_T18DKPHORfSMkWTbZZUPQ9SUCWYFZaIjVrnWiiZ`\ eaTxLjpSahZTUTvp_MkaLfcLL2kPCdUMYYWRlATfQPHEHSSJkM\ dhR_fWVc`QFzDLtFRoHXiJYFaZMY_ST`ZPRequxRnqPgjNbyqa\ n`3YCagNafMaeL4QVGVRR_OkwAcS9m5wgNchd7VEiXLcZSX`ZR\ W_UY`SZbP`cNkPRQFUWSPbJYbPVaURa_ODinRlqVifZfWFPvNV\ iV_XFhSLgQRfOXeM_OCWIASC8 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-05-13 (The Ultimate Reality [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 28, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= TheUltimateReality { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=+0.01233031649858841/0/436.7201/1/-90/0 params=0.98/0.76/-0.23/0.45/1.00087/0/0/0 float=y maxiter=95 inside=bof61 logmap=yes periodicity=6 colors=00006600501802B03D03G04J05M06P07S08W09_09c0\ Af0Bj0Cl0Hf0c_zQU5mOzZHFzCzZIPzzUSzczzoLzqzjsFztzu\ vzzrCxnGwiKueOtaSrYWpT_oPcmQdjRegSfdTgbTh_UiXVjU21\ 5325435545655765875985A92BA5CB8DCCEEFEGJGHMGJQGLTH\ MUINWJOYKP_LQaMRcNSeOTgPUiQVkRWmSXoTYqUZsV_uW`wXaz\ YbzZcz_dz`ezagzbizckzcmzcmzcmzcmzcmzcmzcmzcmzcmwcm\ wcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwAjZHhVO\ gSVeOk0IhAJfLKcVLFmpLkhRh`XfTRDSxmkrjdlhYffRbmqah`\ P9DWPHduQMExSNjXWYGgyxOKlXLJ0cQEXWSRYi3Zh8_fC`eHY4\ 7_HC`THORLTWLY`Lc_LbaLacLpgnDT6JWAQZEWaIPOvUUiY_X2\ KsBPjKVaT_T18DKPHORfSMkWTbZZUPQ9SUCWYFZaIjVrnWiiZ`\ eaTxLjpSahZTUTvp_MkaLfcLL2kPCdUMYYWRlATfQPHEHSSJkM\ dhR_fWVc`QFzDLtFRoHXiJYFaZMY_ST`ZPRequxRnqPgjNbyqa\ n`3YCagNafMaeL4QVGVRR_OkwAcS9m5wgNchd7VEiXLcZSX`ZR\ W_UY`SZbP`cNkPRQFUWSPbJYbPVaURa_ODinRlqVifZfWFPvNV\ iV_XFhSLgQRfOXeM_OCWIASC8 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-05-13 (The Ultimate Reality [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 28, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= TheUltimateReality { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=+0.01233031649858841/0/436.7201/1/-90/0 params=0.98/0.76/-0.23/0.45/1.00087/0/0/0 float=y maxiter=95 inside=bof61 logmap=yes periodicity=6 colors=00006600501802B03D03G04J05M06P07S08W09_09c0\ Af0Bj0Cl0Hf0c_zQU5mOzZHFzCzZIPzzUSzczzoLzqzjsFztzu\ vzzrCxnGwiKueOtaSrYWpT_oPcmQdjRegSfdTgbTh_UiXVjU21\ 5325435545655765875985A92BA5CB8DCCEEFEGJGHMGJQGLTH\ MUINWJOYKP_LQaMRcNSeOTgPUiQVkRWmSXoTYqUZsV_uW`wXaz\ YbzZcz_dz`ezagzbizckzcmzcmzcmzcmzcmzcmzcmzcmzcmwcm\ wcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwAjZHhVO\ gSVeOk0IhAJfLKcVLFmpLkhRh`XfTRDSxmkrjdlhYffRbmqah`\ P9DWPHduQMExSNjXWYGgyxOKlXLJ0cQEXWSRYi3Zh8_fC`eHY4\ 7_HC`THORLTWLY`Lc_LbaLacLpgnDT6JWAQZEWaIPOvUUiY_X2\ KsBPjKVaT_T18DKPHORfSMkWTbZZUPQ9SUCWYFZaIjVrnWiiZ`\ eaTxLjpSahZTUTvp_MkaLfcLL2kPCdUMYYWRlATfQPHEHSSJkM\ dhR_fWVc`QFzDLtFRoHXiJYFaZMY_ST`ZPRequxRnqPgjNbyqa\ n`3YCagNafMaeL4QVGVRR_OkwAcS9m5wgNchd7VEiXLcZSX`ZR\ W_UY`SZbP`cNkPRQFUWSPbJYbPVaURa_ODinRlqVifZfWFPvNV\ iV_XFhSLgQRfOXeM_OCWIASC8 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-05-13 (The Ultimate Reality [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 28, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= TheUltimateReality { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=+0.01233031649858841/0/436.7201/1/-90/0 params=0.98/0.76/-0.23/0.45/1.00087/0/0/0 float=y maxiter=95 inside=bof61 logmap=yes periodicity=6 colors=00006600501802B03D03G04J05M06P07S08W09_09c0\ Af0Bj0Cl0Hf0c_zQU5mOzZHFzCzZIPzzUSzczzoLzqzjsFztzu\ vzzrCxnGwiKueOtaSrYWpT_oPcmQdjRegSfdTgbTh_UiXVjU21\ 5325435545655765875985A92BA5CB8DCCEEFEGJGHMGJQGLTH\ MUINWJOYKP_LQaMRcNSeOTgPUiQVkRWmSXoTYqUZsV_uW`wXaz\ YbzZcz_dz`ezagzbizckzcmzcmzcmzcmzcmzcmzcmzcmzcmwcm\ wcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwAjZHhVO\ gSVeOk0IhAJfLKcVLFmpLkhRh`XfTRDSxmkrjdlhYffRbmqah`\ P9DWPHduQMExSNjXWYGgyxOKlXLJ0cQEXWSRYi3Zh8_fC`eHY4\ 7_HC`THORLTWLY`Lc_LbaLacLpgnDT6JWAQZEWaIPOvUUiY_X2\ KsBPjKVaT_T18DKPHORfSMkWTbZZUPQ9SUCWYFZaIjVrnWiiZ`\ eaTxLjpSahZTUTvp_MkaLfcLL2kPCdUMYYWRlATfQPHEHSSJkM\ dhR_fWVc`QFzDLtFRoHXiJYFaZMY_ST`ZPRequxRnqPgjNbyqa\ n`3YCagNafMaeL4QVGVRR_OkwAcS9m5wgNchd7VEiXLcZSX`ZR\ W_UY`SZbP`cNkPRQFUWSPbJYbPVaURa_ODinRlqVifZfWFPvNV\ iV_XFhSLgQRfOXeM_OCWIASC8 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-05-13 (The Ultimate Reality [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 28, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= TheUltimateReality { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=+0.01233031649858841/0/436.7201/1/-90/0 params=0.98/0.76/-0.23/0.45/1.00087/0/0/0 float=y maxiter=95 inside=bof61 logmap=yes periodicity=6 colors=00006600501802B03D03G04J05M06P07S08W09_09c0\ Af0Bj0Cl0Hf0c_zQU5mOzZHFzCzZIPzzUSzczzoLzqzjsFztzu\ vzzrCxnGwiKueOtaSrYWpT_oPcmQdjRegSfdTgbTh_UiXVjU21\ 5325435545655765875985A92BA5CB8DCCEEFEGJGHMGJQGLTH\ MUINWJOYKP_LQaMRcNSeOTgPUiQVkRWmSXoTYqUZsV_uW`wXaz\ YbzZcz_dz`ezagzbizckzcmzcmzcmzcmzcmzcmzcmzcmzcmwcm\ wcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwcmwAjZHhVO\ gSVeOk0IhAJfLKcVLFmpLkhRh`XfTRDSxmkrjdlhYffRbmqah`\ P9DWPHduQMExSNjXWYGgyxOKlXLJ0cQEXWSRYi3Zh8_fC`eHY4\ 7_HC`THORLTWLY`Lc_LbaLacLpgnDT6JWAQZEWaIPOvUUiY_X2\ KsBPjKVaT_T18DKPHORfSMkWTbZZUPQ9SUCWYFZaIjVrnWiiZ`\ eaTxLjpSahZTUTvp_MkaLfcLL2kPCdUMYYWRlATfQPHEHSSJkM\ dhR_fWVc`QFzDLtFRoHXiJYFaZMY_ST`ZPRequxRnqPgjNbyqa\ n`3YCagNafMaeL4QVGVRR_OkwAcS9m5wgNchd7VEiXLcZSX`ZR\ W_UY`SZbP`cNkPRQFUWSPbJYbPVaURa_ODinRlqVifZfWFPvNV\ iV_XFhSLgQRfOXeM_OCWIASC8 } 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=========================================

1 0

FOTD 27-05-13 (Crab and Amoeba [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 27, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= Crab_and_Amoeba { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt01 center-mag=-76.8401/54.8944\ /0.006431008/1/22.501/0 params=-5.8/1.05/-3.4/-0.5\ /1.6/-0.3 float=y maxiter=90 inside=bof60 outside=tdis periodicity=0 colors=000000Zya_x_`wZ`uXatWbsUcrTdqRepQfnOdlLfiNg\ gPheRicSj`UkZWlWYmUZnR`oPbpMdqKerHgsFitCkx9nuAlrBj\ oBhlCfjCdgDbdD`aEZ_EXXFVUFURGSPGQMHOJHMGIKEIIBJG8J\ E5KC3KB4JD4IE4HG4GH4FI4EK4DL4CM5CO5BP5AQ59S58T57U5\ 6W55X34_55Y75X96WB6UD6TF7SH7RJ8PL8ON8NP9MR9KTAJVAI\ XAHd6Dk3Azq8z07w38s59r8AqAApDBoFCnICmKDlNEkPFjSFiU\ GhWHhZHg`IfcJeeKehKdjLcmMcoMbrNatOavO`uP_uPZtQYtQY\ sRXsRWrSVrSVqTUqTTpUSpURoVRoVQnWPnWOmXOmXPeSQYNRRJ\ SJEW77TCAQHCNLFKQHHVKEZMBcP8hR5lT7kU8kU9kVAkVBkWCk\ WDkWEkXFkXGkYIkYJkZKkZLkZMk_Nk_Ok`Pk`QkaRkaRjbSkaT\ kaUk`Vl`Wl_Xl_YlZZmZ_mY`mYanXbnXcnWdnWeoVfoVgoUinR\ goUfpXeq_drbcrdbsgatj`um_vp`ytZvrYtpXrnVplUmjTkhSi\ gQgePecObaM`_LZYKXWIXUJVVJTWKRWKPXKOXLMYLKZMIZMG_N\ BYMF_LJaLMbKQdJTeJXgI_hIcjHfkGjmGmnFqpFtqHrnJqlKoj\ MnhNlfPkcQiaSh_TfYVeWWcUYbR_`P`_NbYLcXJeVGfUEPAqQC\ pREnSFmTHkUJjULhVNgWOeXyd } frm:MandNewt01 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-(p1*c) b=3*z^2+(p2*c-1) z=z-p3*a/b 0.00005 <= |a| } END PARAMETER FILE=========================================

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FOTD 02-06-13 (Lesser and Greater [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- June 02, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= Lesser_And_Greater { ; time=0:03:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-8.91670602/+3.43021479/126.3/1/106.45/0 params=0.9/1/64/-1/0/10008/0/0 float=y maxiter=5000 inside=atan logmap=yes periodicity=10 colors=000zh9aGAbFAcEBcEBdDCeCCfBDgADh9Ei8Ei8Fj7Fk\ 6Gl5Gm4Gl3Dm3Em3Gn4Hn4Io4Ko4Lzczp5Oq5Pq5Rr5Szzzs6V\ s6Ws6Xu5XtmYs6Yr7Zq7Zp8_o9`n9`mAakAajBbiBbhCcgDdfD\ deEedEecFfTDobFflHZwXYvJRy0Gw2Iv4Lt6Nr9PpBRoDUmFWk\ HYjJ`hLbfOddQfcSiaUkzWzzzpZYpYYpzzzWZoW_oV_oU`oTan\ SanRbnQbnPcnPdnOdmNemMemLzzKfmJglIhlHhlzzzGilqUkpU\ koUknUgmUkkUniUrhUugUteTsdTrbSqaSp_RoZRnXQmWQlUPkT\ PjROiQOhOOgNNfLNeKMdIMcHLbFLaEK`CK_BJZ9JY5IYAJWFKU\ KLSOMQSNOMOMUOKTPIRPGPOEPOCPOAPO9PNAPNATNBRNCRMCSM\ DQMDOMENLFMLFLLGIKHFKHJKIGKIRJJSJKTJKAJLAILAIM00KB\ JOCKPDKQELRFLTGMUGMVHNWINXJOYKP_LP`MQaNQbORcPRdPSe\ QSgRThSTiTUjTUhUVfUVeVWcVWaVX_WXYWYWXYVXYTXZRYZPY_\ NY_LZ`KZ`I_aG_aE``G`_HaYJbXKcWMcVOdUPeTReRSfQUgPVg\ OXhNZiM_jKajJbkIdkHejMajQYiVUiZQhbMhfIgkEgoAfs6eq9\ epCdnFcmIbkLbiOahR`fU`eWafXafXafYbfYbfYbfYbfZbfZcg\ ZcgZcg_cg_cg_cg_dg`dg`dg` } 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 01-06-13 (Mandelbrot Marina [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- June 01, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= Mandelbrot_Marina { ; time=0:45:00.00 SF5 at 2000MHZ reset=2004 type=mandel passes=1 center-mag=0.3219145087671323692/-0.03521313068405\ 13389/2.82383e+014/1/30/0 params=0/0 float=y maxiter=7500 inside=0 logmap=2180 periodicity=6 colors=000B0UB0XB0_B0cD0cE5cF5eF5kJ5mJ7mKAmKHmOIiR\ IeVIbYNZ`OVdOSgOOjOLs_r3REUXHsbJhcOZcSOdWEd_FZbGTe\ GOhHIjHDmI7pI2rJ6oJ9lJCiJFfJIcJL`JOYJRWOTVSVVXWV`Y\ Ue_Ui`UXgVKnW8uWNfd`SmnEuaJdQNOER8HXDKaHMgMPlQSrVU\ wZhXrfK_d7H`JBXV5Tf0lUQXZcHcpNerSgtXhvajxfkyZ`sSQm\ LGgNOiPVkRblTinVqpWxqXfgYQZZ9QbAMfBIjBE`QPSd_JriKe\ ZLUOMIDmMexL_xOYxRWxTVxWTxZRx`QxcOxfMxhLxkJxnHxpGy\ qJyrLyrNysQytSytUyuXyvZyv`ywcyxeyxgvvetudrsbpranp_\ loZjmXhlWekUciTahR_fQYeOWcNUbLSaKT`JU`IU_IV_HW_HId\ wFSwRQqaOkwaPx`NxZLxYJxXHlcTaicQonFuyDTeB1NCKLDUJE\ cIEmGFrFGvDGzCGrEGmGGhHGcJGWKEQQCQWAP`8ef6hk4kq2nv\ 2tq2yl5un7ro9oqBlrEhsGeuIbvK_wOatSbqWcpZcobcmfbkia\ ik`gl_emZcnYaoX_pWYqVWrUUsTStSQuROvIGw98z3JF19USzK\ LzA7zI3hC2A615`cAwP5cG3K81lVuOFT7O05I03C01605Qi3JY\ 2DN16B8wQ5cH2K8mvE`gAPT7CE3D2m81X40GI_DCO86C4H5H82\ 8vtYTSHPbtITeCJS69EAeawzH } END PARAMETER FILE=========================================

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FOTD 31-05-13 (A New Rectangle [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 31, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= A_New_Rectangle { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=trashed.frm formulaname=testrot-XY-ZW function=flip/ident center-mag=-0.071007/-0.0544167/1.310716/1/12.499/0 params=93.1/86.3/0/0/-0.2/0.05 float=y maxiter=255 inside=bof61 periodicity=6 colors=000PXeQWjRUoSTtVRpYPl`NhcLdfJ`iHXlFToDPqBLp\ EJoHInKGmNFmQDkTCjWAiW9hWCfWFdWKbWP_WUXWZVWcTWhRWm\ PVrNSuLTuJUvHVvEWuHXtJYsL_rNaqPcpQeoQgnQimQklQmmRq\ oRtzRwzUzzczzmzzvzzzzzzzzYQGTMOOIWKEcFAkB7sLBrUFqb\ JpkNpcLnXJmQHkJGjKFgLEeMDcNDaOCZPBXPBVQATR9RS8OT8M\ U7KV6IV6GW9IXBKYDMZFOZHQOPPOQPPRQPRRPSSQTTQUUQUVRV\ WRWWRWXRXYSYZSY_SZ`T_aT_aT`bUacUadUbeUcfVcgVKhVKhW\ KiWKjWKkXKlXKmXKnXKnI_l2Pl3Qk3Qk3Qj4Qj4Qi4Qi4Rh5Rh\ 5Rg5Rg6Rf6Rf6Re6Se7Sd7Sd7Sc8Sc8Sb8Tb8Ta9Ta9T`9T`AT\ _AT_AUZAUZBUYBUYBUXCUXCVWCVWCVVDVVDVUDVUEVTEWTEWSE\ WSFWRFWRFWQFWQGXQGXPGXPHXOHXOHXNHYNIYMIYMIYLJYLJYK\ JYKJZJKZJK0IK0IL0HL0HL0GL0GM0FM0FM0EN0EN0DN0DN0CO0\ CO0BO0BP0AP0AP09P09Q08Q08Q07R07R06R06R05S05S04S040\ 02Y03S04M04G05A065066076076076F76G86G86H86H86I96I9\ 7J97J97KA7KA7LA7LA7MB7MB7NB7NB8NB8OCKHDLHELIFLJGLJ\ HMKIMLJMLJNMKNNLNNMOONOPO } frm:testrot-XY-ZW {; draws 6 planes and many rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p3: z=4*((-z)^0.9+z^0.9)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 30-05-13 (Troubled Times [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 30, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= Troubled_Times { ; time=0:03:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=EllipticVB passes=t center-mag=-0.1826\ 798464813407/+0.6229800782469389/64.0711/13.109 params=0/0.667/1/0 float=y maxiter=32767 inside=253 periodicity=6 ranges=0/-1/250/-1/550/600/800/1100/\ 1500/2000/2600/3500/32767 sound=off colors=000_KJF00MDNLOc0Pz0Zz0cz0fz0kz0oz0szZzz0000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000zzz000000 } frm:EllipticVB {; Jim Muth z=flip(imag(pixel))+real(p1), c=real(pixel)+flip(imag(p1)), a=sqr(p2): z=sqr(z)+c, |z| <= a } END PARAMETER FILE=========================================

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FOTD 29-05-13 (Etheric Spiral [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 29, 2013 (No Rating) Fractal visionaries and enthusiasts: START PARAMETER FILE======================================= Etheric_Spiral { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt04 passes=1 center-mag=17.0932\ /2.36671/0.004749907 params=-3.3333/-2.3498/0.1908\ /-0.5703/1.6286/1.2902 float=y maxiter=400 inside=bof60 logmap=yes periodicity=10 colors=000cGF`FDZECWEATC9QB7OA5L84I62A42G52M69R7FU\ 8MX9TZ9`_A`ZB_YB_XB_WC_VCZUDZTDZSDZTEYUEYUEYUFYUFX\ UGXTGXSGXRHWQHWPHWOHWNIVMIULISKIRJJQIJPHJNGKMFKLEL\ KDLKCLJBMJAMK9NK8NL7NM6OM5ON4OO2NO3OQ4OR5OR6PR7PR8\ PS9QSAQSBRSCRSDRSDSSESTFSTGTTHTTITTJUTKUTLVUMVUNVU\ OWUPWUQWURXUSXUTXVUYVUYVVYVWZVXZVY_VZ_W__W``Wa`Wa`\ WbaXbaXbaXbaXcaXcaXcaXdaXdaXdaXeaXeaXeaXfaXfaXfaXg\ aXgaXgaXhaXhaXhaXiaXiaXibXibXjbXjbXjbXkbXkbXkbXlbX\ lbXlbXmbXmbXmbXnbXnbXnbXobXobXobXpbXpbXpbXqbWqcVqc\ UrcTrcSrcRsdQsePsfPtgPthPuiPujPukPvlPvmPwnOwoOxpOx\ rOxtOyvOyxOzzOzzOzzOzzOzyOywOyuOxsOwqPvpQuoRunStmT\ tlUskVrjWriXqhYqgZpfZpeZpdZocZobZna_n`_m__mZ_lY_lX\ _kW`kV`jU`jT`iS`iS`hS`hS`gR`gR`fQafQaeQaePadPadOac\ OacOabNbbNbaMbaMb`Mb`Lb_Lb_Kb_KcZKcZJcYJcYIcXIcXIc\ WHcWHdVGdVFdUFdSFcRFdREdREdREdRDeRDeQDeQDePDfPCfOC\ fOCgOCgNChNChMChMChNCgOCf } frm:MandNewt04 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^2+c-1 z=z-p2*a/b p3 <= |a| } END PARAMETER FILE=========================================

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FOTD 26-05-13 (A Solid Platform [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 26, 2013 (No Rating ) START PARAMETER FILE======================================= A_Solid_Platform { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=multirot-XY-ZW-new function=flip/ident center-mag=1.39793/0/0.4733975/1/90/0 params=90/12/2/0/0/0/-2/0 float=y maxiter=400 inside=255 logmap=yes periodicity=6 colors=000D07G0AK0DP1GU2JZ3Mc4Ph5Tm6Xr7`u7dy7hzDmz\ BrzAvzAzwBztCzqDznEzkFzhGzeHzdIzdJzdKzeLzeJzeHzeGz\ fEzfUzfUzfUzhUzgUzfUzfUzeUzdUzdUzcUzbUzbUzaUzaUz`U\ z_cz_czZczYczYczXczWczWczVczVczUczTczTczSczRczRczQ\ czPczPczOczOczNczMczMczLczKczKczJczJczKczKczKczLcz\ LczLczLczMczMczMczNczNczNczNczOczOczOczPczPczPcmPc\ mQcmQcmQcmRcmRcmRcmRcmScmScmScmRcmScmScmScmS`aS``S\ ``S`_S`ZS`ZS`YSaXSaXSaWSaVSaVTaUTaTTaTTaSTaRTbRTbQ\ TbPTbPTbOTbNTbNTbMTbLTbLUcKUcKUcJUcIUcIUcHUcGUcGUc\ FUcEUdEUdDUdCUdCUdBVdAVdAVd9Vd8Vd8Ve7Ve6Ve6Ve5Ve4V\ e4Ve3Ve2Ve2Ve1Ve1Yd3`c4bb5ea7g`8j_9rW6oY8l_Ai`CfbE\ ccG`eIYfKVhMTiNQkPNlRKnTHoVEqXBrZ8t`6uaPnhggny`twb\ rucpsdnqelofjmghkhfjjehkcfladm_bnY`oWZpUYrTWsRUtPS\ uNQvLOwJMxHIzHKyGLyGMyFOyFPxEQxESxDTxDUxCWwCXwCYwB\ _wB`wAavAbv9dv9ev8fv8hu8iu7ju7lu6_lT`lU`kUakU`oSam\ TakUajUahVbfWbeWbcXbaYPPz } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 25-05-13 (Red Riot [No Rating])
by Jim Muth 03 Jun '13

03 Jun '13

FOTD -- May 25, 2013 (No Rating) To get caught up, I am posting the FORD's since May 25 without comment. The regular FOTD's will resume on June 03. I have given no ratings to the images, since they are mostly tweakings of earlier images. START PARAMETER FILE======================================= Red_Riot { ; time=0:20:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=-0.3070163132509978/+0.219156404541476/\ 6.96e+9/1/-7.5/0 params=0.5/2/0.1/3/0/0/0/0 float=y maxiter=5700 inside=0 logmap=784 periodicity=6 colors=000UQZUR_US`UTaUUbUVcUWdUXeUYfUZgU_hU`iU_gU\ ZfUYdVXcVWaVV`UUbUTcVSdWRfXQgYPhZOk_Nn`MqaLtbKrcJp\ eIogJmfKkfLjeNheOgdPecRccSbbT`aVZaWY`XW`YVZdNXkGVr\ 9Tx2Sw4Sv5Ru7Rt8Rs9QrBQqCQpDPoFPnGOmIOlJOkKNjMNiNN\ iOLgNJeNIcNGaNF_MDYMCWMAUM9SL7QL6OL4ML3KL7MKBNJFPJ\ IQIMSIQTHUVGXWG`YFdZFh`EkaDocDsdCveCqjIlnN6aL8YJAU\ HCQFENEGJCIFAKB8M87OAAQBCSDEUEGWFIXHLZIN`JPbLRdMTe\ NVbPS_QPXSMUTKSVHPWEMYCJZ9G`6Ea4RQnQRmQSlPSkPTjPTi\ OUhOVgNVgNWfNWeMXdWZcaacjdhrgmwjrwipugnsdlrajqZhpX\ foUdmRblO`kMZjJXiGVgDTfBRe8Pd5Nc2Lb0Ja5Ma9PaDRaHUa\ LW`PZ`T``Yc`ae`eh_ij_mm_qo_gr0dt5Ki8IgBHfEGdHFcKEb\ ND`PC_SAZV9XY8W`7Vc6Tf5Sh4Rg5Tf5Ve6We6Yd6_c7`c7bb7\ da8e`8g`8i_9jZ9lZ9mICc2EVEG`QHeaIkmJpxKuc`7cZ8cX8c\ W9mU9mSAmRBmPBmNCzMCzU9zU8zU8zc7zc7zc6zm5zm5zm4zz4\ zz3zz2zz2zz1zz1zz0zz4zz3zz3zz3zz3zz3zzzzzzzzzzzzzz\ 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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No demise of the FOTD!
by Jim Muth 29 May '13

29 May '13

Fractal fanatics: Rumors might be spreading that after sixteen years I have abandoned the FOTD. The fact is that we are undergoing major renovations here at Fractal Central, and the FOTD will return when we are again up and running. The best time estimate is about one week, but as is always the case, there are no guarantees implied. Until whenever, take care, and don't be bored. JIM

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Jim Muth had 3 very slow FOTD images in April...
by Hal Lane 28 May '13

28 May '13

Jim Muth had three very slow FOTD images in April, 2013 that I did not have time to calculate the anti-aliased version of back then. I've now calculated them and put them onto my April, 2013 FOTD web page. The fractals are: - Floating Continents [7] - F130412J.jpg - Bottom of the Pile [5] - F130416J.jpg, and - Superluminal [7] - F130418J.jpg If you'd like to look at them, and/or compare them with their unanti-aliased versions, I'd appreciate it if you navigated to the April, 2013 page through my home page to see the above images -- to keep my site counters operating correctly: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html Simple instructions for how to compare two similar images (like the unanti-aliased (.GIFs) and anti-aliased versions of a FOTD) are below the grid of image links on each of the last year's (or so) monthly pages. Some comparison results can really pop out at you. My "Home" page (at the link above) has a short discussion about anti-aliased fractals -- and anti-aliased images in general -- at the bottom. Thanks, - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 21-05-13 (The Littlest Angle [M-6,A-6])
by Jim Muth 22 May '13

22 May '13

FOTD -- May 21, 2013 (Rating M-6,A-6) Fractal visionaries and enthusiasts: Today's image is named "The Littlest Angle", not "The Littlest Angel", which is a Christmas story. I gave it this name because when I first saw the fractal object, it resembled a tiny angel, but when I zoomed in, it turned into the curious angular pattern in the image. The scene was created by the HyperMandelbrot2 formula, though it could just as easily have been created by the hard-coded 'manzpwr' formula. The location is on the X-axis, on the western edge of Seahorse Valley of the parent HyperMandelbrot set, which has begun to collapse into the X-axis. Typical 4-D overlapping and blending fills the scene, the features with the lower iteration count always prevailing. The whole image rates a 6 for both mathematical and artistic worth. Actually, the artistic value could have been raised a point or so if I had replaced the sickly green outer regions with a healthier hue. Perhaps the best feature on the image is its very brief calculation time of 45 seconds. The web sites can cut this time even more. Enrich your life by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and the high-resolution variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Scads of the older FOTD images are online at: <http://www.Nahee.com/FOTD/> Lots of sun prevailed all morning here at Fractal Central, leading to a sunny afternoon with a temperature of 90F 32C, which was quite warm enough to please the fractal cat, who kept busy watching for stray cats. In the human department, the most exciting event came in the morning when two aspiring tomcats got into a fight in the back yard. The next FOTD will be posted when the time is right, which means at any time more than 20 hours from now. Until whenever, take care, and there has been another disaster. I wonder why, in times of such disasters, people pray for help to the same power that sent the disaster or could easily have prevented it, but decided instead to sit on its divine butt and blithely watch its so-called beloved children suffer. I guess we feel it's necessary to keep the faith even when it makes no rational sense. But we surely do admit our ignorance and confusion when we lamely state that God works in mysterious ways. As I see it, something must be very wrong with our popular image of God. When I get to the divine throne to be judged, I'll bring a good defense lawyer and have lots of questions to ask the judge! BTW, Despite all this, I am a confirmed believer. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Littlest_Angle { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-0.751204809666/0/1050025/1/90/0 params=0/0/0/0/0/0/0.03/0 float=y maxiter=1750 inside=255 logmap=218 periodicity=0 colors=0001902A03C04E06G08I0AK0CM0EO0GQ0IS0KU0IW0H\ Y0G_0Ea0Dc0Ce0Ag09h28h5Ag9BfCDeFEdIGcLHaOJ`RK_UMZX\ NY_PWbQVeSUhTTkVSnWRqTUmRUiOUeMUbJUZHUVEUSCUO9UK7U\ H4UD2U90U66UBCUGIUKOUPUUT_UY`UbaUfbUkcUocUmcUkcUic\ UhcUfcUqcUmcUicUecUacUXcUTcUPcULcUHcUDcUFcUHcUIcUK\ eVMgWNiXRkYUmZYo_`q`cs`fs`isakobhkeehibdj_aja_jcYj\ hWjmVlrTnvXpzYrzZtw_vr`xoaymWvhQseKpaEmZ8jV2gS5dT7\ aUAZVCWVFTWHQXKNXMKYOHZREZTB_W8`Y5``3ab2bd1bi9enGg\ sNjxUlwWnvXouZpu_qtarsbssctobolbjhbeeaaaaXZaSV`OS`\ JO`EL`AMaDMaFMbHMbJMbLMcNMcPMdRMdTMdVOaRPZNQXJSUFT\ RBUP8PN6KM5GK4BJ37I2CM6HQ9LUDQYGVaKZeNUPRP8VM7SK6Q\ I5OG4ME4KB3H92F71D50B30945A59A5DA6HB7LB7PB8TB9YC9a\ CAeCBiDBmDCqDCuDdvFctLcrQcpVcn_cldcjichnmndvtVuiWt\ ZWsPWrEWq4Wo7UnASlDQkGOjJMhMKgPIfSGdVEcYCb`A`c8_f6\ Zh4_f5_d6_c6`a7`_8`Z8aX9aVAaUAbSBbQCbPCZTDWXES_FPc\ GLfHIjIFmIHjGIgFJeDKbCL`B } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 21-05-13 (The Littlest Angle [M-6,A-6])
by Jim Muth 22 May '13

22 May '13

FOTD -- May 21, 2013 (Rating M-6,A-6) Fractal visionaries and enthusiasts: Today's image is named "The Littlest Angle", not "The Littlest Angel", which is a Christmas story. I gave it this name because when I first saw the fractal object, it resembled a tiny angel, but when I zoomed in, it turned into the curious angular pattern in the image. The scene was created by the HyperMandelbrot2 formula, though it could just as easily have been created by the hard-coded 'manzpwr' formula. The location is on the X-axis, on the western edge of Seahorse Valley of the parent HyperMandelbrot set, which has begun to collapse into the X-axis. Typical 4-D overlapping and blending fills the scene, the features with the lower iteration count always prevailing. The whole image rates a 6 for both mathematical and artistic worth. Actually, the artistic value could have been raised a point or so if I had replaced the sickly green outer regions with a healthier hue. Perhaps the best feature on the image is its very brief calculation time of 45 seconds. The web sites can cut this time even more. Enrich your life by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and the high-resolution variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Scads of the older FOTD images are online at: <http://www.Nahee.com/FOTD/> Lots of sun prevailed all morning here at Fractal Central, leading to a sunny afternoon with a temperature of 90F 32C, which was quite warm enough to please the fractal cat, who kept busy watching for stray cats. In the human department, the most exciting event came in the morning when two aspiring tomcats got into a fight in the back yard. The next FOTD will be posted when the time is right, which means at any time more than 20 hours from now. Until whenever, take care, and there has been another disaster. I wonder why, in times of such disasters, people pray for help to the same power that sent the disaster or could easily have prevented it, but decided instead to sit on its divine butt and blithely watch its so-called beloved children suffer. I guess we feel it's necessary to keep the faith even when it makes no rational sense. But we surely do admit our ignorance and confusion when we lamely state that God works in mysterious ways. As I see it, something must be very wrong with our popular image of God. When I get to the divine throne to be judged, I'll bring a good defense lawyer and have lots of questions to ask the judge! BTW, Despite all this, I am a confirmed believer. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Littlest_Angle { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-0.751204809666/0/1050025/1/90/0 params=0/0/0/0/0/0/0.03/0 float=y maxiter=1750 inside=255 logmap=218 periodicity=0 colors=0001902A03C04E06G08I0AK0CM0EO0GQ0IS0KU0IW0H\ Y0G_0Ea0Dc0Ce0Ag09h28h5Ag9BfCDeFEdIGcLHaOJ`RK_UMZX\ NY_PWbQVeSUhTTkVSnWRqTUmRUiOUeMUbJUZHUVEUSCUO9UK7U\ H4UD2U90U66UBCUGIUKOUPUUT_UY`UbaUfbUkcUocUmcUkcUic\ UhcUfcUqcUmcUicUecUacUXcUTcUPcULcUHcUDcUFcUHcUIcUK\ eVMgWNiXRkYUmZYo_`q`cs`fs`isakobhkeehibdj_aja_jcYj\ hWjmVlrTnvXpzYrzZtw_vr`xoaymWvhQseKpaEmZ8jV2gS5dT7\ aUAZVCWVFTWHQXKNXMKYOHZREZTB_W8`Y5``3ab2bd1bi9enGg\ sNjxUlwWnvXouZpu_qtarsbssctobolbjhbeeaaaaXZaSV`OS`\ JO`EL`AMaDMaFMbHMbJMbLMcNMcPMdRMdTMdVOaRPZNQXJSUFT\ RBUP8PN6KM5GK4BJ37I2CM6HQ9LUDQYGVaKZeNUPRP8VM7SK6Q\ I5OG4ME4KB3H92F71D50B30945A59A5DA6HB7LB7PB8TB9YC9a\ CAeCBiDBmDCqDCuDdvFctLcrQcpVcn_cldcjichnmndvtVuiWt\ ZWsPWrEWq4Wo7UnASlDQkGOjJMhMKgPIfSGdVEcYCb`A`c8_f6\ Zh4_f5_d6_c6`a7`_8`Z8aX9aVAaUAbSBbQCbPCZTDWXES_FPc\ GLfHIjIFmIHjGIgFJeDKbCL`B } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 19-05-13 (Patterns in a Void [M-8,A-6])
by Jim Muth 19 May '13

19 May '13

FOTD -- May 19, 2013 (Rating M-8,A-6) Fractal visionaries and enthusiasts: Today's image highlights one of the mystery buds of the 4-D HyperMandelbrot set. But the mystery bud is not the reason I posted the image. The most striking part of the scene is the fine display of moire patterns filling the bud. And this pattern will change with every change, however small, of overall image size, resolution or magnitude. 0+0i is the critical starting point of the 2-D Mandelbrot set, so I assume 0+0i+0j+0k would be the critical starting point of the 4-D HyperMandelbrot set. At the same time, I have no idea what the perturbed Hyper-sets might look like. Today's scene might be critical, it might be perturbed. One thing for sure is that much more exploration needs to be done. The name "Patterns in a Void" refers to the Moire patterns filling the open area of the bud. The math interest rates a very respectable 8, the artistic value however is worth no more than a humdrum 6. I leave it to the individual fractalist to decide whether the image is worth the quarter hour required to calculate it. If the decision is negative, the web sites are there to bring relief. The finished image is posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are available at: <http://www.Nahee.com/FOTD/> Heavy clouds, (stratocumulus for the weather-wise), prevailed all day yesterday and today here at Fractal Central, though no rain fell. Because of the high humidity, the temperature of 66F 19C felt just about right. The fractal cat had an active day, often dashing up and down the hallway as though chasing or being chased by an invisible cat. The humans had a slow day, which is boring to read about but was relaxing to experience. The next FOTD will be posted soon. Until soon arrives, take care, and in June 1976 I spent two days in Seattle. On both days the weather was sunny and quite warm, proving that despite its reputation of being a cloudy and rainy city, Seattle is a sunny and warm city. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Patterns_in_a_Void { ; time=0:15:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-0.010735/0.113631/41 maxiter=12000 params=0/0/0/0/0/11/1e-111/1e-111 inside=0 logmap=-590 periodicity=0 colors=000r6Sr6Sr6Sr6Tr6Tr6Tq6Tr6Us6Us6Ut6Uu6Uv6Vv\ 6Vw6Vx6Vx6Vw7Uw7Uv8Uv8Tv8Tu9Tu9SuAStAStARtBRsBRsBQ\ sCQrCQrDPrDPqDPqEPqEOpFOpFOpFNoGNoGNoGMnHMnHMnILmI\ LmILmJKlJKlJKlKJkKJkLJkLJjLIjMIiMIiNHiNHhNHhOGhOGg\ OGgPFgPFfQFfQEfQEeREeRDeRDdSDdSDdTCcTCcTCcUBbUBbVB\ bVAaVAaWAaW9`W9`X9`X8_Y8_Y8_Y7ZZ7ZZ7ZZ7__8__9__9_`\ A_`A_`B_`B_aC`aC`aD`aD`bE`bE`bF`cF`cGacGacHadHadIa\ dJadJaeKaeKbeLbeLbfMbfMbfNbgNbgObgOcgPchPchQchQchR\ ciRciSciTdiTdjUdjUdjVdkVdkWdkWdkXelXelYelYelZemZem\ _em_en`fn`fnafnbfobfocfocfodfpdgpegpegpfgqfgqggqgg\ rhgrhhrihrihsjhsjhskhslhtlhtmitmitniuniuoiuoivpivp\ ivqjvqjwrjwrjwsjwsjxtjxtjxulzvkyukzujzvjzwjzxizyiz\ zizzhzzhzzhzzgzzgzzgzzfzzfzzfzzezzezzezzdzzdzzdzzc\ zzczzczzbzzbzzbzzazzazzazz`zz`zz`zz_zz_zz_zzZzzZzz\ ZzzYzzYzzYzzXzzXzzXzzWzzWzzWzzVzzVzzVzzUzzUzzTzzTz\ zTzzSzzSzzSzzRzzRzzRzzQzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 17-05-13 (The Parent Unleashed [M-4,A-6])
by Jim Muth 19 May '13

19 May '13

FOTD -- May 17, 2013 (Rating M-4,A-6) Fractal visionaries and enthusiasts: Today's image is not a scene in a parent fractal; it is the parent itself. This parent came to be when I checked to see what would happen when the formula Z^(1.237)+C is iterated 14 levels up the hyperladder. What happened was hardly overwhelming, but when rendered with the inside set to bof60 and the outside set to tdis, it was interesting enough to rate a 4 for math value and a 6 for artistic value. The name "The Parent Unleashed" is intentional hyperbole, but it might get a few reluctant fractalists to check the implied wild-animal ferocity in the image. The running time of the parameter file is 1-3/4 minutes, which is about average, but setting up and running a parameter file is far more complicated than checking the FOTD web sites, where the image is already rendered. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images may be accessed at: <http://www.Nahee.com/FOTD/> Today brought ample sun along with a fine display of cirrus clouds and a temperature of 68F 20C to Fractal Central. The fractal cat, now nearing senior cat status, slept through most of it, while the humans busied themselves with human things. There will be no FOTD for May 18; the next FOTD will be posted most likely on the 19th. Until whenever, take care, and a lot of people are being injured by . . . so let's pass a law to ban . . . (fill in the blanks) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= TheParentUnleashed { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.590338/-0.280652/0.6230116/1/-12.5/0 params=1.237/0/14/0 float=y maxiter=1150 inside=bof60 outside=tdis colors=000G0XRKgVUhYci_ihanhcigecggZfiWfkSemPeoNdq\ RdsUcuXcw_bzcbzg_zlYzl_zneznjzppzrvzvzzzzzzzzzzgDB\ gDBgDBgDBhCBhCBhCBhCBhCBgBAfBAeB9dB9cB9bA8aA8`A8_A\ 7ZA7Y96X96W96V95U95T85S84R84Q84P83O73N72M72L72K71J\ 61I61H60G60F60LE1RL2XS3bZ3he4nl5ts6yz6wxAuvDstGqrK\ opNmoQnnRonRpnRqnRrnRsnRtnRunRvnRwnRxnRynRynRxoSxo\ SxpSxpSwpSwqSwqSwqTvrTvrTvrTvsTvsTutTutUutUuuUtuUt\ uUtvUtvUtvUirSZnQOjODfMEeOFePFdRGdSGdUHcVHcXIcYIbZ\ Jb`JaaKacKadL`fL`gM`iM_jN_kNZmOZnOZpPYqPYsQYtQXvRX\ wRXxSZwS`wSbwTcwTewTgwThwUjwUlwUnwVowVqwVswVtwXpxY\ mx_ix`fxbcyc_yeXyfUygTxgTxgTxgTwhTwhSwhSvhSvhSviSu\ iSuiRuiRtiRtjRtjRsjQsjQskQrkQrkQrkQqkPqlPqlPplPplP\ plPpmNomLnnJmnHlnFkoDjoBioAimCgkEejGdhIbfKaeM_cNYa\ PX`RVZTUXVSWXRUYPS_NRaMPcKNeJMgHKiGIjEHlCFnBDp9Cr8\ At69u5Ds6Hq6Lo6Pm6Tk6Wj6_h7cf7gd7kb7o`7r_7tZ6eFBeF\ BeFBeFBeFBfEBfEBfEBfEBgDB } 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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so if you started Fractint with debug=3200 and...
by Hal Lane 19 May '13

19 May '13

---- David wrote: --------- Author: david Date: 2013-05-18 19:18 -400 To: Fractint and General Fractals Discussion Subject: Re: [Fractint] FractInt does arbitrary precision math only for... Hmmm, so if you started Fractint with debug=3200 and a formula par, it would calculate the formula using arbitrary precision? --------------------------- Unfortunately, no -- I believe that their is not code in Fractint to support what you suggest. Debug modes: 3200 fracsubr.c disable auto switch //back// from arbitrary precision debug=3200 appears to assume that you are in arbitrary precision mode *already*, which is not available for the "type = formula" -- only the listed fractal types that specifically the docs say support arbitrary precision: "...mandel, julia, manzpower, and julzpower." - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Re: [Fractint] FractInt does arbitrary precision math only for...
by Hal Lane 18 May '13

18 May '13

------ Mike wrote: ----------- >Author: Mike Frazier >Date: Fri, 10 May 2013 07:48:08 -0600 >To: Fractint and General Fractals Discussion >Subject: Re: [Fractint] Mike Frasier used Fracton to render Jim's >FOTD for May 6th, 2013 > >Unless I am mistaken, FractInt does arbitrary precision math only for >Mandelbrot and Julia built in formula types. You can't select arbitrary >precision math for formula types. --------------------------------- Page 166 of Fractint.doc for 20.4: Wes Loewer wrote an arbitrary precision library in both 80x86 assembler and C, and the Stone Soup team incorporated Wes's library into Fractint. Initially, support was added for fractal types mandel, julia, manzpower, and julzpower. . . . So how far can you zoom? How does 10^1600 sound--roughly 1600 decimal digits of precision. . . . Note: many of Fractint's options do not work with arbitrary precision. To experiment with arbitrary precision at the speedier ordinary magnifications, start Fractint with the debug=3200 command-line option. With the exception of mandel and manzpower perturbations, values that would normally be entered in the Parameters and Coordinates screens need to be entered using the command-line interface or .par files. Other known things that do not yet work with arbitrary precision are: biomorph, decomp, distance estimator, inversion, Julia-Mandel switch, history, orbit-in-window, and the browse feature. - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 16-05-13 (17-Year Minibrot [M-7,A-7])
by Jim Muth 17 May '13

17 May '13

FOTD -- May 16, 2013 (Rating Math-7,Art-7) Fractal visionaries and enthusiasts: Today's image lies on the main spike of an oversized Mandelbrot set that is just starting to morph into a Z^17+C Mandeloid. The first signs of transition are already visible from the surface, in the finer detail. Today's scene lies just inside the point where the main spike is cut off by the escape radius. A small outzoom will show how close it lies. The name "17-Year Minibrot" refers to the generating formula, and also to the 17-year cicadas, (magiciada septemdecem), which are due to emerge in the Fractal Central vicinity in a few weeks. I rendered the image with the outside set to 'tdis'. This gave the image enough detail to make it interesting. Both the mathematical and artistic ratings are 7, which means that both are somewhat above average. The calculation time of 15 seconds will probably be cut by at least half on a SOTA (state of the art) machine, but the minor annoyance of setting up and running this letter as a parameter file will remain. This minor annoyance can be eliminated at the web sites. Thanks to the wonders of modern technology, the image may be viewed without the need of calculating it by surfing over to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and scads of back images are online at: <http://www.Nahee.com/FOTD/> Really pleasant weather was appreciated as best as possible by those here at Fractal Central today. The fractal cat questioned the partly cloudy skies, but approved of the temperature of 82F 28C. The fractal humans alternated between commercial work and weather enjoyment. The next FOTD will be posted in the near future. Until the near future arrives, take care, and terrorists are said to be enemies of freedom, which I guess gives us the right to over-run their land and drop bombs on them. But I fail to see how anyone could be an enemy of freedom. Would the terrorists rather be slaves than free people, or could they simply be fighting back as best they can against what they see as our aggressive intrusion into their sovereign territor- ies? After all, some people say we must keep them suppressed if we are to maintain access to the raw materials that lie in their territories but that we need to maintain our comfortable but extravagant life style. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 17-year_Minibrot { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot3 center-mag=-23.99999459284\ 184/0/3.647139e+011 params=15/12/475.99974045665/0 float=y maxiter=15000 inside=0 outside=tdis symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=0008ZH9YIAXJAWKBVMCUNDTODRQEQRFPSGOTGNVHMWI\ LXGLXIKYKKZMJ_NJ`PIaRIaSHbUHcWGdXGeZFe`FfaEgcEheBi\ dHffIihKkjNmlQonTrpWtrZvsaztdxtgwujuumtupsvsqvvpvx\ owzmwzlwzkszhozflzchzadzZazXYzUUzSRzPKzNJzKGyICyF8\ yD6z85yB5vD4sG4oI4lL3iN3eQ2bS2_V1R`2XX4VY6UZ8T_AS`\ CRaEPbGOcHNdJMeLLfNJgPIhRHiTGjVFkWElVFkUGjTHjTHiSI\ iRJhQJhQKgPLfOLfNMeNNeMNdLOdKPcKPcKP_KPWKPSKPOKPJK\ PFKPBKP7KO1KP3KQ5KR7KR9KSBKTDKTFKUGKVIKWKUWMVXOWYQ\ XYSYZUZ_V_`X`zZa7`btbctddtfethetnftietggueitcktblt\ `nt_ptYqtXotZmt`ktbitcgteetgcthatj_tlYtnWtoUtqStsQ\ ttRtqRtnStkSthTteTtbTt_UtXUtUVtRVtOVtMTtLRtLQtKOtK\ MtJLtJJtIBtF8tC5tA2t63t84t95tA5tC6tD7tE8tF000070`t\ GetMjtSotYstc_tkHtrKtpMtnOtmRtkTtiVth_tbdtXitRntLi\ tNetPatQXtSTtTDtQFtSHtUJtWLtYNtyitYdt``tcWtfStiNtl\ _tiitnKtrntqktphtpetoatnZtnWzmTzmUzgmzmJzoFzqHz`Jz\ KKz3bzfjznrzvjzqbzmWzhOzd } frm:DivideBrot3 { ; Jim Muth z=0, c=pixel, a=real(p1), b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 15-05-13 (Crystal Cities [M-4,A-6])
by Jim Muth 15 May '13

15 May '13

FOTD -- May 15, 2013 (Rating M-4,A-6) Fractal visionaries and enthusiasts: In today's image we take a brief break from hyperland and check the parent fractal that results when the formula Z^(1.37)+C is iterated 1.37 levels up the hyperladder with no function applied. This parent appears as a shapeless main bay with an equally large and shapeless period-2 bud attached to the northwest side. Today's image is located in a twisting filament just inland of the eastern shore line of the parent's main bay. I named the image "Crystal Cities" for no apparent reason. The math interest rates a rather boring 4, the artistic worth, a not much better 6. The calculation time of a mere 45 seconds will remove some of the disappointment if the image lays an egg. The finished image should be posted on the official web site at: <http://www.crosscanpuzzles.com/Archives.html> but the host site has been having problems and has been hard to access lately. It might be down. If it is down, check the hi-def version of the image at Hal's site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Hopefully, his site is up to date: Regardless, the back images are online at: <http://www.Nahee.com/FOTD/> A rather pleasant day passed virtually un-noticed today here at Fractal Central, with ample sun and a temperature of 75F 24C. The fractal cat enjoyed the few beams of sunlight that managed to sneak into F.C. (We get little inside sunlight during the high-sun-angle time of year.) The humans made the best of things. The next FOTD will be posted in a matter of hours. How many hours is yet to be determined. Until whenever, take care, and get hot under the collar about climate-change-global-warming. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Crystal_Cities { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.80267755/+0.71031711/117.094/1/65/0 params=1.37/0/1.37/0 float=y maxiter=16000 inside=0 outside=tdis logmap=28 periodicity=6 colors=000zJnzEozAsz6uz2wy6ys9zlCzfCz7CcUCcOCcJCcD\ Cc9CcKCcRCY`CHdC4_C1OA0E20500000200605A0AE0GJ0MP0R\ U0Y_0cd0li0so0yq0wq0wq1wq5wqAwqEwqLwqPwsUus`usfusn\ ussuszuszuszuUgfRidOn`Lo_HsWEwTCyR9zO6zM4zJ1zH2zG4\ yG5uG6oG6lE7fE9bEAYEAUE7YG6`G5dH2gH1lJ0oJ0sL0wL0zM\ 0zM0yL1sL4nL7gLCbLEYLJTJMOJRJJWEJ_AJd6Jg4JlADoH9sP\ 5wY1zf0zo0zw0uy0lz0bz0Uz0Mz0Ez07z0Az0Dy0Eu0Hq0Ln0M\ l0Pg2Td5U`6YY9`WCbTDfPGiMJlJLoHOsERuCTy9Wz6_z`GzdG\ zfGzgGziGzlGznGzoGzqGzsGzuGzzHzwGzuEzsEzqDznDzlCyi\ CwgAwd9ub9s`7sb7qd6of6og5ng4lg4lg2ig2gq1lq0gq1fq2b\ q4`q4_q5Wq6Uz6Tz7Pz9Oz9MzAJzCHzCGzDDzECzGAzG7zH6zJ\ 5zJ2zL1zM0zM0zO0zP0zT0zR0zP0zO2zM6zLAzLEzJHzHMzGRz\ EWzE`zDfzClzAqz9wzAuz9uz7uz7uz6sz5sz5sz4sz2qz2qz1q\ z0qz0oz0oz0oz0oz0nz0nz0nz0nz0lz0lz0lz0iz0lz0lz0nz0\ nz0oz0oz0qz0qz0sz0sz0uz0uz0uz0qz0oz0nz1lz6izAgzGlz\ MzzHzzHzzHzzHzzHzzGzzGzzG } 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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Another Black Hole !?
by JackOfTradeZ＠comcast.net 15 May '13

15 May '13

. Here is what I saw: http://dl.dropboxusercontent.com/u/33642054/image/fotd_20130510_1200_5.jpg . If you zoom in, the black hole eventually fills the screne, as in my recent viddie. If you increase iterations, it appears to "retreat" to distance and get smaller. The black is not really "lake" region, it is simply "high iteration count to escape" region, and it increases the closer to the "center". This continues to infinity - there is no minibrot or anything else there. .

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FOTD 13-05-13 (Surprise Test [M-7,A-7])
by Jim Muth 14 May '13

14 May '13

FOTD -- May 13, 2013 (Rating M-7,A-7) Fractal visionaries and enthusiasts: The discussion is brief because the day was very busy. Today's image shows a tiny minibrot in the East Valley area of a larger but still small minibrot on the main stem of the Mandelbrot set. The minibrot has been almost totally filled in by hyper-stuff, with the only remaining open area a black dot at the center of the main bay. The math value is down 2 points from yesterday's, since the effect is not as surprising as the title would imply. The artistic worth is up a point however, due to the extra effort I hurriedly put into the coloring. The name "Surprise Test" is an exaggeration. I was really not very surprised when I saw the image The calculation time of a mere 30 seconds will make all fractal troubles vanish like a black cat on a dark night. See the light! Enjoy the finished image posted at: <http://www.crosscanpuzzles.com/Archives.html> Thrill in the hi-def version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And if today's image leaves you hungry for more, check the thousands of FOTD back FOTD fractals and hair-raising discussions online at: <http://www.Nahee.com/FOTD/> A definite chill was in the air here at Fractal Central today, with a mix of sun and clouds and a temperature of 52F 11C. The low tonight is forecast to be 27, which could be the lowest ever recorded in May. No wonder the local farmers are worried. The fractal cat is not worried however. An extra treat of tuna kept him happy most all day. The fractal people made it through a very busy day with a minimum of distractions. The next FOTD will be posted, tomorrow if all goes well, the next day if it does not. Until whenever take care, and where is the outrage about the bombing in Afghanistan and the 19 people shot at the parade in New Orleans? I guess people get outraged only when the news media jumps on a story, thereby telling the public, (Are we a flock of such easily manipulated sheep?) that it's time to be angry again. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Surprise_Test { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-1.832274747051162/0/1.349499e+010 params=0/0/0/0/0/1/1e-050/0 float=y maxiter=1600 inside=0 logmap=198 symmetry=xaxis periodicity=0 colors=0000680740820A10B00C00E00F00G00H01K02M04P05\ R15U25W55Z75`85cB5eC5gF5iH5mJ5qL5sM5vP5yRHzSUzVezW\ kzZez_UzbHzc6td6pe6lg7hh7ei7bj7_k7Xm8Un8Ro8Nq8Kr8H\ s7Hq7Jo7Mn6Om6Sk6Vj5Yh5Zg5_e4`d4`c4bb2c_2cZ2dY1eW1\ gV1gU0hR0iQ0iP0jO0kM0mL0mJ0nH0oG0oF0qE0rC0rB5_2EC0\ FE0FF0GF0GG0GG0HH0HH0JJ0JJ0JK0KK0KL0LM0LM0LN0MM0MN\ 0OO0OR0OS0PU0PW0QZ0Qa0Qb0Re0Rf0Sh0Sh0Sl0Ul0Us0mx0m\ z0Wv0Wr0Ym1Zh2Zc4_Z5`Y7`V8bUAcRBcQCdOEeMFeMHgLJhKK\ hJLiHMjGOjFPkERmCSmBUnAVo8Wo7Yq6Zq6_k6Wg6Uc6RZ6PU6\ LQ6JL6GC7BG6EdUEbSC`RC_QCAQOAPPAPQBORBMSBMUBLVBLWB\ KYCJZCJ_CH`CHbCGcEFdEFeEEgEEhECiECiCEjCEjCEjCEkCEk\ CEkCFmCFmCGmCFnCGnCFnCGoCGoBGoBGqBHqBHqBJrBJrBKrBK\ rBLsBLsBMsBMtBOtBOtBPvAPvAQvAQwURwURwUZxedxeexrkyr\ myzzzzzzzzzrozeizUhxHhw8gv8gt8gr8eq8eo8dn8dk8djrci\ 7ch7beebd7bcr`b7`_7_Zz_Y7_W7ZU7ZSzZR6YQ6YP6WM6WL6W\ K6VJ6VG6UF6UE6UC6SA5S8zR7 } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 12-05-13 (Oh_I_See_You [M-9,A-6])
by Jim Muth 14 May '13

14 May '13

FOTD -- May 12, 2013 (Rating M-9,A-6) Fractal visionaries and enthusiasts: Today's rating is in two parts, a math part and an art part. The mathematical interest is quite high, the artistic interest, just so-so. The scene lies well inside the main bay of the Mandelbrot set, where nothing but a blank screen should be expected, but today's image is anything but blank. The 'ghost bud' peeking out from behind the dark foreground stuff on the left is the first sign I have found of minibrots in the hyper part of the HyperMandelbrot set. True, the scene is not critical, but it is a sign that interesting discoveries might lie ahead. So far however I have been unable to bring the partially hidden bud out into the open. The hole at the center of the parent fractal closely resembles the mandel-object found by Mike Frazier at the bottom of what I had previously assumed was an endlessly shrinking series of concentric fractal starbursts. Today's scene lies inside a second-order bud at the edge of the circluar hole at the center of the main bay of the M-set. The superior math rating of a 9 is held down by the merely average artistic-worth rating of a 6. The name "Oh I See You" describes how I felt when I first caught sight of the unexpected bud. The calculation time of 7 minutes is slow, let's face it. The way to avoid time frustration is to find relief on the web sites. Enjoy the finished image posted at: <http://www.crosscanpuzzles.com/Archives.html> Thrill in the hi-def version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And if today's image leaves you hungry for more, check the thousands of FOTD back fractals online at: <http://www.Nahee.com/FOTD/> A mix of sun and ragged clouds, a temperature of 59F 15C and a brisk northwest wind made today feel unseasonably chilly here at Fractal Central. The fractal cat managed to find a stray shaft of sunlight in the afternoon, and curled up in comfort, but a cloud covered the sun after only 10 minutes and he retired to claim my favorite chair. With no mothers to visit, the fractal humans had a pleasant day at a local barn that has been conver- ted into an antique shop. The next FOTD will be posted in the proper time. Until that wonderful moment arrives, take care, and if the right is right, how can the left be right? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Oh_I_See_You { ; time=0:07:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-0.1237598874/+0.0164735574/3530/1/-23/0 params=0/0/0/0/10/0/1e-060/0 maxiter=7200 inside=0 logmap=459 periodicity=0 colors=00060I50K70J70K80K90LA0LB0KC0KD1LE2MF3OH4PJ\ 5RL6SN7UP8WR9XTAZWB_ZC`aD`cEacFacGbcGdcHccIbcHacIa\ cJ`cI_cJZcJZcJYcJXcKWcKWcLVcMUcMTcNTcOScORcPQcPQcP\ PcPOcPNcPRcPPcPNbPMaPK`PJ`NH`MG_ME_KDZJBZIAXJBWKCV\ LDUKETKFSKGRKGQKHPKIOKJNKKMKLLKMKKMJJNIIOHHPHGQKMR\ JMSIMSHMTGMUFMVEMWDMXCMXDMWEMWFMVFMVGMUHMUHMTDGTEH\ SFISFJRGKRHKQHKQIKPJKPKKOKKOLKNMKNMKNNKMOKMPKLPKLQ\ KKRKKRKJSKJTKIUKIUKHVKHWKGWJGXIFYHFZGEZFE_FE_JG_JG\ ZIGZIGZIGZHGZHGYGGYGGYGGYFGXFGXFGXEGXEGXEGWDHWDHWC\ HWCHVCHVBHVBHVBHUAHUAHUAHU9HU9HT8HT8HT8HT7HS7HS7HS\ 6HS6HS6HT7GT8GT9GT9GTAGTBGUCGUCFUDFUEFUFFUFFVGFVHF\ VIEVIEVJEVKKWLKWLKWMKWNPWNPWOPXPPXQUXQUXSUXTUXTZYT\ ZYUZYWZYXcYYcYZcZ_cZahZahZbhZchcembkmbkmbkmbkrbkrb\ krbkrbkwhkwhkwhkwhkzhkzblzhlzhlzhlzhlzhlzhlzhlzhlz\ hlzhgzhgzhgzhhzmmzmmzmmzmmzmmzmmzmwzmwzmwzzwzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 11-05-13 (Hyperscene [7.5])
by Jim Muth 11 May '13

11 May '13

FOTD -- May 11, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image begins an investigation of the 'hyper' parts of the HyperMandelbrot set. The investigation will continue in the days to come, when hopefully, we will stumble upon some far better hypervistas. Today's hyper vista lies in the East Valley area of the minibrot on the main stem of the parent M-set. The name "Hyperscene" is a description. The rating of 7-1/2 is a come-down, but still a bit above average. The calculation time of 2-1/4 minutes is fair enough, but the wait can be cut somewhat by visiting the web sites. The calculated image is at: <http://www.crosscanpuzzles.com/Archives.html> A hi-def rendering is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> FOTD back images are at: <http://www.Nahee.com/FOTD/> An all-day rain watered down the planned outside activities here at Fractal Central today. The temperature of 66F 19C was fine, that is for the ducks. The next FOTD will be posted when it is ready. Until then, take care, and don't look here for a clever closing remark. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Hyperscene { ; time=0:02:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-1.7499737\ 29001535/+0.00000626490393988/1.235225e+011/1/100/0 params=0/0/0/0/0.5/0/1e-050/0 float=y maxiter=5200 inside=255 logmap=590 periodicity=0 mathtolerance=0.05/1 colors=0000FT0FU0FV0FW0FX0FY0FZ0F_0F`0Fa0Fb0Fc0Fd0\ Fe0Gf0Hf0Ig0Jh0Ki0Li0Mj0Nk0Ok0Ql1Sl2Um3Vm4Xn5Zn6`o\ 7ao8cp9epAgqChqEjrHlrKnsOosSqtWst_uucvuhxwmzzrzzzz\ zUFWUI_WLcYPgXUeWZcVbaUe_TeYTeWSeUReTQeRPePPeNOeLN\ eJMeHLeFLeEKaFJYFJUGIQGIMHHIHKEIHFHFGHDHHBIH9JH6IJ\ 7KH8LG9NFAOEBPDCRCDSAEU9FV8GW7HY6IZ5J_4LX7NU9PRBRO\ DTLGVIIXFKYDMRGVLIcKGdJFeJEfIDgICgHAhG9iG8jF7kF6kD\ 9cCCXAFP9IIeX88KBDNAHP9MR8QT7VV6ZX6bZ5g`4kb3pd2tf1\ xh1qa8kWEePKZJQTCWN6aIA`DE`8I`3L`8JYDHWHGUMESQCQVB\ NZ9Lc7Jg6Hl4Ft48p3Dm3Hi3Mf3Qb3V_2ZW2cT2gP2lM2pJ2tO\ GhTUXXfLYfMYfNYfOYfPZfQZfQZfRZfS_fT_fU_fU_fV`fW`fX\ `fYYc``fYciVelShoPjrMmuJoxGlnDieAfX7dO5_N3WM2RL1NK\ 0QJ3SJ6UJ8WJBYJE_JGaJJcJMeJOgJRiJUkJWmJZoJ`pKYpKWp\ KUpKSpKQqKOqKMqLKqLIqLGrLErLCrLArL8vN5rL6nK6kJ6gI7\ dG7cF7cE8cD8cB8cA9m99m89m6AzUAzUAzXazWAzcBzUBzUCzU\ CzUCzUDzUDzYEzaEzeEziFzmF } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 10-05-13 (Variation [8.5])
by Jim Muth 11 May '13

11 May '13

FOTD -- May 10, 2013 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image lies in the same area of the same parent fractal that gave us yesterday's image, though it is located deeper in the parent's East Valley than yesterday's. It would have rated a 9 if it had not been a virtual repeat, but the actual rating of 8-1/2 is still high enough to do justice to its dark somber mood. Once again, there is no minibrot lurking at the center of the image, which apparently continues down forever, with the number of arms increasing in the same irregular manner. In fact, I have yet to find a single minibrot in any of the strange higher- dimensional parts of the HyperMandelbrot set. This is really not surprising, since HyperMinibrots would be four-dimensional and unable to be squeezed onto a flat 2-D screen without huge distortion. The name "Variation" points out that the image is a variation of yesterday's theme, rather than something new. The good news is the fireball calculation time of 40 seconds, which will be cut substantially if the parameter file is run on one of the present-day multi-processor hot-rod units that the Fractint program cannot yet (if ever) take advantage of. The not-so-secret path to total freedom from parameter-running chores lies on the FOTD web sites, where fractal enlightenment abounds. The official FOTD web site, where the basic finished image is posted, may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> with studies of the image in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back fractals from April 1997 are filed at: <http://www.Nahee.com/FOTD/> The day began with dense fog here at Fractal Central. The fog lifted later in the morning, but the sun had a hard time break- ing through higher clouds. We did have enough sun however to raise the temperature to 73F 23C, which made the fractal cat happy even from his lookout post inside FC. The humans had one more in the apparently endless string of normal days. But this does not imply boredom. After all, who needs sensational happen- ings in their daily lives when there is quite enough sensation coming from the mass media. The next FOTD will be posted in a nominal amount of time. No temporal anomaly is implied however. Until next time, take care, and mythological stories are symbols that, when properly understood, describe the spiritual world; just as mathematical expressions are symbols that, when properly understood, describe the physical world. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Variation { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=+0.2564007\ 14981565/-0.000985574462821/3.572718e+007/1/-90/0 params=0/0/0/0/0.9/0/1e-020/0 float=y maxiter=1000 inside=0 periodicity=0 colors=000eFLfIKiKJkMIlOGnSEpWDrZCscBvfAyk9zo8zr9z\ u6GCQEDMDEJBEF9FC8G95I50O14J3BF4GC5O88V49f1Am0Bh2F\ d6J`AMXEQTJUQMZOScKXfI`kFeo9kyDisGinKiiOidSi`WiWZi\ SchMfhIkhEohAsh6xh2zn0zh0xd1sZ3oW6kS9fMBcJDZFGWBJS\ 8LO4PK0SG0UD0UE0XF0YF0ZG2`G5aI9cJCdJEeKIfKLhLPkMSl\ MWnOZoOcpPerQisQnuSrv2k`Sux0yX0pW0iW0cU0XU2QT4KT6E\ S99SB3QA0UC0QE0OF0LI0IK0FL0DO0AQ08S05U02X00W00Y00Z\ 53`B9cGEdMKeUQh`Xifckniizuluonnipfdr`ZsUUvOPxIKz9D\ yCGyEKxGMxKQvMUzTZvPXsKYrLWpLUoMTnMSlOQlOPkPMiPLhQ\ KfQJeSIcMCeSGfWLh`QidWki`lnenrkoofoncolZoiWohSofOo\ dKocIoaEoZBoY8oX4oU1oT0pP0sS0vU0yX0zZ0za0zd0zf1zi2\ zk2zn3zp4zs5zv5zy6zz8zz9zz9zz6zz4zz3zz100000210320\ 430540650760860970A82BA4DC6EE8FGAGJCIIFKIILGLMGOOF\ RPFUQIWTKYWM_YPaZQcaTedWgfYihZkk`mncoofrriuukwxnxy\ pzzszzuzzsszqpylorghsd`p`JnYDkU8hQ2eL0`H0aD0Y80Q60\ H40E11D23CA5GG6LO9PWBOdDM } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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Mike Frasier used Fracton to render Jim's FOTD for May 6th, 2013
by Hal Lane 10 May '13

10 May '13

Mike Frasier used his Fracton program (on a Mac) specifying ~28 decimal digits of precision and anti-aliasing to render a version of Jim's FOTD for May 6th, 2013 without loss of precision artifacts. To see the improvement, the two images to compare are Fractint's anti-aliased version, and Mike's version. You can also compare the unanti-aliased Fractint version with Mike's... Don't forget to click on the image in your browser to view it actual size Â- to prevent it from being re-sampled by your browser! If a browser re-samples an image, it can significantly change what you see and make comparisons between images meaningless. Please navigate to May 6, 2013 thru my home page: Thanks. http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html Jim always uses: float=y and, assuming that Fractint uses IEEE 754 double-precision binary floating-point format for its floating point calculations, Fractint is using 15 to 17 decimal digits during its number crunching: http://en.wikipedia.org/wiki/Double-precision_floating-point_format // Would a Fractint developer please comment on my assumption? Of course, errors can accumulate during computation -- especially in repeated calculations as are used in fractals. I typically find visible anomalies starting to appear in Fractint fractals at magnifications of around 10^(11) or 10^(12) depending on the fractal. You can really see the improvement in Mike's ~28 decimal digit anti-aliased version clearly by using my "blink microscope" method (described at the bottom of each monthly page on my site of Jim's FOTDs.) The method is described where my page says: "Here's a nifty way to compare..." Please ignore the slight image shift when 'blinking' between the two versions of anti-aliased images. I'm really partial to using the keystroke method of switching the viewed tab -- since you don't have to take your eyes off the fractal to switch the tab you're viewing. The differences between the images will then hit you in the face like a wet mackerel. - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 09-05-13 (Out in Left Field [9])
by Jim Muth 09 May '13

09 May '13

FOTD -- May 09, 2013 (Rating 9) Fractal visionaries and enthusiasts: I have no idea why I named today's image "Out in Left Field", but that's how it goes sometimes. The lack of a logical reason for the name is no problem however. With a rating of a 9, the image needs no fancy, logical name. The image is a scene in the East Valley area of a Hyper- Mandelbrot set that is filling in around the edges of the main bay and inside the buds. The brilliant white hole at the center is not an under-resolved minibrot. It is all that remains of the period-21 bud on the south side of East Valley of the M-set. The rest of the bud is filled in with patterns similar to those in today's image, which, like the stack of world turtles, goes down forever. One of these days, someone like Mr. Mandelbrot (may he rest in fractal land) will determine exactly what is going on in images like today's. Unfortunately, I am not that person. The rating of a 9 is no mistake. The unusually brilliant colors, for which I *am* responsible, earn the rating. The calculation time of 50 seconds is a joy to experience. It's so fast that the calculation is dangerously close to finishing before it starts, thereby creating a time paradox. Checking the image on the web sites will eliminate this threat. Be safe! Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the augmented version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the back images at: <http://www.Nahee.com/FOTD/> After yesterday's deluge, today, even with its heavy clouds and chilly temperature of 68F 19C, was an improvement. It was also the fractal cat's day for a check-up at the doctor. He endured the discomfort bravely, but showed a bit of resentment when he returned to FC. The next FOTD will be posted when it is ready. Until this readiness arrives, take care, and the paranormal does indeed exist. It is nothing more than natural things we do not yet understand. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Out_in_Left_Field { ; time=0:00:50.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=+0.27135683245/-0.00622833825/105332 params=0/0/0/0/0.9/0/1e-020/0 logmap=190 inside=255 maxiter=1500 outside=imag logmap=190 periodicity=0 colors=00000210320430540650760860970A80BA0DC0EE1FG\ 3GJ6IIAKIDLGGMGKOFOPFUQIWTKYWM_YPaZQcaTedWgfYihZkk\ `mncoofrriuukwxnxypzzszzuzzpoznhykavfWsdPp`JnYDkU8\ hQ2eL0`H0aD0Y80Q60H40E11D23CA5GG6LO9PWBOdDMeFLfIKi\ KJkMIlOGnSEpWDrZCscBvfAyk9zo8zr9zu6GCQEDMDEJBEF9FC\ 8G95I50O14J3BF4GC5O88V49f1Am0Bh2Fd6J`AMXEQTJUQMZOS\ cKXfI`kFeo9kyDisGinKiiOidSi`WiWZiSchMfhIkhEohAsh6x\ h2zn0zh0xd1sZ3oW6kS9fMBcJDZFGWBJS8LO4PK0SG0UD0UE0X\ F0YF0ZG2`G5aI9cJCdJEeKIfKLhLPkMSlMWnOZoOcpPerQisQn\ uSrv2k`Sux0yX0pW0iW0cU0XU2QT4KT6ES99SB3QA0UC0QE0OF\ 0LI0IK0FL0DO0AQ08S05U02X00W00Y00Z53`B9cGEdMKeUQh`X\ ifckniizuluonnipfdr`ZsUUvOPxIKz9DyCGyEKxGMxKQvMUzT\ ZvPXsKYrLWpLUoMTnMSlOQlOPkPMiPLhQKfQJeSIcMCeSGfWLh\ `QidWki`lnenrkoofoncolZoiWohSofOodKocIoaEoZBoY8oX4\ oU1oT0pP0sS0vU0yX0zZ0za0zd0zf1zi2zk2zn3zp4zs5zv5zy\ 6zz8zz9zz9zz6zz4zz3zz1zzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 08-05-13 (Sinuous Discharge [8])
by Jim Muth 08 May '13

08 May '13

FOTD -- May 08, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image with its lightning-like filaments reflects the weather today here at Fractal Central. The formula causing all the bad weather on the screen takes 1.5 parts of Z^(-1.1) and combines it with 0.3 part of Z^(-7.4) before adding (1/C) on each iteration. The resulting parent fractal is a hugely oversized thing resembling an upside-down figure eight, with today's scene lying on the filament extending east from the east branch of the valley separating the two large lobes of the parent. The name "Sinuous Discharge" refers to the image's sinuous outer curves as well as the electrical effect of the brilliant inner curves. The rating of an 8 is getting to be a habit, a habit that I hope continues. The calculation time of 1-1/3 minutes is appropriate for the image, neither too fast nor too slow. But a chore remains -- the chore of setting up this e-mail as a parameter file and running it. Thankfully, this is when the web sites are there for the rescue. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> The weather took a turn for the worse here at Fractal Central today, as a series of severe thunder-storms moved in during the morning and dropped 3.15 inches, 8cm, of rain by noon. During the storm an apartment building was struck by lightning and set afire. The temperature hung around 61F 16C most all day. Luckily, the fractal sump pump did its job and we had nothing worse than a couple puddles on the basement floor. The fractal cat, who doesn't like thunder, became uneasy until the noise stopped. The next FOTD will be posted in a reasonable time. Until reason prevails, take care, and presidential assassins are buried in the U.S. with no fuss; the Oklahoma City bomber, who killed well over one-hundred, was buried in the U.S. with no fuss; the Newtown school shooter, who killed 20 children was buried in the U.S. without a fuss. Why then is there so much silly fuss finding a place to bury the Boston bomber, who killed only four people? If we claim it is because he used a weapon of 'mass destruction', then shouldn't the automatic gun used by the Newtown shooter and the bomb used by the Oklahoma City bomber also be considered weapons of mass destruction? IMO, everyone, even those we consider the most evil, deserves a proper burial! God will deal with the evil-doer. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Sinuous_Discharge { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+84.76284793287175/+1.51704663727301/\ 119/1/-96./0 params=1.5/-1.1/0.3/-7.4/0/0/0/0 maxiter=1200 inside=0 logmap=135 periodicity=16 colors=000A60A80AA0AC0AE0AG0AI0AK0AM1AO2AQ3AS49U5A\ V6BW7CY7DZ8E`9Ea9FcAGdAHeBIgCJhCJjDzzDzzEzzFzzFzzG\ z0zz0zz0zz0zz0zz0zz0zz0zz0zcicchfcgicdkcenJbrJcpJ_\ rJbsHZoGZmFXjEWhDUeCSaAQY9PV8NR7LN6JJ5IG7KH9LHBMHC\ OHEPHGQHISIUUIUUKcccccczzzzzzzzzzzzzzz00000000000K\ 00K00KilKjmKhlJglJfkJdkJbjJajJ`iJ_iJZiJYhJXhIWgIUg\ ITfISfIRfIPeIOeINdIMdIKcIJcHIbHHbHFbHEaHDaHC`HA`H9\ _H8_H7_H8YI8XI8VJ8UJ9TK9RK9QK9PLANLAMMALMAJMBINBHN\ BFOBEOCDPCBPCAPC9QD7QD6RD5RD3RE2SE1SE0TE0TE0TF0SG0\ RG0QH0PH0PI0OI0NJ0MJ1MK1LK2KL2JL2IM3IM3HN3GN4FO4FO\ 5EP5DP5CQ6BQ6BR6AR79S78S78Q89P9AOABNBBMCCLDDJEEIFE\ HGFGHGFIHEJHCKIBLJAMK9NK8OL7PM6QM7PO7OP7NR7NS7MT7L\ V7KW7KX8JZ8I_8H`8Hb8Gc8Fd8Ff8Eg8Dh9Cj9Dk9Gl9Jn9Mo9\ Pp9Sr9Vs9YtD`iGcZKfPNiEQl4So6Tr7Vr8Wr9YrBZrC`rDarE\ brFdrHerIgrJtrWhrKjrMkrNlrOnrPorQqrSrrTtrUurVzzLzz\ NzzOzzQzzRzzSzzUzzVzzKzzF } 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 07-05-13 (Busy-Body [8])
by Jim Muth 08 May '13

08 May '13

FOTD -- May 07, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image has some very unlikely parameters, which is a sign that I was led to the parent fractal by the Fractint evolver feature. But regardless of where the image came from, it still rates an 8, which has been the standard for the past several days. The parent combines 2.475 negative parts of Z^(-1.05) with 0.275 negative parts of Z^(-5.5) then adds (1/C) on each iteration. This parent is a huge Mandeloid with a circular main bay edged by several large buds and a series of rings. Today's scene lies in a filament leading to a degenerate ring on the eastern edge of the large circular bay. The rating of an 8 is perhaps a bit more than the image deserves, but then again, perhaps I'm a bit too humble. The name "Busy Body" refers to the clutter of detail filling the frame. The calculation time of 12 minutes is slow. It's at times like this that the web sites come in handy however. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> The weather was near perfect all day today here at Fractal Central. The fractal cat enjoyed it, as did the fractal humans. The next FOTD will be posted well before the world disintegrates into a de-sitter soup. Until whenever, take care, and maybe I'm a Boltzmann brain inside a larger Boltzmann brain, and it's Boltzmann brains all the way up. BTW, when will these fascinat- ing hypothetical creatures be mentioned on one of the pop-science TV shows? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Busy-Body { ; time=0:12:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-3.216611489264434/+0.5748460602506155/\ 2.249254e+012/1/49/0 params=-2.475/-1.05/-0.275/\ -5.5/0/0/0/0 float=y maxiter=12000 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000zzzzzzxzztzzpzwlzthxsdwq`vqXtqTsqPqqMpqI\ opFmpBlo8jo7io5ho7fo8eoAeoCdoFdoHcoJaoMaoN`oP_oS_o\ VYoXXo_XoaWocWo`Vm_TlYSjXSiWQhVPfTPeQOdPNcONaNI`ML\ _LGYJ8XHFWG2VFCTD2SCAOB2PA2M92N521825A88D9DGAJMBPP\ DWVFaXFhaGoeGvhHzjHzoIzsIzwIzzIzzIzmAxf9q`8iV7cO5W\ I3PD2I91C50500000000000000000100200500500800900A00\ C00D00G00H00I20J85LD9MJDMPINWNOzSPzWPvVOoVOoXShYVa\ _XWa`JccGde3NB3OC3PC2PD2QD2oFozF2eF3aG5YH5aH5YI5NJ\ 7MJ7LL8GM9BM07N02O00O0020020Do0020Pa002F7oG5WG5oF5\ VDPzC5VC7oB7VAPz98T98o88T7Pz59T59o57N55o55o53o52o5\ 10500800A01C05F08H0BJ0FM0IO0MQ0PT0TW0XY0``0da0h`0f\ _0eY0dX0cX2aW5`V7_T8_dMNeQQfWVh`Yfa_ec`da_c`Y`_X_Y\ WYXVWWTVTSTSQQQPPPOOONNNMLMLJLJIIIGHHFGGDFFBDDACC9\ BB8AAACCCFDFGGGIHIJILMLMNMOPNQSPSTQVWSXXV__W``Xcc_\ ee`ffaiidmlfppitsmxwpzzzzzzzzzzzzzzzvzzvzzzzzzzzzz\ 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 06-05-13 (In Deep Territory [8])
by Jim Muth 07 May '13

07 May '13

FOTD -- May 06, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image lies very deep in the parent fractal that comes about when 0.1 part of Z^(4.4) is combined with 2 parts of Z^(0.4) and straight C is added on each iteration. This parent resembles a Mandelbrot set facing northeast with a large triangular area sprouting behind it from its East Valley area. Today's scene is located in the northwest valley forming the entrance to this triangular area. The name "In Deep Territory" refers to the unusual magnitude of the image, one of the greatest of all time. The rating of an 8 reflects my opinion of the image at the time I rated it. I may soon shift to an more informative rating system that gives two ratings, one for the artistic value, the other for the mathematical interest. A good part of the artistic effect was achieved by rendering the image with the inside set to 'fmod'. The magnitude of over 2.5*(10^13) is at the verge of resolution breakdown. In fact, the breakdown is already becoming visible along some of the sharp edges. Luckily, the image calculates in 3-1/2 minutes, surprisingly fast for a scene that uses the 'fmod' feature. And the web sites are always there for instant enjoyment. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Another absolutely perfect day prevailed here at Fractal Central today. The few angel-hair cirrus clouds that appeared in the morning, and the few cotton-puff cumulus clouds that popped up over the ridges in the afternoon did nothing but add to the perfection. The temperature of 73F 23C and gentle southeast wind were also perfect. The fractal cat admired the outdoor conditions . . . from the inside. The fractal humans also admired the outdoor conditions. The next FOTD will be posted in a number of hours. Until that number passes, take care, and I am still waiting for someone to solve the very interesting and quite puzzling 'Boltzmann brain' paradox, which currently has physicists pondering and rational skeptics a bit concerned also. I'll forget the convoluted line of thought about entropy that led to the problem, since it is on the internet. At this time, I'll merely state that either the existence of the universe involves more than pure blind chance, or the universe is filled with disembodied 'Boltzmann brains' which somehow can exist and be conscious while floating in empty space. The apparently 'logical' deduction is that, if the universe is merely a random accident, then it is many googols of times more likely that, instead of existing in a real physical universe, I am a pathetic deluded Boltzmann brain, floating in empty space and imagining everything I have ever experienced, including the physical world and everything else that appears to be so real. I doubt that this is true, but, despite convoluted claims to the contrary, no one has yet been able to show beyond doubt that it is untrue without invoking an intelligence of some kind to elimi- nate the random element. And we know what rational scientific skeptics think of the idea of 'God'. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= In_Deep_Territory { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=-1.122707213001586/-0.1067224794760605/\ 2.545255e+013/1/-15/0 params=0.1/4.4/2/0.4/0/0 float=y maxiter=1000 inside=fmod proximity=0.932 periodicity=6 mathtolerance=0.05/1 colors=000giWgkZgmafocfqffsifukbog_icXd`UZXRUUOOQL\ JNNMQPPSRSVTUXVX_X_aZbd`dfbghdjkfmmhopjrrluunxwozy\ jsqflibeaZZVVSNRLFNE7J70UCEdGSbMU`RW_WYY`ZWe`VjbTo\ dSteVufYvh`wjcxkfymhzneyocxo`woZwoWvpUupRupPtpMsqK\ sqHrqFqqDqqCokCmfCkaCiWCfRBSMBMGBCBB76B21G36K4BO5G\ S6LX7Q`7Ud8Zh9cmAhqBmuCryCvuEurFunHukIugJudLu`MuYO\ uUPuRQuZRdeROlR8fV7`Z7Vb7Pe6Ji6Dm68p6DnAImENkIRjMW\ hQ`gUeeYid`mbdpaht`lw_pzZtyXrxWqwVpvTouSntRlsPkrOj\ qNipLhoKfnJemHdlGclFbYD`KBZ6AX8F_9KaAOdBTfCXhDakEf\ mFjpGorHstLrpOqmRpiUpfXob_n_bmWemThlPkkMnjIqjFtiBw\ h8zh5vg6rf7ne8kd9gcAccA_bBXaCT`DP_EM_ELaFKbFJcFIeF\ HfFHgFGhFFjFEkFDlFDmFMnPUoYbofjporpxpouoornnolnmkm\ jjmgimeglbfl_ekXckVbjSajP`jNbfQccTe_WfXZhTaiQdkMgl\ JjnFmoCpq8sr5vs2yo3vl3si4qf4nb5k_5iX6fU6dQ6aN7ZK7X\ H8UD8RA9P79M49KGJLRTMaaNlkOwtOtqMqoLolKljJigIgdGda\ Fb_E_ZDXYCWWAUU9SR8QN7KF6 } 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 05-05-13 (Lopsided Basin [8])
by Jim Muth 06 May '13

06 May '13

FOTD -- May 05, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that results when the simple formula Z^(1.75)+C is iterated 9 levels up the multi- dimensional complex-logarithmic hyperspiral. This fractal consists of a large main bay split along the X-axis, with a prominent disconnected smaller Mandeloid lying some distance to the southeast. Today's scene lies in a valley in this smaller Mandeloid. The name "Lopsided Basin" refers to the unbalanced nature of the basin surrounding the central minibrot, where the iteration count and therefore the appearance of the fractal elements on the left and right sides are vastly different. The rating of an 8 includes a bonus for the coloring effort, though I'm not saying how much of the rating includes the bonus. The calculation time of 1-2/3 minutes will pass fast enough to keep boredom in the realm of remote possibilities. Boredom may be done away with altogether by viewing the image on one of the FOTD web sites. Accept the obvious. Fractals are great! For rational proof, check the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and if further proof is needed, check the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The ultimate in proof may be found at: <http://www.Nahee.com/FOTD/> where thousands of similar fractals are posted. Cloudless skies prevailed all day on the 4th and 5th here at Fractal Central, with a temperature of 72F 22C both days and gentle breezes. The fractal cat saw the sun outside and wondered why it failed to reach his shelf. The humans spent the 4th working and the 5th relaxing. The next FOTD will be posted soon enough to prevent withdrawal and with enough delay to prevent fractal overload. Until whenever, take care, and to me it seems as though we're so obsessed with political correctness that we have no way to even recognize the causes of our problems much less to accept the causes and rationally discuss possible solutions. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Lopsided_Basin { ; time=0:01:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=+1.266621276199444/-0.148359824796705/\ 2.008047e+007/1/75/0 params=1.75/0/9/0 float=y maxiter=1800 inside=0 logmap=238 periodicity=6 colors=00050B60970780B90EA0HB1LC2OD3RE4VF5YG6`I7cK\ 8fMBhNEiNHjOKlONmPQnPToSXjU_fWbaYfY_iUalUcpUesUgvU\ isUkqZlocnmhommqmrrmvtmzumzvmzvmzvmzwmzwmzwmztkzqi\ zngzkeziczgbzeazd`zc_zbZzaYv`Xr_WmZVhYUcXSZWQ_VO`U\ NZSMXQMWONUMNTKORITQGQGFR6FRDFSAFS2JO3ML4QH5SE6UA7\ S78P39M0ALC8RO7S_6IRB9LG0IL7MEDY8Jh2Kc6L_9MWCMSFSO\ GYKGcGHhDHXPEL`C9kA5p51t0PpLlleEU0Dc5DcACcFCcKCbPJ\ eLPhIWkFamCgp9ns6tv3zw0zx1zy1zz2zz2AzHAzWAzj9zm8zo\ Qzjgzeyzaqz_izYzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzyzzxzzwzzvzzuzztzzszvriuohwjgwifw\ hcwh`rdYm`VmaSmcPmcMmcJmZDmZ7mZ2mZLmUbhQtZRfVSUQTG\ MP3RK`TF_UA_W6ZX6ZZ6Z_7Ya7Yb7YZDaVIeRNiNTmJYqFbtKX\ jPSaPHOOCEcBAh61i88jAFkBMlDTmF_nGfoImpJtiLpbNlWPiP\ ReISbL_hOfnQmsSMSUOUWQWYSY_TZaV`cXbeZzg_zi`zkazmbz\ mbzmczmdzmezmezmfzmfzmfzmgzrgzrgzrhzrhzrhzrizrizri\ zrjzrjzrjzrkzrkzrkzrlzrlz } 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 03-05-13 (Well Shielded [8])
by Jim Muth 03 May '13

03 May '13

FOTD -- May 03, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image resembles a shield decorated by fractal heraldry. I appropriately named it "Well Shielded". The fractal, which is rotated 90 degrees, lies on the main stem of its parent, an oversized Mandelbrot set that is on its way to becoming a cubic Mandeloid. The exact location of the scene is in a blunt valley jutting eastward into the second bud out the main spike, which is already splitting into the cubic-bud shape, with two lobes. The rating of an 8 is based on the unusual cubic shield-like pattern and also on my semi-expert coloring, which some say is great and others say is amateurish. All I can say is that great art is not created in the matter of the minutes that I spent on today's image. I went back to the 'DivideBrot5' formula for today's image because this formula does some types of mixed-power images better than the 'FinDivBrot-2' formula that I usually use. The calculation time of 2 minutes might be just slow enough to give restlessness a chance to appear. The wiser way to see the finished image is to visit the FOTD web sites. Find your happiness at: <http://www.crosscanpuzzles.com/Archives.html> where the image is posted already calculated. And clarify your vision at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the high-definition versions are posted. The thousands of back images are online at: <http://www.Nahee.com/FOTD/> bringing joy beyond comprehension to those who venture there. Perfect weather still prevailed here at Fractal Central today, with a cloudless sky, gentle breeze and temperature of 70F 21C. The fractal cat took it in stride, being more concerned with pigeons roosting in the area. The humans had an average day, which is pleasant to experience but boring to write about. The next FOTD will be posted quite soon, and that is not boring. Until soon arrives, take care, and we should not be angry at big corporations such as oil and phone companies for making such obscene profits at our expense. We should be angry at ourselves for having allowed ourselves to become addicted to their flashy products, thereby assuring these powerful conglomerates that their obscene profits will continue to grow. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Well_Shielded { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 float=y maxiter=1900 center-mag=-3.866658236650682/0/7.70961e+009/1/90/0 params=3/3 inside=0 logmap=268 periodicity=6 colors=000B2bB5aB8_ABZAEYAHX9KW9NV9RU9VTI_RQd7YhBm\ nAqzAut9wo9wi9wd9wZ9wU9009006IJ9IOBHUDHZFGdH9gFUF`\ VFaWGbYGcZGd_GeaGgbGhdHieHjfHkhHliHmjHnfMjcQg_VcXZ\ `TcXQgUMlQJpNGtKIsLKsLMsLOrLQrMSrMUqMWqMYqNZqN`pNb\ pNdpOfoOhoOjoOlnPnnPpnPqnPrkUrhYrearber_irXmrUqrSu\ mUphVkcWfZ_aUbYYbbaefeikimomqtqrxouvmvtlwrjxpiyngz\ mfzkdzibzgaze_zdczbgv`krZooXrlWviUwfSwcQwcOzhNzhQK\ KSKKUHKWGKYFK_FKaoE`oAio6ro2zk9yhFyeLyaRyZXyWbyYOm\ ZAbaFadJagOajSaeUf`WjWYoRZsUarXdq_gpajpdmogpnjsmlu\ mYhcJXU5LKESTNZ`Weidlqmryfpk_nZTlLNj8CbH2WQ5SY7Pd9\ MlBJsDGzbCJZIIWNITTIPYHMcHJhHGmHzZIzLIs7Ic7DL78J73\ D9BGBJJCQMEYPGeSHlPIjNIhLIfIIdGIbEIaPLdZOghRjrUm7G\ bONZdUWu`TpXUlUVgRWcOXZLYVIZRFZSF_EncDpeCqgBriAtk9\ um9vozjDzhHzgKzfNzdRzcUzbXz`_zmczmfzmizmlzmpzmszmv\ zmyzmuzzqzzmzzizzfzzbzzZzzVzzRzzOzzKzzGzzCzz9zzCzz\ FzzHzzKzzMzzPzzRzzUzzWzzT } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 02-05-13 (Aliens Among Us [7.5])
by Jim Muth 02 May '13

02 May '13

FOTD -- May 02, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image bears footprints, which is not surprising, since it lies in yesterday's parent fractal, very close to yesterday's scene. But these footprints were not made by bigfoots, they were made by aliens from outer space, which explains why they resemble the pea-pods of the body snatchers. The actual location is East Valley of the large minibrot on the main stem of the parent, where a tiny minibrot is located. Today's scene lies at the tip of the main spike of this minibrot. The name "Aliens Among Us" merely tells it like it is. For all anyone knows, the space aliens may very well be living among us, unrecognized and disguised as the man and woman next door. The rating of 7-1/2 is quite average. The extra half point is a reward for the coloring, which was more difficult than first appears. The calculation time of one minute will leave just enough time to go into the next room and pour a drink. Viewing the image on the web sites will avoid the drink. Be cheerful anyway! View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Be joyful! Check the high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Be in total bliss! Check the thoudands of FOTD images at: <http://www.Nahee.com/FOTD/> Today brought another round of cloudless skies, gentle winds and dry air to Fractal Central. The temperature of 73F 23C made it the second consecutive perfect day. Nicholas, the cat of the fractal variety made it through the day uneventfully, sleeping all afternoon in my favorite chair. The fractal humans made it through the day by working. The next in the inexhaustible series of FOTD fractals will be posted soon. Until whenever, take care, and everyone wants peace, but the evil other side will not let it happen, and this is true regardless of which side a particular person is on. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Aliens_Among_Us { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-17.53500853358189/0/2.109337e+010 params=0.1/2/1/-1000/0/800/0/0 float=y maxiter=1500 inside=0 logmap=126 symmetry=xaxis periodicity=6 colors=0000L40M70O90QB0SD0UF0XH0_J1bL2eN3YK4QH5IE6\ AB51472893CB3FD4JE5MG5QI6TK7XM7_N8cP9fR9jTAmVBqWBt\ YEtZHt`KtaNtcQtdTtfWtgZtiatjdtnevkfthgrfhpcho`imZj\ kWjjUkhRlfOleMmcJnaGn`EoZBpX1nX9lWHiVOfUWcTc`Sc`Nf\ `RbaUZbXUcdPd_KeWDfSHgPLgNOgKSgIWfFZfDbfAff8ac0if6\ qiCzoHzvGzzGzvGzrGvmGriGmhGihFegFcgF`fFZfFXeFVeFVd\ DTeFRfGPfHNgILhJEqGKhKQ`OWTSaKWgC_k0im4cn8ZoCUqGPr\ JKsNFuRAvV5wY0p_7iaEbbLXdSQeZJgeBejDhkEkkFnlAtqGql\ LngRkcWhZaeVfbQk`Mj_KiZIhZHhYFgXEfXCeWBeV9dV8cU6dR\ 0cU5cXAc_FcbKbePbhUbkZdqdbmb`jaZg_XdZWcXUcWScVQcTO\ cSNcQLcPJcNHcMCcMGcLKcKOcJScJWcIZcHbVGfZGjaFneEqhE\ meOicYe`gaZp_`mZbjYdhXfeWhcUj`TlYSnWRpTQqROnSNlSLi\ SKhSIhSHhSFhSEhSChVDhSEhQFhOGhMGhKHiPIlUJoZJqc1yhA\ umIzrQzvZzzfzznzzvzzrzzozzlzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzZzzZzzZzzZzzVzzRzzOzz\ KzzGzzDzz9zz6zz7zz7zz7zz7 } 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 02-05-13 (Aliens Among Us [7.5])
by Jim Muth 02 May '13

02 May '13

FOTD -- May 02, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image bears footprints, which is not surprising, since it lies in yesterday's parent fractal, very close to yesterday's scene. But these footprints were not made by bigfoots, they were made by aliens from outer space, which explains why they resemble the pea-pods of the body snatchers. The actual location is East Valley of the large minibrot on the main stem of the parent, where a tiny minibrot is located. Today's scene lies at the tip of the main spike of this minibrot. The name "Aliens Among Us" merely tells it like it is. For all anyone knows, the space aliens may very well be living among us, unrecognized and disguised as the man and woman next door. The rating of 7-1/2 is quite average. The extra half point is a reward for the coloring, which was more difficult than first appears. The calculation time of one minute will leave just enough time to go into the next room and pour a drink. Viewing the image on the web sites will avoid the drink. Be cheerful anyway! View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Be joyful! Check the high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Be in total bliss! Check the thoudands of FOTD images at: <http://www.Nahee.com/FOTD/> Today brought another round of cloudless skies, gentle winds and dry air to Fractal Central. The temperature of 73F 23C made it the second consecutive perfect day. Nicholas, the cat of the fractal variety made it through the day uneventfully, sleeping all afternoon in my favorite chair. The fractal humans made it through the day by working. The next in the inexhaustible series of FOTD fractals will be posted soon. Until whenever, take care, and everyone wants peace, but the evil other side will not let it happen, and this is true regardless of which side a particular person is on. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Aliens_Among_Us { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-17.53500853358189/0/2.109337e+010 params=0.1/2/1/-1000/0/800/0/0 float=y maxiter=1500 inside=0 logmap=126 symmetry=xaxis periodicity=6 colors=0000L40M70O90QB0SD0UF0XH0_J1bL2eN3YK4QH5IE6\ AB51472893CB3FD4JE5MG5QI6TK7XM7_N8cP9fR9jTAmVBqWBt\ YEtZHt`KtaNtcQtdTtfWtgZtiatjdtnevkfthgrfhpcho`imZj\ kWjjUkhRlfOleMmcJnaGn`EoZBpX1nX9lWHiVOfUWcTc`Sc`Nf\ `RbaUZbXUcdPd_KeWDfSHgPLgNOgKSgIWfFZfDbfAff8ac0if6\ qiCzoHzvGzzGzvGzrGvmGriGmhGihFegFcgF`fFZfFXeFVeFVd\ DTeFRfGPfHNgILhJEqGKhKQ`OWTSaKWgC_k0im4cn8ZoCUqGPr\ JKsNFuRAvV5wY0p_7iaEbbLXdSQeZJgeBejDhkEkkFnlAtqGql\ LngRkcWhZaeVfbQk`Mj_KiZIhZHhYFgXEfXCeWBeV9dV8cU6dR\ 0cU5cXAc_FcbKbePbhUbkZdqdbmb`jaZg_XdZWcXUcWScVQcTO\ cSNcQLcPJcNHcMCcMGcLKcKOcJScJWcIZcHbVGfZGjaFneEqhE\ meOicYe`gaZp_`mZbjYdhXfeWhcUj`TlYSnWRpTQqROnSNlSLi\ SKhSIhSHhSFhSEhSChVDhSEhQFhOGhMGhKHiPIlUJoZJqc1yhA\ umIzrQzvZzzfzznzzvzzrzzozzlzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzZzzZzzZzzZzzVzzRzzOzz\ KzzGzzDzz9zz6zz7zz7zz7zz7 } 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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AOTD 5_1_13
by JackOfTradeZ＠comcast.net 02 May '13

02 May '13

. ""Just have one question, what was the background music??"" Domenico Scarlatti. One of the lesser known composers from the Bach/Baroque period, but one of my favorites. I downloaded a zillion MIDI files from the classical archives web site; many of them marry quite well to fractal animations. .

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FOTD 30-04-13 (Deep Green [8.5])
by Jim Muth 02 May '13

02 May '13

FOTD -- April 30, 2012 (Rating 8.5) Fractal visionaries and enthusiasts: Today's 8.5 rated image lies in the parent fractal that results when 0.2 part of Z^2 is combined with 15 parts of Z^(-1.5). This parent appears as an oversized but skeletal Mandelbrot set with a well-defined much smaller M-set in the area of its East Valley and two minibrots symmetrical to the X-axis in the area of its main spike. Today's scene lies in the intricate debris between these two minibrots. I named the image "Deep Green" because of the vivid green ring surrounding the central minibrot. The rating of 8-1/2 includes a sizable and perhaps too liberal bonus for my coloring. The calculation time of 1-3/4 minutes borders on slowness, making the web sites a good calculation alternative. Find this calculation relief on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and classy variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Hordes of back images are posted at: <http://www.Nahee.com/FOTD/> Lots of clouds hung overhead here at Fractal Central today, and a few flurries of drizzle drifted down now and then, but the sun also broke through several times, and the temperature of 66F 19C was so close to average that it left no grounds for complaint. The fractal cat took it all in stride, satisfying himself when he evicted me from my favorite chair and took it over with a satisfied smirk on his face. The humans meanwhile checked the latest news, seeing nothing new, of course. The next FOTD will be posted when I get a round tuit. Until I can find a tuit shop, take care, and there is a question I want a clear answer to. It is, 'why are we here on earth?' (Answers such as 'to get to heaven' 'to propagate the species' 'it's a lucky accident' or 'it's up to each of us to decide' are rational enough but not really satisfactory.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Deep_Green { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-13.76762576559253/+0.00003824191632297\ /8.95286e+011/1/88.25/0 params=0.2/2/15/-1.5/0/800\ /0/0 float=y maxiter=1600 inside=0 logmap=126 periodicity=6 mathtolerance=0.05/1 colors=000zKzzKzyPzyRszXzzUxz_qz`xzZzzWzsUzxRzsPzq\ OzoMznLzlKzhJzkLqfMueOjePedQKdRfcT3cU09TV8MO6II5DB\ 0850320800A20D00L00V20f30T42Q55I69D66A848924A02A5F\ FFKGJOIORIRVJP_KOcKLfLKjLRiGZhDdf9ke4sd0yc0neIdh`V\ itUdiT_ZRPOUaPVUPY`QZaQ_dQaeRchRdiRdaPdVMdOLdGJdAI\ cIJcPKcVLcaMchOdkOinGlo9pp2tq0np0ip2co5Zo9TnDOnFJh\ EEcE9YD4TDEYEOaFYeGfjIonJZqOIuT2xW6pVAiVEaVIWVMPUQ\ IUUAUY4U`RIdl5xT0qW0l_0fc0af0Wj2Rn2Lq3Gt3LuBQvJUvR\ ZxZcyffynkzvozzxffzPKzTPuWTpZWka_fecchfWcdPZaIU_BQ\ YMZ_Yf`hocqvdkjVeZM_MDUA4O00R94VJBZTJaaRekZiuekzl`\ qpRdtGRx6FzEAvL6sT3oZ0ka5neAohFqkKsnPuqUvtZxi`yZhz\ OjzLizJnzGrzErzBpz9kz6kzBnzFkzJnzMpzQszUpzYqzRqzcs\ zcszctzctzcuzcuzcvzevzmxzmxzmyzmyzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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 30-04-13 (Deep Green [8.5])
by Jim Muth 02 May '13

02 May '13

FOTD -- April 30, 2012 (Rating 8.5) Fractal visionaries and enthusiasts: Today's 8.5 rated image lies in the parent fractal that results when 0.2 part of Z^2 is combined with 15 parts of Z^(-1.5). This parent appears as an oversized but skeletal Mandelbrot set with a well-defined much smaller M-set in the area of its East Valley and two minibrots symmetrical to the X-axis in the area of its main spike. Today's scene lies in the intricate debris between these two minibrots. I named the image "Deep Green" because of the vivid green ring surrounding the central minibrot. The rating of 8-1/2 includes a sizable and perhaps too liberal bonus for my coloring. The calculation time of 1-3/4 minutes borders on slowness, making the web sites a good calculation alternative. Find this calculation relief on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and classy variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Hordes of back images are posted at: <http://www.Nahee.com/FOTD/> Lots of clouds hung overhead here at Fractal Central today, and a few flurries of drizzle drifted down now and then, but the sun also broke through several times, and the temperature of 66F 19C was so close to average that it left no grounds for complaint. The fractal cat took it all in stride, satisfying himself when he evicted me from my favorite chair and took it over with a satisfied smirk on his face. The humans meanwhile checked the latest news, seeing nothing new, of course. The next FOTD will be posted when I get a round tuit. Until I can find a tuit shop, take care, and there is a question I want a clear answer to. It is, 'why are we here on earth?' (Answers such as 'to get to heaven' 'to propagate the species' 'it's a lucky accident' or 'it's up to each of us to decide' are rational enough but not really satisfactory.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Deep_Green { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-13.76762576559253/+0.00003824191632297\ /8.95286e+011/1/88.25/0 params=0.2/2/15/-1.5/0/800\ /0/0 float=y maxiter=1600 inside=0 logmap=126 periodicity=6 mathtolerance=0.05/1 colors=000zKzzKzyPzyRszXzzUxz_qz`xzZzzWzsUzxRzsPzq\ OzoMznLzlKzhJzkLqfMueOjePedQKdRfcT3cU09TV8MO6II5DB\ 0850320800A20D00L00V20f30T42Q55I69D66A848924A02A5F\ FFKGJOIORIRVJP_KOcKLfLKjLRiGZhDdf9ke4sd0yc0neIdh`V\ itUdiT_ZRPOUaPVUPY`QZaQ_dQaeRchRdiRdaPdVMdOLdGJdAI\ cIJcPKcVLcaMchOdkOinGlo9pp2tq0np0ip2co5Zo9TnDOnFJh\ EEcE9YD4TDEYEOaFYeGfjIonJZqOIuT2xW6pVAiVEaVIWVMPUQ\ IUUAUY4U`RIdl5xT0qW0l_0fc0af0Wj2Rn2Lq3Gt3LuBQvJUvR\ ZxZcyffynkzvozzxffzPKzTPuWTpZWka_fecchfWcdPZaIU_BQ\ YMZ_Yf`hocqvdkjVeZM_MDUA4O00R94VJBZTJaaRekZiuekzl`\ qpRdtGRx6FzEAvL6sT3oZ0ka5neAohFqkKsnPuqUvtZxi`yZhz\ OjzLizJnzGrzErzBpz9kz6kzBnzFkzJnzMpzQszUpzYqzRqzcs\ zcszctzctzcuzcuzcvzevzmxzmxzmyzmyzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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 01-05-13 (Sasquatch Bigfoots [7.5])
by Jim Muth 02 May '13

02 May '13

FOTD -- May 01, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image reminds me of bigfoot footprints. Bigfoots (not 'bigfeet') are also known as sasquatches, so I named today's image "Sasquatch Bigfoots". These enigmatic creatures cannot possibly exist. If they did, we would long since have found hard evidence of their existence such as their bodies, excrement and dwelling places. But despite the impossibility, many people still claim to have seen bigfoots, and unless one is a hard core devoted CSICOP-type skeptic, it is hard to believe that every one of these people are mistaken or lying. Today's image gives proof that bigfoots are lurking around FC. I mixed 1/10 part of Z^2 with one part of Z^(-1000) and found the proof I was not really searching for. This unlikely combination of parameters produced an oversized parent fractal that appears to be a Mandelbrot set with flat disks filling the smaller buds and floating in the center of the larger buds as well as the main bay. The situation looked rather hopeless at first, but knowing how tricky fractals can be, I checked Seahorse Valley of the large minibrot on the main stem of the parent, where two disks are tangent, and found an interesting area of chaos. This area is where the bigfoots thrive, and it took little additional time to find the evidence. If I had found an actual bigfoot, I might have rated the image at a 10. As it is, with only the mysterious footprints to show, I could give a rating no higher than 7-1/2. Perhaps the best feature of the image is its starship speed of 20 seconds. But be warned, when calculated at faster-than-light warp speed, the image finishes before it is started. So be sure to avoid the time paradox that would result if you failed to start the calculation after the image had appeared on the screen. Or better still, forget such time-travel paradoxes by checking the image on one of the web sites. Be happy in your fractal work by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and check the glories of high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> More FOTD back images than one can shake a stick at are posted at: <http://www.Nahee.com/FOTD/> After viewing the back images, forget about shaking the stick. You'll be too exhausted to lift it. The weather was absolutely perfect here at Fractal Central today. Perfection is described by a cloudless deep blue sky, pleasantly warm sun, gentle breezes, low humidity and a temperature of 75F 24C. The fractal cat took it in stride. FL spent the afternoon puttering in her garden, while I took a pleasant walk to the Susquehanna River, which is 1/2 mile from FC, 1/2 mile wide, and home to a variety of common eastern water fowl. The next FOTD will appear, though not by magic, in the proper universal time. Until whenever, take care, and be aware that, according to relativity, there is no universal time. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Sasquatch_Bigfoots { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-17.88773677769922/+0.0002296224951834\ /9.344237e+007/1/-7.5/0 params=0.1/2/1/-1000/0/\ 800/0/0 float=y maxiter=300 inside=0 logmap=33 periodicity=6 colors=000GFjFGiDIhCKfCMeCOdDQbDSaDW`LZYRcWYhUcmRj\ rPptNvrLtmKneKhYKbPKYHKT9KOBKL8JI6JF6ED78A937A35B8\ IA4RA8SKBTUEUcIVkLWiOXgSYeVZcYYb_YbaYbcYaeYagYaiY`\ kY`mY`oY_qY_sY_uYZwYZyYZzWWvVTsUQpTOmSLjQIgPGdODaN\ AZM8WN7VN7UN7UN6TN6SN6SN5RN5RN5QN4PN4PN4ON3NN3NN3M\ N3MRALVGLZMKaSKeZJidJmjIppImoJjoKgoLdoLboM_nNXnOUn\ ORnPPnQMmRJmRGmSDmTBmTDnVEnXFnZGn`HobIodJofKohLpjM\ plNpnOppMokLngKmbJlZHkUGkQFjMEiHChDBg8Af49z08z09z1\ 9z2Az3Az3Bz4Bz5Cz5Cz6Cz7Dz7Dz8Ez9Ez9FzAFzBFzBSzlUz\ iWzgYzdZzb`z_bzYczWazU_zTZzRXzQVzOUzNSzLRzKUzJWzIY\ zH_zGazFdzEfzDhzDjzClzBozAqz9sz8uz7wz6yz6uz9rzCozF\ kzIhzLezObzRZzTWzWTzZQzaMzdJzgGzjCzjDzlEzmFznGzoHz\ pHzqIzrJzsKztLzuMzvKzwMzwOzwQzw9zyRzwkzwhzueztbzs_\ zrXzqUzpRzoOznLzmIzlFzkCzj9zi6zh4zg5zh5zh6zi6zi7zj\ 7zj8zk8zk9zl9zlAzmAzmBznBzn8zsBznEziHzdKz_NzVOzPQz\ QSzRUzSVzSYzqXzpVznUzmSzl } 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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AOTD 5_1_13
by JackOfTradeZ＠comcast.net 01 May '13

01 May '13

. The "black gold" animation is posted, but it doesn't really look like black gold anymore. It just looks awesome! The compiled video is much larger than usual; I don't know why that is - I was expecting it to be smaller due to the simplicity and redundancy in the colors. The original 1024 AVI is 1 GIG! http://www.fractal-animation.net/vid/tesla.zip 33 MEG download, 1 min 47 sec run time. It is also on my youtube page if you don't wanna download it: http://www.youtube.com/FractAlkemist Comments welcome as always. Cheers! JoTz .

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FOTD 29-04-13 (Five [7])
by Jim Muth 29 Apr '13

29 Apr '13

FOTD -- April 29, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a nice soft, soothing, low-contrast scene showing a quintic minibrot against a greyish-blue background. I named it "Five" because of the Z^5 energies infesting it. (There is also an almost-forgotten movie named "Five".) The parent fractal is a Mandelbrot set caught halfway through the process of morphing into a quintic Mandeloid, at the moment when it is at the peak of shapelessness. Today's scene is located near the X-axis of the parent, at the western extremity of its main body. The circular colors ringing the minibrot came about when I rendered the scene with the inside set to 'fmod'. (Having the background a flat black also works quite well.) The rating of a 7 is getting quite commonplace, but with it's unspectacular effect, that's what I think the image is worth. The calculation time of 5-3/4 minutes is slow. Luckily, the web sites are always there to make life easier. Enjoy life to the max. See the image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> with variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and slews of older images at: <http://www.Nahee.com/FOTD/> Heavy clouds kept a blanket over Fractal Central today. The rain was very light, yet just enough to keep things wet. The fractal cat spent the day watching the local pigeons and asking for food, while the fractal humans caught up on the news. The next FOTD will be posted, that much is sure. The big question is exactly when. Until whenever, take care, and if it takes two to tango, how many does it take to boogaloo? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Five { ; time=0:05:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip float=y center-mag=-1.461801752982463/+0.00126522280599655\ /1817040/1/-75/0 params=5/10/0/0 maxiter=2000 inside=fmod proximity=0.04 logmap=78 periodicity=6 colors=000U_kU_kU_kU_kU_kU_kU_kU_kU_kU_kU_lU_jU_hT\ ZfSYdSWcSTaSQ_SOYSLWSJUSGTSERSBPS9NS6LS4KT6MU8NVAO\ VCPWEQXGRXISYKTZMUZOW_QX`SY`VZaX_bZ`b_ac`bc`cb_d`Z\ `YXYWUUSQRPNOMJKKFHGCDD8AA57B68C69D7AE7BE8CF8DG9EH\ 9FI9GIAHJAIKBILBJLCKMCLNCMODNPDOPEPQEQRFRSFSSFSTER\ TEQTEQTEPTEPUDOUDNUDNUDMUDMVCLVCKVCKVCJVCJWEOXFTXG\ YYHbYIfZJkZKp_Lu_MyYNvWNsUNpSNmRNjPNgNNeLNbJM_ILXG\ KUEJRCIOAIM9IJ7IG5ID3IA1I70I51J81JB1JE1JH1JK1JN1JQ\ 1JT1JW4KU7KT9KRCKQFLOHLNKLLNMKPOISPHVQGXRE_SDbSBdS\ AgS8jT7lT5oT4qU3oU7mUAkUDiUGgUKeUNcUQacz_czZczZczY\ czYczXczXczZcz_cz`czaczFczEczCczBczsczrczrczrczrcz\ rczrmzrmzrmzrmzrmzqmzqmzqmzqmzqmzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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Jim's copper & verdigris green 'Black Gold' color map.
by Hal Lane 29 Apr '13

29 Apr '13

JackOfTradeZ, I like Jim's copper and verdigris-green color map for his 'Black Gold' FOTD for April 21st, 2013, too. I did a few minimal magnification zooms into the parent of Jim's Black Gold image and put them with my large version of his FOTD on my site of FOTD 'variations': http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html You've got a nice-looking image!: http://www.fractal-animation.net/tesla.gif I'm looking forward to your animation... Do you use PAR2BAT for your animations? <---<< - Hal Lane ######################## # hallane(a)earthlink.net ######################## =========== Forwarded email ======================== Author: JackOfTradeZ Date: To: fractint Subject: [Fractint] BlackGoldAOTD The zoom-in to the Black Gold image is looking seriously cool, especially with Maestro Muth's new color map, which after trials, looked way better than the original, or my own "gold" map. I see an intricate pattern of copper nano-wires in a molecular chip, with bursts of bluish electricity as the Log2 zoom progresses. That, along with the formula from electronics (parallel resistance, but don't take it too seriously; such formulas, an inverse of summed inverses, occur quite frequently in physics), suggest I should give this animation a "cool" sounding "electric" name. Alternatively, the images also strikingly resemble native copper minerals, with elemental copper dispersed among the blue-green mineral. I expect the animation will be finished in 2 weeks +/- ; but it is always hard to predict! Until then, fetch a preview here: http://www.fractal-animation.net/tesla.gif =========================================================

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FOTD 28-04-13 (A Round Pentagram [7])
by Jim Muth 28 Apr '13

28 Apr '13

FOTD -- April 28, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's scene shows a quintic minibrot, which unlike most minibrots in the Z^5+C Mandeloid is actually interesting. This is because it is combined with the Z^2+C Mandelbrot set in such a way that the excessively large and numerous minibrots found in the Z^5+C Mandeloid are separated much more widely and the in-between space filled in. The parent fractal is an oversized Mandelbrot set already starting to look a little weird in places. Today's scene is located in the basin of a larger quintic minibrot that lies in a small island of debris inside the bud located just beyond the large bud on the X-axis of the parent. I named the image "A Round Pentagram" after the rounded pentagram immediately surrounding the central minibrot. A pentagram is the familiar 5-pointed star, which is a religious symbol when oriented with a point facing upward, and a symbol of occultism when rotated 36 degrees so that it resembles a goat's head, with a point facing downward. The rating of a 7 is in the ball park of average. If I had put extra effort into the coloring, the image might have rated an 8. The calculation time of a speed-of-light 45 seconds will pass in a flash. The flashing, which might be confused with bomb testing, thereby causing a sudden unwelcome arrival of security forces, may be avoided by checking one of the web sites. The finished image is posted online on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High-quality renderings are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images are at: <http://www.Nahee.com/FOTD/> A near perfect day prevailed here at Fractal Central today, with lots of sun, gentle breezes and a temperature of 70F 21C. Clouds arrived later in the afternoon, but by then all the outdoor activities were nearly finished. The fractal cat seems to be resigned that no more sun will be falling on his window shelf until autumn, and has claimed my favorite chair as his bed. The humans are resigned that autumn will eventually come, followed by winter. The next FOTD will be posted in the divinely ordained time. Until whenever that is, take care, and believe it or not, some people actually are puzzled by the way I feel at peace when I am out alone without a cell phone. The truth is that it is quite easy to be at peace when out of contact with others. After getting hooked on computers, I simply refused to become addicted to any additional absolutely necessary conveniences of modern technological life, without which survival would be in doubt. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Round_Pentagram { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip periodicity=6 center-mag=-8.120884801079228/+0.01070920339951809\ /3.235e+011/1/9.5/0 params=5/6 float=y maxiter=1500 inside=0 logmap=96 mathtolerance=0.05/1 colors=0000Si0Rf0Qd0Pa0O_0MX0KV0IS0GQ0EN0CL0AI08G0\ 6D44A53B66B78B8AB9CCAECAFCBHCCJCDLDENDFPDFPDGQEHRE\ ISEJTEKUELVFMVFOWFQXFSYGUZGZaGcdGhgGmjHrmHmrHhmHch\ FZeGUhHPmIDrGEvIFwKFrLGmNHhPHcQIZSJWUJVVKUXLSZLR_H\ KXIKZINVJMXFLZFJ_GIaHHcHFdIEfJDhG5nJCiQJeSQfUXg_Z_\ YYa`_cZ`eXagV`zT`zR_zP_zNZzJYzLZzM_zN`zO`zPazQbzRc\ zSczTdzUezVezWfzXgzYhzZhz_iz`jzajzbkzclzdmzemzfnzg\ ozhozaizWczPYzJSzCMz6Gz7Hz8Hz9IzAIzBIzBJzCJzDJzEKz\ FKzFLzGLzHLzIMzJMzJMzKNzLNzMOzNOzOOzOPzPPzQPzRQzSQ\ zSRzTRzURzVSzWSzXTzWSzVSzUSzTSzSSzRSzQSzPSzOSzNSzM\ SzLSzKSzJSzISzHSzUSzUSzUSzUSzUSzUSzUSzUSzUSzUTzUTz\ cTzcUzcUzcUzcVzcVzcVzcWzcWzmWzmXzmXzmXzmYzmYzmYzmZ\ zzZzzZzz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz\ _zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zz_zzbz\ z`zz_zzZzzZzzZzzZzzZzzZzzZzzZzzZzzZzzZzzZzzdlzblza\ lz`kzZkzYjzXjzVjzUizTizTl } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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BlackGoldAOTD
by JackOfTradeZ＠comcast.net 28 Apr '13

28 Apr '13

. The zoom-in to the Black Gold image is looking seriously cool, especially with Maestro Muth's new color map, which after trials, looked way better than the original, or my own "gold" map. I see an intricate pattern of copper nano-wires in a molecular chip, with bursts of bluish electricity as the Log2 zoom progresses. That, along with the formula from electronics (parallel resistance, but don't take it too seriously; such formulas, an inverse of summed inverses, occur quite frequently in physics), suggest I should give this animation a "cool" sounding "electric" name. Alternatively, the images also strikingly resemble native copper minerals, with elemental copper dispersed among the blue-green mineral. I expect the animation will be finished in 2 weeks +/- ; but it is always hard to predict! Until then, fetch a preview here: http://www.fractal-animation.net/tesla.gif .

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FOTD 26-04-13 (Fairies on the Lawn [6.5])
by Jim Muth 26 Apr '13

26 Apr '13

FOTD -- April 26, 2013 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is named "Fairies on the Lawn". I have heard it said that even though we never see fairies dancing on the lawn, it is no sign they are not there. Well, in today's image the fairies are dancing on the screen and they are quite visible. True, they do not resemble tiny people, and why should they? They are 'arupa' fairies, basically bright little bundles of energy with no definite shape. I came upon the fairies as I was exploring the fractal that results when 0.1 part of Z^2 is combined with 2 parts of Z^(-3) and the whole thing is iterated with the bailout radius set to 900. This fractal is an oversized, well-decorated Mandelbrot set overflowing with extra goodies such as islands inside the main bay and superfluous minibrots everywhere. Today's scene lies just off the main stem near the spot where the large minibrot should be. The rating of 6.5 includes the half-point bonus for my coloring efforts. I'm not sure that the bonus was fully earned, but it gives me a feeling of satisfaction to pat myself on the back occasionally. The calculation time of a fireball-fast 30 seconds will pass in about 8 breaths. Checking the finished image on the FOTD web sites will save your breath. The fairies dance online in finished form at: <http://www.crosscanpuzzles.com/Archives.html> where the image has been calculated and is posted. The high-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> With photoshop blue skies, a few puffy white clouds, gentle breezes and a temperature of 61F 16C, today's weather was near perfect here at Fractal Central, and the fractal cat made the most of it. The fractal humans made the most of it also, while we were busy on more important things however. The next FOTD will be posted in the near future. Until the future arrives, take care, and most everyone, even the wealthiest, has occasional feelings that despite modern technology something is missing in his or her life. But it's not so simple to pin down exactly what is missing or where it might be found. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fairies_on_theLawn { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-18.910519601936/+0.0644882255628/\ 3.41531e+007/1/-72.5/0 params=0.1/2/2/-3/0/800/0/0 maxiter=800 inside=0 logmap=50 periodicity=6 colors=000KGqJFpIEoHDnGCmFBlEAjD9gC8cB7ZA6U95P84K7\ 3F62A000uzxtmuscrgUrXKrM7r20nj0GqULzz0whPwVOwHNw3M\ v8QvDTuHWuMZuRbtVet_htckjdg`ddRe`IeYJgVJiSJkPJlNJn\ KJzHUzEczCmzJmcQVTXZKcZYLZj3`lFanRbpbcqmanl_lkYikW\ gjUdiSbiW`k__mbZofXqiWsmVupUvgao_hhRpaJwVNpZRibVbf\ ZWibPmfIqjBthASf90p4Bk9DjEEjJFiOHhTIhXJKzNGrPDjR9b\ T6VV3OW9QZFR`LTcQUeSWdUXcVYbX_aY``_b_acZbeYdUXfUWg\ UViUUjUTlUSnURoUQqUPrUOtUNvUMwULyUKrUTtfRucPvcOxcM\ ycKxcHycIycIycIycIycIycIycIycIzcJzcJzcJzmJzmJzmJzm\ JzmJwmwxmrxmmxmiymdym`ymWzmSBmq7muzmqMmnTmk`mggmdn\ maumZqmUnmPjmKgmFcmA`m5Ym0xclpcahcR`cGTc5dc4gcJicX\ kOkmSygWwbZvYatTdsNhqIkpDnn8qmicbjc`jcZkcXkcWlcUlc\ SlcRjcLi`Fgf9fk3ej2ej1fk2gl3hl4im4jn5kn6lo7lp7mp8n\ q9orAprAqsBrtCxuKstDsuDtvEuvFvwGwxGxxHyyIzzJZzv`zt\ azsbzqczpdznezmfzkgzjhzhizgjzekzdlzbmzanz_ozZpzXqz\ WrzUszTtzRuzQvzOwzNxzLcze } 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 25-04-13 (Butterfly Cookies [7])
by Jim Muth 25 Apr '13

25 Apr '13

FOTD -- April 25, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Butterfly Cookies". The obvious reason is that it reminds me of butterfly cookies. In fact, it reminds me so much of the cookies that, when I saw the image, I ran to the local store to pick up a box. The recipe behind the cookies combines a measly 0.1 part of Z^2 with a full part of Z^(-3) then adds C on each iteration. The resulting parent fractal is an oversized thing closely resem- bling some of those created by the parallel-resistance formula posted on the list a week or so ago. Its Mandelbrot shape is apparent, but the normally empty inside parts are filled with all kinds of superfluous decorations. Today's scene lies on the X-axis just beyond a large minibrot on the skeletal negative spike. The rating of a 7 is an improvement over yesterday's, but still leaves lots of room for improvement. Hopefully, tomorrow's image will rate an 8, but there is no guarantee that it will not check in at a rating of an embarrassing 6. One thing not in dispute is the speed of today's image. On my far from SOTA machine it finishes in 20 seconds. Some of the current units will finish it in far less time, that is if they can run the old Fractint DOS program at all. Regardless, the image is available on the FOTD web sites. The official FOTD web site with the finished image may be found at: <http://www.crosscanpuzzles.com/Archives.html> Augmented variations of the image are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the FOTD back images are at: <http://www.Nahee.com/FOTD/> The weather was near perfect here at Fractal Central today, with photoshop (old-kodachrome) blue skies and white cotton-puff cumu- lus clouds. The only thing not perfect was the temperature, which at a high of 57F 14C was notably chilly for late April. The fractal cat would have preferred more sun on his shelf. But now that the sun is at a much higher angle it strikes only the edge of the shelf closest to the window. The humans, not very concerned with sun angles, had an average day. The next FOTD will be posted in a number of hours. Until that mysterious number of hours passes, take care, and thanks to science we have life better today than at any time in the past. Why then are so many people dis-satisfied with their lives? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Butterfly_Cookies { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-14.05247665674564/0/1.18392e+009 params=0.1/2/1/-3/0/800/0/0 float=y maxiter=750 inside=0 logmap=88 symmetry=xaxis periodicity=6 colors=000000012034556A78FAAKDCPGEUJGZMIcRKhXNmcPr\ jRe_WSQ`EGe06i9KjIXkRikLmrPpzUtzZwzczzhzzmzzrzzzzz\ K6KHAUEEcBIoHNiNRcTVYZZS_bO_eL_iH`lE`pAcs7ms7ms7ms\ 7zs7zszzszzozflLfiSffZfcef`khcSie9iaIjYQjUZkQgkMom\ YinhcosZgta`udUugOdiQfjThkVjlgqTsx9nlFjaKfQQbFV_JW\ XNXURXRVYOZZMaZL`zL_zLZzLZzPbzTfzXjz`nhdrphuxevobw\ g_x_XySVzKchclRwpIjs9Zv1No5Oi8PcBQYERRHSLKTFNU9QU9\ Ob9MkmKsmA1mD8mFEzILzKRzNYzPcQghjylountqoympunmrok\ npikqfgrddsbas`YwWKri6nv5mn4mf3m_2mS1mL0mD0m61iC2f\ I2bO3_U4W_4Te8W_BYVF_QIaLLdFPfASh5Vj0Si8QhFOgMMfTN\ bROZQPWPZXGbWEfWCiWAmW8qW6tW4pY8m_CiaGfcKbeO_gSWiW\ TjZWkYZkXakXdlWglVilVzdTzXRzPQzHOz9NzOdzauzZozXjgV\ ddT_aZ`ZcaWhbTmcQrdUs_XsV`tRctMgtHjuDnu8qu4rrCspJt\ zQqzPnzOkzNizMdzR_zWVz`QzdLziGznBzs7zwDzmJzdPzWVzM\ `zDfz4ez9dzDczIbzMazRazV`zX_zZZz`YzbXzdMzfBzh1ziBz\ ZKzOTzDWzHZzKazOdzRgzU`zT } 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 24-04-13 (A Spiked Fractal [6])
by Jim Muth 25 Apr '13

25 Apr '13

FOTD -- April 24, 2013 (Rating 6) Fractal visionaries and enthusiasts: Today's minor fractal diversion is a scene on the X-axis of the fractal that results when 0.1 part of Z^(-4) is combined with Z^2, and straight Z is added on each iteration. The resulting parent fractal is an oversized but skeletal Mandelbrot set, with today's scene located in a blank area on the phantom X-axis. With too little time to really work up a good coloring, (that is if any colors could have helped the image), I could rate the scene no higher than a 6. The name "A Spiked Fractal" refers to the sharply pointed dark areas surrounding the rather large minibrot. Without doubt, the best feature of the image is its unbelievably fast calculation time of under 5 seconds. But of course, this does not include the time required to set up and run the parameter file. The web sites will eliminate the need to run the parameter file however. The completely calculated image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> with high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back imaged may be accessed at: <http://www.Nahee.com/FOTD/> Sunny weather and a temperature of 72F 22C made today near ideal here at Fractal Central. Clouds and a rain shower moved in at 6:00pm, but by then the fine day was in the bag. The fractal cat and the fractal humans both enjoyed the fine weather while it lasted. The next FOTD will be posted before too long. Until whenever that happens, take care, and I hear that some teen-aged girls around town are swooning over the surviving Boston bomber, and even planning to have his picture tattooed on their bodies. I guess they think he's cute or something, but to me it seems strange to be honoring a 19-year-old man who is almost certainly a mass murdering terrorist. At the same time, it is also a relief for any worried men, since it appears that such frivolous women will be totally unable to replace men in any significant numbers in the prestigious but formidable high-paying fields of science and technology. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Spiked_Fractal { ; time=0:00:05.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-3.254107804724713/0/5524.303 params=0.5/2/0.1/-4/0/0/0/0 float=y maxiter=265 inside=0 logmap=7 symmetry=xaxis periodicity=6 colors=000SQmUSmWUmYWm`Ymc`mfcmifm005K00000BJFIUHP\ cJWmL_kIczGfzDjhBmz9i_FeTKaMQYcVUc_QUWNUSJUOGcKCcG\ 9cDDkaJmZPoWVcU`cRfcPhcRjcSkcTmcVnmWpmXqmYkmXemW`m\ WHmlAmf3m`7mWBmRAmV8mZ6mb5mf3mj2mn9mlGmjNmiTmg_mef\ mdmmbsmanmcjmefmfjmJjmJjlJjlJjlIjlIjlIjlIjlIklIklI\ klIklIklHklHkkHkkHkkHkkHkkHkkHkkGkkGlkGlkGlkGlkGlk\ GlkGljFljFljFljFljFljFljFljFljFmjEmjEmjEmjEmzEmzEm\ zEmzEmzDmzDmzDmzDmzDmzDmzDnzDnzDnzCnzCnzCnmCnmCnmC\ nmCnmCnmBnmBnmBnmBomBomBomBomBomAomAomAozAozAozAoz\ AozAozAoz9oz9pz9pz9pz9pz9pz9pz9pz8pz8pz8pz8pz8pz8p\ z8pz8pz8nz9lzAkzAizBizAhzBhzBhzBhzChzChzCgzDgzDgzD\ gzEgzEgzEfzFfzFfzFfzFfzGfzGfzGezHezHezHezIezIezIdz\ JdzJdzJdzKdzKdzKdzKczLczLczLczMczMczMbzNbzNbzNbzOb\ zObzOazPazPazPazPazQazQazQ`zR`zR`zR`zS`zS`zS_zT_zT\ _zT_zU_zU_zU_zUZzVZzVZzVZzWZzWZzWYzXYzXYzXYzYYzYYz\ YZzZYzYYzYYzYYzYYzYYzYYzY } 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 23-04-13 (A Long Journey [5])
by Jim Muth 24 Apr '13

24 Apr '13

FOTD -- April 23, 2013 (Rating 5) Fractal visionaries and enthusiasts: Today's quick fractal diversion shows a minibrot in the East Valley area of what is left of the large minibrot on the skeletal main stem of the fractal that results when 3 parts of Z^(-2) are combined with 0.333 parts of Z^2 and straight C is added on each iteration. The rating of a meager 5 shows that the image is little more than a filler to help bring the lagging FOTD up to date. The name "A Long Journey" came to mind when I had the impression of a wheel with 16 spokes surrounding the minibrot, with a shoe attached to each spoke. There is little else to be said about the image except that it is fireball fast even on non-SOTA units. And the web sites are always ready to simplify things by eliminating the need to run the parameter file. The official web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The augmented versions of the image are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the thousands of FOTD back images are at: <http://www.Nahee.com/FOTD/> The morning was dreary here at Fractal Central today, with low clouds and a temperature of 43F +6C. But at noon the clouds evaporated, leading to a sunny afternoon with a temperature of 61F 16C. The fractal cat tried to enjoy the sun on his shelf, but the sun angle is so high in spring and summer that it mostly misses the shelf. The humans spent the day at work with no play. The next FOTD will be posted before long. In all likelihood, it will have a higher rating than today's. Until whenever, take care, and why don't we all try to stop fighting about religion? We could begin by agreeing that the deep truths of all religions are the same even as the surface details differ widely. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Long_Journey { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-7.041083174077353/+0.03648089706941075\ /1.598147e+009/1/32.5/0 params=0.333/2/3/-2/0/0/0/0 maxiter=750 inside=0 logmap=44 periodicity=6 colors=000F00K25P4AU6FZ8KcAPhCUmEcrGlvIuoJkhKb_KSU\ FIOAAH50000UzzUmzAczDZmGUcAUU0QK0UAAXCA`EAcGAgJAjL\ KnNmuRGzQmzPOoORmNVkMZiLZlFagLdcQjdKg_VeWdbRo`NyXT\ iUYVRbGUcPWcXYceXorZio_cmaYjbShcMfeGcfAag4_dCYaKXZ\ RWWZVTeUQmTcsJWtOOtSGuX8u`1ud9`QGGBFGBDGBCGBBGBBGC\ BGDBGFBGGBFGBDGBCG000000000000000000000000SkYSkYRk\ YQlYPlYPlYOmYNmXMmXLnXLnXKnXJoXIoXHpWIoXJoXKoXLoXM\ oXNoXOoXPoXQoXRoXSoXToXUoXVoXWnYXnYYnYZnY_nY`nYanY\ bnYcnYdnYenYfnYgnYhnYimXilXilXikXikXijXjiXjiXjhXjh\ XjgXjgXkfXkeXkeXkdXkdXkcXkcXlbXlaXlaXl`Xl`Xl_XmZXm\ ZXmYXmYXmXXmXXmWXnVXnVXnUXnUXnTXnTXoSXoRXoRXoQXoQX\ oPXoPXkNShLOdKKaIFYHBVF7QD2RE3SE3SE3TF4UF4VF4WF4XG\ 5YG5ZG5_G6`H6aH6cH6eH7gI7iI7kI8mI8mJ8mJ8mJ9mJ9mK9m\ K9mKAmKAmLAmLBmLBmLBmMBmMCmMCzMCzNDzNDzNDzNDzOEzOE\ zOEzNFzOEzOEzPEzPEzPEzQEzQEzQDzRDzRDzRDzSDzSDzSDzT\ CzTCzTCzUCzUCzUCzVCzVBzWB } 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 21-04-13 (Black-Gold Minibrot [No Rating])
by Jim Muth 23 Apr '13

23 Apr '13

FOTD -- April 21, 2013 (No Rating) Fractal visionaries and enthusiasts: On April 17 Mike Frazier posted an interesting image named "Black Gold". Today's FOTD is named "Black Gold Minibrot". The name indicates that I checked the center of Mike's image and not surprisingly found a minibrot. That minibrot appears at the center of today's FOTD image. I tweaked the colors to add a little variety, but made no changes to the parallel resistance formula itself. Since the image is a borrowed one I could give it no rating, but it's still a rather spectacular one to look at. The calculation time of one brief minute will cause no pain even for those with the busiest schedules. And the web sites are always ready to shorten even that brief minute. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Nothing but sun fell on Fractal Central today, though the temperature of only 50F 10C was hardly spring-like. The fractal cat passed most of the day on his window shelf, watching for passing stray cats. When he finally saw one, his growl of defiance could be heard throughout the room. FL spent several hours working in her garden. As for myself, I simply spent the day. The next FOTD will be posted within a reasonable time. Until a reasonable time passes, take care, embrace the good and eschew the evil. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BlackGold_Minibrot { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=F_20130417_1555 passes=1 center-mag=-10.19977132535179/0/1907.836 params=0/4.5 float=y maxiter=2750 inside=0 logmap=48 symmetry=xaxis periodicity=6 colors=000wzXmvUcrRUmPKhRAcT0ZV2UQ4PM6KH7FD9A8B84C\ 10C10O40ZA0hIAoSKubUyjczomyjcubUoSKhIAZA0O40C10K00\ C10O40ZA0hI0oS0ua0yh0zzmyh0ua0oS0hI0ZA0O40C10U00C1\ 0O40ZA0hI0oS0ua0yh0zocyh0ua0oS0hI0ZA0O40C10c00C10O\ 40ZA0hI0oS0ua0yh0zoUyh0ua0oS0hI0ZA0O40C10m00C10O40\ ZA0hI0oS0ua0yh0zoKyh0ua0oS0hI0ZA0O40C10z00C10O40ZA\ 0hI0oS0ua0yh0zoAyh0ua0oS0hI0ZA0O40C10z00C10O4zZA0h\ I0oS0ua0yh0zo0yh0ua0oS0hI0ZA0O40z10z00z10O4zZAzhI0\ oS0ua0yh0zo0yh0ua0oS0hI0ZA0O40z10z00z10O4zZAzhIzoS\ 0ua0yh0zo0yh0ua0oS0hI0ZAzO4zz10z00z10O4zZAzhIzoSzu\ a0yh0zo0yh0ua0oS0hI0ZAzO4zz10z00z10O4zZAzhIzoSzuaz\ yh0zo0yh0ua0oS0hIzZAzO4zz10z00z10O4zZAzhIzoSzuazyh\ 0zo0yh0ua0oSzhIzZAzO4zz10z00z10O4zZAzhIzoSzuazyhzz\ ozyhzuazoSzhIzZAzO4zz10z00z10O4zZAzhIzoSzuazyhzzoz\ yhzuazoSzhIzZAzO4zz10z00z10O4zZAzhIzoSzuazyhzzozyh\ zuazoSzhIzZAzO4zz10z00zb_ } frm:F_20130417_1555 { ; Similar to the parallel resistance formula z=0,c1=pixel-p1,c2=pixel+p1,c3=pixel: f1=z*z+c1, f2=z*z+c2, f3=z*z+c3, z=1/(1/f1+1/f2+1/f3), |z|<100 } END PARAMETER FILE=========================================

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FOTD 19-04-13 (A Forest on Alpha-X [8])
by Jim Muth 19 Apr '13

19 Apr '13

FOTD -- April 19, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "A Forest on Alpha-X", but to actually see the forest with its strangely tinted sky beyond, it is necessary to step back from the screen. The impression of a forest of trees lies in the overall shading, not the finer details, which are more Mandelbrot than tree-like. Apparently, on planet Alpha-X, the air is also filled with flying insects, especially during the times of twilight, which is the time of day illustrated in the image. The clouds of bugs are scattered all over the background. The image was created by the MandNewt08 formula, which I wrote quite a few years ago. This formula is part of a series that was intended to do something that I have long since forgotten. The only thing I am sure of is that the series creates images that share both Mandelbrot and Newton characteristics. The rating of an 8 seems about right for the image, with a full point of the rating due to the coloring, which took about 45 minutes to get almost but not quite right. The calculation time of 2-3/4 minutes is close to FOTD average. The fastest way to enjoy the dusky forest scene is to view it in finished form on one of the FOTD web sites. To see the dusky scene without calculating it, surf over to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and check the interesting variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> The cloudy breezy weather today was offset by a temperature of 73F 23C. Light rain showers began in the afternoon, but by post time had not amounted to much. The fractal cat passed most of the afternoon sleeping in my favorite chair and the rest of the time asking for food. The humans spent most of their time watching the TV news. The next FOTD will be posted in a day of two. Until whenever it actually appears, take care, and now it looks like we'll need tighter controls on home-made bombs. And we'll also need to keep more careful watch on those outgoing people with a lot of friends, who never do anything suspicious. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Forest_on_AlphaX { ; time=0:02:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt08 passes=1 float=y center-mag=0.651181/-1.47796/6.963012/1/-62.5/0 params=0.941/-0.627/-0.909/-0.706/0.416/-0.527 maxiter=768 inside=bof60 logmap=yes periodicity=0 colors=0006Ac6Ac6Ac6Ac6Ac6Ac6Ac6Ac6Ac6Ac6Ac6Ac6Ac7\ Ac7Ac7Ac7Ac7Ac7Ac7Ac7Ac7Ac7Bc7Cc7Dc7Ec7Fc7Gc7Hc8Ib\ 8Jb8Jb8Ja8J`8J_8J_8JZ8JY8JY8JX8JW8JW8JV8JU8JT8JT9I\ S9IR9IR9HQ9GP9FP9EO9DN9CN9BM9AL99K98K97J96I95H95H0\ 0A00A00A00A00A00A00A00A00A00A00A00A00A00A00A00ABD8\ BE9CFADGBEGCFGDFGEGFFHFHIFIIFJIFKHELGEMFENEEPDDQCD\ RBDSADTADUADVADXACYACZAC_AC`ACaABbABcABcABcABdACeA\ DfABgA9hA7iA5jA0kA2lA4mA6nA7oA9pAAqABrACsAFtAGuAIv\ CFwCLwBMwBFwBQwARwAQw9Ow9Xw9Uw8Ww8Yw7_w7aw7bw6cw6b\ w6gw7dw8kw8hw9iwAiwAnwBmwCmwCnwDnwEowEowFowFpwGpwH\ pwHqwIqwJqwKrwMrwOswQswSswUtwWtwYtw_uwauwcuweuwguw\ iuwkuwmuwouwquwsuwuuwwuwzzwzzwzzwqtwotwmswkswjrwhr\ wfqwdqwcpwapw_owYowXnwVnwTmwRmwQlwOlwMkwKkwJjwHjwG\ jwHiwIiwJiwKhwLhwMhvNhvOhuPhuQhtRhtShsThsUhrVhrWhq\ XhqYhpZhp_ho`hoahobhnchnbgnegnffngenienkdnmcnocnqb\ msbmuamw`mz`mz_mzZmzZmzYm } frm:MandNewt08 {; Jim Muth z=c=(pixel*p1): a=z^p2+(c-1)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END PARAMETER FILE=========================================

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BlackGold
by JackOfTradeZ＠comcast.net 19 Apr '13

19 Apr '13

. I recall the parallel resistance formula from my 4th grade advanced electronics class; something like if you have a number of resistors in parallel the total resistance is less than the least, like taking the inverse of all the inverses: Rt = 1 / (1/R1 + 1/R2 ...... + 1/Rx) or something like that. But what does it have to do with the fractal formula? I don't see it, except the last line has a similar format. Anyway, cool image. And if you zoom back a little you see the parent fractal - one of the freakyest Mandelbrot monsters I have ever seen! I will see if I can do a zoom animation of this. Gold is so like, way cool! .

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FOTD 18-04-13 (Superluminal [7])
by Jim Muth 18 Apr '13

18 Apr '13

FOTD -- April 18, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows a minibrot in the Z^(1.04)+C Mandeloid. Despite the impossibility of moving through space faster than light, the minibrot appears to be doing just that. I appropriately named it "Superluminal". The parent fractal is shaped much like the minibrot in today's image, though the parent is zooming toward the east. Today's scene is located in a narrow band of chaos on the southern shore line of the parent, near its rounded tip. The rating of a 7 is close to average. The rather muddy colors prevent me from giving the image a higher rating. The calculation time of 8 minutes is slow. I admit it. But the web sites are up and running, and will eliminate the need of booting the 30-year-old DOS-OS just to run the parameter file. Enjoy the convenience of viewing the image without the chore of calculating it by viewing the completed image online at: <http://www.crosscanpuzzles.com/Archives.html> and don't forget the interesting variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> or the thousands of back FOTD images at: <http://www.Nahee.com/FOTD/> A heavy bank of clouds hung over Fractal Central all day, while the temperature reached a relatively pleasant 61F 16C. The fractal cat didn't complain about the lack of sun, but he did grumble about being served the wrong flavor of food at his midday meal. (He wanted turkey; he got beef.) The humans passed the day working and wondering about the current spate of disasters. The next FOTD will most likely be posted in 24 hours. If it is not, then it will be posted in 48 hours. Until whenever, take care, and we can avoid future fertilizer plant disasters by moving fertilizer plants far away from residential areas. (The only good thing in all the recent bad news is the disappearance of the Jodi murder trial from the news media. Apparently God has had mercy on us.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Superluminal { ; time=0:08:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-1.030010403518456/-1.732735590658575/\ 2.622e+007/1/122.5/0 params=1.04/0/525/2400 float=y maxiter=10000 inside=0 logmap=800 periodicity=6 colors=000OSeOSdPSdPSdQSdQScRScRScSSbSSbTSbTSaUSaU\ SaVSaVR`VR`WR`WR_XR_XR_YRZYRZZRZZRZ_RY_RY`RY`RXaRX\ aRXaQWbQWbQWcQWcQVdQVUVVUVUUVUUVUUVTUVTUVTUUT`SN`S\ N_SN_SN_SNZSNZSNYSNYSNXSOXSOXSOWSOWSOVSOVSOVSOUSOU\ SOTSOTPITOISOISNIRMJRMJQLJQKJQKJPJJPIKOIKOHKNGKNGK\ MFKMELLELLDLKCLKCLKBLJAMJAMI9MI8MH8MH7MG6NG6NF5NF4\ NE4NE3ND2OI6EI6DH6CH6CG6BF6AF6AE69E69D68D67C67B66B\ 65A65A649639638627518628628728728228828929129A29A2\ 952952962942A62JCKKFHKDDLBAE97G73I73821B4KC5KD7KE8\ UF9UHEUIHcJIcKPcLQmMUmOUmPUm3cz3Xz3cz3Uz3cz3Uz2cz2\ Uz2cz2Uz2_zUPzUKzUKzUPzULzUSzUPzUYzUPzUZzUPzUZzUPz\ UZzUPzUZzcVkcbjmeimhhmkgmnfmlemjemhemfemdemcemcemc\ emcemcemczmczmczmczmczmczmczmczmczmmzmmzmmzmmzmmzm\ mzmmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 17-04-13 (Rainbow Rider [!!!])
by Jim Muth 18 Apr '13

18 Apr '13

FOTD -- April 17, 2013 (Rating !!!) Fractal visionaries and enthusiasts: Today's image rates three 'bangs'. Last evening I actually found a passable fractal image in the parent mandeloid that results when the expression Z^(1.001)+C is iterated 37.21 levels up the hyperladder. That fractal appears as today's FOTD. The parent fractal is a squashed and distorted oval with mostly smooth edges on the southeast half and sawtooth edges on the northwest half. A most unexpected valley lies on the southern shore of the oval, while some slight irregularities appear on the southeast shore line. Today's image lies in these southeast irregularities. I named the image "Rainbow Rider", since the open area appears to have a head somewhat like a horse's, while the rest of the open space is drawn out into a rainbow-like arc. The smoothly- blended rainbow colors supplied the final inspiration. The open area in the image is not actually a minibrot, since it fills in if the maxiter is increased, but it is certainly more than I expected to find way down here in the bottom lands. The down side of the image is its calculation time, which at a half-hour is beyond all resemblance of reason. Luckily the web sites are online to save time and tempers. Check the completed image at: <http://www.crosscanpuzzles.com/Archives.html> Enjoy the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Look back at the past images at: <http://www.Nahee.com/FOTD/> Today was as close to perfect here at Fractal Central as it is possible to come. The blue sky, brilliant sun and temperature of 66F 19C could hardly have been improved upon. The fractal cat enjoyed the sun on his shelf, but the sun is now getting so high in the sky that it misses half the shelf. The humans meanwhile attended to everyday things. The next FOTD will be posted soon. Until whenever that might be, take care, and it appears someone is spreading ricin through the mail. I guess we'll have to ban either the mail or the castor bean plants. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Rainbow_Rider { ; time=0:30:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-3.15118/-3.4669/34.75141/1/-17.5/0 params=1.001/0/37.21/9900 float=y maxiter=4500 inside=0 logmap=-3110 periodicity=6 colors=000GcHFcJFcNEcKDcIDcGCcECcBBc9Bc7Ac5Ac1Ad3A\ d4Ad5Ad6Ad7Ad8Ad9AeAAeBAeCAeDAeFAeGAeHAfIAfJAfKAfL\ AfMAfNAfOAfPBfQCfRDfSEfTFfUGfVGfWHfXIfYJfZKf_Lf`Lf\ `MfaNfbOfcPfdQfeQffRfgSfhTfiUfjVfkWflWflXfmYfnZfo_\ fp`fq`frafsbftcfudfvefwdeyefwfguggthhrihpjiojimkjk\ lkjmkhnlfolepmcrnaqmbpmbolcnlcmkclkdkjdjjeiiehiegh\ ffhfeggdggcfgbfhaeh`ei_diZdiYcjXcjWbkVbkUakTalS`lR\ `mQ_mP_mOZnNZnMYoLYoKXoJXpIWpHWqGVqFVqEUrDUrCTsBTs\ 9StATsATsAUsBUsBUsBVsBVsCVsCWsCWsCXrDXrDXrDYrDYrEY\ rEZrEZrFZrF_rF_qF`qG`qG`qGbqGcqHdqHfqHgqLUnJXpH_qF\ brDesBht9ju7lv5nw6lu7jt7hs8gr8ep9co9anA`mAZlBXjCWi\ CUhDSgDQeEPdENcFLbFKaHJbJJbKIbMIbNIcPHcQHcSGcUGcVG\ dXFdYFd_Ed`EdbEedDeeDegCehCfjCfkBfmBfoAfpAgrAgs9gu\ 9gv9gqBemCdhEbdFa`H`WIZSKYNLWJNVFOUGQSHSRHTQIVPJWO\ JYNKZMK`LLaKMcIMeHNfGNhFOiEQkDRlCTnBWm5VoAUpFSqKRr\ OUsTZtYcuahw`mx_ryZwzYzxX } 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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Black Gold
by Mike Frazier 18 Apr '13

18 Apr '13

This fractal looks a bit like gold filigree. The formula is a variation of the parallel resistor formula with three z^2 components. The components are centered at -4.5, 0, and +4.5 along the imaginary y axis. Here is a link to an image: http://dl.dropboxusercontent.com/u/33642054/image/black_gold_1200_5.jpg The Fractint compatible PAR file for the image is: Black_Gold { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20130417_1555 passes=1 float=y center-mag=-10.19972708650225/0/121.2121227272727/\ 1/0/0 params=0/4.5/0/0/0/0/0/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O\ 40C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40\ C10000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C1\ 0000C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C100\ 00C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000\ C10O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C1\ 0O40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O\ 40ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40\ ZA0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA\ 0hI0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0h\ I0oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0\ oS0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS\ 0ua0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0u\ a0ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0\ ym0zy0ym0ua0oS0hI0ZA0O40C10000C10O40ZA0hI0oS0ua0ym\ 0zy0ym0ua0oS0hI0ZA0O40C10 } frm:F_20130417_1555 { ; Similar to the parallel resistance formula z=0,c1=pixel-p1,c2=pixel+p1,c3=pixel: f1=z*z+c1, f2=z*z+c2, f3=z*z+c3, z=1/(1/f1+1/f2+1/f3), |z|<100 } -- Mike Frazier www.fracton.org

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FOTD for April 17, 2013
by Brian Prentice 18 Apr '13

18 Apr '13

Here are two more details from Jim's fractal for today: http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_14a.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_14b.png Brian Prentice

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FOTD 16-04-13 (Bottom of the Pile [5])
by Jim Muth 17 Apr '13

17 Apr '13

FOTD -- April 16, 2013 (Rating 5) Fractal visionaries and enthusiasts: In today's image it looks like we have come to the end of the road. The exponent of Z is 1.004, and even searching as much as I could, I found none of the fractal semi-chaos that produces the most interesting designs. What I did fine was today's image, which is quite fractal in nature, remaining the same no matter how deeply into it one dives. So I guess this is the end of the road as we approach an expo- nent of unity, at least with my less-than-light-speed 12-year- old fractal dedicated machine. A super-speed SOTA unit might find that some interesting stuff does lie beyond the edges of today's image, but I'm not going to try to find it. The rating of a 5 is below FOTD average. The name "Bottom of the Pile" indicates the position of the generating expression. The calculation time is inexcusably slow. Over 1/4 hour will pass between the time the <enter> key is struck and the image- finished chirp sounds. I recommend turning to one of the web sites for relief. The finished image may be viewed at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and back images at: <http://www.Nahee.com/FOTD/> Lots of clouds, a little sun and a few showers, with a tempera- ture of 68F 19C made today a pretty average one here at Fractal Central. The fractal cat Nicholas grabbed my chair when I got up from it at lunch time to reach for the remote control, and turned defiant when I tried to return to it. FL was on Nico's side in the chair dispute. The next FOTD will be posted within a reasonable time. Until reason prevails, take care, and it looks like we need tighter controls on those household items and substances that could be used in the creation of explosives. It might be impractical but at least it would make us feel better. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Bottom_of_the_Pile { ; time=0:16:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-1.04288/-9.26179/34.5/1/163.7/0 params=1.004/0/1.54/2400 float=y maxiter=5000 inside=0 logmap=-737 periodicity=6 colors=000I6GH6GG5HF4IE4JD3JC3KBCLAEL94M96N9EO9EP9\ AQ9CR9ER9GS9HT9JU9LV9MW9PX9SX9UY9XZ9__9b`9ea9haEkV\ JoPOrJStDRvEQsEQpEPnEPkEOhFOfFNcFM`FMZFLWFLTGKQGKO\ GJLGIIGIGGHDHHAHG8HG5HF2HF0H52786AAADCDGFHJHKMJOOM\ SROVUQZXSa_VebXidZlgapjcsmewpgzrjnambLpS4nR6lQ8kP9\ iOBhNChSLhWUh_ahcjhgridqjaqj_pkXplVolSomPnnNnnKmoI\ mpFlpClqAkr7kr5js2js0jpChmNflPelQdlRdlTclUckVbkXak\ YakZ`k``ja_jbZjdZjeYjfYkfYleZmeZme_nd_od`ocapcaqbb\ rbbracsadt`dt`eu_ev_fv_fuZeuYdkLLtYctXbsXasW`sV`rV\ _rUZqUYqTXpTWpSWpRVoRUoQTnQSnPRmPQmOQmNPlNOlMNkMMk\ LLolknihngfnedmbbm`_mZYlWWlUUlSRkPPkNNu0vt1ut1tt2s\ t2rs3qs3ps4os4or5nr5mr6lr6kr7jq7iq8iq8hq9gp9fpAepA\ dpBcpBcoBboCaoC`oD_nDZnEYnEXnFXmFWmGVmGUmHTmHSlIRl\ IRlJQlJPkKOkKNkLMkLLwluvktvjsvjruiquiquhpugotgntfm\ tfmtelsdksdjsciscirbhragrafr`fq`eq_dqZcqZbpYbpYapX\ `pW_oWZoVZoVYoUXnTWnTWnSV } 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 15-04-13 (Undersea Garden [!!])
by Jim Muth 16 Apr '13

16 Apr '13

FOTD -- April 15, 2013 (Rating !!) Fractal visionaries and enthusiasts: In today's image we're down to Z^(1.009) yet the interesting images keep coming. I named the scene "Undersea Garden" because something about it reminds me of an undersea scene. The parent is another oversized torpedo-like open area with patches of semi-chaos spotted along the edges. Today's scene is obviously located in one of these chaotic areas. The rating of two 'bangs' indicates my surprise at finding something worthwhile this close to Z^(1) (or straight Z). If I find anything even closer to unity in future FOTD's, I'll increase the number of 'bangs' in the rating. The big drawback is the calculation time of 12 minutes, but relief is available as always on the web sites. Nobody runs DOS programs nowadays, so make life easy by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And be sure to check the hi-def versions and the variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The thousands of back images are online at: <http://www.Nahee.com/FOTD/> A great mid-April day was fully enjoyed by both cat and humans here at Fractal Central today. The temperature of 66F 19C and partly cloudy sky could hardly have been improved. The next FOTD will soon be posted. Maybe we can find something even closer to unity. Until whenever, take care, and a certain woman I know well, who claims to want nothing more than peace on earth, feels that we should withdraw all US military troops from foreign countries. This makes good sense, but this same woman's favorite music is 'classic rock', including protest music from the Vietnam War era, which all too often seems violently angry to me. And when I played 'The Planets' for her, thinking she would enjoy 'Venus, the bringer of peace' she surprised me by naming 'Mars, the bringer of war' as her favorite section. Women are sometimes truly hard to understand. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Undersea_Garden { ; time=0:12:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip center-mag=-0.7609181081167751/+4.589745372939182/\ 649/1/42.5/0 params=1.009/0/1.9/3500 float=y maxiter=7500 inside=255 logmap=334 periodicity=6 colors=000HnkHnkHpkIpnIrnIrnKtnKvnMvnMxpMxpOzpOzpQ\ zpQzpQzrSzrSzrSzrUzrUzrWztWztWztXztXztUzxXztZzp`zn\ bzjdxfftdhn`jjXkfWnbSpXOrUMtQIvKFxHDzDAz87z55z22z2\ 0z00z00z05z0Az0Dz0Iz0Oz0Uz0kz0dz0Xz0Qz7IzFCzO7zX0z\ f0zp0zz0zz0zz0zr0xj0r`0kU0hM4fK4fK4fK4fK4fK4fK4dK4\ dK4dK4dK4dI4dI4bI4bI4bI4bI4bI4bI4`I4`I4`H4`H4`H4`H\ 4ZH4ZH4ZH4ZH4ZH4ZH4WK0XI2ZH4ZH4`F5`D5bD7bC8dC8fAAf\ 8Ah8Ch7Dj5Dj5Fk4Fk4Hn2Ip0Ip0Kr0Kr0Mt0Ot0Ov0Qx0Qx0S\ z0Uz0Uz0Wz0Wz0Xz0Xv0Sn0Mf0IZ0DS0AM05F0280020000000\ 0000000000000000200M70700800C00J50RB0I40K50O80QA0U\ D0WF0XI0`K0bO0fQ0hU0jW0nZ0p`0td0vf0zk0zp0zv0zz0zzz\ zzzzzzzzzzzzzzzzzzzzzzz0zz0zv0zr0nn0jk0fj2bh2Zf4Wd\ 5Sb5O`7OW2MX5MZ7M`AMbCMdFMfHMhKMjMMkQMnSMpWMrXMt`M\ vbMxfMzhMzkMznKzrMzpMznOznOzkOxkQvjQtjQrhSphSkfSjf\ UhdUfdUdbWbbW``XZZXXZXUXZSXZQWZOW`MU`KU`ISbHSbFQbC\ QdAOd8Of7Mf5Kf4Kh2Ih0IYYu } 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 14-04-13 (Not Quite Linear [7.5])
by Jim Muth 15 Apr '13

15 Apr '13

FOTD -- April 14, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a scene in one of the Z^(1.02)+C parent fractals. Since the complex logarithm is multi-valued, there are multiple fractals the expression can create. Most of these fractals are over-sized torpedo-shaped things, though only some have the interesting fractal semi-chaos along their edges. Today's scene lies in a bit of this semi-chaos along the southwest shore line of its parent. This parent fractal is unusual in that it has a small island-arc of debris lying inside its main bay, totally disconnected from the nearest shore. I have not yet checked this island, though at first glance it appears relatively unpromising. The name "Not Quite Linear" describes the generating expression. The rating of 7-1/2 is about average. I did put a little extra effort into the coloring, though it is debatable whether my work made much of an improvement. If you run the parameter file, do not be concerned if nothing appears on the screen for a minute or two. The top inch or so of the image is a flat color. With a calculation time of 12 minutes, the image is a slow one. The web sites can relieve impatience however. The completed image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> A perfectly average mid-April day passed uneventfully here at Fractal Central today, with partly cloudy skies and a temperature of 59F 15C. The fractal cat ignored the weather, exhausting his energy playing under an afghan. The humans had a day as average as the weather. The next FOTD will be posted in one day, maybe two. Until whenever, take care, and when the going gets tough, get going. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Not_Quite_Linear { ; time=0:12:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-21.7682/0.605373/1.223368 params=1.02/0/0/3500 float=y maxiter=3500 inside=255 logmap=80 periodicity=6 colors=000GC8AFMADLAGLAEKAHKAGJAIIAHIAJHAIHAKGAIGA\ LFAKFBMGBMHCNICOICPJDQKDRLDSLETMEUNEVNFWOFXPGYQGZQ\ G_RHaSHbTHeTIfUIiVIkVMmWPnXToXWpY_qYbrZfs_it_mu`pv\ `twawvasu_ptYlsWitUetSbuQ_uOWvMTvLPwJMwHJxFFxDCyB8\ y95z72z6BqBJiGSaL_TQhLVpD_x5cv8buAbtCbsFbrHaqJapLa\ oOanQ`mS`lU`jX`iZ`h`_gc_fe_eg_diZclZbnZapZ`rZ_p`Zn\ aYlbXjcWhdVffUdgUchTaiS_jRYkQWmPUnOSoNQpNPqmNrmLtm\ JumHvmFwmDxmCymGpmJgmMZmL`mLbmLcmLemLfmLhaLiaKkaKm\ bKnbKpbKqbKsbKteQjhVak_TndKqiBsn2mh8hbDccJccOccUcc\ Zcccccacc_ccYccXccVccTccSccQccOccMccLpbvpcvpdwpewq\ fwqhwqiwqjwrkwrlwrmwrnxsoxsqxsrxssxttxtuxtvxtwxuyy\ txxtwxtvxtvxtuwttwtswtswtrwtqvtqvspvsovsnusnusmusl\ uslusktsjtsitsitshtrgsrgsrfsresrmrrmrrmrrmrrmrrmqr\ mqqmqqmqqmpqmpqmpqmpqmpqmoqmoqzoqzoqzorzprzprzqszq\ szrtzrtzstzsuztuztuzuvzuvzvvzvwzwwzwwzxxzxxzyxzzxz\ ywzxvzxuzwtzwtzwszvszvA0F } 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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AOTD 4_14_2013
by JackOfTradeZ＠comcast.net 14 Apr '13

14 Apr '13

. The "pentagon-heptagon" image FOTD 1/26/08. I animated this and uploaded it around Feb 2008, but it wasn't so good; I have long wanted to re-do it and finally have. Much better I think. 1 min 55 sec, 34 meg download. http://www.fractal-animation.net/vid/j2bh.zip comments welcome as always enjoy! JoTz .

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FOTD 12-04-13 (Floating Continents [7])
by Jim Muth 14 Apr '13

14 Apr '13

FOTD -- April 12, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a trip into the world of close-to-linear fractals. The exponent of Z is 1.009, which is not quite linear but close enough to give a good idea of how things might go as the exponent approaches ever closer to unity but never quite reaches it. I gave the image the unlikely name "Floating Continents". The inspiration most likely was a painting by Magritte, which depicts large chunks of landscape floating in a vast empty space. The parent fractal is another of those very low order torpedoes, with today's scene located in a bit of debris at the edge of the nearly featureless main bay. There might possibly be minibrots hidden somewhere in this debris, but so far I have found none. The rating of a 7 is only average; the calculation time is an annoyingly slow 13 minutes, but this annoyance can be avoided by checking the finished image on one of the FOTD web sites. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the hi-def versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Rain with occasional grumbles of thunder hung on most all day here at Fractal Central, while the temperature stopped short at a rather chilly 50F 10C. The fractal cat wanted more sun but satisfied himself with more food instead. The humans wanted less rain. The next FOTD will be posted in a number of hours. The question is the exact value of that number. Until whenever, take care, and why have those 'end of the world' shows become so popular on TV? Could it be that people are disturbed by what they see coming in the not-too-distant future? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= FloatingContinents { ; time=0:13:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-3.893895417262991/-1.242689299920607/\ 1.939e+009/1/-177.7/0 params=1.009/0/2/3500 float=y maxiter=3600 inside=255 logmap=-1238 periodicity=6 mathtolerance=0.05/1 colors=000rzztycsxGrwGqvGtucrtGnsGmrIlqGkpFjqEinDh\ mCglAfk9ej8di7ch6bg5af6`e6_d7Zc7Ya7W`8V_8UZ8TY9SW9\ RV9PUAOTANSAMQBLPBKOBINCHMCGKCFJDEIDDGDBEEABE99E87\ F75F71D64F76H88I9BKBDLCFNDIOEJQFKRHLTINUJOWKPXMRZN\ S_OTaPVbQWdSXeTYgU_hV`jXakYcmZdn_ep`fqadrbcrcard`r\ dZseYsfWsgVshTshStiQtnFznEznDznCzuFzqDznCzkBzhAze9\ zb8z_7zX6zU5zS2zR4zR5zR7zR8zRAzRBzRDzQEzQGzQHzQJzQ\ KzQMzQNzPPzPQzPSzPTzPVzPWzPYzPZzMWzKTzIQzGNrEKsBHt\ 9Eu7Bv58w07z26y36x56w66v86u96uB6tC6sE5rF5qH5pI5pK5\ oL5nN5mO5lQ4kR4kT4jU4iW4hX4gZ4g_4fa3eb3dd3ce3bg3bh\ 3aj3`k3_m2Zm2zm2zm2zm2zm2zm2zm1zm2zm2zm3zm3zm4zm4z\ m5zm5zm6zm6zm7Vm7Vm8Vl8Vl9Vk9VjAViAzhBzhBzgCzfCzeD\ zdDzdEzcEzbFzaFzaGz`Gz_HzZHzYIzYIzXJzWJzVKzUKzULzT\ LzSMzRMzQNzQNzPOzOOzNPzMPzMQzLQzKRzJRzISzJRzJRzKRz\ KRzKRzLRzLRzMRzMRzMRzNRzNQzOQzOQzOQzPQzPQzQQzQQzQQ\ zRQzRQzSPzSPzSPzTPzTPzUPz } 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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Jim's FOTD for April 12th 2013
by Brian Prentice 13 Apr '13

13 Apr '13

No minibrots but some beautiful shapes! http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_13a.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_13b.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_13c.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_13d.png Brian Prentice

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Three More Torpedoes
by Brian Prentice 12 Apr '13

12 Apr '13

Here are three more pictures generated with Jim's formula published in his FOTD for April 10 2013: http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_12a.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_12b.png http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_12c.png Brian Prentice

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FOTD 10-04-13 (The Mighty Midget [8.5])
by Jim Muth 11 Apr '13

11 Apr '13

FOTD -- April 10, 2013 (Rating 8.5) Fractal visionaries and enthusiasts: The formula behind today's image is Z^(1.09)+C, a hopeless expression if ever there was one. But as today's image shows, things need not always be as hopeless as it first appears, and an expression as close to linearity as today's can produce interesting fractals when calculated with one of the alternate complex logarithms. The parent fractal is shaped like a torpedo, much as the minibrot at the center of today's image. In the range of exponents so close to unity, most all the fractals tend to resemble torpedoes, but this does not mean they are necessarily all the same. Check the minibrot in today's image, which actually creates a rather pronounced 3-D effect. Most of this effect is due to my semi-skilled coloring of course, and I rewarded myself with a full half point for the effort. The name "The Mighty Midget" is a comment on how the image gets so much from so little. The calculation time of 2-1/2 minutes borders on slowness. The web sites are there to avoid impatience. So make life easy. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are filed online at: <http://www.Nahee.com/FOTD/> Midsummer arrived with a bang here at Fractal Central today, with a temperature of 86F 30C and an afternoon thunder-shower. The fractal cat said enough heat is enough and started searching for a cooler spot than the window shelf. The humans meanwhile had an average day. The next FOTD will be posted before long, though I'm not sure of the route. Until whenever and however, take care, and be ever aware of the dangers inherent in making hasty decisions that will do nothing but make someone feel better. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Mighty_Midget { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident center-mag=-0.192308145885724/-1.991515836863857/\ 2998.507/1/57.5/0 params=1.09/0/525/0 float=y maxiter=5000 inside=0 logmap=140 periodicity=6 colors=00060F70F70F80F90F90FA0FA0EB0EC0DC0DD0DD0EE\ 0EF0FF0EG0DG0BH09I08I06J14J03K14K24K34L44L54L64M74\ M84M94NA4NB4NC5ND5OE5OF5OG5PH5PI5PJ5QK5QL5QM5QN5RO\ 6RP6RQ6SR6SS6ST6TU6TV6TW6UX6UY6UZ7U_7V`7Va7Vb7Wc7W\ d7We7Xf7Xg7Xh7bn7_k7Xh7Ve7Sb7Q_7NX7KU7IR7FO7DL7AI7\ 7H58G68G78G78G88G98G98GA8GB8GB8GC8GD8GD8GE8GF8GF8G\ G8GG8FH8FI8FI8FJ8FK8FK8FL8FM8FM8FN8FO8FO8FP8FQ8FQ8\ FR8FR8ES8ET8Qh8Qg8Qf8Qe8Qd7Qc7Qb7Qa7Q`5UeN6SQBWTGZ\ VLaYQe`Vhd`mbZkaXj_VhZTgXReWPdVOcTMaSK`QIZPGYNEWMC\ VN9WLBUKDSJEQIGPGINFJLELKDMIBOGAQF9RD8Tz6Vz5Wz4cz4\ `z3cz3Xz3cz3Uz3cz3Uz2cz2Uz2cz2Uz2czUUzUUzUUzUUzUcz\ UczUczUczUczUczUczUczUczUczUczUczc_kcbjceichhckgcn\ fclecjechecfecdeccecceccecceccecczcczcczcczcczcczc\ czcczcczmmzmmzmmzmmzmmzmmzmmzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 09-04-13 (Mandy in the Sky [8])
by Jim Muth 11 Apr '13

11 Apr '13

FOTD -- April 09, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us back in time to the halcyon days of the MandNewt series of formulas, in particular the MandNewt11 formula. Don't ask what this series of formulas does or was supposed to do. I haven't the foggiest idea, but one thing it certainly does is create some unusual images. I named the image "Mandy in the Sky". If I had more room, I might have added 'with diamonds' since the sky surrounding the not-quite-critical Mandelbrot set is filled with rings of sparkling points that could be either stars or diamonds. The rating of an 8 indicates that, even though the image may not be the best of all time, it is new and different enough to be given a rating that is notably above average. The fireball fast calculation time of 15 seconds will seem to pass in a flash once the diamonds begin appearing at the top and bottom of the screen. And viewing the image on one of the web sites will eliminate the flash. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> without the task of calculating it. Variations in high-definition are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the FOTD back images are posted at: <http://www.Nahee.com/FOTD/> The preview of summer continued here at Fractal Central today, with a temperature of 81F 27C, gentle winds, and a blue sky filled with puffy white clouds. The fractal cat spent most of the day watching the birds, which were quite active in the area. The humans made it through another day with nothing going wrong -- a task that is not as easy as it might first appear. The next FOTD will be posted in the appropriate time. Until whenever, take care, and we know that physical matter is real because it is there even when no one is looking, but if no one ever looks, how do we know that the matter is there? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mandy_in_the_Sky { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt11 passes=1 center-mag=1.87368\ /0/0.08274124/1/180 params=1/-1/1/-1/1/-1 float=y maxiter=250 inside=253 logmap=27 symmetry=xaxis periodicity=0 colors=00000FB9FF00G3EM6JS8OZBTdDYjGbpIgyKnwKltKjr\ KgoKemKckKahK_fKXcKVaKT_KRZJKYJPXJTWJYWKbVKgUKkTKp\ WGvUKtSOrPRpNVnLZlJbjHfhEifCmdAqb8u`4yY5yZ7y_zUzzy\ `ByazzbmzbzzcGzdmzzzzzKzfLzgLzoMzhNz`NzUOzMPzFQzGR\ zHSzITzIUzJVzKVzLWzMXzNYzNZzO_zPYzR_zPazOczMezKfzJ\ hzHjzFlzEnzCgzL_zTTzaLziEzr6zz6zz6zz6zy6zy5zy5zy5z\ x5zx5zx5zx5zw5zw4zw4zw4zv4zv3zi2zX1zK0z74z98zBCzEG\ zGKzIOzKTzNXzP`zRdzThzVlzYpz_tzaozbkzbfzcbzcYzdUzd\ PzePzf6zA8zEBzJDzNGzRIzVLz_Nzcpz3oz5nz6mz8lz9kzBiz\ DhzEgzGfzIezJdzLczMbzOazQ`zRZzTYzVXzWWzYVzZUz`yzUy\ zVyzWxzXxzYxzPwzHwz8mzHdzPfzRhzSizUkzWmzXozZpz_rza\ `zlKzvMzpNzjPzdQzZSzTTzNVzHTzIRzJOzKMzLKzLIzMFzNDz\ OHzTLzXPzaSzfWzj_zoWzmSzjOzhLzeHzcDz`9zZ5zWCz_IzbP\ zfVzjazmgzqdzlbzh_zcXz_UzVSzQPzMMzHazPqzXqzTqzPqzL\ rzIrzErzArz6mzDhzJdzQ_zXVzbQziQziQziQziPzjPzjPzjPz\ j6zT6zP6zL3zI6zHLSnPzPSzP } frm:MandNewt11 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-f j=c*z^d+g z=z-e*h/j, .0000000000000000000000000000005 <= |h| } END PARAMETER FILE=========================================

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FOTD april 9
by Susan Brown 09 Apr '13

09 Apr '13

FOTD -- April 09, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us back in time to the halcyon days of the MandNewt series of formulas, in particular the MandNewt11 formula. Don't ask what this series of formulas does or was supposed to do. I haven't the foggiest idea, but one thing it certainly does is create some unusual images. I named the image "Mandy in the Sky". If I had more room, I might have added 'with diamonds' since the sky surrounding the not-quite-critical Mandelbrot set is filled with rings of sparkling points that could be either stars or diamonds. The rating of an 8 indicates that, even though the image may not be the best of all time, it is new and different enough to be given a rating that is notably above average. The fireball fast calculation time of 15 seconds will seem to pass in a flash once the diamonds begin appearing at the top and bottom of the screen. And viewing the image on one of the web sites will eliminate the flash. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> without the task of calculating it. Variations in high-definition are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the FOTD back images are posted at: <http://www.Nahee.com/FOTD/ <http://www.nahee.com/FOTD/>> The preview of summer continued here at Fractal Central today, with a temperature of 81F 27C, gentle winds, and a blue sky filled with puffy white clouds. The fractal cat spent most of the day watching the birds, which were quite active in the area. The humans made it through another day with nothing going wrong -- a task that is not as easy as it might first appear. The next FOTD will be posted in the appropriate time. Until whenever, take care, and we know that physical matter is real because it is there even when no one is looking, but if no one ever looks, how do we know that the matter is there? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mandy_in_the_Sky { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandNewt11 passes=1 center-mag=1.87368\ /0/0.08274124/1/180 params=1/-1/1/-1/1/-1 float=y maxiter=250 inside=253 logmap=27 symmetry=xaxis periodicity=0 colors=00000FB9FF00G3EM6JS8OZBTdDYjGbpIgyKnwKltKjr\ KgoKemKckKahK_fKXcKVaKT_KRZJKYJPXJTWJYWKbVKgUKkTKp\ WGvUKtSOrPRpNVnLZlJbjHfhEifCmdAqb8u`4yY5yZ7y_zUzzy\ `ByazzbmzbzzcGzdmzzzzzKzfLzgLzoMzhNz`NzUOzMPzFQzGR\ zHSzITzIUzJVzKVzLWzMXzNYzNZzO_zPYzR_zPazOczMezKfzJ\ hzHjzFlzEnzCgzL_zTTzaLziEzr6zz6zz6zz6zy6zy5zy5zy5z\ x5zx5zx5zx5zw5zw4zw4zw4zv4zv3zi2zX1zK0z74z98zBCzEG\ zGKzIOzKTzNXzP`zRdzThzVlzYpz_tzaozbkzbfzcbzcYzdUzd\ PzePzf6zA8zEBzJDzNGzRIzVLz_Nzcpz3oz5nz6mz8lz9kzBiz\ DhzEgzGfzIezJdzLczMbzOazQ`zRZzTYzVXzWWzYVzZUz`yzUy\ zVyzWxzXxzYxzPwzHwz8mzHdzPfzRhzSizUkzWmzXozZpz_rza\ `zlKzvMzpNzjPzdQzZSzTTzNVzHTzIRzJOzKMzLKzLIzMFzNDz\ OHzTLzXPzaSzfWzj_zoWzmSzjOzhLzeHzcDz`9zZ5zWCz_IzbP\ zfVzjazmgzqdzlbzh_zcXz_UzVSzQPzMMzHazPqzXqzTqzPqzL\ rzIrzErzArz6mzDhzJdzQ_zXVzbQziQziQziQziPzjPzjPzjPz\ j6zT6zP6zL3zI6zHLSnPzPSzP } frm:MandNewt11 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-f j=c*z^d+g z=z-e*h/j, .0000000000000000000000000000005 <= |h| } END PARAMETER FILE=========================================

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fotd april 9
by Susan Brown 09 Apr '13

09 Apr '13

1 0

FOTD 08-04-13 (Another of the Trees [7])
by Jim Muth 08 Apr '13

08 Apr '13

FOTD -- April 08, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is an almost-Julia set of the X-axis at the western extremity of the (-Z)^(1.55)+C Mandeloid. It's almost a Julia set because it is double-rotated 0.01,0.01 degree from the true Julia orientation. (To see the true Julia version, change the (p1) and (p2) parameters to 90.) I might have rated the image a point or so higher if there were not so many similar tree-like images in FOTD history. As it is, the rating of a solid 7 is perfectly average. The name "Another of the Trees" indicates my dis-satisfaction with a fractal theme that is becoming hackneyed. The calculation time of 4 minutes is rather slow, and I'm not sure the image is worth the wait. This is where the web sites become a blessing in disguise. Check the finished image posted at: <http://www.crosscanpuzzles.com/Archives.html> And the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Spring was in full bloom here at Fractal Central today as the temperature reached 72F 22C and the sky remained nearly cloudless. The fractal cat enjoyed his appointed time in the sun on his shelf, though with the sun now at an increasingly high angle it is missing the back edge of the shelf. The humans passed the day working and sometimes pondering the pathetic state of our 'modern' culture. The next FOTD will be posted in the proper time. Until whenever, take care, and what will we do when the internet is turned off by the same dark forces that created it and then were satisfied at how easily we became addicted? (I'm not serious of course . . . or am I?) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= AnotherOfTheTrees { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 center-mag=0.218919/0/13.36618/0.8579/90/0 params=89.99/0/89.99/0/-1.1352113/0/0/0/1.55/0 float=y maxiter=1500 inside=255 periodicity=6 colors=000ES000a00a00a00_00_00Y00Y00Y00X00X00X00W0\ 0W00W00U00U00S00S00S00Q00Q00Q00O00O00O00M00M00K00K\ 00K00K00I00I00I00G00G00G00E00E00C00C00C00900900900\ 80080080060060030030030000000000000000000000000000\ 00000000000000000000000000000000000000000000000jzw\ jzwhzufzrezqcxoawn_tlYrjYqhXofWneUjcShaQf_QdYObXM_\ WKYUIXSGWQGUOEQKCOI9MG8KE6GC3E93C80960830300000000\ 00000000000000000IzzGzzEzzCzz9xz8ux8qu6nq3hl0eh0_c\ 0XY0SW0OQ0IK0EG089033000000000W8fU6eU6cS6cS6aQ3aQ3\ _O3YO3YM0XM0XK0WK0UK0UI0SI0SG0QG0OE0OE0MC0MC0K90I9\ 0I80G80G80E60C60C309309008006006003003000000000000\ 000000000000000000000000000000000000xS0tO0qM0nK0jI\ 0eG0aE0Y90W80S60M30I00E00900600000000000000tz0rz0q\ z0qz0oz0oz0nz0nz0lz0lz0jz0jz0hz0hz0fz0fz0ez0ez0cx0\ aw0au0_u0_t0Yr0Yq0Xq0Xo0Wn0Wl0Ul0Uj0Sh0Sf0Qf0Qe0Oc\ 0Oa0Ma0K_0KY0IX0IW0GW0IOO } 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 07-04-13 (Pi in the Sky Bye and Bye [8.5])
by Jim Muth 07 Apr '13

07 Apr '13

FOTD -- April 07, 2013 (Rating 8.5) Fractal visionaries and enthusiasts: We are taught in religion class that if we are good while on earth and obey all the rules, we will have our pie in the sky bye and bye when we die. My opinion is that it's too bad we have to be dead to enjoy our pie. But maybe it's not all that bad. In today's image we can have our pie while we're still alive. The pie in question is not the kind we eat, but the kind that describes the ratio of a circle to its diameter -- the kind of pie that is spelled pi and has a transcendental numerical value of 3.14159.... To add to the confusion with today's image, it is not straight Z that is raised to the power of pi, it is (-Z), and what a difference that little minus sign makes in the appearance of the parent Mandeloid. The parent has been turned on its side and is splitting apart along the parts that would normally lie on the Y-axis, resulting in a totally new fractal. Today's image is a Julia set of the point where the X-axis intersects the split-apart western extremity of the parent fractal. The name "Pi in the Sky Bye and Bye" refers to the exponent of Z, and might also be a warning to the youngsters that they had better be good if they want their pie. The rating of 8-1/2 includes the standard half-point bonus for the coloring, which might even be a little too intense. The calculation time of 2-1/3 minutes is about average, but viewing the image on the web sites will save a good part of that time. Enjoy the completed image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Another near-perfect spring day graced Fractal Central today. The day began with a temperature of 36F +2C but under full brilliant sunshine warmed to an afternoon high of 64F +18C. The fractal cat fully enjoyed the strong afternoon sun on his shelf in the southwest window. The humans enjoyed the entire day's weather, thinking of the coming summer activities. The next FOTD will be posted in a certain number of hours. To find the exact number of hours check back every so often. Until whenever, take care, and ambiguity can sometimes be confusing. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= PiInTheSkyByeAnBye { ; time=0:02:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 center-mag=-0.250391/0/0.9363296/1/-90/0 params=90/0/90/0/-1.0876775/3e-008/0/0/3.141592653\ 58979/0 float=y maxiter=2500 inside=0 periodicity=0 colors=000A00G30N52XABgFKnKUsJczKqzPzzUzzZzzezqhzZ\ 0vB0c00P0060000000000000G20lG0zP0zc2zl0zZ0zK0zBcz0\ ml0mU0ch0cq0cz0cz0cz0cz0mz0mz0mz0mz0mz0rz0vz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz6zz0zz0zz0zz0zz0Zz00zP0zz0\ zq0zh0zZ0zP0zG0z60z00z00z00z00z00z00v00q00z00z00z0\ 0z00z00z02z0Kz0Zz0qz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz06v0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0vz0q0zz0zz0zz0zz\ 0zz0zz0zzBzzPzzczzqzzzzzzzzzzzvzzqzzhzzZzzUzzKzzBz\ z6zz0zz0zz0vz0qz0lz0hz0qz0vz0zz0zz0zl0zP0z60z00z00\ z00z00z00z00z00z00q02Z0BB0K00U00q00Z00G000000000B2\ 0PG0c60Z20U00P06K0hl0zz0zz0zz0zz0zz0zz0zz0zq0zh0zZ\ 0zU0zK0zB0z20z00z06z0Gz0Pz0Uz0cz0lv0vh0zU0zG0z20z0\ 0z00z00z60zh0hz0lz0lz0qz0 } 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 05-04-13 (The Great East [7.5])
by Jim Muth 05 Apr '13

05 Apr '13

FOTD -- April 05, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a different view of a tiny minibrot in the east valley area of a larger minibrot on the main stem of the Mandelbrot set. The minibrot is sliced in the Rectangular direction, which explains why it looks nothing at all like a Mandelbrot minibrot or a mini-Julia set. As is usually the case with fractals created by taking odd slices of the Julibrot, the image has been stretched and skewed to bring it to reasonable proportions. The thin diagonal yellow lines through the open area are parts of the west branch of the large valleys on the north and south shore lines of the main bay of the underlying minibrot. The rating of 7-1/2 is largely earned by the coloring, which is just about all the image has going for it. The name "The Great East" simply tells that the scene lies to the east of a larger minibrot. The calculation time of 3-1/4 minutes is within reason. The web sites can completely remove the need to calculate. The official FOTD web site is again up and running at: <http://www.crosscanpuzzles.com/Archives.html> High definition versions are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Spring arrived with a day of total sun and a chorus of bird song here at Fractal Central today. The temperature of 59F 15C was the warmest in at least one entire month. The fractal cat, taking advantage of the strong sun, passed the afternoon on his shelf in the southwest window. The humans passed the day working, though FL's gardening enthusiasm is growing fast. The next FOTD will be posted when it is ready. Until that glorious moment arrives, take care, and political correctness might keep people happy, but it all too often fails to admit and solve the problems. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Great_East { ; time=0:03:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/3.920133e+007/1.6807/102.3920236694\ 89504/35.4 params=90/90/0/90/-1.7857285921/0/\ -1.7857285921/0/2/0 float=y maxiter=7500 inside=0 logmap=314 periodicity=6 colors=00000F00G00H00I00J00K00L00M00N00O00P01Q02R0\ 3S04T05U06V07W08X09Y0A_0B_0Ca0Dc0Ec0Df0Dg1Ch2Dk3Cm\ 4Cn5Cq6Bs7At89v99xA9zBBzCDzDFzEHzFJzGLzHNzIQzJSzKU\ zIWzFYzC_v9ar5fm6ch7ac7_c8Yc8WZ9UZ9SZAQUAOUBMKCKKC\ IEDGEDEEECEEAEF8ED7FF6EH6EJ6EL5EN5EP5FR4JS4MU4PW4S\ Y3U_3Wa3Yc2`e2af2bh2cj1dl1em1gn0ip0kq2mr4os7qtAquF\ qvKpwQoxRomYmcPmUEm8HmdIXdLYcO_cR`cUacXcb_dbbebegb\ hhakiankaqlJwVatmUtqNttJqjGo`DlRAjH2g77h8Bh9FhAJiA\ NgBReCVcDZbDdaEeaFeaGdaGd`Gd_HdYHdVHbRH`NHaIHdDHj8\ Hz5Gp4Hj3Hd3HZ2HU2HO1HI1HC0H70H83L95PA7TB9WBB_CEcD\ GfEIjFKnFMqHOnIPkKQhLReNSbOT_QUXRWUTXRUYOWZLX_IZ`F\ _aDZ`GY`JX`MW`PV_SU_VT_YS_`RZcQZfPZiO`lNcoMhrLmuLr\ xNvvPzuQumRqeTmYViQXeI_aA__6_Y2`Z5`Z7`ZAaZCaZFaZHa\ cKbcMbcPbcRbcUccWcmZcm`cmacmbzzJzz0zz3zz5zz8zzAzzD\ zzFzzIzzKzzJzzJzzJzzJzzJzzJzzJzzJzzJzzJzzJzzJzzJzz\ JzzOzzSzzXzz`zzczzdzzezze } 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 03-04-13 (No Ifs Ands or Butts [8])
by Jim Muth 04 Apr '13

04 Apr '13

FOTD -- April 03, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a Julia set of the point where the positive X-axis crosses the eastern extremity of the main bay of the (-Z)^(2.5)+C Mandeloid. A kind of East Valley lies at this point, though it is too small to be seen without enlargement. I named the image "No Iffs Ands or Butts". I refuse to admit the inspiration for the name. At least a full point of the rating of an 8 is due to the coloring, which I put almost an hour into. The calculation time of 3-3/4 minutes borders on slowness. Relief may be found at one of the web sites however. The web site at: <http://www.crosscanpuzzles.com/Archives.html> is temporarily down, but the image will soon be posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, with a temperature of 43F +6C and brisk winds made today feel unpleasantly cool here at Fractal Central. The fractal cat enjoyed the periods when the sun was out, while the humans tried to figure out why we cannot gain access to the FOTD-crosscan web site web site. The next FOTD will be posted soon. Until whenever, take care, and the environmentalists who protest against oil pipelines should be ready to set an example and stop consuming the oil that makes the pipelines necessary. If they are unwilling or unable to kick the oil habit themselves, they should remain silent and stop pushing for laws to force others to comply with their own particular ideas. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= NoIfsAnds_or_Butts { ; time=0:03:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 center-mag=-0.388106/0/1.04/1/90/0 params=90/0/90/\ 0/0.372582/0/0.372582/0/2.5/0 float=y maxiter=12000 inside=255 logmap=yes periodicity=6 colors=0006LS3KU0KW3KZ6La9MdCNfFNjKRhPUeUXbZeZcmWh\ uTmyWrzZvzdzzmzzzzzzzzzzmzzmzzmzzmzzkzziJzgKzeLzcM\ zcMzcQzcUzcXzc`zcdzcgzckzcozcrzcvzcyzcuzcqzcnzcjzc\ fzacz__zYWzWTzUPzSLzQIzPEzPAzP7zSAzVDzXFz_IzbKzdNv\ cQrcSmcVmcXmc_mcamcmmcmmcmVcmKcmKcmK_mKamKcmKamK_m\ KYmKWmKUmKSmKQmKOmLMmJJqIInHHkGGhFFfEEcDDZCCUB9PA5\ K90580A705000000000000KUKNkkNkkNkjMjjMjjMjjMijMijL\ ijLijLhjLhjKhjKgjKgjKgjMilLhkKgjJgiJfiIfhHegHefGdf\ FdeFcdEccDbcDbbCaaB``B``A__9_Z9ZY8ZY7YX7YW6XV5XV5W\ U4WT3VS2UR3VS3VS4VS4VT4VT5VT5VU5WU6WU6WU6WV7WV7WV7\ WW8WW8XW9XW9XX9XXAXXAXYAXYBXYBYYBYZCYZCYZCY_DY_DY_\ DY_EZ`EZaEZbEZbEZcE_dF_eF_eF_fF_gF`hF`hG`iG`jG`kG`\ kGalGamGanHanHaoHbpHbqHbqHbrIbsIctIctIcuIcvIcwGdxI\ cwJbwLavMavO`uP_uR_tSZtUYsVYsXXrYWr_Vq`VqbUpcTpeTo\ fSohRnjNriPpiRniSmhUkhVjhXhgYfg_eg`cfbbfc`feZefYeh\ WhlWfjVeiVdgUcfUbeUacT`bT } 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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Jim's FOTD for March 31st is on my server now.
by Hal Lane 03 Apr '13

03 Apr '13

Jim's FOTD for March 31st, its 'parent' and some zooms into the parent ('variations') are on my server now. Sorry for the delay. Most of April 1 is done, so it should be up soon. - Hal Lane ######################## # hallane(a)earthlink.net #######################

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FOTD 01-04-13 (A Rectangular Set [No Rating])
by Jim Muth 01 Apr '13

01 Apr '13

FOTD -- April 01, 2013 (No Rating) Fractal visionaries and enthusiasts: Today's image is a new view of a minibrot hole on the main stem of the Mandelbrot set. The minibrot looks so unusual because it is sliced in the Rectangular orientation, which lies at a right angle to the Mandelbrot orientation and is determined by the imag(z) and imag(c) axes. The brilliant green bars slicing diagonally through the open area are actually Mandelbrot valleys viewed at a right angle. The bars are straight edged because regardless of where points in the M-set are initialized, they will eventually settle into the same orbits unless they escape first. There is no way I could give a rating to such an overworked theme, but being fascinated by things beyond visualization, I continue returning to the four-dimensional Julibrot for ever new surprises. The name "A Rectangular Set" is a bit misleading. The image is merely a small part of one of an infinity of Rectangular sets. The calculation completes in 25 seconds, fast enough to waste no one's time. The web sites are more convenient but probably no faster. When the official FOTD web site is back in operation, it will be found at: <http://www.crosscanpuzzles.com/Archives.html> Until then, the finished images may be seen in hi-def at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> The day began pleasant enough here at Fractal Central today, with breaking clouds and a temperature of 50F 10C, but by midday the clouds and rain had returned, and the temperature had dropped to 45F +7C. The fractal cat observed all this with dis-interest, while the humans made it through another day with no unexpected disasters happening. The next FOTD will be posted soon. Until we find out how long 'soon' is, take care, and when disasters happen, look to the bright side. But before you look, be sure a bright side actually exists. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Rectangular_Set { ; time=0:00:25.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/10166.07\ /1.3984/29.6185420924715608/28.9858769262522351 params=90/90/0/90/-1.690128/0/-1.690128/0/2/0 float=y maxiter=3200 inside=0 logmap=28 periodicity=6 colors=000BamCalD`kE_jFZiGYgHXeIWcJVaIU_ISYHQVHOSG\ MQGKNFIKFGIDDGBADA89846713940B72E94HC6KF8OHARKCUME\ YPG_SGbUFdXEf_DiaCkdBmfAlgClhDkiEkjFjkHjlIilJimKhn\ LhoNgpOgqPfrQfrRhoUjmXlk_nibpgerehtckvanx_qqXlkUgd\ RbZOYSLTMIONJJOLPWSUpfGoaHnYHmTHlPHkLHgNIcOI_PIWRJ\ SSJPTJSPGVMEYIC`FAaJDaNGbRJbVMcYOcaRdeUdiXem_epadm\ bdjbdgbLTRLUQKVQKWQJXPJYPIYPIZPH_OH`OGaOGbNGcNFcNF\ dMEeMEfMDgMDhLCiLCiLBjKBkKBlKAmJAnJ9oJ9oJ8pI8qI7rI\ 7sH6tH6uH6uH7tI7sI8sJ8rJ9rK9qK9qLApLApMBoMBnNBnNCm\ OCmODlPDlPDkQEkQEjRFjRFiSFhSGhTGgTHgUHfUHfVIeVIeWJ\ dWJdXJcXKbYKbYLaZLaZM`_M`_M_`N_`iSVgTVeTVdTVbUV`UV\ _VVYVVWVVVWUTWURWUQXUOXUMYULYUJYUHZUGZUE_UC_UB_U9`\ U7`U6`U7aT8bT9bT9cTAcSBdSCdSCeSDfSEfRFgRFgRGhRHhQI\ iQIjQJjQKkQLkPLlPMlPNmPNmPOnOPoOQoOQpORpNSqNTqNTrN\ UsNVsMWtMWtMXuMYuLZvLZwL_wL`xLaxKayKbyKczKczKbxLaw\ L`vM`uM_tNZsNYrNYqOXpOWoP } 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 31-03-13 (End of the Line [7])
by Jim Muth 01 Apr '13

01 Apr '13

FOTD -- March 31, 2013 (Rating 7) Fractal visionaries and enthusiasts: We are still trying to gain access to the official FOTD web site. Neither we here at FC nor the technicians at the host site can figure out why the site continues to reject our password, which everyone agrees is correct. But web site or not, there will always be fractals. Today's image lies in the oversized parent that results when 5.5 negative parts of Z^(-1.1) are combined with 0.55 negative part of Z^(-11) and (1/C) is added on each iteration. This parent includes a huge spectacular 'fan' but today's image does not lie in this fan. It lies near the terminal of the filament extending south from the southernmost large bay. The name "End of the Line" indicates that the filament terminates not far beyond the scene. The rating of a humdrum 7 indicates that I put too little effort into working on the colors. The calculation time of 3-1/2 minutes is rather slow. But the web sites can relieve that problem. The official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> is still down. I recommend checking the finished image on Hal's web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Clouds and a cold rain spoiled Easter Sunday here at Fractal Central. The temperature of 45F +7C with the rain kept the Easter finery under wraps and umbrellas. The fractal cat grew alert when the cries of fighting tomcats drifted into the house. When the tomcats settled their differences, the fractal cat remembered that he was hungry. The humans were a bit grouchy because of the weather. I guess we'll have to ask the Big Guy in the sky why He spoiled His biggest day. The next FOTD will probably be posted to the list in 24 hours. It's hard to say when it will be posted to the official web site. Until next time, take care, and I sure would like to know what actually happened on the first Easter. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= End_of_the_Line { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=-2.506677199191898/-10.18811576459481/\ 1.663562e+011/1/-120/0 params=-5.5/-1.1/-0.55/-11\ /0/525/0/0 float=y maxiter=3200 inside=0 logmap=468 periodicity=6 mathtolerance=0.05/1 colors=000505505606707808909A0AB0BC1CD2DE3EF4FG5GH\ 6HI7IJ8JK9KLAGMBCMC8MD5LE7KF9JHBJICIKEHLGHNHGOJFQL\ ERNETODXQCWSCaZK_WRbZZeaUdXmkgQbUdiYK`UBbB9XU8RI6c\ c5GPFmmObgfzzfxzdkVcP0bd7aQDa_J`QP_QV_Q`ZQfYQlYQrj\ f1he3gd5fc6dc8cb9baB`aC_`EZ_FX_HWZIVYKUYLUVKUSJUPI\ UMHUJGUDEU7BU19V3AV5BW7CW9DWBEXDFXFGXHHYJIYLJYNKZP\ LZRMZTMYWSYZXYabXdgXgmXjrXmwZjt_gq`dnbakcZhdWefTbg\ Q_hNXiKVgMTeOSdPQbRP`TN_UMYWKXXJVZIT`GSaFQcDOeCNfA\ Lh9Ki8WcEgYJsSOoVRlYUh`WebZae`ZhcVjeSmhOpjLrmHuoEx\ rBztqzVltTgnSbiRYcPTYOPTNKNMFHKACJ56I11H42F62E93DB\ 3CD4BG4AI59e58f67P66S75U74k73X65w67Y69Y6BY6DZ5FZ5H\ _5J_5L_5NW7QS9SPAULCXIDZEF`AHc7Ie3Kg0LiGRjWWjSXiPX\ hLYhIYgEZfBZf7_e4_d1_dHZhWZljYpyYtp`mhcf_f`SiUKlOH\ kSFkWCk_Akb8kf5kj3kn1kq2in3gk4eh4ce5ab6_`7YY7WV8US\ 9SPAQNAOKBMHCKEDIBDH9EGEEGIEFMFFQFFUFEZFEbGEfGDjGD\ nGDrHFnHHjHJgILcIM_IOXIQT } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-03-13 (Quadraquintic Brot [8.5])
by Jim Muth 28 Mar '13

28 Mar '13

FOTD -- March 28, 2013 (Rating 8.5) Fractal visionaries and enthusiasts: Today's long-awaited FOTD image rates a solid 8-1/2, most of which is due to the coloring. The striking colors were not a result of any artistic talent. They are a result of programmed randomness, though I did give myself a 1/2 point bonus for being the one who struck the <enter> key. The image shows a scene in a minor minibrot on the main stem of the grossly oversized parent Mandelbrot set. This minibrot is halfway through the process of morphing from quadratic to quintic, with today's scene located in debris on the degenerate northwest shore line of the minibrot's main bay. I named the image "Quadraquintic Brot" because the obviously quintic minibrot at the center is surrounded (beyond the frame edges) by purely quadratic stuff. The calculation time of 1-3/4 minutes will pass in a flash. To avoid being dazzled, I recommend visiting one of the web sites. If the finished image is not already posted to: <http://www.crosscanpuzzles.com/Archives.html> it soon will be. The high-definition versions are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images may be checked at: <http://www.Nahee.com/FOTD/> A blustery mix of sun and clouds with a temperature of 48F +9C made today a disappointing one for those impatient for spring to arrive. The fractal cat was equally disappointed with the come-and-go sunshine on his shelf, and soon retired to my favorite chair. Meanwhile the humans continued working on the work room. The next FOTD will be posted when the work room work is finished, most likely in 24 hours. Until whenever, take care, and those who think fracking for natural gas and oil is harmful to the environment should calculate the number of square miles that would need to be covered with solar panels to supply an equal amount of energy. People should do the math before clamor- ing for solar energy! And monstrous wind turbines not only kill the birds that fly into them, they create subsonic pressure waves that are disorienting to both animals and humans within a half mile or so. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Quadraquintic_Brot { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip passes=1 center-mag=-83.71508047424459/+0.0075262435899841/\ 3.99368e+010/1/81.25/0. params=5/50 float=y maxiter=1500 inside=0 logmap=193 periodicity=6 colors=000LWpJTlHRhFPdEN`CLXAJT8HP7FL5DH3BD1990755\ 66967D68I68M69Q6AV6AZ6Bb6Cg6Ck6Do6Et3Bs6Es9HsCKsFM\ rIPrKSrNXrQ_qTaqWcqZeq_gq`hr_is_jtakuelvimwknxmoyp\ pxrjvvexzZuy`rxbowclveiufguhdtjcskhrmmqnrppvrvzpqz\ omzmhzldvj_riWmgRhfNcdIcf8ccEcaJcZPcWU`S_YObVKdSJY\ RHWQGVPFTOESMEQKEPIENGEREDPCCTACR8CQ7DO7FN7HN6IM6J\ M6KL5ML5OK5RK4UJ4XJ4_I3bI3eH3hH7iGAjFEkEHlDKmCOnBR\ oAVp9Yq8`r8bl8dg8ea8gX8iR8jM8lG8nB8s22o68lADhEJeIO\ aMUZQZVUdRVgSYiS_jTakTclUemUgnVipVkqWmrWosXqtXsuXu\ vWqpWnkWkfWhaWeXWbRW_MWXHWUCWR7YOEZMK_JR`HXaFcbCic\ Apd8vcBrbDnbGjaIfaLc`N__QW_SSZVOZXLQbMHgM5kL9lMDmM\ HnNKoNOoOSpOVqPZrPbrQesQitRmuRpuRktQftPatPYtOTtNOs\ NJsMFsLAsL5sz2sz1sz7nzCjzHezMazRzzWzz`zzezzjzzozzt\ zzyzzZzz8zz9zzAzzAzzBzzCzzCzzzzczzczzczzczzmzzmzzm\ zzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 28-03-13 (Quadraquintic Brot [8.5])
by Jim Muth 28 Mar '13

28 Mar '13

FOTD -- March 28, 2013 (Rating 8.5) Fractal visionaries and enthusiasts: Today's long-awaited FOTD image rates a solid 8-1/2, most of which is due to the coloring. The striking colors were not a result of any artistic talent. They are a result of programmed randomness, though I did give myself a 1/2 point bonus for being the one who struck the <enter> key. The image shows a scene in a minor minibrot on the main stem of the grossly oversized parent Mandelbrot set. This minibrot is halfway through the process of morphing from quadratic to quintic, with today's scene located in debris on the degenerate northwest shore line of the minibrot's main bay. I named the image "Quadraquintic Brot" because the obviously quintic minibrot at the center is surrounded (beyond the frame edges) by purely quadratic stuff. The calculation time of 1-3/4 minutes will pass in a flash. To avoid being dazzled, I recommend visiting one of the web sites. If the finished image is not already posted to: <http://www.crosscanpuzzles.com/Archives.html> it soon will be. The high-definition versions are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images may be checked at: <http://www.Nahee.com/FOTD/> A blustery mix of sun and clouds with a temperature of 48F +9C made today a disappointing one for those impatient for spring to arrive. The fractal cat was equally disappointed with the come-and-go sunshine on his shelf, and soon retired to my favorite chair. Meanwhile the humans continued working on the work room. The next FOTD will be posted when the work room work is finished, most likely in 24 hours. Until whenever, take care, and those who think fracking for natural gas and oil is harmful to the environment should calculate the number of square miles that would need to be covered with solar panels to supply an equal amount of energy. People should do the math before clamor- ing for solar energy! And monstrous wind turbines not only kill the birds that fly into them, they create subsonic pressure waves that are disorienting to both animals and humans within a half mile or so. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Quadraquintic_Brot { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip passes=1 center-mag=-83.71508047424459/+0.0075262435899841/\ 3.99368e+010/1/81.25/0. params=5/50 float=y maxiter=1500 inside=0 logmap=193 periodicity=6 colors=000LWpJTlHRhFPdEN`CLXAJT8HP7FL5DH3BD1990755\ 66967D68I68M69Q6AV6AZ6Bb6Cg6Ck6Do6Et3Bs6Es9HsCKsFM\ rIPrKSrNXrQ_qTaqWcqZeq_gq`hr_is_jtakuelvimwknxmoyp\ pxrjvvexzZuy`rxbowclveiufguhdtjcskhrmmqnrppvrvzpqz\ omzmhzldvj_riWmgRhfNcdIcf8ccEcaJcZPcWU`S_YObVKdSJY\ RHWQGVPFTOESMEQKEPIENGEREDPCCTACR8CQ7DO7FN7HN6IM6J\ M6KL5ML5OK5RK4UJ4XJ4_I3bI3eH3hH7iGAjFEkEHlDKmCOnBR\ oAVp9Yq8`r8bl8dg8ea8gX8iR8jM8lG8nB8s22o68lADhEJeIO\ aMUZQZVUdRVgSYiS_jTakTclUemUgnVipVkqWmrWosXqtXsuXu\ vWqpWnkWkfWhaWeXWbRW_MWXHWUCWR7YOEZMK_JR`HXaFcbCic\ Apd8vcBrbDnbGjaIfaLc`N__QW_SSZVOZXLQbMHgM5kL9lMDmM\ HnNKoNOoOSpOVqPZrPbrQesQitRmuRpuRktQftPatPYtOTtNOs\ NJsMFsLAsL5sz2sz1sz7nzCjzHezMazRzzWzz`zzezzjzzozzt\ zzyzzZzz8zz9zzAzzAzzBzzCzzCzzzzczzczzczzczzmzzmzzm\ zzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 25-03-13 (The Missing Mandy [7.5])
by Jim Muth 25 Mar '13

25 Mar '13

FOTD -- March 25, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image takes us on a trip into a higher dimension. The scene is in a valley of a sub-bud on the north shore of the main bud of the HyperMandelbrot set. The ill-defined thing at the center is a potential minibrot that has not yet fully formed but is well on the way. The name "The Missing Mandy" refers to the not quite fully formed minibrot at the center of the image. (To reveal the actual minibrot raise the maxiter to 2500 and change all parameters to zero.) The rating of 7-1/2 is boringly average. The calculation time of 2 minutes ia about average also. Due to technical computer difficulties there will be a delay of perhaps a day or two before the image is posted to the official web site at: <http://www.crosscanpuzzles.com/Archives.html> as soon as a computer problem is solved. It will be posted sooner at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are posted at: <http://www.Nahee.com/FOTD/> Light snow fell most all day here at Fractal Central today, but with a temperature of 36F +2C it melted as fast as it fell. The fractal cat passed the afternoon sleeping. The humans passed the day thinking of better days. The next FOTD will be posted in the proper time. Until then, take care, and when light battles darkness, the light always wins. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Missing_Mandy { ; time=0:02:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-0.99327427717631/+0.250652899394853/\ 2130000/1/-32.5/0 params=0/0/0/0/0.75/0/1e-100/0 maxiter=850 inside=0 logmap=-441 periodicity=0 colors=00086S0KOmzN0KNzzM0KMzzL0KKzzK0KJzzJ0KIzzH0\ KHzzGEKGzzFCKEzzEBKDzzDAKCzzB9KBzzA8UAzz97U8zz87U7\ zz75c6zz54c5zz43c4mm32c2cc21c1cc1cc0babY_bUZbPScKL\ dFEeB7fCCdCGbCKaDP_DTYDXXEUZER_FO`FLaSK`dJ_qIZiOdb\ UjVZoOduHizLeiPaUSZEXM5eNEnOMwOUzG`d`bKucHreFofCmg\ Ajh8gj5ek3bl1`mIcfZe`ngVSOZ65aALYE`VKZZPXbUVe_UidS\ liQpnPsiNheMZ`LOXKETJ4XQB_WIcaOfhVjn`mtgpzmUpR8g59\ e89dAAcCAbEA`GB_IBZKBYMCWNCVNCUNDSODRODQOFNKGKHDID\ 9FA6D62A30800C60GB1JH2NM3RS0UXWjUzzSoqUeiWW`YLT_BK\ a1Cb2I`3OZ4UY5ZW6dV7jT7oS8bO9QKADGB0D7S`4sxIooWkgi\ gZvdRX_I8V9RM9hD9cIRZNhWQbUSYSVTQXOOZJQYIRXISWHTVH\ UUGVTGWTG_WIcYJf_KjaLmcMhaRd_V`ZZWXcSWgOUkKToNQpQO\ qSMqVKrXIr_GsaEscLodRkeXhfcdmiaznYzzV`nRTfOKZKCRH4\ GEUz9CoF7fK2YP1PQ1rQ1`Q1tQ1bQ1zQ1cQUzR0eRczR0gRmzR\ 0iRzzR1zX1za2zfczzmzzzzzzzzLzoTzmazjjzgrzenzckzbhz\ `ez_bzYZzXWzVTzUQzSlzcgzc } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 22-03-13 (Hyper Hi-Jinks [7.5])
by Jim Muth 23 Mar '13

23 Mar '13

FOTD -- March 22, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image shows a hyper scene in Scepter Valley of the HyperMandelbrot set. I named it "Hyper Hi-Jinks" because that's what I see happening in the image. The rating of 7-1/2 is about average for these hyper images. Most of the features inside the outer circle consist of higher- dimensional stuff that lies in the HyperMandelbrot part of the Julibrot. To see the pure but under-resolved Mandelbrot scene with the minibrot undistorted change all the parameters to zero. I have ideas of what might be happening in these weird images created by the HyperMandelbrot2 formula, but as of today, it still doesn't add up. I still wonder whether it's some kind of mathematical quirk, but many of the things I find with the HyperMandelbrot2 formula are consistent with the overlapping images created by the hypercomplex formula hard coded in Fractint. Today's image calculates in 45 seconds, which leaves lots of time for other activities. And the web sites are always there with the finished image. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Another un-springlike day passed unappreciated here at Fractal Central today. The mix of sun and clouds with snow flurries and a temperature of 37F +3C felt more like late December than early spring. The fractal cat, who seemed notably unconcerned with the weather, spent most of his time playing, eating and sleeping. The humans spent the day fighting a computer virus. We finally won. (We hope.) The next FOTD will be posted in two days, since we are taking a trip back to Old Fractal Central tomorrow. Until next time, take care, and all the world's problems could be solved if they would just listen to me. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Hyper_Hi-Jinks { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-1.250884071513/+0.022468556515/407144/\ 1/137.5/0 params=0/0/0/0/1.2/0/1e-075/0 float=y maxiter=1000 inside=255 logmap=201 periodicity=0 colors=000ZQX_RY`SZaT_bU`cVadWbeXcfYdgZeh_fi`gjahk\ bilcjmdkieeeg_ajUIcWYlOznMZpLZczZRJzUHZvGZzFZyEZAD\ QlN9Le17n5Ai8DeCFaFIYJKUMNQQPMTSIXUE_XAbZ6_b5Xf5Uj\ 4Xm4_p3bs3eu3hw2kz2nz1qz1um0zc8zU0zKJcBGK9DC7A9586\ 35312Y_dTVZPRULMPHIKCDFbZz_WzXTyUQsRNmOLhLIbIFXFDS\ CAM97G65B3258hWHaaCSS8JJ499T3oL2bE1Q70DqWGlTEhRDdO\ C`MBXJ9zzzzzzzzzzvmzrczlZzfUwbOqZLlVJfSHaOFWLDRHAL\ E8GA6A74532UVBSSAQQ9OO8MM8KK7II6GG5EE5CC4AA3882662\ 441220fc7c`6`Z6YW5WU5TR4QP4OM3LK3IH3GF2DC2AA187155\ 0220XRbUOZRMWOKTMIQJFMGDJDBGB9D869546223mLUgIQaGNX\ EKRBGM9DG7AB465232Ux10tcUp10l1Nh10dc0a1DYcAU0AQ09M\ m7J06Fz4B037013wS5kM4_G3OB2C51IomGciFceccaccYccUcz\ QmzNmzJmzFmzBzz7zz3zzQzzLzzHzzDLz8Az4SzGOzDKzBGz9C\ z68z44z2hzhazaWzWPzPJzJCzC6z6TzWQzTOzRMzPKzMIzKGzI\ EzGCzDAzB8z96z64z42z2izvbzmWzeQzXJzPDzG6z8xzBszAoz\ 9jz8fz7bz7Yz6Uz5Qz4Lz3Hz3 } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 21-03-13 (Tentacles [8])
by Jim Muth 21 Mar '13

21 Mar '13

FOTD -- March 21, 2013 (Rating 8) Fractal visionaries and enthusiasts: One of the more unusual things I have discovered while exploring the hyperMandelbrot set is the predominance of tentacles. Sometimes these tentacles have definite points of convergence; at other times they simply wander aimlessly or turn back on themselves. Today's image shows a nest of these tentacles, with the longer ones converging on a point and the shorter ones wandering aimlessly. There also appears to be something more solid hidden in the background of the image, but for the time at least, this hidden thing will remain unseen. The name of the image is not surprisingly "Tentacles". The rating of an 8 indicates that I consider the image to be one of the best of the past week or so. The calculation time of 3-3/4 minutes is slow however, but this problem may be remedied by checking the image on one of the web sites. The image has been calculated, and posted at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> With a temperature of 34F +1C, biting winds, dark scudding clouds, a few flakes of snow, and a sun that did nothing on the rare occasions when it appeared, today felt like a return to January here at Fractal Central. The fractal cat complained of too few bursts of sun and decided to exhaust his energy begging for an extra serving of turkey and cheddar. The humans had an average day, though FL is becoming impatient for gardening weather to arrive. The next FOTD will be posted soon. Until 'soon' arrives, take care, and I hear that the FOTD has gone viral! Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Tentacle_Madness { ; time=0:03:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=hypermandelbrot2 passes=t center-mag=-0.60303739/0/133.912 params=0/0.3/\ 1e-009/0/1.5/0/1e-045/0 float=y maxiter=10000 inside=0 logmap=66 symmetry=xaxis periodicity=0 colors=000R6HR6IR6IR6JR6KS6KS6LT6LT6MU6MU6NV6OW6OX\ 6PY6PZ6Q_6Q`5Ra5Sb5Sc5Td5Te5Uf5Vg5Vh5Wi5Wh5Xh5Xh5Y\ h5Zh5Zg5_g5_g5`g5ag5af5bf5bf5cf5cf5de5ee5ee5fe5fe5\ ge5ge6fe6fe6fe7fe7ee7ee8ee8ee8de8de9de9de9deAceAce\ AceBceBbeBbeBbeCbeCaeCaeDaeDaeDaeD`eE`eE`eE`eF_eF_\ eF_eG_eGZeGZeGZeHZeHZeHYeIYeIYeIYeIXeJXeJXeJXeKWeK\ WeKWeLWeLWeLVeLVeMVeMVeMUeNUeNUeNUfOWeNVeNVeNUeNUe\ NUeNTeNTeNTeNSeNSeNSeNReNReNReNQeMQeMQeMPeMPeMPeMO\ eMOeMOeMNeMNeMNeMMeMMeMLeMLeMLeLKeLKeLKeLJeLJeLJeL\ IeLIdLIdLHdLHdLHdLGdLGdLGdKFdKFdKFdKEdKEdKEdKDdKDd\ KCdKCdKCdKBdKBdKBdKAdKAdJAdJ9dJ9dJ9dJ8dJ8dJ8dJ7dJ7\ dJ7dJ6fVGgWGgWGhXGhYGiYGiZGjZGj_Gk`Gk`GlaGlbGmbGmc\ GndHmcGmbGlbFlaFk`Fk`Ej_EjZEiZDiYUhYUhXUgWUgWUgVUf\ UUfUUeTceScdScdRccRccQcbPcbPcaOmaNm`Nm`MmYPmZTm_Qm\ `MmaJzbFzcCzcCzcCzdBzdAzd9zj7zq7zp6zp6zp6zp6zp6zo6\ zo6zo6zo6zo6zn6zn6zn6zn6z } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 20-03-13 (Hyperbud [?])
by Jim Muth 21 Mar '13

21 Mar '13

FOTD -- March 20, 2013 (Rating ?) Fractal visionaries and enthusiasts: Today's image illustrates what I take to be a bud in the hypercomplex Mandelbrot set. But the bud is not perfect. The straight arms converging on the mouth of the bud show that the bud is not a critical one. In fact, I changed the starting point to 0,0.3,0.3,0 to see what other slices might look like. I doubt that the hypercomplex set has a single critical point. The hyperset is actually a four-dimensional hyperslice through the 8-D Julibrot. But enough of the bud shows through the converging arms to give an idea of the gothic-arch shape of the four-dimensional hypercomplex buds. I gave the image no rating since almost all its impact is in the mathematical aspect, and its color leaves much that could be improved. The name "Hyperbud" describes the scene. The calculation time of 4-3/4 minutes is rather slow. To avoid delay I recommend viewing the finished image on one of the web sites. Time may be saved by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Higher definition versions are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are at: <http://www.Nahee.com/FOTD/> Today here at Fractal Central featured a mix of clouds and sun with a few flurries of snow and a temperature of 39F +4C. The fractal cat slept through most of it, though he did come to life when tuna and cheddar appeared in his dish. The humans simply had a human day. The next FOTD will be posted soon. Until soon arrives, take care, and I heard on the midday news that if an asteroid were ever to be spotted coming our way, our govermnemt would be ready to take action. The action would be to tell everyone to start praying. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Hyperbud { ; time=0:04:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=t center-mag=-0.49291912/+0.10220297/268/1/-2.5/0 params=0/0.3/0.3/0/1.5/0/1e-045/0 float=y maxiter=12000 inside=0 logmap=67 periodicity=0 colors=000R6HR6IR6IR6JR6KS6KS6LT6LT6MU6MU6NV6OW6OX\ 6PY6PZ6Q_6Q`5Ra5Sb5Sc5Td5Te5Uf5Vg5Vh5Wi5Wh5Xh5Xh5Y\ h5Zh5Zg5_g5_g5`g5ag5af5bf5bf5cf5cf5de5ee5ee5fe5fe5\ ge5ge6fe6fe6fe7fe7ee7ee8ee8ee8de8de9de9de9deAceAce\ AceBceBbeBbeBbeCbeCaeCaeDaeDaeDaeD`eE`eE`eE`eF_eF_\ eF_eG_eGZeGZeGZeHZeHZeHYeIYeIYeIYeIXeJXeJXeJXeKWeK\ WeKWeLWeLWeLVeLVeMVeMVeMUeNUeNUeNUfOWeNVeNVeNUeNUe\ NUeNTeNTeNTeNSeNSeNSeNReNReNReNQeMQeMQeMPeMPeMPeMO\ eMOeMOeMNeMNeMNeMMeMMeMLeMLeMLeLKeLKeLKeLJeLJeLJeL\ IeLIdLIdLHdLHdLHdLGdLGdLGdKFdKFdKFdKEdKEdKEdKDdKDd\ KCdKCdKCdKBdKBdKBdKAdKAdJAdJ9dJ9dJ9dJ8dJ8dJ8dJ7dJ7\ dJ7dJ6fVGgWGgWGhXGhYGiYGiZGjZGj_Gk`Gk`GlaGlbGmbGmc\ GndHmcGmbGlbFlaFk`Fk`Ej_EjZEiZDiYUhYUhXUgWUgWUgVUf\ UUfUUeTceScdScdRccRccQcbPcbPcaOmaNm`Nm`MmYPmZTm_Qm\ `MmaJzbFzcCzcCzcCzdBzdAzd9zj7zq7zp6zp6zp6zp6zp6zo6\ zo6zo6zo6zo6zn6zn6zn6zn6z } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 19-03-13 (Hyper-Minibrots [7])
by Jim Muth 20 Mar '13

20 Mar '13

FOTD -- March 19, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows what I take to be parts of minibrots in an East Valley section of the Hypermandelbrot set. Since the HyperMandelbrot set is four-dimensional, its minibrots must be four-dimensional also, which means it will never be possible to show all of one on a flat two-dimensional screen. The name "Hyper-Minibrot" simply describes the image. The rating of a 7 indicates that I did too little work on the colors. The calculation time of 1-1/4 minutes will pass quickly enough considering that a 2-D slice of an 8-D object is being calculated. But calculation may be avoided entirely by checking the web sites. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Yesterday's snow made a quick exit from the Fractal Central area today when the temperature reached 48F +9C under partly cloudy skies. The fractal cat, now in the senior cat category, passed the afternoon sleeping on top of his tall bookcase, while the humans finished the work. The next FOTD will be posted in 24 hours. Until then, take care, and have a good day. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Hyper-Minibrots { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-0.6555077\ 854/0/39173.06 params=0/0.3/0.3/0/1.5/0/1e-045/0 float=y maxiter=5000 inside=0 logmap=181 symmetry=xaxis periodicity=0 colors=000m_am``l``k`_k`_j`ZiaZiaYhaYgaXgaXfbWebWe\ bVdbVcbUcbUbcTbcTacS`cS`cR_dRZdQZdQYdPXdPXeOWeOVeN\ VeNUeMUeMTcLTbLT`LT_KTYKTXKTVKTUJTTJSRJSQJSOISNISL\ ISKISIHSHHSGHREHRDGRBGRAGR8GR7FR5FR4FR3FS4GT5HT6IU\ 7IU7JV8KW9LWALXBMXBNYCOYDOZEP_FQ_FR`GR`HSaITaITeJS\ hLSkMSjKTjITiGUiFUiDUhBVh9Vh8VfAUeBTdCSbERaFQ`GP_H\ P`IQaIRbISbJTcJUdJUdKVeKWfKXfLYgLYhLZhM_iM`jMahMah\ K_gJZeIYdHXbGVaFU_FTZGSXHRWIPUJOTKNRKMQKLRKESK7TK0\ VK2WK4YM6ZO8`Q9aSBcUDcUFcUHcUIcUEcUBcU7cR4cQ1cP2cO\ 3cO3cN4dM5cM5aL6`L6_K7YJ8XJ8VI9UHASHARGBQGBKC6F92E\ D7EGCDJHDMLDPQCSVCV_CYcB`hBcmBfqAij8ld7oYjZcj`djbd\ jcdjeejgejieligjjeijcgjafj`dkZckXbkc`kc_kcYlcXlmVl\ mUlmTlmRmwQmwOmwNmwMmzNkzOizOhzPfzPezQczQbzR`zR_zS\ YzTWzTVzUTzUSzVQzVPzWNzWMzVLzVLzUKzUKzTKzTJzSJzSIz\ SIzRIzRHzQHzQGzPGzPGzPFzOFzOEzNEzNEzMDzMDzDLzMDzV3\ zU5zU7zT8zTAzTCzSDzCaz9Zz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 18-03-13 (8-Dimensional Landscape [7.5])
by Jim Muth 18 Mar '13

18 Mar '13

FOTD -- March 18, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a scene in the eastern part of the main bud of the HyperMandelbrot set, just west of Seahorse Valley. I posted it as a FOTD because of its interesting repeating patterns, which almost but not quite repeat identically. The image rates a 7.5 and would have rated higher if similar near-repeating patterns were not so plentiful in the classic Mandelbrot set. The name "8-Dimensional Landscape" indicates that the image is a slice of the 4-dimensional HyperMandelbrot set, which itself is a 4-D slice through the center of the 8-D HyperJulibrot figure. I am beginning to make some sense of these hyper images, but I still have a long way to go before everything adds up. The calculation time of 2-1/4 minutes borders on slowness. The web sites can bring relief however. Time may be saved by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High definition variations are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And back images are online at: <http://www.Nahee.com/FOTD/> Today brought thick clouds then heavy snow to Fractal Central, while the temperature hovered just at freezing. As of post time, about 2 inches (5cm) had piled up. The fractal cat took a quick glance out the shelf window, then settled to sleep. The humans spent the day getting the routine things done. The next FOTD will be posted in a reasonable time. Until reason prevails, take care, and take time to think things out. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 8-Dimens_Landscape { ; time=0:02:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-0.7978139292256579/-0.016458707578773\ 58/2177/1/-157.5/0 params=0/0/0/0/0.5/0/1e-018/0 maxiter=750 inside=0 logmap=-358 periodicity=0 colors=000UYWOQcMO`LNYKMWJLTIKRHJOGIMCXG8kB4z62tN1\ ob3qc5rd6te8uf9wgBxhCyhFxZHxPJxFLqDNjBPc9QX7SQ5UJ3\ VC2OI8INECSK6XQUYXpZbkafgdjcgmZjqVmuRoxXhsbaogVjmO\ fsHaxAYqH`kNbeTe__gUejOglTinYgg_caU`iNbpG`wIZpKUiM\ QcOLXQHRSCKT8EUDDVICWNBXRAYW9Z`8_d7`eD`eJaePaeVbe`\ befcblaaqZbjUadP_ZLYTGWNBUH6SB2Q5I`6Yj6mt6ghDaXKWL\ RR9XZCVeFTlIRsLPmRSgXVabYWg_VQVV8R_C_cFghIplLxpFqr\ Ajp5dm6Tj7HcBDZF7TL7OT8PX9Q`ARaASXBSKCNFBI9AJ4AJ8A\ L9ANAAPBARCATDAVEAXFFYFL_FN`FPaFRbLTcQVdWXe`ZadWfg\ _kkcpoguokznnvkktfhrZepSboOanL_nOVoRUoULeUUXObNIkI\ GoEDsFJnFOiFTdFY`FdWFiREoQFjNGbLHTJIJHI9FLFEOKERQE\ UVEX`E_eEXr2ajEkbUecQ`cNWcKQcHLcEGcBBc8H`7MZ7SX7XU\ 6bS6gQ6fR8eSAdSCcTEhWHbTFXRDSOCMMAHJ9BH76F6KJ5XN4j\ R3wV2oS6hPAaMEVJINGMGDQ9AU27Y8HXERXK`WQjWUrRVsWVt_\ VudWvhWwmWxqWyu_vvcsvfqvjnvnkvqivpewpaxpYxpUypQzpN\ zmQtjTohWjeZeHnJca`jHOyPr } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 17-03-13 (Green for the Day [7.5])
by Jim Muth 18 Mar '13

18 Mar '13

FOTD -- March 17, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today is Saint Patrick's Day here at Fractal Central, and over the rest of the world as well. In honor of the occasion, I added a touch of green to today's image, which shows a partially eroded minibrot on the northwest shore line of the main bay of the HyperMandelbrot set, which lies in an 8-dimensional Julibrot that I have no intention of getting into. Change the real(p3) or real(p4) (or both) parameters to zero and see the minibrot before it was eroded. Surprisingly, the maxiter is now far too low to show the uneroded minibrot, which indicates that everything within the outer circle of the image is new stuff existing only in the higher-dimensional part of the Julibrot. The rating of 7-1/2 includes a bonus for honoring the day. The name "Green for the Day" acknowledges that it is a special day for the Irish. The calculation time of 6-1/4 minutes is slow. Luckily, the web sites can relieve fractal slowness. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Cloudy skies and a temperature of 39F +4C made the outdoors rather unpleasant here at Fractal Central today. The fractal cat and fractal humans had a typical uneventful day indoors. The next FOTD will be posted in the proper time frame. Until whenever that is, take care, and be of sound mind and body, but don't let the mind and body get too noisy. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Green_for_the_Day { ; time=0:06:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-0.7329867\ 340546847/+0.2212534245722819/3.30344e+010/1/168.7\ /0 params=0/0/0/0/0.13/0/1e-070/0 float=y maxiter=2450 inside=0 logmap=-1916 periodicity=0 colors=00005A05A05A05A05A05A25A35A55A65A85A95AB5AD\ 5AE5AG5AH5AJ5AK5AJ5AI5AI5AH5AG5AG5AF5AE5AE5AE5AE5A\ F5BG6CH6DI7EK7FM7GN7HP7IR7JT7KV7LW8MW8NW9OV9PTAQSA\ RRASPATOAUNAVLAWKAXIAYIAZIA_HA`HAaHAbGAcGBdFCeFDfF\ EfDFgCGhBFh9Kc8P_7UW6YS5bO4gK1mH3kG5jG7iF9gFBfFDeE\ FdEHbDJaDL`DN_COYCQXBSWBUVBWTAYSA_R9aQ9cO9eN8gM8hL\ 8uaft_etZesYesXerVerUerTeqSeqRdpPdpOdpNdoMdoLdnJdn\ IdmHcmGcmFclDclCckBckAcj7hk9clAZmCVmDQnFMoGHoHDpKE\ pMFpOFpQGqTGqVHqXIqZIr_Jr`JraKrbLscLseMsgMsiNtkOtm\ OtoPtpPsqQsrRrsSrtSquTqvUpwVpxVpycozmozrnzvnzzmzzm\ zzmzzjzzgzzdzzK3OI8KGDHEIDDNAHNBLOCPODSYEUgGVcHWhJ\ YmKZrM_vNazPxzpsnqnhqiardWr_PsVJszzsOzVzzaEzg9an4Y\ tJdmYkflr_zyUxpQwhNu_KtSHrJEqBBp38uK7y_7ZrbXj_VcXT\ WUSPRQHOOALN3ILAFKHDIOBHU9G`7Eg5Dn3Ct1Iq0No0Sl0k_G\ lRHlIIm9Jm1KoGUpVcrimsxvHmvccecpQcyAcc7coKccXcmizm\ uzztzzszzrzzrzzpzznzzlzzF } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 16-03-13 (Into a Magic Land [7.5])
by Jim Muth 16 Mar '13

16 Mar '13

FOTD -- March 16, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image continues the adventures in the land that is not supposed to exist but has not heard the bad news and exists anyway. The scene of the image is at the pseudo-origin of a minibrot, which is the spot at the center of the main bay of the minibrot. I rated the image at 7-1/2, mostly because of the extra work I put into the coloring. Most of the color palette however was lifted from the FOTD image of March 4. I can say nothing about the number series of the circular elements surrounding the center of the image because I know nothing about the series. The name "Into a Magic Land" is a bit overblown, though in some ways, fractals are quite magical. The calculation time of 3-2/3 minutes is slower than some recent images but still well within reason for today's image. Relief from the calculation chores may be found at: <http://www.crosscanpuzzles.com/Archives.html> with high-definition diversions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images at: <http://www.Nahee.com/FOTD/> Moderate to heavy snow fell here at Fractal Central today, but the temperature of 34F +1C kept it from building up on the pavements. On the grass however, about 3 inches or 8cm accumulated. The fractal cat spent much of his time watching the pigeons flapping around on the outside window sill. The humans spent the day doing human things. The next FOTD will be posted in the proper time. Until whenever that might be, take care, and if everyone knows how to solve the world's problems, why do the problems still exist?. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Into_a_Magic_Land { ; time=0:03:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 center-mag=+0.261738445061591/-0.002047573531171/\ 1.060901e+009/1/-5/0 params=0/0/0/0/1/0/1e-100/0 float=y maxiter=3200 inside=0 periodicity=0 colors=000XEHYBIZ9I_6J`8JaAK`CJ_EI_GIZIHYKHYMGXOGW\ QFWSEVUEUUDUUDTUCQUBTUCVUCYUC_UCbUCdUCfUDiUDkUDnUD\ pUDqU8rUDrUHrWLsYPs_Ts`Ysbaqdeogimemkcqiahg__eYScW\ JeUAgSFiQKkOPmMUmKZlIgkGfjEfjFfjGfjGfjHfjIfiJfiKfi\ KfiLfnMfnNfhGAiHAjIAkLAlOAmRAnUApWArZAtbDzjGzqcxzz\ zzzfZOWPPPHQMDQLBMLBRJDSHGSIITKJTMLWOLYQMYSM`UNcVN\ fWOiXPlYRoZUr_Wv`Zya`yc`zd_zfYtdWqeRocMiaId_F`YCXW\ 9TX6SX3SY7SYASZESZIS_MS_PS`TS`XSa`SacSbgSbkSfoQbnS\ ZpTVsVSqWOqXKoZGmcDkh9im5gr2ezNjzRd`UeZXeX_eVbeTeb\ Rh_PkXNnUMlSNjRNiQNgONeNNdMObLO`JO_IOYHORDPXGObJNc\ MMcPLcPKcPIcOHcUGcUFcUDcUCcUBcUAcU8cU7cU6bP5`P3_O2\ YM1XK0YK2ZK3WK1ZL4`L7bLAdOCfVFhVIkUKoUNrUQtUSzWVzY\ Yz__zcXkbVeaS_`QVZOPZLJZJDZG7ZE2ZC4ZF6ZI8ZKAZNCZQD\ ZSFZVHZcJZmLZmLZzMZzM_zNazNYzNUzOPzOLmPNcPPUOPVPQT\ PRRQRPQTNRUMRWKSWISWGTWETXDUYBUZ9VZ7YY2VX6SW9PVCQU\ DRUDSUETSETQFUPFVMGWJGXHH } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 15-03-13 (Minibrot Madness [?])
by Jim Muth 16 Mar '13

16 Mar '13

FOTD -- March 15, 2013 (Rating ?) Fractal visionaries and enthusiasts: Today's image is a variation on a minibrot. I named it "Minibrot Madness" because the minibrot is unlike any I have seen so far in Fractal Land. Actually, the image is a continuation of the recent explorations in the 4-D HyperMandelbrot set created by hypercomplex numbers. The 'stuff' condensing around the edges of the bays and buds of the minibrot is just as much a mystery as the eroded 'stuff' that obscures the minibrot in the image of March 04. It has no right to be there, but there it is anyway, violating all the rules of common-sense math. This 'stuff' is sensitive to the value of the real(p3) and real(p4) parameters. And if the maxiter is increased, the 'stuff' expands and soon fills in the remaining open areas inside the minibrot. The image might be a real fractal; it might be an artifact of math imprecision. But until I find out exactly what is going on with these hyper-images, I will rate them with a question mark. One thing not in doubt is the speed of the parameter file, which on the modern day speed-demons will finish in 45 seconds or less. Of course, the simplest way to see the image is always to check it on one of the FOTD web sites. View the finished image at leisure at: <http://www.crosscanpuzzles.com/Archives.html> And check the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The thousands of FOTD back images are at: <http://www.Nahee.com/FOTD/> Clouds and a temperature of 45F +7C prevailed today here at Fractal Central, while the fractal cat prevailed in my favorite chair. The humans simply prevailed, which requires no further elaboration. The next FOTD will be posted in the appropriate time. Until whenever, take care, and they say heaven exists in four- dimensional space. No wonder we can't spot it with our three- dimensional scientific devices. All we can see are 3-D slices. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Minibrot_Madness { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-0.7329986\ 40931621/+0.2212681808037857/4510/1/-158.75/0 params=0/0/0/0/0.135/0/1e-070/0 float=y maxiter=2625 inside=0 logmap=-54 periodicity=0 colors=000mtImtFltDjtAit8gvBcvD_wGWwISxLOxNKxPJtRI\ pSHmTHiUGfVFbXE_YEWZDT_CP`COaEOZFQWHSTIURJVOLWLMYJ\ OZGP`DQbBSd8Tg5Ui3Wj8YkD_lHamMcoQeoVgpZipckqgmrlor\ pqsursyntyktyhuyeuybuyZvyWvyTvyQwyNwyJxyGxyDxyAyy7\ yy4yyEstOmoYgkgafqXboYdmYekYfiYhhZifZjdZlbZmaZn`Uo\ _QoZMpYIpXDqW9qV5rU1rX3qZ5qa6qc8qf9qhBqkDqmEqpGqrH\ qpJrnKrmLrkNrjOrhPrfQreSscTsbUs`VsZXsYYsWZsV_sYWn_\ SjaOecKafGXhCTj8Ol4Kn0Gm3Em6Dm9CmCBmEAmH9mK8lN7lQ6\ lS5lV4lY3l`2lc1le0hb4d_8`XCXUGTRKPPNLMRHJVDGZ9Db5B\ e8AfAAgC9hE9hG8iI8jK7kM7kP6lR6mT5nV5nX4oZ4p`3qb3qX\ 6nS9kNChIFeDHcFJaHL_JMYKOWMQUORSPTQRUOTWMUYKWZIY`G\ ZbE`cCbeAcf8Uk6Lo5Cs43w35t66q87nB8kDAhFBeICbK8eLD`\ MHXMLSMPONTJNXFN`BNaHQbMTcRWdXZeaaffdBJZfegfkfRrqm\ mlfpe_s_TvTNxNKnUIe`FWfDNm89yBEsEJnHNhKSczFJqKLmLO\ iLReMUbMXZN_VNbROeNOhKPkOgYN0UN0UEB0NAAWAKdAUmAanG\ dnMfoRioXkpbmpgpqmrzzzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 15-03-13 (Minibrot Madness [?])
by Jim Muth 16 Mar '13

16 Mar '13

FOTD -- March 15, 2013 (Rating ?) Fractal visionaries and enthusiasts: Today's image is a variation on a minibrot. I named it "Minibrot Madness" because the minibrot is unlike any I have seen so far in Fractal Land. Actually, the image is a continuation of the recent explorations in the 4-D HyperMandelbrot set created by hypercomplex numbers. The 'stuff' condensing around the edges of the bays and buds of the minibrot is just as much a mystery as the eroded 'stuff' that obscures the minibrot in the image of March 04. It has no right to be there, but there it is anyway, violating all the rules of common-sense math. This 'stuff' is sensitive to the value of the real(p3) and real(p4) parameters. And if the maxiter is increased, the 'stuff' expands and soon fills in the remaining open areas inside the minibrot. The image might be a real fractal; it might be an artifact of math imprecision. But until I find out exactly what is going on with these hyper-images, I will rate them with a question mark. One thing not in doubt is the speed of the parameter file, which on the modern day speed-demons will finish in 45 seconds or less. Of course, the simplest way to see the image is always to check it on one of the FOTD web sites. View the finished image at leisure at: <http://www.crosscanpuzzles.com/Archives.html> And check the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The thousands of FOTD back images are at: <http://www.Nahee.com/FOTD/> Clouds and a temperature of 45F +7C prevailed today here at Fractal Central, while the fractal cat prevailed in my favorite chair. The humans simply prevailed, which requires no further elaboration. The next FOTD will be posted in the appropriate time. Until whenever, take care, and they say heaven exists in four- dimensional space. No wonder we can't spot it with our three- dimensional scientific devices. All we can see are 3-D slices. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Minibrot_Madness { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=-0.7329986\ 40931621/+0.2212681808037857/4510/1/-158.75/0 params=0/0/0/0/0.135/0/1e-070/0 float=y maxiter=2625 inside=0 logmap=-54 periodicity=0 colors=000mtImtFltDjtAit8gvBcvD_wGWwISxLOxNKxPJtRI\ pSHmTHiUGfVFbXE_YEWZDT_CP`COaEOZFQWHSTIURJVOLWLMYJ\ OZGP`DQbBSd8Tg5Ui3Wj8YkD_lHamMcoQeoVgpZipckqgmrlor\ pqsursyntyktyhuyeuybuyZvyWvyTvyQwyNwyJxyGxyDxyAyy7\ yy4yyEstOmoYgkgafqXboYdmYekYfiYhhZifZjdZlbZmaZn`Uo\ _QoZMpYIpXDqW9qV5rU1rX3qZ5qa6qc8qf9qhBqkDqmEqpGqrH\ qpJrnKrmLrkNrjOrhPrfQreSscTsbUs`VsZXsYYsWZsV_sYWn_\ SjaOecKafGXhCTj8Ol4Kn0Gm3Em6Dm9CmCBmEAmH9mK8lN7lQ6\ lS5lV4lY3l`2lc1le0hb4d_8`XCXUGTRKPPNLMRHJVDGZ9Db5B\ e8AfAAgC9hE9hG8iI8jK7kM7kP6lR6mT5nV5nX4oZ4p`3qb3qX\ 6nS9kNChIFeDHcFJaHL_JMYKOWMQUORSPTQRUOTWMUYKWZIY`G\ ZbE`cCbeAcf8Uk6Lo5Cs43w35t66q87nB8kDAhFBeICbK8eLD`\ MHXMLSMPONTJNXFN`BNaHQbMTcRWdXZeaaffdBJZfegfkfRrqm\ mlfpe_s_TvTNxNKnUIe`FWfDNm89yBEsEJnHNhKSczFJqKLmLO\ iLReMUbMXZN_VNbROeNOhKPkOgYN0UN0UEB0NAAWAKdAUmAanG\ dnMfoRioXkpbmpgpqmrzzzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 14-03-13 (Hyper Something [?])
by Jim Muth 15 Mar '13

15 Mar '13

FOTD -- March 14, 2013 (Rating ?) Fractal visionaries and enthusiasts: Today's date is 3-14, which makes it international PI day. In two years it will be 3-14-15, which will make it an even more accurate PI day. And in three years it will be 3-14-16, which is the rounded value of PI that I learned in elementary school. In honor of the number PI, today's image has absolutely nothing to do with 3.141592654.... In the last FOTD, I said I was finished with the hypercomplex stuff for a while. I lied. I am becoming so fascinated with the theme that I'll probably continue with it for a number of days. I will give no rating to the images because I have no idea what I am dabbling in. Today's image shows another scene that should not be there. The location is at the center of the main bud of a minibrot in an elephant on the southern shore line of East Valley of the parent HyperMandelbrot set. The eighteen arms are arranged around the center in six groups of three. But the six groups are not identical, with each group having its own particular arrangement of its arms. The name "Hyper Something" indicates that the appearance of the image indicates that it involves hypercomplex numbers, but at the same time I have no idea what the period of the arms means. Regardless of what is going on, the image is a pretty good one, which, if I had given it a rating, would have rated an 8. The calculation time of 40 seconds will pass quickly, leaving ample time to ponder the mathematical mysteries of the image. For even more pondering time, check the completed image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Today came on like a day in mid-January here at Fractal Central, with biting winds, scudding clouds and a temperature only a degree or two above freezing. The fractal cat took advantage of the sun while it was shining, and found comfort in my favorite chair when the sun failed him. The humans simply had another day with nothing to report, The next FOTD will be posted in the proper time. Until whenever that might be, take care, and now is the time for action. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Hyper_Something { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=+0.2536635\ 94488/-0.000352077249/4318949/1/-147.5/0 params=0/0/0/0/1/0/1e-075/0 float=y maxiter=600 inside=0 periodicity=0 colors=000bELdHMeKNfNPhQQiTRjXTl_UmbWneXphYqk_rn`s\ qaondkkfgihcfj_clWanSZpOWrKUtGRvCOx9MzEKuJJpOIkTHf\ YGabFX`JXZMXXPXWSXUVXSZXQaXPdXNgXLjXJnXIqXGtXEwXDz\ XIwSNtOSrJXoFalAej6af8YcAU_CQXEMTGJQHIFdGJhFMkEQnD\ TqCWtLevUowZTBYbSXlhLLrRcunM0iWGedV`mifUjbco_mtYl0\ XpLXsddkf`qopk2fqWM3bQMjUdqH`RNhbSomOJPth2hoWCbYpw\ kkvofvravuyOeo_lekrZijGjXLmcPpjTsqjVIedX`mj3scIunk\ DHc_bgjZapkoxFjwRewa`vmF`oLhrRougm8awR_vbYvm7TaGbi\ Plq7WzEbyKiyRpxhd1bmVyB_qNfjZlcjrht2euHbuW_vj2K1AU\ GIcVQmiI`hKXhLUhQYkV`m_dodgq_YoWOnSElO4kfxFkqGpjGt\ dGnK2iUHecWhc_PKxRKwTKvUKuAAKKlgzzz1So2Tm2Tl2Uj2Ui\ 2Vg2Vf2Vd3Wc3Wa3X`3XZ3YY3YW3YV4`S5cQ5eN6hL7jJ7mG8o\ E9rC9t9Aw7Av5It4Qq4Yn4fj3lg3nd3oa6pZ9qWCrTFrRIqOLq\ LOpIRpFUpDWgM__VbSbfKkiCslFomzzmLznzznR_oTWoWSpZOp\ aKqdGqfDqgbrhcoidmiejjfhjgekhcli`ljZmkWmlUqmTunTxo\ TsZVnJWlMUjPThSSfVQdYPb`O } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 12-03-13 (More Vacuum Energy [7.5])
by Jim Muth 13 Mar '13

13 Mar '13

FOTD -- March 12, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is another, and probably the last, of the present series of ventures into the world of the four-dimensional HyperMandelbrot set. To create the image I took the image of March 4 and decreased the value of the real(p4) parameter to 1e-170. As a result I found that the number of arms surrounding the center point, which is the pseudo-origin of the underlying minibrot, has increased. I'll make no effort to explain the number of elements around the center, since I have no idea what determines this number. But the number does appear to increase by increments of two as we venture deeper into the apparently limitless center point. The color palette is the same one that appeared in the March 4 image, with a few tweakings to smooth some rough breaks. The rating of 7-1/2 is a bit conservative, but this is the third image based on the same theme, which detracts from its worth. The calculation time of 2-1/2 minutes is a fair price for the image. And as always, the web sites are even more fair. The completed image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Variations are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> back images are available at: <http://www.Nahee.com/FOTD/> The day began with rain here at Fractal Central. The rain ended by midday, but the clouds hung on all afternoon. The temperature of 50F 10C was pleasant enough. The fractal cat spent the morning watching the world go by and passed the afternoon wrapped in an afghan and visible as only a lump. The humans passed the day pondering existence. The next FOTD will be posted in a day or two. Until whenever, take care, and let a smile be your umbrella on a rainy day, but don't start complaining when you get wet. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= More_Vacuum_Energy { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 center-mag=+0.2587410\ 516089257/-0.0013438824741138/8.974e+009/1/-162.5/0 params=0/0/0/0/1/0/1e-170/0 float=y maxiter=3200 inside=0 periodicity=0 colors=000QDFSEFUFFWGFYHF_IKaJQcKWbIebGgbEpdFrfGzh\ GziHwjIziJziKziKzkLzkMzmNznOznMznOzmPwmRtmVqnXmo_h\ pccrhZtl_vojxpzpmcfajWSPPLQMGQLEMLERJFSHHSIITKJTML\ WOLYQMYSM`UNcVNfWOiXPlYRoZUr_Wv`Zya`yc`zd_zfYtdWqe\ RocMiaId_F`YCXW9TX6SX3SY7SYASZESZIS_MS_PS`TS`XSa`S\ acSbgSbkSfoQbnSZpTVsVSqWOqXKoZGm_Dk`9ib5gc2edNdbRd\ `UeZXeX_eVbeTebRh_PkXNnUMlSNjRNiQNgONeNNdMObLO`JO_\ IOYHORDPXGObJNcMMcPLcPKcPIcOHcUGcUFcUDcUCcUBcUAcU8\ cU7cU6bU5`U3_U2YU1XU0YU2ZU3WU1ZV4`V7bVAdVCfVFhVIkU\ KmUNoUQqUSsUVuUYwU_qZXkbVeaS_`QVZOPZLJZJDZG7ZE2ZC4\ ZF6ZI8ZKAZNCZQDZSFZVHZYJZ_LZbLZfMZdM_cNaaNY`NU_OPY\ OLXPNVPPUOPVPQTPRRQRPQTNRUMRWKSWISWGTWETXDUYBUZ9VZ\ 7YY2VX6SW9PVCQUDRUDSUETSETQFUPFVMGWJGXHHXEHYBIZ9I_\ 6J`8JaAK`CJ_EI_GIZIHYKHYMGXOGWQFWSEVUEUUDUUDTUCQUB\ TUCVUCYUC_UCbUCdUCfUDiUDkUDnUDpUDqU8rUDrUHrWLsYPs_\ Ts`YC6FE7FG8FI9FKAFMBFOCF } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 11-03-13 (More Heptic Stuff [7.5])
by Jim Muth 11 Mar '13

11 Mar '13

FOTD -- March 11, 1013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a scene in the Scepter Valley of the same oversized parent Mandelbrot set that created the March 9th image of two days ago. The overwhelmingly obvious minibrot at the center combines the quadratic elements closer to the minibrot with the heptic (I guess that's the word) elements farther out, to create an entirely new world of high-order images. I named the image "More Heptic Stuff" in the hope that 'heptic' is the right word for Z^7 stuff. (As I see it, the series goes . . . linear, quadratic, cubic, quartic, quintic, hexic, heptic, octic, nonic . . . etc.) The rating of 7-1/2 seems about right while viewing the image, but the rating appears too high when the calculation time of a dragging 20 minutes is considered. Viewing the finished image on one of the FOTD web sites can raise the rating a point or so. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> High-definition renderings are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are at: <http://www.Nahee.com/FOTD/> With near total sunshine and a temperature of 59F 15C, yesterday was infested with spring here at Fractal Central. The fractal cat caught the lazy bug early and stretched on his shelf in the southwest window most of the afternoon to take advantage of the sun, which at this time of the year is as strong on his shelf as it ever gets. Today turned out cloudy but with another quite mild temperature of 55F 13C. The humans had average days both days. The next FOTD will be posted whenever it is. Until then, take care, and I hear from some in the media and also from FL that there is a war against women. But I am uncertain just which group of people is supposed to be waging war against just which group of women. Is it all men against all women, or only right- wing men against left-wing feminists, or is it the entire male- dominated culture itself that is at war against women? I have always assumed there are fewer women in high-paying top executive offices because women have the common sense to avoid the life-shortening dog-eat-dog race to the top, and not because there is a male-created glass ceiling holding back all the aspiring women. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= More_Heptic_Stuff { ; time=0:20:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip passes=1 center-mag=-18.7620116655262/+0.3566079766580704/\ 1.511423e+009/1/-100/0 params=7/15 float=y maxiter=9000 inside=0 logmap=-1600 periodicity=6 colors=000KYDKYDLYDNXCOXCPXBQWBRWASWAUXDWXFXXIZYK_\ YNaYPcYSdZUfZXgZZiZak_cl_fn_ho_j`hiNpi9xiFseLobRj_\ WfXaaUgYRlUOiQLgMIeIFcFCaB9_76Y43Q7II9XABk3Dz4Ew4F\ t4Fr4Go4Hl4Hj9FdED_IBVN9QR7LW5G_3Bd16h01fA4eJ7dS9b\ `CaiF`rH_nLZkPYhTXeWWb_V_cUWgTTjSQnRNrQKvQHyOLxMOw\ KRvJUuHXtF`sDcrCfqAip8lo7oo8kn9hnAenBbnC_mDXmDTmEQ\ mFNlGKlHHlIElIBlLAiN9fQ9cS8`U7YX7VA6A`5Pc5Me4Jg4Gr\ jKngJjeIfcHb`GZZFVXERVECdAEcCGbDIbEKaFM`GO`IQ_JR_K\ TZLVYMXYOZXP`WQbWRdVSeVTp_NzdIwgHtiGqlFnnEkqDhsCev\ BbxA_zAVzARzDMzGKzKIzJHzIFtHEtGDuGRc8TXBVRDXKGZDI`\ 6Lb0NZ4PV7RRATNDVJHXFKZBN`8QaI`bSjcPc`McZJcXGcUDcS\ AcQ7cN4cL1cJ0cO0cT0cY0ca0cf0ck0co5mm9mkDmjHmhLmfPm\ eTmcYmaam`emZimXmmWqmUumSymRnmScmTUmUJmV9mWAmYAmZA\ m`AmaAmcAmdAmfAmgBmhBmjBmkBmmBznBzpBzqBzrLzjVzbdzV\ mzNjzPhzRezTczVazXZzZXz_VzaSzcQzeOzgLziJzkHzlIzkJz\ kKzkLzkMzkNzkOzkPzkQzkRzk } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 09-03-13 (Forever Seven [8])
by Jim Muth 11 Mar '13

11 Mar '13

FOTD -- March 09, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows that heptic minibrots need not always be the dull high-order things one would presume. The parent fractal is an oversized Mandelbrot set that has been corrupted not very far from its surface with order-7 energies. The scene is in the East Valley area of the parent's large main- stem minibrot, which is already well on the way to becoming an order-7 minibrot. This minibrot's East Valley has already vanished and been replaced by burgeoning order-7 lobes, which are surrounded by loosely connected spirals. These spirals still abound in today's image, which lies rather deep in one of the larger spirals. The rating of an 8 is my estimate of the image's worth. The minibrot really is quite unusual. Foe comparison, try to find as interesting an order-7 minibrot in the straight Z^(7)+C Mandeloid. The name "Forever Seven" indicates that from the magnitude of today's image all the way to infinity the order-7 minibrots will prevail. Check the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images are at: <http://www.Nahee.com/FOTD/> We had a preview of spring here at Fractal Central today when the temperature reached 55F 13C and the sky was horizon-to- horizon blue. The fractal cat stretched to his fullest cat length in the warm sun and was as happy as a cat could be. The humans were a satisfied neutral, which is the usual condition of earth-bound humans. The next FOTD will be posted in about one day. Until then, take care, and how did we ever get into a situation where we must have ever-higher technology if we hope to survive? Can no one see that it's a dead end? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Forever_Seven { ; time=0:02:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip passes=1 center-mag=-26.21766685865878/-0.00673733985958567\ /8.354727e+010/1/-63.45/0 params=7/15 float=y maxiter=1800 inside=0 logmap=238 periodicity=6 colors=000A5cA5eA5fA5gA5hA5iA5jA5kA5mA5nA5oA5pA5qA\ 5rA5sA5qA5oA5mA5kA5i95h85f75d65c55c55c45c45c45c45c\ 45c45c55c65c75c85c95cA5cA5cA5cA5cA5cA5cA5cA5cA5cA5\ cA5cA5dA5eA5eA5dA5cA6bA6aA7`A6Z96W95T84Q84M73K72J6\ 2J63J74K74M85O86Q96S97UA7WA8Y99_89a7Ab6Bd6Af5Ah5Aj\ 4Al3An3Ap2Ar1At1Av0Mx0Oy1Gx2Ix3Mw4Qw5WvA5WA5YA5ZA5\ _A5`A5aA5bWTiTVjRXkOZlM`mJbnHdoFepJdqMdqPcrScrVzrY\ zs`zsczsWzjPzbHzUAzMFzLKzKPzKUzQZzVcz`gzelzjqzpvzu\ zzzWzBazEgzHmzKszMpzPnzRzaTzaVzaXz`_z`aa`c_`eY`gab\ eecdidbmeaqf_ugZxhYwf_wd`vbbv`cuZeuXfuWgtUitSjsQls\ OmrMorKprJqmHlhGhcEc_D_cHafKbiNdlQemRcnSanT`oUZpVY\ pgWqXVrYTrZSs_Qt`PtiNubMvcKvdJqhOmkSinWdq``tdXwhTz\ lOujKpiGkhCfg8af4Xe0Sd3Tf5Uh7Uj9VlBWnDWocXqcYscYuc\ ZwcZxc_wc`vcavcbumctmdtmesmfrzgrzhqzipzjpzkozlnzXz\ zUzzRzzOzzMzzLzzKzzIzzHzzGzzFzzJzzNzzQzzRzzRzzRzzS\ zzSzzSzzSzzRzzRzzRzzRzzRz } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 08-03-13 (Vacuum Energy [8])
by Jim Muth 09 Mar '13

09 Mar '13

FOTD -- March 08, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image is an exploration into the detail of the cap over the minibrot that appeared as the 'Translateration' image of March 4. This spurious cap is rather sensitive to parameter changes, most of which I have yet to check. Today's image shows the result of one such change. In it, I increased the exponent of the real(p4) parameter 15 orders of magnitude and checked the chaos the change creates in the minibrot cap. The underlying minibrot lies in the trunk of the period-34 elephant on the south shore line of East Valley of the Mandelbrot set, but this number appears to be totally lost in the image, where the topmost pattern has 8 elements and the next pattern inward has 10. I have named the image "Vacuum Energy". The name indicates that the image overlies the emptiness of the interior of a minibrot, and sometimes, just as in the 'real' physical world, the nothing of a fractal vacuum can be filled with quite a bit of something. The rating of an 8 indicates both mathematical and artistic value. The color palette is a tweaking of the palette I used in the March 4 image. The calculation time of 1 minute, 25 seconds is fast enough. Of course, the web sites are even faster. The big-time business pros will view the finished image at: <http://www.crosscanpuzzles.com/Archives.html> But wait! High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the back images are stacked at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds with a temperature of 43F +6C made today a typical end-of-winter day here at Fractal Central. With all the talk on the big news outlets of snow in the Northeast, one would think FC was buried. Actually, not a flake has fallen in the past week and the ground is bare, with bulbs already popping up in FL's garden. The fractal cat is unconcerned with snow or flower bulbs. All he wants to do is get into the places where he is not permitted, such as storage closets and the outdoors. The humans, with enough to keep them busy, want little. The next FOTD will be posted in a number of hours. Until whenever, take care, and we will never solve our problems until we fully understand them and have the courage to accept them for what they are. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Vacuum_Energy { ; time=0:01:25.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 center-mag=+0.2587410\ 51607766/-0.00134388247424955/4.63764e+010/1/-159/0 params=0/0/0/0/1/0/1e-085/0 float=y maxiter=2700 inside=0 periodicity=0 colors=000E0lF2lG4lH6lI6nK8nM9nOBnQDnSDnUEiXGa_ITb\ JLeJDhJ4kN0nQ0qT0tX0w`0ze0zl1zs6zw_zmYqaVgSJ_GLQ8K\ J1JG0GE0KB1N86N99PDBQGEWJE_NG_QGdTIiVInXJsYLx_OzaT\ zbXzdazfdzidzkbzn_zkXzlOziGsf9kb4d_0YX0RY0QY0Q_0Q_\ 0Qa2Qa9QbGQbLQdRQdYQfdQfiQgpQgwQnzNgzQazRVzVQzXJzY\ Dza6zb1wd0sg0pi0lkIkgOkdTlaYlYblVglRlgOqbLwYIzTGxQ\ ItOIsNIpJIlIIkGJgEJdBJb9J_8JO1LY6JgBIiGGiLEiLDiL9i\ J8iT6iT4iT1iT0iT0iT0iT0iT0iT0gT0dT0bT0_T0YT0_T0aT0\ XT0aV0dV0gV0kV0nV4qV9wTDzTIzTNzTQzTVzT_zTbzaYwgVlf\ QbdNVaJLaEBaB1a60a20a00a40a90aD0aI0aN1aQ4aV8a_BabE\ agEanGakGbiIffI_dITbJL_JEYLIVLLTJLVLNRLOONOLNRIOTG\ OXDQX9QX6RX2RY1T_0Ta0Va0__0VY0QX0LV0NT1OT1QT2RQ2RN\ 4TL4VG6XB6Y88Y28_09a09b0Bd0Bf0Dd0Bb29b69a98_D8_G6Y\ J6XN4XQ2VT2TT1TT1RT0NT0RT0VT0_T0bT0gT0kT0nT1sT1wT1\ zT1zT1zT0zT1zT8zXEz_LzbRzd_zgfzklzpszlzwizsfqpbbl_\ QiXBlT0pQ4sNDwJLzGTC1lD1l } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 07-03-13 (Back to Earth [7.5])
by Jim Muth 07 Mar '13

07 Mar '13

FOTD -- March 07, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: The ship that in yesterday's image was sailing space has foundered. Someone has let the wind out of its solar sails. It is stuck in the intergalactic doldrums, where it will remain forever, a derelict to remind us that our fondest dreams must remain unfulfilled. And despite the technophiles' optimistic pronouncements, technology will never be able to match our ability to dream unfulfillable dreams. Before we will be able to venture peaceably into space, we will need to solve the economic and environmental problems facing us on the surface of our planet. The rest of the world is tired of seeing people in the U.S. and other advanced countries living lives of luxury at their expense. They rightfully demand part of the material action. They claim that it is time for all people in all countries to enjoy lives like we in the West have been living for a century or more. The problem is that it would take at least four planet earths to supply the resources for this to be possible, and it would be politically impossible to squander resources to venture into space until the economic inequalities are solved one way or the other and we are able to live in peace. Since this is not about to happen, we're stuck on earth, where we will continue to dream awesome dreams and watch them pop like bubbles. The time could never be better to turn to fractals for distraction from this harsh reality. Today's image lies in the center of the 'fan' of one of those 'double negative' parent fractals. I rated it a 7-1/2 out of generosity. Most of the color was created by the Fractint program, the DOS program that will not die, and might even outlive the PC it was written to run on. The calculation time of 4-3/4 minutes is slow, but the web sites are still there. The finished image is available online at: <http://www.crosscanpuzzles.com/Archives.html> With hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and thousands of back images at: <http://www.Nahee.com/FOTD/> Today produced a mix of clouds and sun, with more clouds than sun here at Fractal Central. The fractal cat, realizing early that he would have little sun to stretch out in, spent most of the day eating and sleeping, wishing he could have lived back at the Old Fractal Central when it was the one and only official Fractal Central and the old fractal cats (now gone) spent their days outside, watching, chasing and occasionally catching birds and bugs. The humans spent the day feeling down because of what we see on the declining news channels as the declining condition of our culture. As for the next FOTD, it will be posted when the time comes. Until whenever, take care, and what is the evolutionary advantage of the human ability to so vividly imagine so many things that, because of the body's limitations, we will be forever incapable of doing? Jim (what a waste of imagination) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Back_to_Earth { ; time=0:04:45.00 SF5 at 2000MHZ reset=2000 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.744488223675127/-0.04951958592821827\ /1.377578e+010/1/-140/0 params=-1/-11/-11/-1.1/0/\ 800/0/0 float=y maxiter=2400 inside=0 logmap=364 periodicity=6 colors=000hCNbJWXQdEKMHC2KSMKUcbUFUfb9RNCUWFXdI_mO\ vqMls79zCJxHTvo14modcjjUfpJjGKf`580DOTFN_SlsQSTB`V\ czUhRh`VmTZq9n_DjgHfnPqONid6G`BOgGWndwqYpsRitP_MNa\ ci1BcBNXKZRUj557EHOISd16hBNoyfwddv`IHXNRTTaPYkavYT\ liscTjc_abgTbnhp4`kMTfc_e2SzUm37oZmS_cQ`iNao60oBDq\ GQshsorM7aVXk10dBFYKTRUgZG3UOMPWctCHAEHDKRGRaJNka8\ ychzq`f`an9JmVX5G5SA4OGDiOJhVOgbUfiJMo82XUAEnHCjSA\ gb7cm5_xB`wThvGaz8es00FcJYYQeRXmNL4MQIMUVLZhDYUH`g\ rEUrLCaUZqD9iKL`QYTXiQXYN_iBLzGUwA1GJE_KRjoRTgU__X\ gS_nFphX3CTFSPRf18rBOt`KwFa3HbMJbciCYbJcXQiRXoIknK\ fr57zDYvRbdObmPHZNK0y8ykJwYTvETVHPcJelcFrXNsRbzLH9\ LPQcIexUDFviIlosHoaSrzc3zdHzeVcahVUiRUmOUq6jLAkUEl\ cImlknddohYpmRqq6rCBsSGtf_uUWv`SwgOxnsymgzpWzslzye\ zxZzwSzvez1VzULz`LzgLzn6zrkzIYzaeztVzuczhczkczoczr\ czsmztmzumzEmzTmzgzzWzzIzzVzzczzlzzDzz2zzUzzCzzZzz\ KzzXzzizzYzzezzmzzuzzuzzu } 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 06-03-13 (Ship of Space [8])
by Jim Muth 07 Mar '13

07 Mar '13

FOTD -- March 06, 2013 (Rating 8) Fractal visionaries and enthusiasts: A ship that sails on the stellar winds of space -- how romantic. A fractal ship that sails abstract mathematical hyperspace on the winds of numbers -- well, maybe not quite as romantic, but a lot more real than space ships will ever be. Today's image shows a fractal ship plowing through four- dimensional space on its way to who knows where. I named it "Ship of Space" when I luckily turned the original image, which looked nothing like a ship, upside down before discarding it. The formula, MandelbrotBC2, is an early version of the MandelbrotBC3 formula. I like to bring up the old formulas now and then to see what I can do with them. The calculation time of 1-1/2 minutes is a fair price for the scene. And luckily, the FOTD web site problem has been solved for good (I hope) and the image is posted there. The finished images are once again being posted to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Lots of clouds darkened the skies here at Fractal Central today, while the temperature held around a quite reasonable 43F +6C. The fractal cat, now into the 'senior cat' group, spent the day sleeping on his high bookcase. The humans passed the day doing lots of human and a few inhuman things. The next FOTD will most likely be posted in 24 hours. Until whenever, take care, and we will never get any significant part of our energy from things like solar panels and wind turbines for the same reason that we stopped using wind to propel our large sea-going ships. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Ship_of_Space { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.6537202144440802/+0.4582235896757069\ /14661.82/1/-149.4/0 params=1.5/0/-1.5/0 float=y maxiter=1000 inside=0 outside=fmod periodicity=6 colors=000OdDSfEXiG`lIdoKiqLmtNqwPvzRuwRstRqqSomSm\ jTkgTicTg`UeYUcVVaRV_OVYLWWHWUEXSBXQ7YQ7XQ7WP7UP7T\ P7SO7QO7PN7ON7MN7LM7KM7IM7HL7GL7EK7DK7CK7AJ79J78J7\ 6I75I74H72Aw3X2yILlHNjGPhFRfEUdDWbCY`B_ZAbX9dV8fT7\ iQ7hQ7gP8fO8eO9dN9cM9bLAaLA`KB_JBZICYICXHCWGDVFDUF\ ETEESDFQCGQCIQDJQDLQEMQFOQFPQGRPHSPHUPIVPJXPJYPK_P\ L`PLbOMcONeONfOOhOPiOPkOQmNRmORlQRkSRkTRjVRiXSiZSh\ _SgaSgcSfeSefTdhTdjTclTbmTboTaqU`sU`tU_vUZxUYzVZxV\ `vUbtUcrTepSgnSilRjjQlhQnfPpdOpeMpgKpiIokGomEooCoq\ Ans8nu6nw4my2ku6ipAflEdgJacN_ZRXUWXUUXUSXVQXVOWWMW\ WKWXIWXGWYEVYCVZAVZ8V_6V_4U`2U`4U`6U_8V_AVZCVZEWYG\ WYIWYKXXMXXOXWQYWSYVUYVWZUYXSWVQUTNSRLQPJOMGMKEKIC\ IG9GE7EC5C92AU2Nn1_`y`hygqxzzwzwvzttzqrznpzkozhmwe\ kubis_grXfrUdqRbqO`pL_pIYoFWoCUn9UmEWhJ_cPdZUhUZlP\ dmK`nPWkUSgZNccJ`hEYmEVmDTmDRmCPmBNnBLnAJn9Hn9Fn8D\ o7Bo78o50K50K50K50K50K50K } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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Bad link to Hal's March, 2013 FOTD page repaired.
by Hal Lane 07 Mar '13

07 Mar '13

I had a bad link on my main page: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html pointing to the March, 2013 page. It's been repaired and the March fractal offerings are up to date -- although I've got a zoom into the area in this image where the two series of concentric circles are 'kissing,' calculating away right now: http://www.emarketingiseasy.com/TESTS/FOTD/2013/F130304X.jpg - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 05-03-13 (The Fuzzy-Wuzzies [7])
by Jim Muth 06 Mar '13

06 Mar '13

FOTD -- March 05, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Fuzzy-Wuzzies". The name refers to the overall fuzziness of the image, which is due to the limited math precision. If I had backed out a little, I could probably have found a very similar scene with perfect resolution, but laziness prevailed. The rating of a 7 might have been higher if the math routine could have dredged up a little more resolution. But even as it is, the image is striking enough to be declared FOTD. The parent fractal is actually a hugely oversized field of scattered fractals, with today's scene lying in the main stem area of the centermost fractal. The calculation time of 1-1/3 minutes will pass in a flash, especially on newer machines. (And who other than myself still uses those older dinosaurs?) The finished image is at: <http://www.crosscanpuzzles.com/Archives.html> The hi-def versions are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are at: <http://www.Nahee.com/FOTD/> A cloudy morning gave way to a sunny afternoon here at Fractal Central today, while the temperature of 41F +5C brought a feeling of spring to the area. The fractal cat had just about lost all hope when the sun burst forth, giving him an enjoyable afternoon on his shelf. The fractal humans made it through the day without incident. The next FOTD will be posted when it is ready. Until whenever, take care, and why worry about oversized sugary sodas. Let's pass legislation to solve our real problems. Let's make it illegal for asteroids to threaten the earth, and for hurricanes to strike the U.S., and for tornadoes to strike in Oklahoma, and of course for the climate to grow warmer, and for volcanos to erupt. And it certainly should be illegal to carry illegal guns. (BTW, I actually heard on a certain un-named news channel that we can't crack down on illegal guns in the cities because we would end up putting too many city criminals in jail.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Fuzzy-Wuzzies { ; time=0:01:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+3.429528921055554/+0.2562473412832453/\ 2.329006e+012/1/-28.75/0 params=1/-1.5/0.01/-150/0\ /0/0/0 float=y maxiter=1200 inside=0 logmap=135 periodicity=6 mathtolerance=0.05/1 colors=00000G00H00H00I00I12K22K34N44N58Y68Y7EkFEfM\ U`TUQ_zzzq5ki4ob4tW3xP3sRAnTHiVNeXU`Z_WffYla`l`XUY\ TGVQ3SI9QWFbZKgaQldVqedczmRfzEzlJhbNoTRqJVoKReLOcM\ LaHH_IEYEBXE8YFBYGEZMHZRK_SN_TQ`TT`UW`VZaVaaWdbXgb\ XjcYmcZpcZsWaqPdoIgmBil6OC9QEBSGETIGVKIXLLYNN_PQaR\ SbTUdUXfWZgYai_ckaelbdjecigbgiafk`en_cpZbrZatXZrVW\ qTTpRQnPNmNKlLHkJEiHBhF8gD5fLLiS`kRbiRdhRefQgeQhcQ\ jbQkaqhcskZunUwqPytKzwFozKdzPVzUUzWUzXUzYUzZUz`Uza\ UzbUzcUzeUzfUzgUzhUzjUzkUzlUzm`zrfzwmzhtzUzzFwzJtz\ NqzRozVlzZizbfzfdzjaznZzrWzvUzyWzvXztZzr_zpazmbzkc\ ziezgfzehzbiz`kzZlzXmzVYz`Ize2zj6zf9zcDz`GzYKzVNzS\ RzPUzLYzI`zFdzCgz9kz6nz3qz0sz9uzHvzPxzXyzdyzVyzLyz\ CuzBqzBmzAjzAfz9bz9Zz8Wz8Sz7Oz7Lz7Oz9RzBUzDWzFZzHa\ zJczL`zOZzQWzSUzURzWPzYMz`KzbHzdFzfCzhAzj8zlAzfBza\ CzXEzSFzNGzIHzDSzMazUZzTWzSTzSPzWMzZJzaGzdDzgAzj7z\ m4zp7zk9zgszzhzeZzLPz1Oz7 } 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 04-03-13 (Translateration [9])
by Jim Muth 05 Mar '13

05 Mar '13

FOTD -- March 04, 2012 (Rating 9) Fractal visionaries and enthusiasts: Today's highly rated image might not be a true fractal at all. It might be no more than an artifact of math imprecision. But whatever it is, it certainly looks like a fractal. The object at the center is actually a minibrot on the southern shore of East Valley of the Mandelbrot set. (Reset the real(p4) parameter to zero to see the undistorted minibrot.) But I have no idea what the bulish-gray fractal canopy partially covering the minibrot might be. The features of this canopy appear to be true fractal stuff, and may be zoomed into to the limit of reso- lution. And yes, changing the value of the real(p4) parameter an order of magnitude or two will change the image. I totally fail to see how a value as small as one-googlth or 10^(-100) could have any actual effect on a fractal of magnitude 10^(+008), but today's image does not lie. Something certainly has had quite an effect on the minibrot. I have no theories about what is going on in the image. All I have done is show a most curious scene that I stumbled upon a number of years ago. The name "Translateration" sounds like it has a deep scientific meaning. Actually, as far as I know, it is nonsense. I picked up the word from a sci-fi novel I read many years ago. I forget the name of the novel. The rating of a 9 is based on both the artistic and mathematical merit. Until the host of the official FOTD web site has won its 'war against hackers' and is again up and running, the finished image may be viewed at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the FOTD back images may be viewed at: <http://www.Nahee.com/FOTD/> A mix of clouds and sun with a temperature of 37F +3C made today quite typical for a late winter day in central Pennsylvania. Seeing no promise of dependable sun, the fractal cat lured me from my favorite chair and took instant occupancy, defiantly daring me to try to dislodge him. The humans, pretty well recov- ered from the latest bug, had an average day. The next FOTD will indeed be posted, and the most likely time of the great event is around 24 hours from the time this FOTD is posted. Until whenever, take care, and Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Translateration { ; time=0:03:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=+0.2587410547281214/-0.0013438834420757\ /1.0438e+008/1/-162.5/0 params=0/0/0/0/1/0/1e-100/0 maxiter=3200 inside=0 periodicity=0 sound=off colors=000mKZlIgkGfjEfjFfjGfjGfjHfjIfiJfiKfiKfiLfn\ MfnNfnOfkMsnOfmPUoRHmO0nS4nW7p_AreDtjGvmcxmmpgcfZO\ WPPPHQMDQLBMLBRJDSHGSIITKJTMLWOLYQMYSM`UNcVNfWOiXP\ lYRoZUr_Wv`Zya`yc`zd_zfYtdWqeRocMiaId_F`YCXW9TX6SX\ 3SY7SYASZESZIS_MS_PS`TS`XSa`SacSbgSbkSfoQbnSZpTVsV\ SqWOqXKoZGm_Dk`9ib5gc2edNdbRd`UeZXeX_eVbeTebRh_PkX\ NnUMlSNjRNiQNgONeNNdMObLO`JO_IOYHORDPXGObJNcMMcPLc\ PKcPIcOHcUGcUFcUDcUCcUBcUAcU8cU7cU6bU5`U3_U2YU1XU0\ YU2ZU3WU1ZV4`V7bVAdVCfVFhVIkUKmUNoUQqUSsUVuUYwU_qZ\ XkbVeaS_`QVZOPZLJZJDZG7ZE2ZC4ZF6ZI8ZKAZNCZQDZSFZVH\ ZYJZ_LZbLZfMZdM_cNaaNY`NU_OPYOLXPNVPPUOPVPQTPRRQRP\ QTNRUMRWKSWISWGTWETXDUYBUZ9VZ7YY2VX6SW9PVCQUDRUDSU\ ETSETQFUPFVMGWJGXHHXEHYBIZ9I_6J`8JaAK`CJ_EI_GIZIHY\ KHYMGXOGWQFWSEVUEUUDUUDTUCQUBTUCVUCYUC_UCbUCdUCfUD\ iUDkUDnUDpUDqU8rUDrUHrWLsYPs_Ts`Ysbaqdeogimemkcqia\ hg__eYScWJeUAgSFiQKkOPmMU } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 03-03-13 (At the Wrong Angle [8])
by Jim Muth 03 Mar '13

03 Mar '13

FOTD -- March 03, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's scene shows a minibrot in an oversized parent Mandelbrot set that has been corrupted in its depths by Z^9 energies. The location is in the center of the north branch of Seahorse Valley of the large minibrot on the main spike of the parent M-set. But no minibrot lies at the center of the frame. What we see there is a stretched-out slit with almost nothing of a Mandel- brot or Julia nature about it. The name of the image -- "At the Wrong Angle" -- explains the problem. We are viewing the scene from the wrong angle. We are viewing it from some monstrous unimaginable angle in the fourth dimension. To bring the large-scale pattern to near perfection, the entire image has been stretched and skewed to the limit, yet except at the center, the stretching is hardly noticeable. The image earns a rating of an 8 even though it did appear several years ago in a slightly modified form. The parameter file runs in 4-1/3 minutes. Hopefully, with such extreme stretching and skewing, it will run accurately on all machines. (But it sometimes gives me trouble even on the machine that created it.) Until the official FOTD web site is again up and running, I recommend viewing the finished image at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and don't forget the back images posted at: <http://www.Nahee.com/FOTD/> The un-notable winter weather continued today here at Fractal Central, with cloudy skies, only a few breaks of sun, a few flurries of snow, a brisk north wind and a temperature of 36F +2C. The mighty fractal cat, not quite as mighty as he once was, spent the day watching the world go by and plotting mis- chief. The humans simply made it through the day. I will post the next FOTD when the time comes. Until whenever that might be, take care, and what's that! . . . the world did not end . . . what a disappointment! Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= At_the_Wrong_Angle { ; time=0:04:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot center-mag=-0.000000000\ 00020463/+0.00000000023549410/4.597516e+009/0.0131\ /88.53859228715406/-89.1361541431747213 params=-92/189.6/-26.6/58/-442.1377733748792/0.169\ 7133339657901/-442.1377733748792/0.169713333965790\ 1/9/250 float=y maxiter=60000 inside=0 periodicity=10 sound=off mathtolerance=0.05/1 colors=000neSlbUk`WiZZgX`fVbdTddQkcRfcRbcRZcRVbSRb\ SNbSJbSF`OAbSBdVBfZBhaCjdClhCnkDpoDrrDsuDpsCnrClqC\ joBhnBfmBdkAbjA`iAZg9Xf9Ve9Xl0Vh5Td9S`DQXHOTLNPQLL\ UJHYIDaG9eF5iQNZYeP_dO`cNacMcbLdbLeaKgaJh`Ixb0i`IV\ ZZ8VzHYoP_dXaUdcJpb2nd5le8jfAhhDfiFdjIblK`mNZnPXpS\ VqUTrXTuZRsZPrZNpZLoZJmZCpcIlZOhVUeQ_aMeYHkVDqR8Lk\ uc_VvO4rP6oQ7lR8iSAfTBcUC_VEXWFUXGRYIOZJL_KWObh8ue\ CtcFs`IrZLrXOqURpSUoQXoN_nLbmIelGhlEkkBnj9qi7tiArl\ CqnEpqGosInvKmxSamZzbfzSmzIdzHWzGNzFzzEzzDzzBzzAzz\ 5zqhzzMzwRzgKJzDBz6zQECoY9YM6zBMefzzSzzEzzBzz8zz5z\ z2ztENeAGS79z3RsK5rG4dC4z83z4GzV`C6zz3zzCzz9zz6zz3\ zz4zz3zz9zz1PFeO`CZSHhKLrBPz3TbcEWPdXL`WNWVPRURMUT\ IRahiShyUJWE9ORkHHWA8GWKNOEHa9BA05z3Re2KT0DG06U0dN\ 0UG0K94Alnz`ajQPVECFMkECN7znHXKBm_YjYAhWFXUKYOPZPU\ _QZaSccVhfYmg`rhbviezjhzkkzlmzmoznnzoozqpzsqzurzws\ zxtzzuzzvzzwzzxzzyzzzzzzz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), 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)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 02-03-13 (Engulfed Universe [8])
by Jim Muth 02 Mar '13

02 Mar '13

FOTD -- March 02, 2013 (Rating 8) Fractal visionaries and enthusiasts: In today's fractal I raised the escape radius of yesterday's image to an astronomical 10^(11) and zoomed into a curious hole in the rapidly dissolving zombie face. The result is an image that reminds me of a universe being engulfed by a wave of dark energy -- the stuff or non-stuff that is supposed to eventually tear the universe apart. The image also shows what might be a minibrot of order -(7.4), that is if such things do indeed exist. The black open back- ground surrounding the spherical universe does appear to have bays along its edges, though these bays resemble nothing in the world of fractals that I am familiar with. The name "Engulfed Universe" describes my impression of the circular thing floating in the center of the irregular, empty hole. The rating of an 8 means that I consider the image to be a rather good one. I put only a relatively small amount of extra effort into the coloring. The calculation time of 3-1/3 minutes is rather slow. Unfortu- nately, the official FOTD web site is having difficulties and will not be updated for a while, but the image will soon be posted, and in hi-def at that, at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images are still at: <http://www.Nahee.com/FOTD/> The day dawned with a flurry of snow here at Fractal Central. The flurry amounted to nothing, and soon cleared off, leading to a day that featured a mix of sun and clouds, and a temperature of 37F +3C. The fractal cat would have preferred more sun, but still had a reasonably pleasant day on his window shelf. The next FOTD will most likely be posted in 24 hours. Until then, take care, and how unusual would it be if the world ended and nobody noticed? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Engulfed_Universe { ; time=0:03:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.1274/-0.616678/56.56671/1/153.75/0 params=-1.4/-7.4/-7.4/-1.4/0/100000000000/0/0 float=y maxiter=5400 inside=0 logmap=6 periodicity=6 colors=000EH7CQNJbPPRROFdVENVDJVCEVBAIFBOIBLLCIOCF\ RDCUD9XDGWCNVBTUA_T9eS8bJF`BLcGOeLQgQSjVVl_XndZpaX\ rZVsWTuTRvRPxhSzzUzzJzz9zzIzzRzzZZzQkzHxz8RzKNzKJz\ LGzLCzMBzIAzK9zM8zO7zQ6zS6zT5zV4zX3zZ2z`2za5zV8zPB\ zIEzCCz2Jz1Jz1Jz1Gz4Dz6R000U0FDF00N00Y01Q03l15T27p\ K0_2Bt31d3Fx3CV3rz3Dc3Mm4Gh5Oc6PZ7VUKYWX_YiaZlcasc\ cvdfxghzijwfhucgzafzeezQczRbzTazU`zVZzXYzYXzZWz_Vz\ aXzcYzdZzf`zhazibzkdzleznfzphzqizsjztkzslzsmzsmzsn\ zsnznzznzzmzbhzgmzpwzkrzjrzjrzgqzdpzaozZnzWmzUlzRk\ zOkzLozIizGZzDgzAfz7ez4_z2dzFazRZzbWznTzzGzxazvPzt\ PzsPzqPzoPzmPzlPzjPzhPzgPzeOzcNzZWzUdzPmzPlzQjzQhz\ QfzQdzQczYazd`zkZzrYzyXzrXzkXzdXzYXzRXzKXzDXz6Xz0X\ z3_z5az7czAezCgzEizGkzJnzLpzNrzQtzSvzUxzWzzXxzYwzZ\ vz_t_`s`araaqb`qdZrfYrhXrjVslUsnTspSsrUnkWjeYf__bU\ YmRWmNVmKUmJUmIUmHUmGQmCMm8Im5FmBDmHAmM8mS6mXCm_Hz\ bMzezzhzzkzznzzqzzszztzzu } 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 01-03-13 (Zombie Apparition [Not Rated])
by Jim Muth 01 Mar '13

01 Mar '13

FOTD -- March 01, 2013 (No Rating) Fractal visionaries and enthusiasts: Be warned! Prepare! The zombies are coming! No one is safe! They are being spotted more often in large cities such as New York, and I hear reports of scattered zombie outbreaks in other parts of the country. These reports would be about as amusing as the reports of space aliens if the zombies were not real and did not have the unpleasant habit of arising at night to stumble around the neighborhood and feed upon any living beings they might find. And we all know what happens when a living being is fed upon by a horde of zombies -- the being dies! But the situation is not totally hopeless. Protective measures are available. A few days ago I spotted a hungry zombie stumbling along the street near FC in search of food. Before I fled in terror, I managed to take a fractal photo of its gaunt face. Today's image shows a close-up of the creature's face just as it pops from its grave. So if you spot anything like this in your neighborhood, be aware that your life is in dire danger. Do not try to fight it off. You cannot kill it -- it is already dead. Run, do not walk to the closest zombie shelter and start to pray. Hey, maybe I'll make March fractal zombie month. To bring the unworldly demon to light and warn the world of what is coming, I simply raised the escape radius of yesterday's image to 1,000,000, and there the monster was, in his full horror. The name "Zombie Apparition" says it all. Since ratings mean nothing to those who have been devoured by zombies, I did not bother to rate the scene. The calculation time of 45 seconds is optional. A shift to passes=g will cut the time notably but miss a lot of the smaller debris, while the shift to passes=1 will double the time but reveal all the zombie debris. The finished image in 640x480x256 GIF resolution is posted at: <http://www.crosscanpuzzles.com/Archives.html> Higher definition versions are available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Lots of clouds, a brisk north wind and a temperature of 41F +5C kept today feeling like a midwinter one here at Fractal Central. The fractal cat was unconcerned with the temperature, since he was on zombie watch all morning. When nothing showed up by lunch time, he glommed my favorite chair and turned defiant, making me sit elsewhere. FL had a bad day, with her flu bug hanging on longer than we think it should. The next FOTD, hopefully zombie free, will be posted when the time is right. (I couldn't be any more vague than that.) Until whenever, take care, and if God is asleep, as I hear the ex-pope sometimes wonders, maybe someone had better wake up the Deity. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Zombie_Apparition { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=0.201835/0.00487195/0.4183674/1/103.75/0 params=-1.4/-7.4/-7.4/-1.4/0/1000000/0/0 float=y maxiter=5000 inside=0 periodicity=6 colors=000000000FDF00N00h01Q03l15T27p20_2Bt31d3Fx3\ CV3Jv3Dc3Mm4Gh5Oc6PZ7VUKYWX_YiaZlcasccvdfxghzijwfh\ ucgzafzeezQczRbzTazU`zVZzXYzYXzZWz_VzaXzcYzdZzf`zh\ azibzkdzleznfzphzqizsjztkzslzsmzsmzsnzsnznzznzzmzb\ hzgmzpwzkrzjrzjrzgqzdpzaozZnzWmzUlzRkzOkzLozIizGZz\ DgzAfz7ez4_z2dzFazRZzbWznTzzGzxazvPztPzsPzqPzoPzmP\ zlPzjPzhPzgPzeOzcNzZWzUdzPmzPlzQjzQhzQfzQdzQczYazd\ `zkZzrYzyXzrXzkXzdXzYXzRXzKXzDXz6Xz0Xz3_z5az7czAez\ CgzEizGkzJnzLpzNrzQtzSvzUxzWzzXxzYwzZvz_t_`s`araaq\ b`qdZrfYrhXrjVslUsnTspSsrUnkWjeYf__bUYmRWmNVmKUmJU\ mIUmHUmGQmCMm8Im5FmBDmHAmM8mS6mXCm_HzbMzezzhzzkzzn\ zzqzzszztzzuzzwzzxzzyzzzzzwzztzzszzrzzrzzlzzgzzbzz\ YzzTzzOzzXzzezznzzwzzuzzszzrzzpzzozzmzzlzz`zzYzzWz\ zUzzSzzQzzbzznzzczzUzzJzz9zzIzzRzzZZzQkzHxz8RzKNzK\ JzLGzLCzMBzIAzK9zM8zO7zQ6zS6zT5zV4zX3zZ2z`2za5zV8z\ PBzIEzCCz2Jz1Jz1Jz1Gz4Dz6 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-02-13 (Blast of Nothing [Not Rated])
by Jim Muth 01 Mar '13

01 Mar '13

FOTD -- February 28, 2013 (No Rating) Fractal visionaries and enthusiasts: Today's image has been granted no rating. There is a good reason. It is not a new fractal. It is the parent fractal of the past two days' images rotated so that east is up and north is left. The image of Feb 26 lies deep in the stuff at the extreme left edge of the fractal. The image of Feb 27 lies in the East Valley of the medium-sized minibrot on the northwest shore line of the 'fan', which now opens to the north instead of the east. The image is not the exact parent. Though I retained the same color pallette, to add impact, I did change it a bit. The name "Blast of Nothing" was inspired by the thought of the currently popular and always mysterious "Dark Energy", which as far as we know comes from nothing, yet is causing the entire universe to fly apart. Numbers are at least as abstract as Dark Energy. A curiosity of the Julibrot in which today's scene lies is that the image extends far out, to perhaps infinity, in the 'Z' planes. This can be demonstrated by changing the value of initial Z, the (p4) parameter, to extreme values. Doing so would normally soon result in a blank screen, but in today's case, the image, though it changes, appears to go on forever. The calculation time of only 45 seconds will pass in a flash. The blinding flash can be avoided by visiting the FOTD web sites. To view the image without risking blindness, check the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> But remember that this official site is on a schedule that is different from the schedule of the mailing list. Some images may appear on the web site well before or after they are posted to the mailing list. Variations are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> with the back images safely stored and available at: <http://www.Nahee.com/FOTD/> The day brought lots of clouds and showers of both rain and graupel to Fractal Central. The fractal cat, never wondering what graupel is, spent most of the day ensconced in my favorite overstuffed wing chair. The humans, still not up to average after the failure of the flu shot, spent the day wondering just why the pope resigned. My opinion is that, when he realized how bad the situation in the church actuially is and how futile the task of saving it would be, he lost hope and gave up. Most likely, nothing less than another reformation is needed. The next FOTD will soon be posted, and I cannot now be found, nor will I ever be found on 'Twitter' or 'Facebook' or any other new-fangled social-networking sites. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Blast_of_Nothing { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=0.642419/0.0511001/0.5102041/1/103.75/0 params=-1.4/-7.4/-7.4/-1.4/0/3500/0/0 float=y maxiter=5000 inside=0 periodicity=6 colors=00000000000700N00h01Q03l15T27p20_2Bt31d3Fx3\ CV3Jv3Dc3Mm4Gh5Oc6PZ7VUKYWX_YiaZlcasccvdfxghzijwfh\ ucgzafzeezQczRbzTazU`zVZzXYzYXzZWz_VzaXzcYzdZzf`zh\ azibzkdzleznfzphzqizsjztkzslzsmzsmzsnzsnznzznzzmzb\ hzgmzpwzkrzjrzjrzgqzdpzaozZnzWmzUlzRkzOkzLozIizGZz\ DgzAfz7ez4_z2dzFazRZzbWznTzzGzxazvPztPzsPzqPzoPzmP\ zlPzjPzhPzgPzeOzcNzZWzUdzPmzPlzQjzQhzQfzQdzQczYazd\ `zkZzrYzyXzrXzkXzdXzYXzRXzKXzDXz6Xz0Xz3_z5az7czAez\ CgzEizGkzJnzLpzNrzQtzSvzUxzWzzXxzYwzZvz_t_`s`araaq\ b`qdZrfYrhXrjVslUsnTspSsrUnkWjeYf__bUYmRWmNVmKUmJU\ mIUmHUmGQmCMm8Im5FmBDmHAmM8mS6mXCm_HzbMzezzhzzkzzn\ zzqzzszztzzuzzwzzxzzyzzzzzwzztzzszzrzzrzzlzzgzzbzz\ YzzTzzOzzXzzezznzzwzzuzzszzrzzpzzozzmzzlzz`zzYzzWz\ zUzzSzzQzzbzznzzczzUzzJzz9zzIzzRzzZZzQkzHxz8RzKNzK\ JzLGzLCzMBzIAzK9zM8zO7zQ6zS6zT5zV4zX3zZ2z`2za5zV8z\ PBzIEzCCz2Jz1Jz1Jz1Gz4Dz6 } 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 27-02-13 (It's Fractal Time [7.5])
by Jim Muth 27 Feb '13

27 Feb '13

FOTD -- February 27, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Since the flu shot did not work this year, we are both still feeling lethargic from the flu here at FC today, which means the discussion will be brief. I named the image "It's Fractal Time" because even after 24 years, fractals are still fun. The rating of 7-1/2 indicates my lack of real enthusiasm for the image. Today's scene is another dive into yesterday's parent fractal. Today we check very deep into the East Valley area of a minibrot on the northeast edge of the parent's prominent 'fan'. These fractal fans almost always appear with the 'handle' pointing west and the open blade to the east. They are common in fractals that combine two negative powers of Z, but rarely appear in other fractals. Due to its extreme magnitude, the calculation time of the image is a slow 9 minutes, almost all of which may be saved by checking the web sites. So relieve all stress and calculation anxieties by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Variations in hi-def are available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And thousands of FOTD back images are available at> <http://www.Nahee.com/FOTD/> Rain fell all night and morning here at Fractal Central today. The afternoon remained cloudy with a temperature of 45F +7C. Nicholas, the fractal cat, gave up on the sun well before noon, but then laid claim to my favorite TV chair, from which he would not be dislodged. The humans meanwhile made it through another unpromising day. The next FOTD *will* be posted, that much is clear, what is in doubt is the exact time it will be posted. My best guess is in 24 hours. Until whenever, take care, and if the Catholic Church ever starts changing its standpoint, who knows where the changes will stop? Maybe the church will go so far as to admit that its most important articles of faith such as the existence of God, salvation and heaven are not quite as certain as it has always taught. After all, one would think that by this time science would have found at least a hint of something. Jim (A true believer still) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= It's_Fractal_Time { ; time=0:09:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.543534421205797/+0.7283066746232452/\ 2.874541e+012/1/55/0 params=-1.4/-7.4/-7.4/-1.4/0/\ 3500/0/0 float=y maxiter=6000 inside=0 logmap=-950 periodicity=6 mathtolerance=0.05/1 colors=00000800A00C00E00G01I02K13L24N25P26Q37S38U3\ 9V3AX38Z36_4DY5JX6PV7VUKYWX_YiaZlcasccvdfxghzijwfh\ ucgzafleejQchRbfTadU`bVZ`XYZYXXZWV_VXaXZcY`dZbf`ch\ aeibgkdilejnflphnqipsjqtkpslpsmosmosnnsninzhnzhmzb\ hzgmzpwzkrzjrzjrzgqzdpmaojZngWmdUlaRkZOkWLoTIiQGZN\ DgKAfH7eE4_B2d8Fa9RZ9bWAnTAzGAxa9vP9tP8sP8qP8oP7mP\ 7lP7jP6hP6gP6eOEcNLZWNUdOPmPPlNQjLQhIQfGQdEQcCYaFd\ `IkZLrYOyXQrXTkXWdXYYX`RXbKXeDXg6Xj0Xl3_j5ai7chAeg\ CgeEidGkcJnbLpaNr_QtZSvYUxXWzWXxXYwYZvZ_t_`s`araaq\ b`qdZrfYrhXrjVslUsnTspSsrUnkWjeYf__bUYmRWmNVmKUmJU\ mIUmHUmGQmCMm8Im5FmBDmHAmM8mS6mXCm_HzbMzezzhzzkzzn\ zzqzzszztzzuzzwzzxzzyzzzzzwzztzzszzrzzrzzlzzgzzbzz\ YzzTzzOzzXzzezznzzwzzuzzszzrzzpzzozzmzzlzz`zzYzzWz\ zUzzSzzQzzbzznzzczzUzzJzz9zzIzzRzzZZzQkzHxz8RzKNzK\ JzLGzLCzMBzIAzK9zM8zO7zQ6zS6zT5zV4zX3zZ2z`2za5zV8z\ PBzIEzCCz2Jz1Jz1Jz1Gz4Dz6 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 26-02-13 (Filament Jungle [7.5])
by Jim Muth 27 Feb '13

27 Feb '13

FOTD -- February 26, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Since both FL and I are down with a bug of some kind, today's discussion will be brief. The image is therefore left to speak for itself. The parent fractal came about when I combined 1.4 negative parts of Z^(-7.4) with 7.4 negative parts of Z^(-1.4) and added (1/C) on each iteration. Today's image is located in the northernmost part of this parent. The name "Filament Jungle" refers to the twisting filaments that infest the scene. The rating of 7-1/2 means that I put only a minor extra effort into the coloring. The calculation takes only 1-1/4 minutes, which will waste no one's precious time. And the web sites will be even faster. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Variations in hi-def are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> back images are at: <http://www.Nahee.com/FOTD/> The sky was cloudy all day here at Fractal Central. Light rain began in the afternoon, but a temperature of 39F +4C made it too warm for any frozen stuff. The fractal cat accepted the lack of sun early, and retired to the cozy bed we have set up for him on top of the tall bookcase in the spare room, where he can feel like king of the (cat) world. The under-the-weather humans somehow made it through the day. The next FOTD will be posted shortly. Until then, take care, and I hear that those who live near wind generators have been complaining about ill effects. Apparently, in addition to killing lots of birds, the generators create subsonic sound waves that disorient and sicken those who live nearby. I guess the greenies who are so concerned about climate change had best pin their hopes on solar panels. But I wonder how many thousand square miles we would need to cover to satisfy our ever-increas- ing demand for electric energy. There is a real solution, but no one wants to do it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Filament_Jungle { ; time=0:01:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.5380106218817268/+2.065537317552037/\ 889259/1/92.5/0 params=-1.4/-7.4/-7.4/-1.4/0/0/0/0 maxiter=1500 inside=0 logmap=75 periodicity=6 colors=000UAWT9VS8UR7TQ6SP5RO4QN3PM4OL4NK4MJ5LI5IL\ 8FG8CLB9KA7NEAODDQHGSKJUMMWRPYTS_YUa_Xcd_efbgkeimh\ krkmpnmvoowqowsqxuqxwsyzsyzuzzuzzwzzL9YMAXMAXNAWNA\ WOAWOAVPAVPAVQAUQAURAURATSATSATVEJYH9_K0aJ1bI1cH1d\ K1eK2fK2gK2iP2jU2kZ3lZ3mZ3nZ3oZ3_LGKZT4ke9egD`iIVj\ MQlRKmVFoZApXFkVKgTObSTZQXUOaQNeMMgJMhHLiFLjDKkBKl\ 9Jm7Jn5Io3Ip1Kj2Le3M`4NW4OR5QM6RH6SC7T78U28h1Fv0Mt\ 0Ls0Lq0Kp0Ko0Jm0Jl0Ik0Ii0Hh0Hg0Hf1Ie1Jd2Kc2Lc3Mb3N\ a3O`4P_4Q_5RZ5SY6TX6UX6VioQgpTfpVepXcqZbq`aqb`qdZr\ fYrhXrjVslUsnTspSsrUnkWjeYf__bUYfRWjNVmKUhJUdIUcHU\ cGQcCMc8Ic5FcBDcHAcM8cS6mXCh_HcbMZezVhzQkzLnzHqzOs\ zVtz`uzgwzmxztyzzzzqwzitzYszMrzBrzzlzzgzzbzzYzzTzz\ OzzXzzezznzzwzzuzzszzrzzpzzozzmzzlzz`zzYzzWzzUzzSz\ zQzzbzznzzczzUzzJzz9zzIzzRzzZZzQkzHxz8RzKNzKJzLGzL\ CzMBzIAzK9zM8zO7zQ6zS6zT5zV4zX3zZ2z`2za5zV8zPBzIEz\ CCz2Gz6JzANzERz_mzbizcezc } 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 24-02-13 (The Test of Time [7])
by Jim Muth 25 Feb '13

25 Feb '13

FOTD -- February 24, 2013 (Rating 7) Fractal visionaries and enthusiasts: The expression behind today's image combines 1.96 negative parts of Z^(2.3) with 0.98 parts of Z^(4.6), then adds C on each iteration. When written as a function, this expression has two critical points, zero and -1. (I previously had this wrong.) The MandAutoCritInZ formula automatically initializes Z to zero, but Z can be initialized to -1 by entering that value as the real(p4) parameter. For some strange reason, the minibrots in the fractal that is produced when initial Z is set to zero are quadratic M-sets, while the minibrots in the fractal with initial Z set to -1 are of order 2.3. This might be because the value of -1 is a point of inflection on the graph of the function, while the value of zero is the tip of a parabola. In both cases the derivative is zero and the fractal will therefore be undistorted. I'm not sure if this is true of all fractas created by expressions with multiple critical points. Regardless of the correctness of the math, today's image lies in the fractal that results when Z is initialized to -1. The minibrot at its center is of order 2.3 as expected. The rating of a 7 is perhaps a bit conservative. I did put a half hour or so of effort into the coloring. The calculation time of 8 minutes is slow. Much time may be saved by viewing the finished image on one or more of the FOTD web sites. Check the finished image at the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And the variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images are at: <http://www.Nahee.com/FOTD/> A typical late winter day passed uneventfully here at Fractal Central, with lots of clouds during the morning and a clearing in the afternoon. The temperature of 37F +3C was right on the mark. The fractal cat played with his catnip ball until the sun appeared. Then he stretched out on his shelf in the southwest window. The humans made it through the day with a minimum of annoyances other than the usual miseries of the flu. The next FOTD will be posted when it is ready. Until whenever, take care, and I hear from Old Fractal Central back in Bodymore Murderland, (as the locals there call Baltimore, Maryland), that the weather forecast there today is partly cloudy with a near 100-percent chance of scattered bullets. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Test_of_Time { ; time=0:08:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=cosxx float=y center-mag=+0.102350608821/-0.60041985916/3.4e+008\ /1/150/0 params=-1.96/2.3/0.98/4.6/0/0/-1/0 maxiter=5400 inside=0 logmap=365 periodicity=6 colors=000KMUKMUKMUKMUKMUJMUIMWGOXEQXCSXAUX8WX6X`B\ YdG`gLbkQfnVjrZnuTrzNvzIxzCzz7pzIczTUmcUcmbWzHvMJn\ zPNzPNzPNzQNzQNzRNzRNzRNzSNzSNzTNzTNzgQyfPxfPwePwe\ PvePudPWSxBt9JoGQjNXeUc``jWgqRmrTkrVjrXhsZgs`esbds\ dbteatg_tiZtkXumWuoUuqTurSsnUqkVphWneYlbZk__iXagUb\ fRcdOebLfaIg_FiYCjX9k`WScY9o_KzIUzJTzJTzKSzKSzLSzM\ RzMRzNQzOQzOQzPPzQPzQOzROzSOzSNzTNzdWzaTzZRzWPqqJp\ pKooKonKnnKnmKmlKmlKlkKzjLziLziLzhLzgLzgLzfLzeLzdL\ zdMzlJzrGzzCpzEmuGguIgvKfvMewOewQbsR`pSYmSWjTTfTRc\ UP`UMYVKVWHRWFOXCLXAIY8FY7JX7NX7QW6UW6XW6`V5cV5gU5\ jU4nU0zm0zmmzTmzQGSNTT_RVaQXbOZdNaeKdfKhhKizUpkUpl\ Uomcnocmpcmqcqnhozjnpmmfmmcrm`vmZzmWzmQzmTzmWzkZzm\ VzmQzmMzmIzmIzmIzmIzmJzcJzcJzcJzcJzcJzcJzcJzcJzcJz\ cJzcKzcKzXKzXKzXKzTOzXKzWKzWKzWKzWKzWLzWLzWczWczWc\ zVczVczVmzVmzVmzVmzVmzVzzVzzUzzUzzUzzUzzUzzUzzUzzU\ zzUzzTzzTzzTzzTzzTzzTzzTz } 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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I've filled in the missing links to...Jan,'13
by Hal Lane 24 Feb '13

24 Feb '13

I've filled in the missing links to the images I calculated for Jim Muth's FOTDs for January, 2013. The only one marked as coming "soon..." is January 27th's F130127W, which I'm calculating as I write this, and should have a live link, well, "soon..." The links on my February, 2013 page are also effectively up to date. They're only missing February 22nd, which Jim says is a "very slow" one. Please visit my pages using this link: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html I'd be much obliged if you'd let me know of any problems you find on the site. Thanks! - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 22-02-13 (Slowly I Turned [7.5])
by Jim Muth 23 Feb '13

23 Feb '13

FOTD -- February 22, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is named "Slowly I Turned". The name has nothing to do with the image. It is actually a phrase from an old Abbott and Costello comedy skit. Those aged enough to be considered venerable will remember the movie. The rest must forever wonder why the phrase was so funny. Today's image is no joke however. It shows a Z^(2.3) minibrot in the phantom parent fractal of two days ago. This parent consists of a large three-lobed central bay with smaller bays on the west and east and west ends. Today's image is located in a blunt valley on the western edge of a bud on the northwest edge of the western lobe of the large central bay. The rating of 7-1/2 indicates an image just slightly above average. The calculation time of 11-1/2 minutes is very slow, making a trip to one of the web sites by far the better choice. Much time may be saved by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Variations in high-definition are or soon will be posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> If the variations are not yet posted, it is because some of the hi-def variations can be quite time consuming to generate. The many thousands of FOTD back images are online at: <http://www.Nahee.com/FOTD/> The day dawned clear, but clouds moved in as the sun rose, and the rest of the day was cloudy with a temperature of 32F 0Z and a few light flurries of snow. The fractal cat quit the window shelf as soon as he saw the lack of sun. The humans had a busy day. With too much work and both of us feeling under average, testiness prevailed. The next FOTD will be posted when the time is right, and there is a good chance that might not be for two days. Until then, take care, and everyone knows the solutions to the nation's problems. Why then have the problems not yet been solved? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Slowly_I_Turned { ; time=0:11:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=cosxx float=y center-mag=-0.776166017979/+0.444260643139/4.4421\ 5e+008/1/-152.5/0 params=-2/2.3/1/4.6/-0.02/0/-1/0 maxiter=5400 inside=0 logmap=487 periodicity=6 colors=000UUZTU_RUaQUbOUdNUeLUfKUhIUiHUkFUlEUmCUoB\ UpAVq9Wn8Xk8Yh7Zf7_c6``6aZ5bW4cT4bQ3aO3`L2_I2ZG3YK\ 4XO4WR5VV5UY9`bAXeBThCQkDMnEIqFEtFBwHCtJDrLEoNEmPF\ jRGhTHeVHcXIaZJZ`KXbKUdLSfMPhNNiNLkSJmXHnaFpfDqkBs\ p9tt8YcLCNYFO_IPaLRbOSdQTfTVhWWiZXkaZmd_of`pddrchs\ alu`pvZtxYxyUtsQpmMlhIhbEdYA`S7YN8VO9SO9QOANPAKPBI\ PBFQCCQCAQFCTHEVKGYMI_PJbRLdUNgWPiZRl`SncUqeWshYvj\ Zxi_th_qg_mf_je_gd_cc_`b_Ya`U``R_`NZ`KY`HX`DW`AV`7\ TbAScCRdEPeGOfINhKLiMKjPJkRHlTGnVFoXDpZCq`BrbJqWRp\ OZoHfn9nm2lc6kUAjUEiUHYUMNURBUW0U_CXWOaS_fOjkLqpPu\ qSqoXnl`geda`hXWlSRpNMtLQrJUqHYoF`nDdlBhkAkjFbaJUU\ NLMUKNYKOZLOWMNbMmhNMONMLOLJPLGPKcQKmQKm3Re5S_6SY8\ TV9zTBURCUPDSNDQLEOJEMIFKGFIEGGCUEAZC9cA7c85c63c41\ c20c08h7FiDMkKTmQVlVXkZYjc_igzikzkmzlnzjhziczhZzgT\ zfOzeJziPzmVzr_zvezzjzzhzzfzzdzzbzz`zzZzzXzzVzz_zz\ czzgzzkzzozzlzz`zz_zzZzzZ } 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 21-02-13 (In the Phantom [8])
by Jim Muth 22 Feb '13

22 Feb '13

FOTD -- February 21, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene in yesterday's 'phantom' parent fractal, which was revealed by switching the value of initial Z of the Feb. 18 image to the second critical value of the generating function, which is -1. The location is near a larger minibrot in a tiny valley on the western shore line of the large western bay of today's parent. Today's parent fractal, which appeared as yesterday's FOTD, is quite unusual. It is filled with minibrots, but the minibrots are not the expected quadratic variety as they are in the other parent fractal of today's function. Instead, as is illustrated in today's image, they appear to be of an order somewhere around 2.5. Actually, today's entire parent is strange, and deserves a more careful examination, which I will do in the next few days. The rating of an 8 is divided half-and-half between mathematical interest and fractal artistic value. The name "In the Phantom" describes the location of today's scene -- in a fractal that first appeared as a buried 'phantom' fractal in the background of the image for February 18. The calculation time of 6-1/2 minutes is slow. Checking the web sites can cut the wait to seconds. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Variations in hi-def are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds, complete with a few flakes of snow, made today a typical sample of midwinter weather here at Fractal Central. The temperature of 34F +1C was almost exactly average for the day. The fractal cat spent several hours on the shelf in the southwest window, trying to enjoy the off-and-on sun, while the humans passed the day working. The next FOTD will be posted, that much is certain. The only question is exactly when it will be posted. Until whenever, take care, and have fun. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= In_the_Phantom { ; time=0:06:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=cosxx inside=1 center-mag=-1.759337223588773/+0.04880086507460096\ /1.244e+010/1/-97.5/0 params=-2/2.3/1/4.6/-0.02/0/\ -1/0 float=y maxiter=5400 logmap=470 periodicity=6 colors=000F0F64X85TA6PC7LA8HD9EHAGHBIICKHDMD0OD4KA\ 5PDBTHOXKR_OUcRXgV_k_`uZaqYanXbjWbgVbdUc`TcYScVRdR\ QdOPeKOeHNeEMfALf7Ht0Lf4PT7TFAX1DW6FVAGUFHUJITNJSS\ LRWMR_NQdOPhPQkOPlQPmSPmTPnVOoXOoYOp_OqaNrdOqbPq`Q\ pZRpXSoWToUUnSVnQWmPXmNYlLZlJ_lIdhMhdQlaUpYYtUaxRd\ neUzzHzzLzmOzcRqDRpTTczuktksnbqqNoYKrFcuPiDqCEpBGo\ 9Hm8Jl7Kk6Mi5Nh4Ki0Og3Re6Uc9XaC__EbYHeWKhUNkSQnRSn\ QRnQRnPRnPQnPQnOQnOPnNPnNPnNOnMOnMOmNRnMPnMOnLNnLM\ nKLoKKoJJoJIoIHoIGpHFpHEpGDpGCpFBu92pFAkLIfQQaWYyI\ NjSXX`eIjoAzz4sxczz8luAzzCwqCzzEwpFzzGsjIpgJndKlaL\ tZNfWOeTPcQR`NSZKTXH850JI7UVEleDgfHcgKZhNVhQRiTMnX\ Ij_Dkb9leCcq5oz8jfBhdEgbHeaKj_NbYQ`WT_VW`TZXRaVPdT\ OgSMjQKmPJkSLiUNhWPfYQe_ScaUbcWyeXzgZzi`zkbzmczoez\ qgzshzkgzcfzWezOdzGcz8czAdzBezDfzEfzFgzHhzIhzJizLj\ zMkzNkzPlzQmzWozRmzQlzOkzNkzMjzLjzKizJizIhzHhzGgzF\ gzEfz6ozAjzDfzHbzhlzfhzed } 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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fractint on phone
by Tim Wegner 21 Feb '13

21 Feb '13

5 5

FOTD 20-02-13 (The Phantom Revealed [7])
by Jim Muth 21 Feb '13

21 Feb '13

FOTD -- February 20, 2013 (Rating 7) Fractal visionaries and enthusiasts: The FOTD that appeared two days ago on February 18 was named "A Phantom Parent". In that image it is apparent that another fractal lies buried beneath the surface fractal, but because the surface fractal is critical, that hidden fractal must be forever obscured. But things are not nearly as bad as they first appear, for in today's image I take away the surface stuff and reveal that phantom fractal in its full glory, which explains the name "The Phantom Revealed". The trick lies in choosing the alternate critical value of initial Z. The generating expression actually has two critical values. In the previous image, the initial value of Z was automatically set to zero, one of the critical values. In today's image, I have reset the value of initial Z to -1, the second critical value. The result of this change is to move the previously buried fractal to the surface, and bury the fractal that was previously on the surface. Fragments of the previous surface image now appear as the bits of orangish stuff scattered about today's scene. Calculating complex critical values is not much fun. One of these days I might find a formula that can switch the critical values of initial Z automatically, but that day is not in the foreseeable future. Until then, I will continue to find the alternate critical values with the graphic method. The rating of a 7 totally reflects the mathematical value of the image. The artistic value hardly exists. But I will dive into today's image and post what I find there as tomorrow's FOTD. Who knows, I might find something worth a higher rating. Check the fractal phantom at: <http://www.crosscanpuzzles.com/Archives.html> With a deeper analysis at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the spooks from the past at: <http://www.Nahee.com/FOTD/> Typical midwinter weather prevailed at Fractal Central today, with a temperature of 28F -2C and frequent but light flurries of snow. The fractal cat made a break-out but got caught before he got into trouble, and was soundly scolded for his efforts. The humans made it through the day with only one spat, which was due to FL's testiness. My patience, approaching that of Job, kept things under control however. The next FOTD will be posted in 24 hours. Until then, take care, and when will the over-zealous technophiles realize that technology cannot solve all of man's problems because it has created many of them itself? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ThePhantomRevealed { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=cosxx float=y center-mag=0/0/0.69 params=-2/2.3/1/4.6/-0.02/0/-1/0 maxiter=750 inside=0 symmetry=xyaxis periodicity=6 colors=000GSNTT_RVaQXbOZdNaeLdfKhhIliHpkFplEomCnoB\ mpAmq9mn8mk8kh7if7gc6f`6eZ5dW4cT4bQ3aO3`L2_I2ZG3YK\ 4XO4WR5VV5UYzmazmdzmezmfzmfzmgzmgzmbzmZzmVzmQzmMzm\ IzmIzmIzmIzmJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcKzcKz\ XKzXKzXKzTOzXKzWKzWKzWKzWKzWLzWLzWLzWLzWLzVLzVLzVL\ zVLzVLzVLzVMzVMzVMzUMzUMzUMzUMzUMzUMzUMzUNzUNzTNzT\ NzTNzTNzTNzTNzTNzTNzJOzLNzNNzPNzRNzLMzMNzMNzNNzNNz\ NNzONzONzPNzPNzPNzQNzQNzRNzRNzRNzSNzSNzTNzTNzgQyfP\ xfPwePwePvePudPudPtcPscPrcPrbPqbPpaOpaOoaOn`Om`Om_\ Ol_Ok_OkZOjZOiYOhYOhYOgXNfXNfWNeWNdWNzVNzVNzUNzUNz\ UNzTNzTNzBYzCXzDXzDWzEWzFWzFVzGVzHUzHUzIUzJTzJTzKS\ zKSzLSzMRzMRzNQzOQzOQzPPzQPzQOzROzSOzSNzTNzdWzaTzZ\ RzWPqqJppKooKonKnnKnmKmlKmlKlkKzjLziLziLzhLzgLzgLz\ fLzeLzdLzdMzcMzbMzbMzaMz`Mz_Mz_MzZMzYNzYNzXNzWNzVN\ zVNzUNzTNzx`zw_zv_zu_zuZztZzsZzrYzrYzqYzpXroXzoXzn\ WzmWzlWzlVzkVzjVziUziUzhU } 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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software
by JackOfTradeZ＠comcast.net 21 Feb '13

21 Feb '13

. The FracTools 3.0 CD is downloadable here: http://www.fractal-animation.net/fractools.zip It is 365 MEG. It took me 40 minutes to upload with my commie-cast high-speed (LOL) connection. The FracZoom software is only 33Kb: http://www.fractal-animation.net/fraczoom.zip I have tons of old fractal software from the DOS '90's, including the original "Fractal Creations" CD for FractInt which is bound to be an immortal classic. I was living in Philly at the time and they had these computer show / flea markets a few times a year. Got lotsa good stuff then, including the complete VB6 suite for $120 ! .

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Re: [Fractint] My site's version of Jim Muth's FOTD now...
by Hal Lane 20 Feb '13

20 Feb '13

> > Hal wrote: > > <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> > > now has a February, 2013 page that's almost up to date. I'll try to > > keep up with Jim, although some of the images I create take quite a > > while to calculate. > > - Hal > > > John wrote: > Thank you (and Jim) very much! > John > jlewis(a)clara.net > 13/02/2013 You're welcome, John. Thanks for your enthusiasm! - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 19-02-13 (Erosion [7.5])
by Jim Muth 19 Feb '13

19 Feb '13

FOTD -- February 19, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a scene in the debris in the western part of yesterday's fractal. Most of the expanse of the image is inside stuff brought to life by the 'fmod' inside fill, though the more detailed elements consist of 'outside' stuff rendered with the 'tdis' option. All this trickery blends together to create an image that, at least in my opinion, rates a 7-1/2, one-half point of which is a bonus for the extra effort I put into the coloring. The name "Erosion" is a comment on the way the scene appeared when I first saw it, with the inside a flat black. The calculation time of 1-1/2 minutes is brief enough to cause no distress to those with other things to do, and slow enough to let a bit of anticipation build. Be a big-time thinker. View the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and thereby escape the need of calculating it. Enjoy high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And check the back images at: <http://www.Nahee.com/FOTD/> An inch of wet slushy snow fell this morning here at Fractal Central. The clouds continued when the snow ended, but when the afternoon temperature reached 39F +4C the slush vanished almost by magic. The fractal watch cat observed the big fat flakes with interest for a few minutes, then retired to his current favorite sleeping spot, on his blanket on top of the tall bookcase. The humans had a typical day, though FL, who is not feeling up to par and has work to finish, was rather testy. The next FOTD will be posted in the right cosmic time, (if there is such a thing). Until that hopefully eagerly awaited moment arrives, take care, and to solve a difficult problem, become one with the problem. (But don't ask how.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Erosion { ; time=0:01:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=cosxx passes=1 center-mag=-1.01074854/+0.01219294/518.3415/1/105/0 params=-2/2.3/1/4.6/-0.02/0/0/0 float=y inside=fmod maxiter=1800 proximity=0.045 outside=tdis colors=000U69V69X69Y69Z69UBAcebdedeffffhd`ccWZbRUa\ MP`HK_CFXBEVBETBEQBDOADMADJ5CH5CF0CG4DG7DHADHKDHPE\ IYEzzEJzEzzFJzFzzFKzFzsFJpIzlLGiOzfRzbUz_XzX_zTbzQ\ e5mh4mk9mhDmfHmcMmaQmZUmXYmUbmSfmPjmNnmLlmMjmMhmMz\ UzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzUzzcz\ zczzczzczzczzczzczzczzczzczzczzczzczzczzczzcz`mQcm\ NemKhmHkmEmmCTmY8mrBmqEmpGmoJmnLmmMmcMmVKmXJmZHm_G\ maEmbDmdBmeAmg8mi7mj5ml4mm2mo1mpbITdKReMQfOPgQOhSN\ jULkWKlYJm_InaHheKbiNXlQZiP_fO`cNaaMcZLdWKeUJfRIhO\ HiMGjJFkGEmEDnBCo8Bp6AhCD`IGTOJLUMD_P6eR7fT8fU9gVA\ gXAhYBhZCi`DiaDjbEjdFkeGkfGkgGliHjfIhcIg`JeYKcWKbT\ L`QMZNMYL`iKotJmsUlrdjqoipzknxllwmkvkjujizihzggzbg\ zbfzbezadz`cy_bxZawY`vW_uVZtUYsTXrSWpRVnQUlPTjOShN\ ReMQcLOaKN_JMYILWJOVJQUJTUKVTKYSK_SKbRLdQLgQLiPMlO\ MnOMqNMsNEWoHRmBM4CK4DJ5DI5EH6FF7FE7GD8HC8HA9I99J8\ AJ7AL69M69N69P69Q69R69T69 } 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 18-02-13 (A Phantom parent [No Rating])
by Jim Muth 19 Feb '13

19 Feb '13

FOTD -- February 18, 2013 (No Rating) Fractal visionaries and enthusiasts: The fractals I post as FOTD's are almost always scenes deep in larger fractals that I call the parent fractal. These parent fractals, which usually go un-appreciated, are sometimes weird enough all by themselves to be worth FOTD status. Today's image is one of these ridiculously weird parent fractals. It is just crazy enough to be noticed and hopefully appreciated. (It is filled with minibrots, one of which will be posted as the next FOTD.) I named the image "A Phantom Parent" because I have the impression that the orangish valleys toward the east and west edges of the image are parts of a larger unseen fractal that lurks in the background but defies being brought out into the open. The generating expression mixes an unlikely portion of Z^(2.3) with an equally unlikely portion of Z^(4.6), and then adds cosxx(C), which is not a true function at all, but an early complex-math mistake that was retained to keep the wrong images it had created compatible with the corrected program. With XY symmetry and a maxiter of only 750, the image is almost instantaneous. I have listed the calculation time at 10 seconds, though on most SOTA units, the image will run in about 3 seconds. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> with a Hi-Def version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and thousands of back images at: <http://www.Nahee.com/FOTD/> Total sun made today a brilliant midwinter day here at Fractal Central. The temperature started at a cold 12F -11C but under the warm sun reached a more reasonable 34F +1C in the afternoon. The fractal cat enjoyed the afternoon sun on his window shelf, but he still misses his companion, who shared the shelf with him until she went to cat heaven several months ago. The humans had a day that could have been improved upon. The next FOTD will be posted shortly. Until we find out how long shortly is, take care, and every economic problem seems to hit poor people the hardest. I guess this is why poverty is so unpopular. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Phantom_Parent { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=cosxx float=y center-mag=0/0/0.69 params=-2/2.3/1/4.6/-0.02/0/0/0 maxiter=750 inside=0 symmetry=xyaxis periodicity=6 colors=000GSNTT_RVaQXbOZdNaeLdfKhhIliHpkFplEomCnoB\ mpAmq9mn8mk8kh7if7gc6f`6eZ5dW4cT4bQ3aO3`L2_I2ZG3YK\ 4XO4WR5VV5UYzmazmdzmezmfzmfzmgzmgzmbzmZzmVzmQzmMzm\ IzmIzmIzmIzmJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcJzcKzcKz\ XKzXKzXKzTOzXKzWKzWKzWKzWKzWLzWLzWLzWLzWLzVLzVLzVL\ zVLzVLzVLzVMzVMzVMzUMzUMzUMzUMzUMzUMzUMzUNzUNzTNzT\ NzTNzTNzTNzTNzTNzTNzJOzLNzNNzPNzRNzLMzMNzMNzNNzNNz\ NNzONzONzPNzPNzPNzQNzQNzRNzRNzRNzSNzSNzTNzTNzgQyfP\ xfPwePwePvePudPudPtcPscPrcPrbPqbPpaOpaOoaOn`Om`Om_\ Ol_Ok_OkZOjZOiYOhYOhYOgXNfXNfWNeWNdWNzVNzVNzUNzUNz\ UNzTNzTNzBYzCXzDXzDWzEWzFWzFVzGVzHUzHUzIUzJTzJTzKS\ zKSzLSzMRzMRzNQzOQzOQzPPzQPzQOzROzSOzSNzTNzdWzaTzZ\ RzWPqqJppKooKonKnnKnmKmlKmlKlkKzjLziLziLzhLzgLzgLz\ fLzeLzdLzdMzcMzbMzbMzaMz`Mz_Mz_MzZMzYNzYNzXNzWNzVN\ zVNzUNzTNzx`zw_zv_zu_zuZztZzsZzrYzrYzqYzpXroXzoXzn\ WzmWzlWzlVzkVzjVziUziUzhU } 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 17-02-13 (Pattern in Nothing [8])
by Jim Muth 18 Feb '13

18 Feb '13

FOTD -- February 17, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image features a minibrot at its center. (Nothing unusual there). But the minibrot is surrounded by an unusually well-defined and decorative pattern, which gives the image a rating of an 8. The parent fractal consists of two crooked and widely separated Mandelbrot sets symmetrical with respect to the X-axis and connected by a band of debris. A kind of fractal butterfly exists where this debris intersects the X-axis, with today's scene lying in the debris surrounding this butterfly. The name "Pattern in Nothing" is a comment on the abstract nature of numbers, which are about as close to nothing as it is possible to come -- at least in this world. The calculation time of one minute is quite a bargain. After all, one can certainly spend much more time than this and still end up with nothing. But once again, the web sites come to the rescue by saving the minute and making the image labor-free. The finished image is posted online for instant viewing at: <http://www.crosscanpuzzles.com/Archives.html> High-definition variations are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> A brisk partly cloudy day with snow flurries and a temperature of 27F -3C kept the fractal cat as well as the fractal humans near the heat most all day. Stuff that is more exciting did not happen. The daily fractal journal is written to be more factual than exciting The next FOTD will be posted in either 24 or 48 hours. Until a day or two, take care, and several scientists now tell us that the universe might have come from nothing. Is this another way of saying that God created the universe? If God does not exist, as Atheists believe, then God must be nothing. Or am I merely engaging in word play? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Pattern_In_Nothing { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.1174897833/+0.004803/41599/1/25/0 params=1.6/1.5/0.8/3/0/0/0/0 float=y maxiter=2250 inside=0 logmap=45 periodicity=6 colors=000U8vSArPCnMEjJGeGIaEKYBMU8OP5QL2SH0UD4WG7\ YIA_KDaMGaOJbQMcSQdUUhWZmYcr_huamwcrvevugzsizqkzom\ zmrulotllslirlfqlcpl`olYnlVmmSlmPkmMjmJimGhmDgmAen\ 7fm8fl9fkAfjAgiBghCggDggDgfEheFhdGhcGhbHiaIi`Ji`Ji\ _KiZLjYMjXMjWNjVOjYIjWLjVOjUQjTTjSWjRYjQ`jPcmQfjOe\ gNeeMebKe_JdYIdVGdSFdQEcNDcKBcIAcF9bC7bA6b75b54bN8\ tOArPBqQDpREoSGmTHlUIkVKjWLhXNgYOfZPe_Rd`SbaUabV`c\ W_dYYeZXf`WgaVhbUhbUg`Vf_WeYWeXXdWXcUYbTYbSZaQZ`P_\ bMZ`O_ZQ`XR`VTaTUaRWbPYcNZcL`dEbeGadIadKadLadNadP`\ dQ`dS`dU`dZ_aV`dRagOajKbmHboDcrAcu6dxKdzKewKeuKfsP\ fqPfoPglPgjUhhUhfUhdUibUi_UjYUjWUjUckSckQclNclLclJ\ cmHcmFcmEcmDcjFchHchJchKchOchRchUccYcc`cccccgccjcb\ Uc_`cXfcUmcRscGxcKycOycRycVycYycaycdychycjzckyckxc\ kwclwclvclucmtcmtcmscnrcnqcnqmopmoomonmopmnnmmmmml\ mmkmmjmmimmhmmfmmemmdmmcmmbmmamm`mmXmmUmmSmmUmmVmm\ XmmYmm_mmammbmmdmmfmmgmmi } 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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Jan, '13 has 4 FOTD image "variations" added.
by Hal Lane 16 Feb '13

16 Feb '13

My January, 2013 web page with versions of Jim Muth's FOTDs has four more FOTD images and "variations" added to it: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html I'm (very) slowly catching up... - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 15-02-13 (Hairy Caterpillars [7])
by Jim Muth 15 Feb '13

15 Feb '13

FOTD -- February 15, 2013 (Rating 7) Fractal visionaries and enthusiasts: In today's image we dive into a variation of the Z^(2.5)+C Mandeloid, checking the area of the infinitely divided main stem that lies just east of the siamese-twin main minibrot, where we find an area crawling with fuzzy yellow caterpillars. The name "Hairy Caterpillars" refers to the flock of them infesting today's scene. The central minibrot is a quadratic one starting to morph into an order-2.5 minibrot. The surrounding pattern is mostly quadratic, but with breakdowns in the symmetry everywhere. The rating of a 7 is boringly average. Even the blue-and-gold color scheme does little for it. But the calculation time of 45 seconds is brief enough to justify expending the energy to view just another average fractal. Visiting one of the web sites will expend even less energy. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> Variations are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are available at: <http://www.Nahee.com/FOTD/> Today was quite pleasant here at Fractal Central, with ample sunshine and a temperature of 46F +8C. Heavier clouds moved in toward sunset, but by then the pleasant day was in the bag. The fractal cat passed a good part of his day chasing catnip balls up and down the hallway. The humans passed the day working. The next FOTD will be posted in the proper time. Until whenever, take care, and environmentalists are crying that climate change is real and we must do something now to reduce greenhouse gas emissions, such as switching to renewable energy sources such as solar or wind energy. The same environmental- ists are also crying that we must stop cutting down trees. I agree with their concern, but I wonder if they have ever done the math to see how many trees we would need to cut down to make room for the solar panels, and-or how many bird-killing wind generators we would need to replace our present fossil-fuel energy sources. IMO, the problem is the overpopulation of earth. And forget high technology, which would ultimately fail. If we wish to maintain our present life style, a permanent and universally acceptable solution to the population problem does not and never will exist. As silly as it might seem, we would have a better chance of bringing everlasting happiness to mankind by launching a scientific search for heaven. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Hairy_Caterpillars { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-3 function=recip float=y center-mag=-3.426640077239256/+0.00001363879827702\ /4.535646e+007/1/-97.5/0 params=2.5/100/50/100 maxiter=1500 inside=0 logmap=85 periodicity=6 colors=00000J00D00K00F00O00H00S00J00P00L00M02O04Q0\ 6S08U0AX0A`08c06`04Y02V00T00P00Uwz2ww5ts7qoAmkCigF\ gcHcZKZWMUPPPKRKEUFEWBBZ97`74c51eIAmK9oM8qO7sQ6uS5\ wsq`tqazqczqdzqezlfzhgzjczlUznOzpQrqRmqSkqUmqVnqXz\ qYzqZU8YU8ZU8_U8`U8aU7bU7cU7dU7eU7gU6hU6iU6jU6kU6l\ U6mU5nU5oU5qU5rU5sU4tU4uU4vU4wU4xccYbbZba_b`_b_`a_\ aaZaaYbaXbaWc`Wd`Vd`Ue`Tf_Sf_Sg_Rg_Qh_PiZOiZOjZNkZ\ MkYLlYKlYKmYJnYInXHoXGpXGpXFqWEqWDrWCsK6gK5fL8gMBh\ MDhNGiNIiLKgKMfJOeIQdHScFUaEW`DY_C_ZBaYAcXEeWHfWKg\ VNiVQjVTkUWlUZnUaoTdpTgrTjsSmtSpuSnrRloRjlRhiRffRd\ cRb`R`YQZVQXSQVPQTMQRJQPGQNEQQHPSKOUNNWQKYSK_VKaYU\ c`UecUgeUiackZcmWcoTcqPmsMmuJmvGmcQzzSzcUzzWzcYzz_\ zcazzczcezzgzcizzkzcmzzozcqzzszmtzzuzmvzzwzmxzzyzm\ zzzzzmzzzzzmzzzzzmzzzzzmzzzzz9zz7zz5zz3zz1zz0zz1zz\ 1zz1zz2zz2zz2zz4zz5zz6zz7zz8zzAzzBzzCzzDzzEzzGzzHz\ zIzzJzzKzzPzzUzzZzzczzgzz } frm:FinDivBrot-3 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(imag(p2)+16), b=imag(p1), d=real(p2)+1: z=(d)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 13-02-13 (Nothing Much [7])
by Jim Muth 14 Feb '13

14 Feb '13

FOTD -- February 13, 2013 (Rating 7) Fractal visionaries and enthusiasts: To create today's image, I combined 10 negative parts of Z^(-1.6) with 2 negative parts of Z^(-3.7) and added (1/C) on each iteration. When the calculation was finished, I found myself with a parent fractal that was little more than a large irregular open hole with Mandelbrot features along its southern boundary and a large cloverleaf object floating inside its northern part. I found today's scene when I checked the eastern edge of the obviously Mandelbrot stuff on the southern boundary of the large irregular hole. The name "Nothing Much" describes what I found there. But 'nothing much' implies a little something, and a little something is what we find in today's image, which is perhaps most notable for its well-divided areas that are unusually flat. Actually, these flat areas would have been nearly totally flat if I had not used the 'tdis' outside option when rendering the scene. As it is, the image rates a nominal 7, good enough to be worth the 2-1/4 minutes required to calculate it. Curiously, I think this is the first image in which I have used a negative maxiter with the 'tdis' outside. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> High-definition versions are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> A cloudy day with a temperature of 41F +5C ended with a burst of wet snow at nightfall. The snow never amounted to more than an inch (2cm) however, and by midnight, had ended. The fractal cat had an average day for an indoor cat. (Indoor cats live far less exciting but far safer lives than the stray and feral cats that roam the area.) The humans had an average human day. The next FOTD will be posted in approximately 36 hours. Until then, take care, and I hear that our schools now need far more computers and internet access in the classrooms if they hope to do an adequate job of teaching students. But if this is so, how, in primitive classrooms without computers, did we learn enough to develop the present day computers that have now become so necessary? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Nothing_Much { ; time=0:02:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+1.097932482367496/-1.698027822201469/\ 4.926059e+008/1/140/0 params=-10/-1.6/-2/-3.7/0/\ 525/0/0 maxiter=5000 inside=0 outside=tdis logmap=-150 periodicity=6 colors=000zz0Y4nW7gUA`SDUQFNsRtM3lR5iW7f`8cdA`iCYn\ DVsFSwGQdDaMBm49xEEsNJnWOidTdmY`aQWRISGAO53K87NAAQ\ CDTFGWHJZJMaLPdKTdJWdI_dIbdHfdGidFmdFpdGkeGffGafGY\ gGTgGOhGKhONiVQjaTkiWlpZmwamqcgkdafeW`gQVhKQiEZZQf\ P`nEkv4vdGeNRP5a8DXDLSHSOM_JQfFUdEVbEW`EX_EY_EZ_EZ\ _E__E`_E`_Ea_EabCUdAMg9Fi77k60d99YCHSEPeaXsxdtteuq\ evnewkexheyeezbez_escdlfdeicZlcSobMrbRtWWuQ`vKewEj\ mGncIrVJlXHfZF``EVbCPdBJf9Dg8GeAIcCKaEM_GOYHwJ6VDc\ PvzSuqVtiYs``rTcqKfqCw5Ywi8tg7qf6oe5lc4jb3ga2e`1Hu\ OGmNFeMEZLDRKDKJPIQ_HXlOayUfpWcgY`Z_ZQaWIcUFdQCdN9\ dK7dHDZKITNONQTHTZBWc5Zh0a_2UR3NI4G959062031MYB`_H\ cZMgXSjWXnVaqTguSlxRquTrrUsoWtlXtPWX2VA8_BDcCKgDXl\ DgpEntFzzFUcLNUQG3VN8_UDd`IhgNmnSrtXvgThVQWIMJ6J69\ NIBQTDUdFXoH_zRVm_R`hNOqJBrF9rB7r85eLKTYYHjkFfmEcn\ C`oBXq9Ur8RsEOnKLjQIeWFak4df7ba9`XBZSDXNGVIITDKR9M\ QkjpZ`TZXaZUi_Ol_Io_Cq_6t } 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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My site's version of Jim Muth's FOTD now...
by Hal Lane 13 Feb '13

13 Feb '13

My web site's version of Jim Muth's FOTD images: http://tinyurl.com/My-versions-of-Jim-Muths-FOTD or: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html now has a February, 2013 page that's almost up to date. I'll try to keep up with Jim, although some of the images I create take quite a while to calculate. However, the new January, 2013 page only has a few images on it. I'm still adding links to it. Fortunately, all the January 2013 images without links have been calculated and anti-aliased... - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 12-02-13 (Duck Pond [7])
by Jim Muth 13 Feb '13

13 Feb '13

FOTD -- February 12, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a dive into the image of February 11. The apparently morphing minibrot at the center looks so like a swimming duck that I had no choice but to name it "Duck Pond". This minibrot appears to be on the way to becoming an everyday quadratic one, but still has a way to go before passing official inspection. The rating of a 7 appears boringly frequently, but with a normal bell curve distribution of fractal ratings, it is not surprising. The calculation time of 2-3/4 minutes will seem a bit slow for those pressed for time. The web sites can eliminate any undue stress. The stress-free already-calculated image is at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def versions are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Lots of clouds and a temperature of 39F +4C made today a typical mid-February day in Central Pennsylvania. The fractal cat, not at all a typical cat, passed the day watching the show passing by his lookout window. The humans had a typical day of working, which is easy to report but very boring to read about. The next FOTD will be posted in 24 hours, not sooner, but very possibly later. Until that eagerly awaited moment arrives, whenever it may be, take care, and the earth's overpopulation problem may indeed be solved by technology. With so many more people being born, the chance of a super genius being born who will invent the technology to solve the problem will continue to increase until the birth of the genius becomes inevitable. (I guess God will have to send the genius, since no human being could solve our population problem.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Duck_Pond { ; time=0:02:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident center-mag=+0.4486435686791/+0.0000527839348/\ 1.805046e+008/1/37.5/0 params=1/3/-0.35/4/0/0/0/0 float=y maxiter=5400 inside=0 logmap=248 colors=000BHfBIgDHhFGiHGjJGkKHkMIlPLmVSmZZnabodgph\ epkiqnmrQUbNUcKUdHUeHNHDJERNJdQOqTSpMZoGdn9km3qj7g\ gBYeFObJE`N4WK3RH3NE3PPPNNNIIIFFFCCCEK8SbEduKjgVpU\ euHokJgbK`UMULNNh7na8oW9oQAoJAoDBo7Co1CoAGcJJSSNG_\ Q5PZLLOQIEVF4_PgGKkHFnIAqJ5tK0wKXdVoUeyIpoLkfNgYPb\ PRZGTVQWQZZMg`IpcEyeATCrSJlRPfRW`QaVPgPPnJOtDOz77M\ bYNcwNcxSUxWLy`Byd2vcMsbeqayoetnhplllkogischv_gyWd\ vNasF_p7hnFqmMpiNoeOnbOpKDq13mB2iK1fU1bb0_k0Vj5Rj9\ MjDIjHDjL9jPChXFgcHfkKerMdyO_wPVvQRuRMtSIsTKuTLwUN\ yUOz7ABDCEIEHOGKTINYJQ_LU`NXbP`cRceTgfVj0OW4LX8JXC\ HXGFXKDXOBXS9XW7Xq4gn6ik7jh9keAlbBn_DoXEpUFqTMfTTX\ T_MTfCTl2ao8iqErsKzuQdRWeTVfVUgXThZSi`RjbQkdPlfOmh\ NnjMolLpnKqoJrnKsnKtnKunLwnLznLznMznMznMznNzmNzmNz\ mOzmOzmOzmPzmPzmPzmPzmQzmQzlQzlRzlRzlRzlSzlSzlSzlT\ zlTzlTzkUzkUzkUzkVzkVzkVzkWzkWzkWzkXzjXzjXzjYzjYzj\ YzjYzjZzjZzjZzj_zj_zZtzWs } 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 11-02-13 (Something Else is Wrong [7 and 9.5])
by Jim Muth 12 Feb '13

12 Feb '13

FOTD -- February 11, 2013 (Rating 7 and 9.5) Fractal visionaries and enthusiasts: Today's image earns two ratings, a 7 for the artistic worth and a 9.5 for the mathematical interest. The mathematical rating reflects the mystery of what is happening in the image. The iterated expression subtracts 0.35 part of Z^4 from Z^3 and adds straight C on each iteration, yet the image features a lopsided cubic minibrot and a not-quite-critical-looking hexic minibrot, both lying side-by-side. And to add to the mystery, the deeper we go into the image, the closer the minibrots approach the quadratic variety until nothing remains but the usual quadratic ones. The parent fractal is not all that unusual -- a Mandelbrot set rotated 180 degrees with a hole at the terminus of every filament. The hole at the end of the main spike, which in today's parent points east, is unusually interesting in that it has a well-defined valley along the positive X-axis on its east side. Today's scene lies rather deep in this valley. The artistic part of the image reflects my increasingly cynical and depressing view of the modern world we have created for ourselves. As the years pass, I find depressing deep blue colors creeping ever more often into my images, such as those that abound in the outer parts of today's scene. The name "Something Else is Wrong" expresses my feelings when I saw the two incompatible minibrots lying side-by-side in the same area of the same parent. The terraced effect was achieved by rendering the image with the 'outside' parts set to 'tdis', a setting that is quite effective at adding life to images that appear dead with the outside set to 'iter'. The calculation time of 2-1/4 minutes might appear slow to those with only marginal interest in fractals. The web sites can make fractals much more interesting for these few. Check the completed image at: <http://www.crosscanpuzzles.com/Archives.html> and high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the thousands of back images at: <http://www.Nahee.com/FOTD/> Early morning rain ended by 9am here at Fractal Central today, but the heavy clouds and fog hung on for most of the day, while the mild temperature of 45F +7C improved things only a little. The fractal cat passed most of the day sleeping, an activity that is hard to make interesting. The humans passed the day working, an activity that is equally uninteresting to report. The next FOTD will be posted when it is ready, which most likely will be sometime tomorrow. Until that glorious moment arrives, take care, and let's pass a law banning all disagreement. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Something_is_Wrong { ; time=0:02:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.4486436381/+0.00005502463/72716.29/1\ /-107.5/0 params=1/3/-0.35/4/0/0/0/0 float=y maxiter=3000 inside=0 outside=tdis sound=off colors=00000D00E00G00H00J00F00D00B0090070050GV00B0\ 0D02F04H06J08L0AN0CP0ES0GV0IY0K`0Mc0Oe0Qg5SiAUkFWn\ KYqP_tU`vZancaghc`mdUneTneSneSneRoeRoeQoeQoePoeOpe\ OpmNpmNpmMpmMzm0zmDzmCzmCzmBzmBzmAzmArm9xm9vmDumGt\ mJsmNrmQpmTomWzm_zmbzmezmhcmdWmaOmZRmYUmXXmW_mWbzV\ dzUgzTjzTmzSpzRszQuzQtzPszPszOrzOrzOrzPrzQrzRrzSrz\ TrzUrzVrzWrzXrzYrzZrz_rz`rzarzbrzbqz`qzZqzYqsWpsUp\ tTptRptQotOotMouLouJnuHnzGnzEnzDfzOZzZRziWzm`zpezt\ jzwozz6zoXzYwzHyzJvzqdznNzl5zj6ze7za8zY9NUARQBUMBX\ IF`MIcPMgSPjVTnYWq`_ucbxf`naZdYYVTWLPUBKT2GRKmNQjJ\ WgF`dLXUQTKWPA`L0C1IA7Q9DY7Je6PmWTkuXitabsfXrkRqpL\ ptFptEqhGrYHrMJsBKs0Lh9UZHbPQkFYsH_rJ`qLapMboOcnQe\ mSflrv_TglVhkXijZji_lhamgcnfeoefpehqdjscltbmuaov`q\ w_l49m8BmBDnFEnIGnLHoPJoSLoVMpZOpaPpdRqhTqkUqnWrrX\ ruZO3rQ6qR9pTCoUFnWHmXKlZNk_QjaSibVhdYhe`ggbfheejh\ dkkcmmbnpaps`qv_aQ8bSAcUB } 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 09-02-13 (Jewel of the Fractal [6])
by Jim Muth 12 Feb '13

12 Feb '13

FOTD -- February 09, 2013 (Rating 6) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! ----------------------------------------------------------- frm:FinDivBrot-3 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(imag(p2)+16), b=imag(p1), d=real(p2)+1: z=(d)*(z*z*fn1(z^(a)+b))+c |z| < esc } ----------------------------------------------------------- The new formula, FinDivBrot-3, is a minor generalization of the FinDivBrot-2 formula that I use often. But this is the first time I have used the FinDivBrot-3 formula for an FOTD. Today's image lies in the remains of Scepter Valley of the large minibrot on the main spike of its oversized parent Mandelbrot set, which is corrupted just beneath its surface by Z^11 energies. The rating of a 6 indicates an image FOTD lacking in impact, but it's all I could give the contrived image whose main attraction is an unusually symmetrical order-11 minibrot and few carefully tweaked color registers. I named the image "Jewel of the Fractal", a name that promises more than the image delivers. Luckily, the calculation time of a fireball 30 seconds will leave little time for anticipation to build, holding the disappointment to a minimum. Today's finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> Hi-def renderings are available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images and discussions are available at: <http://www.Nahee.com/FOTD/> As expected, the talk of a superblizzard proved to be all hype, at least for the Fractal Central area, where we picked up a whopping 1 inch 2.5cm of slushy snow overnight. Today was partly cloudy and breezy with a temperature of 30F -1C. The fractal cat, who never panics when superstorms are predicted, had another calm day as he sought and found the warmest spots in the house. The humans had a day of antiquing near Harrisburg, where we picked up some bargain books and CD's. Yes they do still exist. The next FOTD will be posted, who knows when. My best guess is within 24 hours. Until that mysterious 'when' arrives, take care, and regardless of the problem, be assured that higher technology will be called upon to solve it and might actually work for a while. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Jewelof_theFractal { ; time=0:30:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-3 function=recip center-mag=-17.75145971129946/+0.02607765322928155\ /6.44325e+011/1/35/0 params=11/10000/1000/1000 float=y maxiter=275 inside=255 logmap=20 periodicity=6 mathtolerance=0.05/1 colors=000zhUiDMuGRcAJN5B603A45E77HA9LDAOGCSJEVMFQ\ QEMUEIYDL`DPdCUhCZmCcrDhvEmzEhvJerNboR_lWXj_UhcRgg\ OafKWeFRdCLcCGbCAaC5aDAdEEfFIhGNjHRlIVnIZpMVrQRsUN\ tYKuaGweCxi8yl5zZRuLlqNhkOefPaaQZXRVSSSNTOIULDQIGN\ FIKDKHAME8OB5Q83SE6RK9QQCPVFPTOVSX_RedQniPvnOtgNr`\ NqUMoNMnGLl9Lk2XbNbZOgVPlRPqNQvKQuZGul7nkEhjKbjQXi\ WRiaLhgFhmBgj8fg5ed2eaGWTUMKfDCiCFlCIoBLrBNuAQxATz\ AVyHZxObwVfvajvhmucntZnsUnrQnqLnpGnoBnn7nj7qf7sb7u\ _7wUGsOOoIXkDdgEeiFfjGglGhmHioIjpIkqIjcIjRIiEIi1Lk\ 8NmEPoLRqRUsYWucYwj_xpYvkXtgWrbVqZUoUTmQSlMQkKOkIM\ kGKjEIjCHjBGfIGbOF_VFW`FTfKWhOZiTakXdl`fmbdnccnebo\ faog`pi_pjZqkYqjfXjnCgpGdqKasOZtRXrSVpSTnSSlTQjTOh\ TNgTMgPLgMLgJMhOMhTJfYHebFdfDckBbo9at7`xCWlGR`KNPO\ IDSE1NC7JBCFAHIBKKCNMCQODTQDVUG`YJfaLleOrhQxkUmmXb\ p`SrcHtf6pcClaHh_MeYRaVWYT`UReRPjWQj`RjdSjiTjmTjoc\ oqntryxfdqVKjK0cXLhiemzzz } frm:FinDivBrot-3 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(imag(p2)+16), b=imag(p1), d=real(p2)+1: z=(d)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 08-02-13 (Something is Awry [7])
by Jim Muth 08 Feb '13

08 Feb '13

FOTD -- February 08, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows a quadratic minibrot surrounded by its typical bifurcating pattern of elements. But wait! Something is wrong. The minibrot must be some kind of circus freak. It bears very little resemblance to a typical quadratic minibrot. The reason is that it is not a pure quadratic minibrot. The minibrot has been caught in the process of morphing from a quadratic to an order-11 one. On its surface, the parent fractal, once you back out far enough to see all of it, is a hugely oversized Mandelbrot set. But in its depths, it is corrupted by order-eleven energies. Today's image lies in an elephant trunk on the south shore line of the parent, at a depth where the order-eleven corruption is just beginning to wreak its havoc on the minibrots. Finding nothing really outstanding in the image, I could rate it no higher than a hum-drum average 7. The colors are blended smoothly enough, but at least in my opinion, they lack harmony. The name "Something is Awry" describes the hopelessly corrupted minibrot at the center. The calculation time of only one minute is quite brief however, and will cause little frustration for those who feel the image has laid an egg. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> High-definition renderings of the FOTD images are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are available at: <http://www.Nahee.com/FOTD/> Heavy clouds prevailed all morning here at Fractal Central, making the ominous media forecast of a super-blizzard seem all the more ominous. But as of post time, the temperature is a rather balmy 37F +3C and nothing has yet fallen from the clouds. I'm beginning to suspect another gross exaggeration from the profit-driven weather media. The fractal cat must agree. All day, he has been notably unconcerned with the weather. The humans are mildly concerned, but expect little more weather action than a mildly inconvenient inch or two of slush, if even that. The next image will be posted in a couple days, but with nothing guaranteed. Until whenever, take care, and we should be ready to accept the truth even when it proves to be something we do not want. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Something_is_Awry { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip passes=1 center-mag=+317.7624490652465/-32.17560651252315/\ 3760/1/-100/0 params=11/1000 float=y maxiter=1500 inside=0 logmap=84 periodicity=6 colors=0007ec7dd7ce8bf8ag9`h9_jAZkCYlEXnGWoIVpKUrN\ TsQStTQvWPwZPxaPudQsgSkjTcmTWpPQqMGqM8qL2pL1oK1nJ1\ lH1iG1fF0bE0_C0XB1UA2R84O86OA8OCALECIGEFIGCKI9MK7O\ M9RQ8SP8RO7PM7OL6MK6LI5JH5IG4GE4FD4DC3CA3A92982761\ 65144032011CmzBiuAerAao9Yl9Vi8Sf7Pc7M`6KY6JV5HR4FO\ 4DL3BI39F27C159136013Hm6Eh5Bc48Z35U22P14K23F13C13A\ 1391281281271261261150150140130130020010010000fbz`\ YvWTrUOmSJhQKcOLZMMUKNPILKGKFEJACI5AH09G08F08E07D0\ 6C06A0590480470360350240130120010xZEuXDrWCpUCmTBkR\ BhQAfO9cN9aL8ZK8XI7UH7RG6PE5MD5KB4HA4F83C72A527415\ 21210cm3cl2cl1cl0ci2cf3mc4m`6mY7mV8mSAmPBmMCmKDmNG\ mQJmSMzVOzYRz_UzbXzeZzgazjdzmgzoizlgziezgczdazb_z_\ YzYWzVUzTTzVRzXPzZOz`MzaKzcJzeHCgFBjEAmC9pA8r97t76\ v56x4zz3zz4zz4zz5zz5zz5zz6zz6zz6zz7zz7zz8zz8zz8zz9\ zz9zz9zzAzzAzzAzzBzzBzzCzzC9zC8zD6zD5zD3zE2zE1zE2z\ H2zJ3zL3zN4zQ4zS5zU5zW6zZ } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } END PARAMETER FILE=========================================

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FOTD 07-02-13 (The Monkey Puzzle [7])
by Jim Muth 08 Feb '13

08 Feb '13

FOTD -- February 07, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that was generated when I combined 1.8 negative parts of Z^(-5.6) with 4.4 negative parts of Z^(-1.9) before adding (1/C) on each iteration. This parent is a NE-SW oriented string of large bays with debris clogging the SW bay. Today's scene is located on a branch of a 'star' on a filament extending from a small bud on the SE shore line of the large central bay of the parent fractal. The rating of a 7 indicates that I have seen a few too many similar images. The name "The Monkey Puzzle" refers to the intricate network of filaments and tendrils radiating from the central minibrot. (It is also the name of a decorative tree native to Chile.) The near average calculation time of 4 minutes can be eliminated by surfing to one of the FOTD web sites. The image has already been calculated and is posted at: <http://www.crosscanpuzzles.com/Archives.html> with the augmented renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are online at: <http://www.Nahee.com/FOTD/> Morning clouds with flurries of snow gave way to a sunny afternoon here at Fractal Central today. After the recent cold and snowy weather, the temperature of 37F +3C actually felt like spring. The fractal cat acted like it was spring, spending several hours in the afternoon sun. The humans spent the day doing boring, routine, but necessary things. The next FOTD will be posted in the near future. Keep checking back, and before you know it, the fractal will be there. Until whenever, take care, and I'm all for clean solar energy, but where would we put the thousands of square miles of solar panels? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Monkey_Puzzle { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+0.8175847835908/+0.2233739092024/2.470\ 83e+009/1/-7.5/0 params=-1.8/-5.6/-4.4/-1.9/0/0/0/0 maxiter=2250 inside=0 logmap=280 periodicity=6 colors=000JQsHOpGNmFMjEKgDJdBIaAGZ9EW8CT79Q57N45K3\ 3H22E11B00864FC8LIBSNFcTKmZOzdSziVzgTzeRzcQzaOr_Nh\ YMeWMcVL`TLYRKWPKTNJQLHOJGLIEIGDGEBDCAAA8887565254\ 0853A65973F8AH9CJAFMBHBCNQDMSEOVFRXFTZGVaGYcG_eGag\ GdjGflGinGkqGmsGpuGrwGtwJswMswPrwRrwUqwXqwZqv_pu`o\ tansamrblqZkp_jo_in`hmahlbgkbfjceiddhecgebffaeg`dh\ _ch_YgcTfgNekIrnCcr7zvzsy6bv9tsDdqGznKelNfiRgfUhdY\ ia`i_djXgkUkrSnzPqzNpzMozMnrMmmMlhLkcLjaLi_LhZKgXK\ fVKeUKdSJcQJbPJaNJ`LI_KIZIIYGIXFHWDHVBHVAHaCOhDUfC\ TdCScBRaBQ_APZAPX9OV9NU8MS8LQ7KP7KN9OMARLCUKDXIF`H\ GcGHfFJiDKmCMpBNsAOv9Qt9Rr9Sp9Tn9Ul9`j9ah8bf8cd8db\ 8f`8gw8mw8nw8owBnwDiWFcXIcYKbZMb_Ob`RaaTabV`cX`d_`\ fa_gc_hfZih_jj`klalobmqcnsdoueptfnsgmrhkrijqjhpkgp\ leomdnnbmoamp_lqZksXkuWjwUiyTizSizThzVgzXfzYez_dza\ czbbzdbzeazg`zi_zjZzlYznXzoWzqWzrSzsPzsMzsJzsmzmpz\ qqzmqziqzfrzbrzZrzWfzcVzk } 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 05-02-13 (Night Watch [7.5])
by Jim Muth 05 Feb '13

05 Feb '13

FOTD -- February 05, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is based on the combination of 4.71 parts of Z^3 and 3.14 parts of Z^4. The parent fractal produced by this unlikely combination is an undersized Mandelbrot set with two open areas some distance to the west. Today's scene lies on the north shore of the southern open area, near what appears to be a mostly-obscured rudimentary East Valley trying to get organized. The buds along this rudimentary valley are not yet fully formed, but appear to be of a cubic nature. The image's stripes were achieved by rendering the image with the outside set to the 'tdis' option. The colors themselves are based on the Fractint default palette, though I have made many changes in this not-very-attractive color scheme. The name "Night Watch" is a comment on the overall darkness pervading the scene. The rating of 7-1/2 is as good a guess as I could make about the final value of the image. Any rating excess is made up for by the very fast calculation time of around one minute. But fractal calculation can be tedious. So be smart and avoid calculation altogether by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> Sharper renderings are or soon will be online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> About 3/4 inch (2cm) of snow fell overnight here at Fractal Central, but the high temperature of 34F +1C had disposed of it by mid-afternoon. The fractal cat kept careful watch over the situation, then, when he saw that everything was under control, retired to his blanket on top of the tall bookcase. The humans, who also prefer things to remain under control, spent the day keeping them that way. The next FOTD will be posted when it is ready, with no promises stated or implied. Until next time, whenever that may be, take care, and if technology is making our lives ever better, why are so many people so unsatisfied with their lives? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Night_Watch { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=+0.1714951778975432/-0.0040565105431643\ /2.40102e+007/1/110/0 params=4.71/3/3.14/4/0/0/0/0 maxiter=1500 inside=255 outside=tdis periodicity=6 colors=000zzezz0zzezz0zzezz0zzezzLzzzzzLzzzzzLQRQR\ RR000000555888BBBEEEHHHKKKMMMOOOPPP___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz0zS7zSEzSLzSSzSSzLSzESz7zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz7zzEzzLzzSzzSzzSzzSzzSzzSzzS\ zzSzzSzzOzzLzzHzzEzzEzzEzzEzzEzzEzzEzzEzzEzzHzzLzz\ OzzSzzSzzSzzSzzSzzSzzSzzSzzSzzQzzOzzMzzKzzKzzKzzKz\ zKzzKzzKzzKzzKzzMzzOzzQzzSzzSzzSzzSzzGzzGzzGzzGzzG\ zzCzz8zz4zz0zz0zz0zz0zz0zz0zz0zz0zz0zz4zz8zzCzzGzz\ GzzGzzGzzGzzGzzGzzGzzGzzEzzCzzAzz8zz8zz8zz8zz8zz8z\ z8zz8zz8zzAzzCzzEzzGzzGzzGzzGzzGzzGzzGzzGzzGzzFzzD\ zzCzzBzzBzzBzzBzzBzzBzzBzzBzzBzzCzzDzzFzzGzzGzzGzz\ Gzz0zz0zz0zz0zz0zz0zz007K } 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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major irritation
by JackOfTradeZ＠comcast.net 05 Feb '13

05 Feb '13

. Do any of you get bombarded with 2 dozen emails per day from that Phrench A-hole sebastien helie or is it just me? I wouldn't mind if he could speak English and it wasn't such nonsense. Sheeeesh! .

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FOTD 04-02-13 (Epsilon Afire [7.5])
by Jim Muth 04 Feb '13

04 Feb '13

FOTD -- February 04, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Let the banners wave, the trumpets blare and the fireworks explode! I'm back with another semi-glorious fractal, this one located in one of the several East Valleys of the 'Zexpe' fractal as it appears 10 levels down the hyperladder with no function applied. The image rates a mildly impressive 7-1/2, but a good part of this is due to the coloring, on which I spent over 1/2 hour. Without the fiery color scheme, the image would be just another chaotic fractal. The name "Epsilon Afire" refers to both the exponent of Z and the fiery colors of the image. The calculation time of four minutes is about average, but the trip to one or all of the web sites is still worth the minor effort. Check the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And thrill to the glories of the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> though I'm not sure Hal is caught up quite yet. The FOTD back images are online at: <http://www.Nahee.com/FOTD/> Typical midwinter cold continued here at Fractal Central today, with partly cloudy skies and a temperature of 30F -1C. The forecast is for another dusting of snow tonight, which will be about the fourth dusting in the past week. The fractal cat took a few glances out the window, but spent most of the afternoon sleeping on his blanket on top of the tall bookcase. The humans had an everyday afternoon. The next FOTD will be posted when things are right, the most favorable time being tomorrow around this same time. Until whenever, take care, and Hooray! Our team held on to win the Stuporbowl! Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Epsilon_Afire { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=+0.393523343081/-0.061624411585/\ 1.439566e+007/1/142.5/0 params=2.71828/0/-10/0 maxiter=3200 inside=0 logmap=-420 periodicity=6 colors=000`NE`PF`QG`SH`TI`VJ`WK`YL`ZL`_M`aN`bO`dP`\ eQ`gR`hSbmV`iSZeQYaOWYMVVJTRHSNFNCDE6AM8BYQCfZDohE\ xwHwtGwqFwnEwkDwhCveBvbAv_9vX8vU7vR6uO5uL4uI3uF2uC\ 1uA1tC2tD3sE4sF5sG6rH7rI8rJ9qKAqMBpNCpODpPEoQFoRGo\ SHnTInUJvYHrWJnVKjULfSNcRO_QPWPQSNSOMlLUmHUzDKz90m\ 60c80U9CKA8AC2ADDAEFKGFUHETIETKESLESMEROEQPEQQEPSD\ OTDOUDNWDMXDMYDL_DL`CKaCJcCJdCIeCHgCHhCGiCGhEHhFHh\ GHhIHhJHhKHhLHgNHgOHgPIgRIgSIgTIgUIfWIfXIfbIfcIfjI\ fkJflJenJeoJekJelJenJeoJepJgqLeqJgeIiZGkRFmKDoDCq6\ BlAFgDJbHN_OlZMaYKRXIGUE3WG5XI6YJ7ZL8_MA`OBaQCbRDc\ TFdUGeWHfXIgZJi`LjaMkcNldOmfQngRoiSpkTqlVrnWsoXtqY\ xu`vs_urZsqYrpXpoWozVmzUlzTjzSizRzzQzzPzzOzzNzzMzz\ LzzKzzJzzIzzHzzGzzFzzEzzFzzEzzEzzDzzDzzCzzCzzCzzBz\ zBzzAzzAzzzvzzxzztzzqzznzzkzzhzzezzbzz_zzXzzUzzRzz\ OzzLzzIzzFzzHzzIzzJzzKzzLzzMzzNzzOzzWzzWzzXzzXzzXz\ zYzzYzzZzzZzz_zz_zz`zz`zz } 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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Old Software2
by JackOfTradeZ＠comcast.net 04 Feb '13

04 Feb '13

. I zipped the FracTools3.0 CD into a single file which unzipps into an empty directory re-establishing the original CD with folder structure etc. It is 365 Meg. I could post it on my web site IF someone willing to download it ....... .

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Links to fractals for Dec 27 - 31 are up.
by Hal Lane 03 Feb '13

03 Feb '13

I'm woefully behind on adding links to my site to point to the hi-def images of Jim Muth's FOTD (and variations) that I've been creating. Fortunately, I've kept up with calculating them -- or I would never be able to catch up... I've just now added links to the fractals for Dec 27 - 31, 2012. More are on the way. Please use this link to my main page to access the images: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html Thanks, - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 31-01-13 (Quadrilateral Arc [7])
by Jim Muth 01 Feb '13

01 Feb '13

FOTD -- January 31, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image will be the last until at least February 4. We're doing a bit of remodeling here at FC. The image rates a 7. I'm not sure why I gave it such a rating. Perhaps it is the most disorganized of all time. I can spot at least a dozen themes in the scene, all trying to predominate but none winning. The arc of quadrilaterals, which inspired the name, is probably the most obvious, though several others are giving notable competition. The parent fractal came about when I combined 10 negative parts of Z^(-1.2) with 0.1 negative part of Z^(-12.2) and added (1/C) on each iteration. It consists of two well-separated parts. The main part, which lies at the center, holds a superb fractal 'fan'. The second part lies well northeast of the main part and consists of a series of rings with a well-defined minibrot within these rings. Today's scene lies at the northeast edge of the superb 'fan'. The calculation time of 3-1/2 minutes borders on slowness. And unfortunately, the image will not be posted on the official web site for several days. It will be available sooner however at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The library of FOTD back images is at: <http://www.Nahee.com/FOTD/> Today brought a mix of sun and clouds with occasional heavy showers of snow to Fractal Central. Luckily, the above freezing temperature of 34F +1C melted the snow about as fast as it fell. The fractal cat spent most of the afternoon in his watch window, chasing the sun and wondering what all the snow was about. The humans passed the day finishing the commercial work. The next FOTD will not be posted before February 4, and maybe not until a day or two later. Until whenever, take care, and as the millionaire who had just gone bankrupt said, "put the past behind you and look ahead to the future." Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Quadrilateral_Arc { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.994509076742968/+1.331693835073464/\ 1322976/1/91.75/0 params=-10/-1.2/-0.1/-12.2/0/\ 1000/0/0 float=y maxiter=2400 inside=0 logmap=246 periodicity=6 colors=000C8LJGMMHNPLPRLQVRRYTS`XTd`UgaUjfUneUplUp\ hSrnQrjPrlNqkMqjLqiJphIpgHpfFoeEodCocBnbAna8n`7ra5\ n_6kZ7hY8dX9aWAZVBVUCSRDPOELLFIIFFFFBDF8BF5AF8AJAD\ ECCEEDEHFFTFPRENPDMNBKLAIJ9HH7FF6ED5CD39C4BC4CC5EC\ 5FC5GC6IB6JB7LB7MB7NB8PB8QB9SA9TA9UAAWAAXABZAB_7AZ\ AB`DCbGDdJDeMEgPFiSFjVGlYHn`HocIqfJsiJtgLqfNoePmcR\ jbShaUf_WdZYaY__W`YVbWUdTSfRRhPGpKQiNZbQhWTpQXqPWq\ PVqOVrOUrOTrNTrNSsNSsMRsMQsMQtLPtLOtLOuKNcKNuKMcJL\ vJLcIKvIJcIJwHIcHIzHHcGGzGGcGFzFEcFEzFDmEDwECmEBzD\ BmDAzDAmEBvFBmGCsHCqIDpJDoKDmLElMEjMFiNFgOFePGdQGb\ RHaSH_THZUIXUIWVJUWJTXJRYKQZKO_LM`LLaLJaMIbMGcNFdN\ DeNCfOAgO9hP7iP6iP6hP5gQ5gQ4fQ4eR3eR3dR3dRDcKMbEVa\ 8ca2ac3`d4Ze4Yf5Wg5Vh6Uj7Sk7Rl8Pm8On9Mo9LqAKrBIsBH\ tCFuCEvDDwDFtFGrGHoIImJJkKKhMLfNMdPNaQO_RPYTQVURTW\ SRXTOYUM_VK`WHbXFcYDdZAf_8g`6hb8gd9feAegBdhCcjDbkE\ amF`oG_pHZrIYsJXuKWvLVxMU } 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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AOTD 1/18/13
by JackOfTradeZ＠comcast.net 01 Feb '13

01 Feb '13

. Zoom In2 the FOTD for 12/28/12 "Into the Aether" is posted: http://www.fractal-animation.net/vid/in2theaether.zip 25 MEG download, 90 second run time. .

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Old Software
by JackOfTradeZ＠comcast.net 01 Feb '13

01 Feb '13

. That software is: ? FracTools ? FracZooms ? FracMusic I have an old CD titled "FracTools 3.0". It contains about 400 Meg of files. If it is what you want, how can I get it to you? On another CD, there is a directory called "FRACZOOM". About 50Kb; it is a "C" program that creates a BATCH file that runs FractInt to generate zoom sequences. (Exactly what my BASIC programs do; I've never used this one so I don't know how it compares) Is that what you are looking for? As for FracMusic, I have a downloaded file called "FractMus" which runs in windows and is very sophisticated - I have used it to generate sound for my animations. It is still available on the web - google it. .

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FOTD 30-01-13 (Cubic Elephant Land [7.5])
by Jim Muth 31 Jan '13

31 Jan '13

FOTD -- January 30, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's semi-glorious image is a simple view of a cubic minibrot in the eastern Elephant Valley of the Z^3+C Mandeloid. (The parent fractal also has an elephant-type valley on the west side of the main bay, but this valley simply mirrors the eastern one.) I chose this particular minibrot because it is a good example of anti-trifurcation, and also because it is an unusually impressive scene in the cubic Mandeloid. The rating of 7-1/2 includes an extra half-point as a reward for the extra effort I put into the flashy coloring. The name "Cubic Elephant Land" is a comment on the exponent of Z and also the cubic elephants that abound all through the scene. The calculation time of 40 seconds is fast by anyone's standards, but the FOTD web sites are always available to make the operation even simpler. Be happy! View the image already calculated at: <http://www.crosscanpuzzles.com/Archives.html> Be happier! See it in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Be happiest! Find thousands more fractals at: <http://www.Nahee.com/FOTD/> The heavy clouds hung on here at Fractal Central today, inter- spersed with heavy showers of rain. The temperature reached a spring-like 64F 18C but could not be enjoyed with rain falling so frequently. Nicholas, the fractal cat, checked the weather outside several times, but spent most of the day asking for more food. The humans, being human, did human things. The next FOTD will eventually be posted, most likely sooner rather than later. Until whenever, take care, and regardless of how bleak the outlook might be, remember that it could always take a turn for the worse. (Then try to think positive.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= CubicElephant_Land { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotCube center-mag=+0.415415021\ 13021440/-0.00759289279330656/4.707256e+011/1/7.5/0 params=0/0/0/0 float=y maxiter=1800 inside=0 logmap=257 periodicity=6 mathtolerance=0.05/1 colors=000KBzKAzK8zK6zK4zK2zK0zH0zE0z90w60r30n00i0\ 0e00a00Y00U00R00P00N00J00G03C0690970C60G30J10N00R0\ 0P00N10N30L40J60J70H90G90GB0EC0CE0CG0BH09J09J0CN1G\ R7JSMNWTRYcSajWcnagtcizcnzfpzckzYgzSezNazJ_yEWy9Uw\ 4Rt0Nr0Lp0Hm0Gj0Cf0Bb06Z01V00Q00L00G00B00600100000\ 10031063074BB6NC7YG9kHBzJBzG4zE0wC0nB0g70_60S40L30\ G00C0090060440C10L0AU0Ke0Up0cz0mz0cw0Ug9aUNzH_rPRk\ UHe_9_e1Uk0Pr0_0zW0yU0tR0pP0kL0gJ0aG0YE0UB0R90N00N\ 00N00N00S34WEG_SSceegg__gWSgRNgNGgJ9gE4iM0pL0zT0zZ\ 0zc0rR0Y70GE0430000140410760B30G00J00N00R00W00_03c\ 06g09_07S07L07E077773G60P60Y60Y60Y60Y60Y30Y10Y00Y0\ 0e00r00p00n00r00w04z0Bz0Jz0Rz0_z0gz0rz0zz0zz0zz0cz\ E4zW0zp0zw4zzLzzczzyzzzzzzzzzzpzzgzzYzzRzzHzzBzz3z\ z0zz0zz0zz0zz0wz0nz0ez0Yz0Rz3Hz7BzB4zG0zL0zR0zU0zN\ 0zH7kBEn6Nn0Up0ap0eW1gECi0P0C_3GW6JS9NPCRLGUHJYENa\ 4Se0Yi0an0_g0Yc0YY0WU6WPE } frm:MandelbrotCube {; Jim Muth real(c),imag(c) z=p1, c=pixel+p2: z=z*(sqr(z))+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 29-01-13 (Grozny [8.5])
by Jim Muth 30 Jan '13

30 Jan '13

FOTD -- January 29, 2013 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image is named "Grozny", a russian word that describes Ivan the Terrible. The exact meaning of the word is somewhere between 'terrible' and 'awesome', kind of how God will appear to Christians when they come face-to-face with Him on judgement day. The name is exaggerated, but it's what came to mind this afternoon when I shut down my thinking. The image does rate an 8-1/2 however, mostly because of its striking coloring. The scene of the action lies in the detail on the 'east' side of the large minibrot on the west branch of the stem extending from the large bud on the north side of the main bay of the parent fractal, which is a Mandelbrot set corrupted in its depths by cubic energies. Now that the description is out of the way, I might add that the image is really a rather pleasant one, well worth the mere 35 seconds required to calculate it on S.O.T.A. computers that are not over-educated. Those whose computers are over-educated and have forgotten how to do DOS, can view the image on one of the FOTD web sites. The completed image is posted on the Official web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the awesome high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> Heavy clouds, dense fog and a temperature of 41F +5C made today easily forgettable here at Fractal Central. The fractal watch cat spent the morning watching for trouble and the afternoon by the heat, recovering. The humans spent the day doing routine things too boring to report. The next FOTD will be found in a few hours and posted most likely in about 24 hours. Until whenever, take care, and since both the political left and right know what is best for the country, and there can be only one thing that is best, why can't they get together and do it? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Grozny { ; time=0:00:35.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-0.1238205930813758/+1.032225706886118/\ 2.948051e+009/1/-59.5/0 params=3/20/0/0 float=y maxiter=900 inside=0 logmap=36 periodicity=6 colors=000D_hC_iB_dA_`9_e8Vb7Q_6LV5GP4CK39G25B0203\ AT2Ib19Ji5na4eU3YN2PF1H708zzzvvvrrrmmmhhhcccZZZUUU\ PPPKKKFFFAAA000q12m01d01`01X01T01P01K00G00C0080040\ 0gPL`LIVHFPECIA9C766336bP5_N5XL4UJ4RH3OF3LD2IB2F91\ C7195OLULJSJIQMLPPOPSQOVTOYVO`YNc_NfbMidMlgMoiLrlL\ umKvoKwqKzsIzuGzwFzqDzmCzmATm90m4Om7Jm6Em49m34m10m\ N0mJ0mF0mB0m70m3MkfKfbIbZGYVEURCQNALJ8HF6DB4mz2mzU\ mzUmzUmzUmzUmzUmzUmzUmzUmzUmzUmzUmzUmzUmzcmzcmzcmz\ cmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzmzxmzzmzzmz\ zmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzHzPEzLCzIAzF8zC\ 6z94z62z3OzTJzNEzH9zB4z55zx2zUHzIDzEAzA6z73z3bzuTz\ fJzT9zEszxnzrizmezh`zcWzZSzUNzPIzKEzF9zA4z5Ezs9z`4\ zIyz4qz3iz3az2Vz2Nz1Fz17z0Izn4zY3zU3zQ2zM2zI1zF1zB\ 0z70z3IzeOzcGzQ8zDiz2Yz1Nz1Bz0nzzjzufzqczl_zhWzcTz\ _PzVLzRIzMEzIAzD7z93z4Ezl } 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 28-01-13 (Un-natural Arch [8])
by Jim Muth 28 Jan '13

28 Jan '13

FOTD -- January 28, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene in Seahorse Valley. It looks nothing at all like the Seahorse Valley scenes we are so familiar with because it is sliced in an odd direction -- rotated 30 degrees from the Julia toward the Rectangular orientation. While viewing the image, (and hopefully enjoying it), the viewer might wonder where Seahorse Valley is located in the frame. Actually, the valley has gone nowhere. The image is immersed in it. Everything in the scene is a part of the valley. The detail in the arch was supplied by the 'tdis' outside coloring option, which colors the points according to how far they travel before finally escaping. I named the image "Un-natural Arch" because of the prominent arch that fills the frame. It almost reminds me of a week or so I spent in Saint Louis quite a few years ago. The rating of an 8 might be a bit excessive. But then again, what is the penalty for padding a rating. The calculation time of 4 minutes is slower than ideal, but the web sites are always available to make life more efficient. So save that time. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back FOTD's are available at: <http://www.Nahee.com/FOTD/> The day began with snow here at Fractal Central, but a rising temperature changed to snow to rain before noon. Occasional rain continued the rest of the day, making a slushy mess of the area. The fractal cat took one look out the window and decided to settle down by the heat. The humans had enough inside stuff to finish to keep their minds off the outside weather. The next FOTD will be posted in the very foreseeable future. Until whenever, take care, and why do they need exploding fireworks at music concerts? Does today's music itself lack power, or have audiences become so desensitized that in addition to the amplified sound, they now need a light show to create total sensory overload? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Un-natural_Arch { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t maxiter=3600 center-mag=0.0774812/-0.0170439/20.36076/1/-90/6.0\ 8852815419518389 params=90/90/60/90/-0.753/0/0.5/0\ /2/0 float=y inside=0 outside=tdis periodicity=6 colors=000I3I_FWpQijSeeUa`WYVYUQ_QLaMFcIAeE5gA0i66\ e8Ca9HYBNUCTQDYMFcIGhEHfHGeKFdNFcQEaTE`WD_ZDZaCYdC\ DsKFrMHrNJqOLqPNpQPpRRoTToUVnVXnWZmX_mY0yDUsRwndm7\ zg9xaBvWDtQFrKHpFJnMKgTK`_KUeKOlKHsKAyP4sU7mZAgcCa\ fFWiIQnKPo8Qr7Qw6Qo5Ql5Qi4Qd3Q`3QX2QT1QP1MW1Ha1Di1\ Fo4Go7HiAJhCKgFLfINeKOeNPdQRcSSbVTaYV`_W_bXZeYZg_W\ iaUjcRlePmgMniKpkHqmFsoCtqAus7wu5xw3ysCwpLvmTtjasg\ iqdrpazo`vn`sn`pn`mm`jm`fm`cl``l`Yl`Vk`Rk`Ok`Lj`Ij\ `Fj`CjZEhXGgVIeTKdSMcQOaOQ`MS_KUYJWXHYVF_UDaTBcRAe\ Q8gP6iN4kM3lLWq`Wq`Xr`Xr`Yr`eEJeELeFMeGNeGPeHQdHRd\ ITdJUdJVdKXdKYdLZdM`cMacNbcNdcOecPfcPhcQidPlcQjcRi\ cShbTfbUebUdaVbaWaaX`aYZ`ZY`ZX`_V_`U_aT_bR_cQZcPZd\ NZeMYfLYgJYhIjeLYhHLkD9mABnBDoBEpBGpCIqCJrCLsDMsDO\ tDQuERvETvEVwFWxFYyFZyFYvIXsKXpMWmOVjQVgSUdUUaWTZY\ SW`STbRQdRNfQKhPHjPElOBnO8pCRJBSLBTMBUNBVOBWPBXQBY\ RBZSB_TB`UBaVBbWBcXBdYAeZ } 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 28-01-13 (Un-natural Arch [8])
by Jim Muth 28 Jan '13

28 Jan '13

FOTD -- January 28, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene in Seahorse Valley. It looks nothing at all like the Seahorse Valley scenes we are so familiar with because it is sliced in an odd direction -- rotated 30 degrees from the Julia toward the Rectangular orientation. While viewing the image, (and hopefully enjoying it), the viewer might wonder where Seahorse Valley is located in the frame. Actually, the valley has gone nowhere. The image is immersed in it. Everything in the scene is a part of the valley. The detail in the arch was supplied by the 'tdis' outside coloring option, which colors the points according to how far they travel before finally escaping. I named the image "Un-natural Arch" because of the prominent arch that fills the frame. It almost reminds me of a week or so I spent in Saint Louis quite a few years ago. The rating of an 8 might be a bit excessive. But then again, what is the penalty for padding a rating. The calculation time of 4 minutes is slower than ideal, but the web sites are always available to make life more efficient. So save that time. Check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition renderings at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back FOTD's are available at: <http://www.Nahee.com/FOTD/> The day began with snow here at Fractal Central, but a rising temperature changed to snow to rain before noon. Occasional rain continued the rest of the day, making a slushy mess of the area. The fractal cat took one look out the window and decided to settle down by the heat. The humans had enough inside stuff to finish to keep their minds off the outside weather. The next FOTD will be posted in the very foreseeable future. Until whenever, take care, and why do they need exploding fireworks at music concerts? Does today's music itself lack power, or have audiences become so desensitized that in addition to the amplified sound, they now need a light show to create total sensory overload? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Un-natural_Arch { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t maxiter=3600 center-mag=0.0774812/-0.0170439/20.36076/1/-90/6.0\ 8852815419518389 params=90/90/60/90/-0.753/0/0.5/0\ /2/0 float=y inside=0 outside=tdis periodicity=6 colors=000I3I_FWpQijSeeUa`WYVYUQ_QLaMFcIAeE5gA0i66\ e8Ca9HYBNUCTQDYMFcIGhEHfHGeKFdNFcQEaTE`WD_ZDZaCYdC\ DsKFrMHrNJqOLqPNpQPpRRoTToUVnVXnWZmX_mY0yDUsRwndm7\ zg9xaBvWDtQFrKHpFJnMKgTK`_KUeKOlKHsKAyP4sU7mZAgcCa\ fFWiIQnKPo8Qr7Qw6Qo5Ql5Qi4Qd3Q`3QX2QT1QP1MW1Ha1Di1\ Fo4Go7HiAJhCKgFLfINeKOeNPdQRcSSbVTaYV`_W_bXZeYZg_W\ iaUjcRlePmgMniKpkHqmFsoCtqAus7wu5xw3ysCwpLvmTtjasg\ iqdrpazo`vn`sn`pn`mm`jm`fm`cl``l`Yl`Vk`Rk`Ok`Lj`Ij\ `Fj`CjZEhXGgVIeTKdSMcQOaOQ`MS_KUYJWXHYVF_UDaTBcRAe\ Q8gP6iN4kM3lLWq`Wq`Xr`Xr`Yr`eEJeELeFMeGNeGPeHQdHRd\ ITdJUdJVdKXdKYdLZdM`cMacNbcNdcOecPfcPhcQidPlcQjcRi\ cShbTfbUebUdaVbaWaaX`aYZ`ZY`ZX`_V_`U_aT_bR_cQZcPZd\ NZeMYfLYgJYhIjeLYhHLkD9mABnBDoBEpBGpCIqCJrCLsDMsDO\ tDQuERvETvEVwFWxFYyFZyFYvIXsKXpMWmOVjQVgSUdUUaWTZY\ SW`STbRQdRNfQKhPHjPElOBnO8pCRJBSLBTMBUNBVOBWPBXQBY\ RBZSB_TB`UBaVBbWBcXBdYAeZ } 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 27-01-13 (The Lost Spiral [7+])
by Jim Muth 28 Jan '13

28 Jan '13

FOTD -- January 27, 2013 (Rating 7+) Fractal visionaries and enthusiasts: Today's image shows a slice of a spiral that lies in the Seahorse Valley area of the Z^2+C Julibrot, a fact that is confirmed by the name "The Lost Spiral". But the image holds no spiral. Instead, it shows a series of concentric rings which break apart into two separate spirals near the center. So what is wrong here? Where is the spiral? Actually, we are looking at a slice of it. Everything in the image is a part of the same great spiral, but sliced in an odd direction. Fractal spirals are four-dimensional things that twist and turn in unimaginable ways, and when sliced in odd directions can produce the most unusual cross-sections. The full 4-D 'object' that is sliced by today's image does not actually appear on the screen. It lies in the nearby hyper- space. The two small spirals at the center are actually two slices of the same hyper-object, which is twisted in 4-D space so that today's image slices through it two times, exactly as a slice through the center of a single donut would produce two apparently separate circles. The outer rings correspond to the rings produced by a slice through a set of nested spheres. The image rates a little over a 7. The plus sign is due to the minor math interest, which adds very little to the artistic worth. Incidentally, the image has been stretched and skewed to a significant degree to clarify the features. The coloring detail of the image was created by rendering it with the outside set to 'tdis'. I would be the first to agree that the calculation time of 7-1/2 minutes is slow. Have no worry when nothing appears on the screen for a minute or two. It takes a while for the calculation to reach the rings, which do not intersect the edges of the frame. All these problems can be avoided however by visiting the web sites. The fastest way to view the spiral fragment is to view it on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High definition variations are posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Though with such slow images as we have had recently, there might be a delay in calculating and posting them. The historic back images are available at: <http://www.Nahee.com/FOTD/> The day here at Fractal Central began with a very chilly temper- ature of +5F -15C. But with clear skies, light winds and an unusually strong sun, it rose to an afternoon high of a rather pleasant freezing. The fractal cat took full advantage of the sun, spending the entire afternoon on his shelf in the southwest window. The humans, meanwhile, took it as easy as possible. The next FOTD will be posted in a minimum of 24 hours, a maximum of who knows what. Until whenever arrives, take care, and first we have inventions, then the inventions become luxuries, and then the luxuries become one more technology-based necessity that we could not possibly survive without. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Lost_Spiral { ; time=0:07:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=-0.09292496257779437/-0.094383497537425\ 95/104097.2/0.01534/-28.0422538333465177/-74.32609\ 02171528954 params=78.41120639667959/58.8488418225\ 6538/89.81383709219642/-44.26099429303873/-0.7537/\ 0/-0.5/0/2/0 float=y maxiter=3600 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000Z8eb7bf6_j6Xn5Ur4Rv3Ow7Qz3Lz9IzEFzKDzPAz\ V7z_5yb7ye9xhAxkCwnEwqFvtHvwIpqJkkJfeJ``KWVKRPKGGG\ MKKRONWSRaWUf_Yngkkb`hYQfTFxrRjrSXrTJrU2sZ5rV7qRAq\ OCpKFoGHoDkaKjbHicFhcCfcAfbEfaIe`Me_QdZUdYYdXacWec\ UibTmbSqbRucPscOqdNodMmeLkeKjcMkbNl`Pl_QmYRmXTnVUn\ UWoSXpRYpP_qO`qMarLcrJdsIftGgtFhuDjuCkvBlvJgrRboZY\ lfThnOeuJbn`7lcAkfDjhGikJhmMgpPfsSeuVdxYcz`YyXSxTM\ wPGwMDuPAtS8rV5qY3p_4lU4iP5fK5cF5`A9aDDbGHbJKcMOcP\ SdSQeXVdVZZRaTNcOKcIGcF7cDD`BJR9PG2bI8VKEOMKHJF2NP\ ARZIVhQapUZqYXraUseStiPumLxwNvpOuiQsbRrWSqQQkTOeWM\ _ZLVaJPdHJgFDjE8lEiwGdqI_kJVeLQ_NLUJ3JOGOTTSXeWa`X\ fWXjRYoMYtHZxDZbjiZjkWjmTjoPjqMjsJjtLcuMYvOSwPMxeK\ XuI5xe3pdCicKbcSWb`PbhIapBaxA`rA_l9_f9Za8ZW8YQ0ZM8\ YLGYLOYLWXKcXKkXKrXKs_IsaHsdFsfEshCskBsm9so8mn9hm9\ clAZkAUjBPiBKhCFgCMeFTcHZbJe`LlZNrYPk`NebMZdLTfKMh\ JGjIJdMMZPPUTROWUJ_XDbV9h } 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 25-01-13 (The Seahorse Valley [No Rating])
by Jim Muth 25 Jan '13

25 Jan '13

FOTD -- January 25, 2013 (No Rating) Fractal visionaries and enthusiasts: I named today's image "The Seahorse Valley", and why not. That's what the image shows. Yes, I know it looks nothing like Seahorse Valley, but it's not the familiar Mandelbrot or Julia views of the valley. Its orientation is off in some remote 4-D orientation not too far from the Julia aspect of the valley. The close-to-Julia nature is apparent in the outer shape of the figure. The more interesting inside stuff exists because the angle of the slice has been rotated six degrees toward the Oblate orientation and one degree in another unimaginable 4-D direction. I declined to rate the image, since Seahorse scenes are so common in FOTD history. If the image had not been such a slow one, I might have rated it at a 7, but 15 minutes is quite a wait for an image to finish, especially when it lies out in a hyperspace no-man's land. Those who view the image on one of the web sites will avoid the calculation wait and get quite a bargain. The finished image is posted in its full glory at: <http://www.crosscanpuzzles.com/Archives.html> and in even fuller glory at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The glorious back images are online at: <http://www.Nahee.com/FOTD/> The 24th brought a mix of sun, clouds and more cold weather to Fractal Central. Today brought clouds and snow. At post time about 1-1/2 in. or 4cm had fallen and the snow was still falling lightly. The fractal cat spent the day watching the flakes come down and lying by the heat. The humans spent the day getting the work finished and readying the snow shovel. The next FOTD will be posted in 24 hours. Until then, take care, and why doesn't the other side see that it is wrong? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_SeahorseValley { ; time=0:15:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0/1.037/1/-35/0 params=84/0/90/1/-0.75/-0.005/0/0/2/0 float=y maxiter=32767 inside=0 logmap=yes periodicity=0 colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\ auhavhcwhcwhcwhdwhdwhewhewhfwhfwhfwhfwhfwT22V68X9D\ ZDI_GNaKScNXdQacP`bP_bO_aOZaOY`NY`NX_NWZMWZMVYMVYL\ UXLTXLTWKSWKRVJRUJQUJQTIPTIOSIOSHNRHMRHMQGLPGLPGKO\ FJOFJNEINEHMEHLDGLDGKDFKCEJCEJCDIBCIBCHBBGABGAAF99\ F99E98E87D87B86B76A75B74A65A65A65C64874E70B61D71F6\ 2F62G72G73H83I83K84L94N94OA5QA5RB5TB6UD6WD6XE7YF7Z\ E8_F8_G8_G9aH9cI9dJAeJAfKAgMBhOBiQBjSCmUCnXCo_DqaD\ pcDogCmmBmoBmqAmsAmq9mo1mm5ml9mkDmiGmeKmaOv_SwYRwW\ RwUQwSQzQPzPPzOPzOOzOOzPNzPNzPMzPMzQMzQLzQLzRKzRKz\ RKzSJzSJySIxSIwTHwTHwTHwUGwUGwUFwVFwVFwWEwXEwYDwZD\ w_CwaCwbCwcBwcBwcAwcAwcAwc9wc9wc9wc8wd8we8wf8wg7wh\ 7wi7wj7wk6wl6wm6wn6wo7wp7wq8wr8ws8wt9wu9wvAwwAwxAw\ yBwzBwzBwzCwzCwzDwzDwzDwzEyzEzzEzzFzzFzzGzzGzzHzzH\ zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\ 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 23-01-13 (Shade of Antiquity [8])
by Jim Muth 24 Jan '13

24 Jan '13

FOTD -- January 23, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's unusually colored image is a near-Julia scene in the Seahorse Valley area of the (-Z)^(2.5)+C Mandeloid. To visualize the Julia set, mentally remove the highly colored inside stuff while retaining the outer shape, which is the Julia set. To see the actual Julia set, change the real(p3) parameter to 0. The thin open slit across the center of the image is a sideways view of the space between the two branches of Seahorse Valley. The angle of the slice is rotated 6 degrees from the Julia direction toward the Oblate direction. The rating of an 8 is largely earned by the coloring, which was created effortlessly by the Fractint program. My part was to tweak a few registers to make the colors blend more smoothly. The calculation time of 3-1/2 minutes is a fair price to pay for the image. (Most of the time is spent calculating the final two lines.) But it is still a bother to set up and run the parameter file. The web sites can eliminate any parameter-file set-up anxiety. For immediate relief view the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And don't forget the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> or the back images at: <http://www.Nahee.com/FOTD/> Some clouds, some sun, a little less wind and a still chilly temperature of 18F -8C made for another bone-chilling day here at Fractal Central today. The fractal cat had an exciting day, surviving his regular trip to the doctor. The humans had another in the endless string of passing days. The next FOTD will most likely be posted in 24 hours. Until whenever, take care, why can't we think four-dimensionally, when even an unconscious computer can do it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Shade_of_Antiquity { ; time=0:03:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 center-mag=-0.056338/0/0.91876 params=84/0/90/0/\ -0.760036618323/0/0/0/2.5/0 float=y maxiter=250000 inside=0 logmap=yes symmetry=xaxis periodicity=12 colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\ auhavhcwhcwhcwhdwhdwhewhewhfwhfwhfwhfwhfwT22V68X9D\ ZDI_GNaKScNXdQacP`bP_bO_aOZaOY`NY`NX_NWZMWZMVYMVYL\ UXLTXLTWKSWKRVJRUJQUJQTIPTIOSIOSHNRHMRHMQGLPGLPGKO\ FJOFJNEINEHMEHLDGLDGKDFKCEJCEJCDIBCIBCHBBGABGAAF99\ F99E98E87D87D86C76B75B74A64A63962952851850851951B6\ 2C62E72F73H83I83K84L94N94OA5QA5RB5TB6UB6WC6XC7ZD7_\ E8aF8bG8dH9eI9gJ9hKAjLAkMAmNBnOBpQBqSCsUCt`CvcDwcD\ xgDqjCmmBmoBmqAmsAmq9mo1mm5ml9mkDmiGmeKmaOv_SwYRwW\ RwUQwSQzQPzPPzOPzOOzOOzPNzPNzPMzPMzQMzQLzQLzRKzRKz\ RKzSJzSJySIxSIwTHwTHwTHwUGwUGwUFwVFwVFwWEwXEwYDwZD\ w_CwaCwbCwcBwcBwcAwcAwcAwc9wc9wc9wc8wd8we8wf8wg7wh\ 7wi7wj7wk6wl6wm6wn6wo7wp7wq8wr8ws8wt9wu9wvAwwAwxAw\ yBwzBwzBwzCwzCwzDwzDwzDwzEyzEzzEzzFzzFzzGzzGzzHzzH\ zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\ 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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FOTD 22-01-13 (Reiterated Numbers [8])
by Jim Muth 23 Jan '13

23 Jan '13

FOTD -- January 22, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's 8-rated image is based on the unlikely expression Z^11+(1.1*Z)+C. The expression seems innocent enough, but when it is iterated 800 times, it creates a parent fractal that appears as a distorted Mandelbrot set with its stem facing northeast and a star burst radiating from its East Valley, which lies on the southwest side of the main bay. Today's scene lies about halfway out the center ray of the starburst. The name "Reiterated Numbers" is a fitting description of today's image as well as almost all other fractals. The rating of an 8 might be a bit overdone. A 7-1/2 might be more accurate. The calculation time of 45 seconds will cause no one distress, especially after the interminable hours-long calculation time of yesterday's image. Make life easy. Dump the calculation wait. View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And view the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> plus the back images at: <http://www.Nahee.com/FOTD/> Conditions more typical of winter in central Pennsylvania arrived with a bang here at Fractal Central today, with an inch (2cm) of snow on the ground, a sky filled with wind-torn clouds, and a high temperature of a bone-chilling 16F -9C. The fractal cat survived the day by the heat; the humans simply survived. The next FOTD will be posted when the time is right. (The most likely time is 24 hours from now.) Until whenever, take care, and I still say we should pass a law to stop this climate change. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Reiterated_Numbers { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-0.1254246947312831/-0.038926514109924/\ 1.570419e+012/1/12.5/0 params=1/11/1.1/1/0/0/0/0 maxiter=800 inside=0 logmap=82 periodicity=6 mathtolerance=0.05/1 colors=00003B04C05D06E07F08G0\ 9H0AI3BK5CM7DO8FQBPVDV`F`zzzzukmzaUzJKoBAk8Ag5Ae3A\ c7LX0W`VbdWcgXckYdoZec_i0`mHSgYJanAXlDBiMLfUVcac`i\ mYlvXhoWXhVQaV_VUjOToHSzASz4Wz8_zCbzGfzJibNmZRpWUD\ uQLpWSk`_fefajj_hnZfqYdzebxoasUboScjQdfOeaMfYKgUJh\ WFcXC_Y8WZ5S_2OZ5MZ8LYBKYEJYHIXKHXNGXQFPctQeoQgkRi\ fRkbXgfacif_mkWppSsqQjqObqMVqKNvRdzXu_iU9u3X_cUbbS\ eaPhaNk`Kn`Iq_FtZcMZZNSUPK`BQS19dMb`OZXQVSSROUNKWJ\ FYFfMbdNZbOW`QSZROXSLVTHTVDQaf6sggMeeOddPcbRcaSb_U\ aZV`XX`WY_U_ZT`YRbYQcXOeWMgVfLcdM`aNY_OVXPTVQQSRNQ\ RKOSHLTFJUCGV9EW6BX3dNb_Q_VSXQVULXRG_OXdZLyRgOafSX\ eVTdZOcaKbeFahB_l6hNehQehTehVehYeg`djJelGfnDgpAhr7\ ijTXmaNojDrs3gNefQeeTedVecYeb`eabe_eeZheYjeXmeVRdT\ TZzzTzzNzzHzzIzzJzzKzzOzzRVzVRzYNz`IzdEzgAzjBzgCze\ DzzEzzEzzBzz9zz7zz5zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ tzzqzzozzlzzjzzgzzezzSzzEzzLzzSzzZzzdzzUzz`zzg } 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 22-01-13 (Reiterated Numbers [8])
by Jim Muth 22 Jan '13

22 Jan '13

FOTD -- January 22, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's 8-rated image is based on the unlikely expression Z^11+(1.1*Z)+C. The expression seems innocent enough, but when it is iterated 800 times, it creates a parent fractal that appears as a distorted Mandelbrot set with its stem facing northeast and a star burst radiating from its East Valley, which lies on the southwest side of the main bay. Today's scene lies about halfway out the center ray of the starburst. The name "Reiterated Numbers" is a fitting description of today's image as well as almost all other fractals. The rating of an 8 might be a bit overdone. A 7-1/2 might be more accurate. The calculation time of 45 seconds will cause no one distress, especially after the interminable hours-long calculation time of yesterday's image. Make life easy. Dump the calculation wait. View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And view the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> plus the back images at: <http://www.Nahee.com/FOTD/> Conditions more typical of winter in central Pennsylvania arrived with a bang here at Fractal Central today, with an inch (2cm) of snow on the ground, a sky filled with wind-torn clouds, and a high temperature of a bone-chilling 16F -9C. The fractal cat survived the day by the heat; the humans simply survived. The next FOTD will be posted when the time is right. (The most likely time is 24 hours from now.) Until whenever, take care, and I still say we should pass a law to stop this climate change. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Reiterated_Numbers { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-0.1254246947312831/-0.038926514109924/\ 1.570419e+012/1/12.5/0 params=1/11/1.1/1/0/0/0/0 maxiter=800 inside=0 logmap=82 periodicity=6 mathtolerance=0.05/1 colors=00003B04C05D06E07F08G0\ 9H0AI3BK5CM7DO8FQBPVDV`F`zzzzukmzaUzJKoBAk8Ag5Ae3A\ c7LX0W`VbdWcgXckYdoZec_i0`mHSgYJanAXlDBiMLfUVcac`i\ mYlvXhoWXhVQaV_VUjOToHSzASz4Wz8_zCbzGfzJibNmZRpWUD\ uQLpWSk`_fefajj_hnZfqYdzebxoasUboScjQdfOeaMfYKgUJh\ WFcXC_Y8WZ5S_2OZ5MZ8LYBKYEJYHIXKHXNGXQFPctQeoQgkRi\ fRkbXgfacif_mkWppSsqQjqObqMVqKNvRdzXu_iU9u3X_cUbbS\ eaPhaNk`Kn`Iq_FtZcMZZNSUPK`BQS19dMb`OZXQVSSROUNKWJ\ FYFfMbdNZbOW`QSZROXSLVTHTVDQaf6sggMeeOddPcbRcaSb_U\ aZV`XX`WY_U_ZT`YRbYQcXOeWMgVfLcdM`aNY_OVXPTVQQSRNQ\ RKOSHLTFJUCGV9EW6BX3dNb_Q_VSXQVULXRG_OXdZLyRgOafSX\ eVTdZOcaKbeFahB_l6hNehQehTehVehYeg`djJelGfnDgpAhr7\ ijTXmaNojDrs3gNefQeeTedVecYeb`eabe_eeZheYjeXmeVRdT\ TZzzTzzNzzHzzIzzJzzKzzOzzRVzVRzYNz`IzdEzgAzjBzgCze\ DzzEzzEzzBzz9zz7zz5zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ tzzqzzozzlzzjzzgzzezzSzzEzzLzzSzzZzzdzzUzz`zzg } 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 21-01-13 (Underwater Scene [Rating 8])
by Jim Muth 22 Jan '13

22 Jan '13

FOTD -- January 21, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene on the east shore line of the north branch of Seahorse Valley of the Mandelbrot set. The scene is rather deep in the valley, requiring a maxiter of 1,500,000, which makes its calculation quite slow, in the range of several hours on older machines. On S.O.T.A. (state-of-the-art) units, with DOS capability, the calculation is much faster, more like 15 minutes, but there is still no denying that the image is a slow one. The individual viewer must decide if the result is worth the wait. I rated the image at an 8, mostly because it is a reasonably unfamiliar scene in the all-too-familiar Mandelbrot set. I named it "Underwater Scene" because it is located deep in the 'watery' Seahorse Valley. Those with slow computers can save a couple hours by viewing the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Those with S.O.T.A. units can still save several minutes. High-definition versions of recent images are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The thousands of back images and discussions may be seen at: <http://www.Nahee.com/FOTD/> Clouds, light snow and a temperature of 30F -1C made for a winterish scene today here at Fractal Central. The fractal cat spent much time by the heat, trying to persuade the humans to turn it up. The humans spent lunch time watching the inauguration ceremonies and the rest of the time keeping busy with the regular work. The next FOTD will be posted when the time is right. Until whenever, take care, and I noticed much less enthusiasm in today's ceremonies than I saw four years ago. Maybe people are disappointed. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Underwater_Scene { ; time=0:15:00.00 SF5 at 2000MHZ reset=2004 type=mandel center-mag=-0.7499986559107\ 32/+0.002303751935777/1.1e+011/1/177.5/0 params=0/0 float=y maxiter=1500000 inside=0 logmap=120000 periodicity=6 passes=t mathtolerance=0.05/1 colors=000RlmRmlRnlPjjOfiMcgL_fJWdITcHPaFL`EIZCEYB\ AWA7VFCXJGZNK`RPbVTdZXfbagfeijikvypnnmrrovvqhb2jd7\ kfBmhGnjKplPqnTspXtravtewvjyxnF9CLGIRNNXUTb_Yhfbnm\ httmKDLZUXljgGnEKoHNpKQqNTrPWrSZsVatYeu_hvbkvenwhq\ xjtymwzpEzRbzdCqGPtQav_nxigCcqakLk2WoGesTpwe0_nrol\ usnxwptByvTvxit8ezMkx_pvZJfZJf`NgbQhdTifWjhZjjakld\ lmfmoinqlnsoopRSoNZnKeoLcoMbpNapN_qOZqPYrPWrQVsRUs\ RStSRtTQuUPuUNvVMvWLwWJwXIxYHxYFyZEy_Dy_CvVAsR9pM8\ mI6TNXg94eB6cD7bF9`HA_JCYLDXNFVOGTQISSJQXLPWMNYOM_\ PKaRIbSHdUFdVEhXCjYBl_9n`8ba7gd6`f6Th5Mj4El47n35d2\ 4W12M01D25C48B6CA7FA9J9BM8DQ7ET7GX6I_5Kc4Lf4Nj3Pm2\ Qp2Pj1Pd1PZ1PU1PO1PI1PD1QH0RL0SO0TS0UV0VZ0Va0Xd4Yf\ 7_hA`kEbmHcoKerOftRhvUixXjsYjnZkj_ke`kaalXblTclOdm\ KemFfmBgkDfjFfiHehIegKeeMddNdcPcbRcaSc`UbZWbYYaXZa\ W`aVb`Uc`Se_Rg_Qi_PmZOoZNqZPsXQuWSwVcyUczTczfcztcz\ sczrmzrmzqmzpmzpmzomznmzn } END PARAMETER FILE=========================================

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FOTD 20-01-13 (Fire Tree [Rating ?])
by Jim Muth 21 Jan '13

21 Jan '13

FOTD -- January 20, 2013 (Rating ?) Fractal visionaries and enthusiasts: Fractal trees are nothing new in the FOTD series, but I have never posted a tree with such simplicity as is seen in today's image. The scene is a Julia set of the (-Z)^(1.618034)+C Julibrot. The corresponding Mandelbrot point lies where the X-axis meets the western edge of the main bud of the Mandeloid. The full Julia set resembles an 'infinity' symbol, a figure eight lying on its side, with an infinity of fractal trees along its edge. The tree in today's image is the largest one, which lies on the X-axis on the east edge of the figure eight. The simplicity was created by lowering the maxiter to 112. This cuts off the finer tree branches, leaving only the most basic tree shape. The name "Fire Tree" refers to the color of the tree. The calculation time of 15 seconds is due to the unusually small maxiter. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition renderings are at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> A sunny day with a temperature of 46F +8C was spoiled by a blustery wind here at Fractal Central today. The fractal cat spent most of the time basking in the sun on his shelf, watching things blowing by in the wind. The humans took it easy most of the day. The next FOTD will be posted in a reasonable time. Until then, take care, and don't wait for a second coming. It isn't coming. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Fire_Tree { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=0.2398/0/15/\ 0.922/90/0 params=90/0/90/0/-1.15/0/0/0/1.618034/0 float=y maxiter=112 inside=255 logmap=69 periodicity=6 colors=0000mzqNIqMFpMDpLAkK7lK5mzwnyvoxupwtqvsrurs\ tqtspsrirqbpqVopOnoHmlAki9jd8i_7hV6gQ5eK4dF3cA2b51\ a01`13_25Z37Y39X4BW5DW5FV6HU7JT8LS8NR9PQARQATYCPdD\ LkEHiiEkkFllFnnFooGqpGrrGtsHuuHwvHxwHwuLwtOvsRvrUu\ qXup_uoctnftmisllskosjrofnkbjg_gcWc_S_XPXUVYR_ZOd_\ Mi`JnaGsbExbJrdNmeRgfVbgZXhbSifNjdMgcLebKcaJ``IZZH\ XYGVXFSWEQVDOUDMXEK_EJbEIeEGhEFkEEgFGcFH`FIXGJTGKQ\ GLMHNJHOFHPBIQ8IR4IS1IT7ORCTQHZPMcORhNWnM`sLexK`rY\ WmjRhwPemOccNaULZKKXAJV1S`8`eFhkMqpTyuZtt`ptalsbhs\ cdrd_rfWqgSqhOpiKpjLkdLf_LaVLYQMTLMOGMJBMF6VR5cb4k\ m4ik8hiBggFfeIecMdaPc`TaZW`X__VbZTfYRiXPmWOpaNqfMq\ kMqpLruKrzKrwMltOfqQ`nSVlTPiVJfXDcZ7a_1bZ3cY5dY6eX\ 8eW9fWBgVChVEhUFiTHjTIkSKkSLgRNdROaRPZQRWQSTQTQPUM\ PWJPXGOYDOZAO`7Na4Nb1Nc3S_5WW7`S9dPBiLDmHFrDGvAIr9\ Kn9Mj8Og8Pc8R_7TW7VT6XP6YL6_H5aE5cA4e64f34d53c73b9\ 3aB3`D3_E3YG2XI2WK2VM20mz } 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 18-01-13 (High-Order Hijinks [Rating 6])
by Jim Muth 18 Jan '13

18 Jan '13

FOTD -- January 18, 2013(Rating 7) Fractal visionaries and enthusiasts: Today's image is another 'almost' Julia set. The parent Julibrot was created by iterating the expression (-Z)^(1.618034)+C. The area of the image lies deep in the west branch of the valley enclosing the large bud on the northeast shore line of the main bay of the associated Mandeloid. The image very clearly illustrates the hairline spirals that lie in the Julia sets of the areas just inside Mandelbrot valleys. The name "Broken Julia Spirals" refers to the spirals on the top side of the grossly enlarged Mandelbrot valley fragment cutting diagonally across the inside of the open area in the image. These spirals are broken because of the limited resolution of the image, which causes many pixels to totally miss the very narrow body of the spirals and print it as an open area. This breakup can be eliminated by the process of anti-aliasing, which calculates the image at a higher resolution, slightly blurs the result then shrinks it down. Unfortunately, the process can be quite time consuming. The rating of a 7 is FOTD average. If such images had not been posted so frequently lately, I might have rated the scene as high as an 8. The calculation time of 7 minutes is a bit excessive. To save time, I recommend checking one of the FOTD web sites. The finished image is online at: <http://www.crosscanpuzzles.com/Archives.html> A sample of what anti-aliasing can do for hairline spirals is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back images are at: <http://www.Nahee.com/FOTD/> Today brought lots of sun to Fractal Central, but the temperature never rose above 30C -1C. The fractal cat basked in the sun all afternoon, having the best day so far this winter. The humans passed the very bright day getting organized. The next FOTD will not be posted before January 20, since I'm going back to Old Fractal Central tomorrow to finish a few things that need to be done. Until whenever, take care, and since everyone claims to do what is right, why does so much wrong exist in the world? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= BrokenJuliaSpirals { ; time=0:07:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 periodicity=6 center-mag=0.10596/0.159292/0.8912656/1/46.75/0 params=89.8/0/89.8/0/0.3125/0.5702/0/0/1.618034/0 float=y maxiter=5000 inside=0 logmap=yes colors=000B36701812923A33B34C44D55E66F66G77G87H98I\ 98JA9KBALCAMCBNDBOECNFBOECOECPECPEDQEDQEDREEREEREE\ SEFSEFTEGTEHUEISEJQGKOILMKMKMNIOOGQPFSQEURDWSCXTBY\ TCbWDgZElaGjcHieIggJfiLdkMcmNaoO`pSYkWWg_UccR_gPWk\ NSqKNoLOmMOlNOjOPiPPgQPfRPdSQcTQaUQ`VQZVRYWRWXRVYR\ TZSS_SQ`SPaSNbTMcTKdTJdTLcVNbWPaXR`ZT`_V_`XZbZYc`Y\ dbXfdWgfVhhUjjUklTlnSnpRorRptQrvPsxOtyOuwNsuNrsNpq\ NooNnmNlkNkiMigMheMgdMebMd`McZMaXL`VLZTLYRLXPLYNLZ\ LK_JK`HKaFKaDKbDKbDKbEKcGKdHKeIJeKIeLHeMIeOJePJeRK\ eSKeTLeVMeWMeXNeZNe_Ob`O``OeUViNamGhq9ou7rw2vyCtqM\ riVpadnUloHmmMnlQnjUoiYphapfeqeiphoqdmralrZjsWisSg\ tPfuMduJcvFavC`w9Zz4Xw6Yt7Yr9YoAYlBYjDYgEYdFYbHY_I\ YYJYZLWZMV_OT_PS`QR`SP`TOaUNaWLbXKbYJb_Hc`GcaFdcDd\ dCfd9deBbeCaeD_eEZfFXfGWfHUfITfJRgLPgMOgNMgOLhPJhQ\ IhRGhSGjSFhTFfTFeUFcUEbVE`VEZVEYWEWWDVXDTXDSYDQYDO\ YCNZCLZCK_CK`CKaCKbCKcCKc } 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 17-01-13 (High-Order Hijinks [Rating 6])
by Jim Muth 17 Jan '13

17 Jan '13

FOTD -- January 17, 2013 (Rating 6) Fractal visionaries and enthusiasts: Today's FOTD is one I found almost automatically in the brief periods of free time that somehow worked their way into an otherwise very busy day. The rating of a 6 might be considered a gift, since I can see little of note in the image. The image is a near-Julia scene in the easternmost East Valley of the Z^9+C Mandeloid. (The parent Mandeloid has eight East Valleys.) The name High-Order Hijinks" refers to the order-9 Julibrot as well as the orientation of the slice, which lies only 0.00003,0.00003 degrees from the true Julia orientation. The 'outside' parts of the image were colored by the 'imag' option, which adds somewhat more life than the flat straight 'iter' coloring. The calculation time of 7 minutes is more than the image is worth. I strongly recommend trying one of the FOTD web sites. Be free of calculation inefficiency! View the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> And enjoy the hi-def versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of back images are at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds with a temperature of 41F +5C made today bearable if not exactly pleasant here at Fractal Central. The fractal cat was more interested with the unwanted cats prowling about than with the weather. The humans had another average day -- pleasant to live through but boring to write about. The next FOTD will be posted within a reasonable time. Until whenever, take care, and always do good, but before doing it, be sure to find out exactly what defines good. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= High-Order_Hijinks { ; time=0:07:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 float=y center-mag=0.13128/0.748246/8.950949/1/-87.5/0 params=89.99997/0/89.99997/0/0.67545/0/0/0/9/0 maxiter=5000 inside=0 outside=imag periodicity=12 colors=000nZqmYplXokWnjWmiVlhUkgUjgTifSheSgdRfcQeb\ QdaPc`Ob`Na_N`ZM_YLZXLZWKYVJXUJWUIVTHUSHTRGSQFRPEQ\ OEPNDONCNMCMLBLKAKJAJI9IH8HG6FH8HH9IHAJICKIDLIEMIG\ NJHOJIPJJQJLRKMSKNTKPUKQVLRWLSXLUYMVZMW_MY`MZaN_bN\ acNbdNceOdfOfgOghOhiPjjPkkPllPmmQnjQnhRnfRodSoaSo_\ TpYTpWUpTUpRVqPVqNWqKWrIXrGXrEYsBYs9Zs7_u4Zs5Zr5Zq\ 6Zp6Zo7Zn7Zl7Zk8Zj8Zi9Zh9Zg9ZfAZdAZcBZbBZaBZ`CZ_CZ\ ZDZXDZWDZVEZUEZTFZSF`UBZRFYPIXNLWLOVJRUGUTEXSC_RAb\ Q8eQ1jP4iP6hP9hPBgPEfPGfPIeOLdONdOQcOScOUbOXaOZaNa\ `Nc_Ne_NhZNjYNmYNoXOqZNqXMqWLqVKqTJqSIqRHqPGqOFqNE\ qLDqKCsIDqJDpJDoJDnJDmJElJEkJEjKEiKEhKFgKFfKFdKFcK\ FbKFaLG`LG_LGZLGYLGXLHWLHVMHUMHTMHRMHQMIPMIOMINMIM\ NILNJKNJJNJINJHNJGNKDOJENJFNJFMJGMJGLJHLJILIIKIJKI\ JJIKJIKIILIIMIIMHHNHHNGHOGHPGHPFHQFHQEHREGRDGSDGTD\ GTCGUCGUBGVBHUCGVBGWBGWBGXBGYBGYAGZAF_AF_AQKKJFANH\ FQJJTLNWNSZPWaR_dTdgVhjXl } 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 16-01-13 (The Unseen World [No Rating])
by Jim Muth 17 Jan '13

17 Jan '13

FOTD -- January 16, 2013 (No Rating) Fractal visionaries and enthusiasts: Today's image is an almost-Julia set of the East Valley of the large minibrot on the northern main spike of the Mandeloid that results when the expression (-Z)^(2.5)+C is iterated. The reddish stuff inside the large open hole is grossly enlarged Mandelbrot stuff. The outer bluish stuff is Julia in nature. I enjoy 'almost' Julia images because they are much more varied. In pure Julia images, every small hole is basically identical, while in the 'almost' images, no two holes are the same. The name "The Unseen World" does not refer to the supposed abode of spirits. It describes the high-iteration Mandelbrot stuff that lies hidden beneath the low-iteration surface Julia stuff. I gave the image no rating, but if I were to rate it, I would have chosen something like 6-1/2. When the calculation begins, it looks like the image will be finished in less than a minute, but things slow down considerably once the central open area is reached, and the calculation will drag on for about 5 minutes. Save energy! Save time! View the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and see the high-definition versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are online at: <http://www.Nahee.com/FOTD/> About 4-1/2 inches (12cm) of sloppy snow fell overnight here at Fractal Central, making for a very unpleasant day with heavy clouds. The temperature of 34F +2C melted just enough snow to fill the gutters with water and make dry feet impossible. The fractal cat, who always keeps his feet dry, had an active day of tearing up old newspapers. The humans had an average day. The next FOTD *will* be posted. The best bet is to look for it in 24 hours. Until whenever, take care, and why is the massacre of 26 people killed together by a single gun more outrageous than 1000 killed one-at-a-time by cheap hand guns every month? Would someone please explain the current politically correct way of thinking. I'm a little befuddled by it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Unseen_World { ; time=0:05:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=t periodicity=12 center-mag=0.202471/-0.225264/56/1/-57.5/0 float=y params=89.898/0/89.898/45.5/-1.422159233/0.2244159\ 71/0/0/2.5/0 maxiter=32767 inside=0 logmap=8 colors=00000H00L10O20S30V40Z50a60e71h82l93oA4sB5vC\ 6wD7wF8wHAwJBwLDwNEwPGxRIxTJxWLxYMx_OxaPxcRyeTygUy\ iWykXymZyo_ymYxkWwjVvhTufSteQscPraNq`LpZKoXInWHmUF\ lTElVGkWIjXKiYMiZOh_Qg`SfaUfcWedYde_dfacgbbhdaifaj\ h`ljamhbkfciddgbee`fcZgaXg_XgZXg_Yg_Zg__g__g_`g_ag\ _bg`cg`dg`eg`fg`gf`hf`ifajfajfakfalfamfanfaofbpfbq\ fbrfbsfbtfbufhyebufYqfSmgNigHegCah6Yh0Vi1Uh2Th3Tg4\ Sg5Rf6Rf7Qe7Qe8Pe9OdApdBccCNcDMbDLbELbFKaGbaHQ`II`\ JI_JH_KQ_LKZMFZNFYOEYPIXQDXQCXRCWSBWTAVUAVV9UW9UW8\ UX7TY7TZ6S_6S`5Ra4Ra4Rb3Qc3Qd2Pe1Pf1Og0Og1Oh2Ph3Qh\ 4Rh5Rh6Si7Ti8Ti9UiAViBViCWjDXjEYjFYjGZjH_kI_kJ`kKa\ kLakMbkNclOdlPdlQelRflSfmTgmUhmVhmWmmXmmYmmZmm_mm`\ mramrbmrcmrcmrcmrcmrcmrcmrcmrcmwczwczwczwczwczwczw\ czwczwczwczwczwczwczwczwczwczwczwczwczwczwczwczwcz\ wczwczwczwczxczyczzczzczzczzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } 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 15-01-13 (Strangely Familiar [No Rating])
by Jim Muth 16 Jan '13

16 Jan '13

FOTD -- January 15, 2013 (No Rating) Fractal visionaries and enthusiasts: I began the day with a question -- when a three-dimensional left hand glove is viewed from the fourth dimension, does it appear as a left or a right hand glove? A few minutes pondering convinced me that the question is meaningless. In 4-D space both left and right hand 3-D gloves are the same shape. They simply lie in different positions. Now on to the important topic -- the fractal for today. Today's image has something strangely familiar about it. In fact, this is the name I gave it. The familiarity arises because the image is actually a view of the familiar Seahorse Valley of the Mandelbrot set. The unfamiliarity exists because in today's image the valley is viewed in the Oblate orientation, centered at the point -0.6 on the imag(z) axis. The scenes of this particular orientation bear no resemblance to either the Mandelbrot or the Julia aspects of the valley. Seahorse Valley is actually a thing with four spatial dimensions, which means it has six mutually perpendicular planes cutting through it, each of which can be translated in an infinity of perpendicular directions. With such a familiar object as the source of the image, I could give it no rating. The calculation time of 5 minutes is longer than I would have preferred, but the new view of an old object that will result will make the effort worthwhile. Those who do not calculate may view the finished image on the web sites. Avoid calculation by viewing the completed image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Don't forget the back images at: <http://www.Nahee.com/FOTD/> Thickening clouds and a temperature of 36F +2C made today less than ideal here at Fractal Central. The forecast of ice and snow later tonight and tomorrow makes the future look even less ideal. The fractal cat passed the day in the front window, watching the world go by and in the back window, watching the stray cats go by. The native humans spent the day watching the work go by. The next FOTD will be posted when the appropriate time has passed. Until whenever, take care, and let's give our congress a kick in the butt. Tell them to pass a law requiring that all our silly disagreements be solved. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Strangely_Familiar { ; time=0:05:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 maxiter=27000 center-mag=0/0/7.466019/1/-36.75/0 params=0/0/90/0\ /-0.75/0/0/-0.6/2/0 float=y maxiter=27000 inside=0 logmap=-13 periodicity=0 colors=000enldmmclmbkmajn`im_hmZglYfkXekWdjVcjUbiS\ aiQ`hO_gMZgKYfIWfGVeEUdCSdARc9Qc8Pb7Na5Ma5L`4J`4I_\ 3H_3GZ3EY3DY2CX2AX29W28V17V15U14U13T12T23U24U25U26\ U37U38U39U3AU3BU4CU4DU4EV4FV5GV5HV5IV5JV5KV6LV6MV6\ NV6OV4OU6PV7QV9RWARWCSWDTXFTXGUYHVYJVYKWZMXZNX_PY_\ QZ_SZ`T_`U`aW`aXaaZbb_bbaccbdccdcaca`b_ZaYY`WW_UUZ\ SSYUQZRO_NM_OK_PJ_PK_QK_QL_RN_SP_TQ_US_UU`VV`WX`XZ\ `Y_`Za`_c``d`af`biaag`bf`be`bc`bb`ba`b``bZ`bZ`cZ`c\ Z`cZ`cZadWbeRckMipInuKotMptNqtPqtRrtSstUttVtt_nkci\ cgdWlZOpUGtP8pS9mV9jYAg`AdcAafBZiBWkBTlDUkEVjGWiHX\ hJYgKZfG_eC`d8ac4bbIcaNd`Re_WfZ_fYdfXhfZl`YfWXaRWX\ MVSHUNCTI7SD8YJ9bPAgVBl`CqfEpXFpOGlSHiWHf_IccJ`gJY\ kKVoKSsNZnQdjSjfVpbXvZYsXYpVZnTZkSZhQ_fO_cM_cLYcQW\ cVVc_TccSchQcmPcqTcmXcj`cgdcdzcazcZzcXzcUzcSzcOzcK\ zcHzcLzcPzcTzcXzc`zcdzchzc1zz2zz2zz2zz3zz3zz3zz3zz\ DzzGzzIzzLzzNzzQzzSzzOzzK } 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 14-01-13 (The Manifestation [7.5])
by Jim Muth 14 Jan '13

14 Jan '13

FOTD -- January 14, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: In yesterday's FOTD, I remarked that calculating the image with the inside set to 'bof61' would work wonders with those solid black areas. In today's FOTD, I go ahead and calculate the image with the inside set to 'bof61', which shows the resulting insanity. I reused the same color palette to make comparison easier. Today's image is still about half 'inside' stuff, but the inside and outside parts blend togehter so smoothly that it is virtually impossible to tell the inside from the outside. The rating of a 7-1/2 is 1/2 point higher than yesterday's. The newly-visible inside stuff adds the additional half-point to the rating. The name "The Manifestation" is a comment about the previously invisible inside stuff being made visible. The big drawback in the image is its slowness. The image takes a full 13-1/2 minutes to calculate. Thankfully, the web sites can eliminate the task of calculation. Save notable time by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Spice things up by checking the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And don't forget the back images at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds and a temperature of 50F 10C made today quite pleasant for a midwinter day here at Fractal Central. The fractal cat enjoyed the sun for a while but soon grew annoyed at the way it kept coming and going. The fractal humans had another back-to-work Monday. The next FOTD will be posted when a nominal amount of time has passed. Until we find out how much time is considered nominal, take care, and I see many popular solutions of non-existent problems, but where are the solutions to the real problems? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Manifestation { ; time=0:13:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.3922690253119078/-0.9833762241149269\ /3570608/1/-165/0 params=1/3/0.6/5/0/0/0/0 float=y maxiter=1750 inside=bof61 logmap=168 periodicity=0 colors=000ttaspcrpeqogpoionknnmmmolmqklsjluhktgjtf\ itehsdgscfsbfs`er_drZdrYcqXeqWeqVijZfiakaelUfmMknE\ hnFenGblG_hHXfIUbIR`JPXKMVKJRLGOMDLMAKN7FO5HO6EQ6G\ R6HS7IU7KV7LW7NX8OZ8Q_8R`9Tb9Uc9Wd9XeDZfG_gJ`gMahP\ biSciVdjZekafkdglghmjimmjnpkookkrklqkipkgpkdokbnk_\ njYmjVljTljQkjOjjLjjJffIbbH__GWWFSSEPPELLDHHCEEBAA\ A77A67A66956956967AIYD9bD0gD4dE7bEB`FEZFIWGLUGPSHS\ QHWNHZLIbJIeHJiEJlCKpAKs8Kn7Ni7Pe6R`6TW5VS5XN5_I4a\ E4c93e43g03i22j32k42l62m72n82nA1oB1pC1qE1rF1sG1sHF\ hISYJdNJqCMpGOoKQoOSnSUnWWm_Zlc`lgbkkdkofjshjvigti\ driaqiZoiWnjTljQjjNijKgjHfgJedLeaNdZPdWRdTTcQVcOXc\ LZbI`bFbaCda9fa6h`3j`1k`2lc3me3ng4oj5pl5qn6rq7ss7s\ u8nv8iv8ew9`w9Ww9Sx9NxAIxAEyA9yA5yIIzQUzYfzerzbtz`\ uzYvzWwzTxzRyzUrzckzmeztZzzSzzMzzFzz9zzAzzAzzAzzBz\ zBzzBzzCzzCzzCzzDzzDzzDzzDzzFzzGzzHzzIzzJzzKzzLzzM\ zzNzzOzzPzzQzzRzzSzzTzzTz } 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 13-01-13 (Hidden Ghost Brots [7])
by Jim Muth 13 Jan '13

13 Jan '13

FOTD -- January 13, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Hidden Ghost Brots". It is probably the first image in FOTD history where the objects that inspired the name do not actually appear in the image. The 'Ghost 'Brots' lie in the black 'inside' areas. When the image is rendered with the inside set to 'bof61', these open areas fill with detail filled in turn with well-defined minibrots. Try it and see. It's kind of hard to rate things that do not appear in an image, so I could give the image a rating no higher than a 7. The calculation time of 2-1/2 minutes is right on the mark. For maximum convenience, the image has been pre-calculated and posted in finished form to the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> High-definition renderings are available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The FOTD back catalog of images is online at: <http://www.Nahee.com/FOTD/> Today dawned damp and foggy here at Fractal Central, and stayed that way most all day. The temperature of 48F +9C was well above normal, but with so much dampness in the air, it still felt chilly. The fractal cat had his eye on the outside conditions that kept even the neighborhood stray cats in hiding. The humans had a do-nothing day, spending more time than usual in front of the fractal TV. The next FOTD will be posted in the right cosmic time. Until then, take care, and solve the country's problems with your head, not your heart. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Hidden_Ghost_Brots { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=+0.3922690253119078/-0.9833762241149269\ /3570608/1/-165/0 params=1/3/0.6/5/0/0/0/0 float=y maxiter=1750 inside=0 logmap=168 periodicity=6 colors=000tqaspcrpeqogpoionknnmmmolmqklsjluhktgjtf\ itehsdgscfsbfs`er_drZcrYbqXaqW`qV`qZdiahaelUhpMktE\ hqFenGbkG_hHXeIUbIR_JPXKMUKJRLGOMDLMAIN7FO5CO6EQ6F\ R6HS7IU7KV7LW7NX8OZ8Q_8R`9Tb9Uc9Wd9XeDZfG_gJ`gMahP\ biSciVdjZekafkdglghmjimmjnpkoslorklqkipkgpkdokbnk_\ njYmjVljTljQkjOjjLjjJffIbbH__GWWFSSEPPELLDHHCEEBAA\ A77A67A66956956967AIYD9bD0gD4dE7bEB`FEZFIWGLUGPSHS\ QHWNHZLIbJIeHJiEJlCKpAKs8Kn7Ni7Pe6R`6TW5VS5XN5_I4a\ E4c93e43g03i22j32k42l62m72n82nA1oB1pC1qE1rF1sG1sHF\ hISYJdNJqCMpGOoKQoOSnSUnWWm_Zlc`lgbkkdkofjshjvigti\ driaqiZoiWnjTljQjjNijKgjHfgJedLeaNdZPdWRdTTcQVcOXc\ LZbI`bFbaCda9fa6h`3j`1k`2lc3me3ng4oj5pl5qn6rq7ss7s\ u8nv8iv8ew9`w9Ww9Sx9NxAIxAEyA9yA5yIIzQUzYfzerzbtz`\ uzYvzWwzTxzRyzUrzckzmeztZzzSzzMzzFzz9zzAzzAzzAzzBz\ zBzzBzzCzzCzzCzzDzzDzzDzzDzzFzzGzzHzzIzzJzzKzzLzzM\ zzNzzOzzPzzQzzRzzSzzTzzTz } 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 11-01-13 (Iterative Challenge [6])
by Jim Muth 11 Jan '13

11 Jan '13

FOTD -- January 11, 2013 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows one of the infinity of things that happen when 0.3 parts of Z^5 are combined with Z^3. The resulting parent fractal appears as a vertically stacked north-south chain of Mandel-like bays with a 'main bay' on the southern end of the chain. The bays grow larger and more distorted the farther north they lie, until at the limit, little Mandel stuff at all remains. Today's scene lies in one of four similar valleys about halfway up the chain. The name "Iterative Challenge" has little to do with the image. I invented the name when, after an hour of futile searching, I had found nothing better than today's image, which rates only a mediocre 6. The calculation time of 4 minutes is more time than the image deserves. But it's still worth a quick glance, especially on one of the FOTD web sites, where the need to calculate it is eliminated. Enjoy the image, already calculated, on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and the high-definition variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are at: <http://www.Nahee.com/FOTD/> Clouds and rain defined today here at Fractal Central. The saving feature was the temperature of 43F +6C, which was notably above average. The fractal cat passed the day lounging by the heat; the humans finished the work on time and then took it easy. The next FOTD will be posted soon. Until whenever, take care, and feel sorry for those fortunate enough to have heavy media coverage of their misfortune. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= IterativeChallenge { ; time=0:04:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.065078360615/-1.793874546443/2774529\ /1/-80/0 params=1/3/0.3/5/0/0/0/0 float=y maxiter=2200 inside=0 logmap=257 periodicity=6 colors=000A5KA5KA5JA5IA5G95E85C75A6585564543622701\ 80090CKABUG9cNKmNUtNczNmzMzvLmrKcnJ`kIYhHWeGZbFb_E\ eXDiUCmRBpOAtL9wI8mKAcLCUMELNGMWHNcIOlJOtKNqNNnPNk\ SNhUNeWNbZM_`MXcMUeMRgMOjMLlMInNHkNGiNGgNFdNFbNE`O\ DYODWOCUOCROBPOBNMAVK9bI8jKCkLFkNIkOLkPOkRRkSUkTXk\ V_kWbkYekZhk_lkankbpkaokZmiXigUdeQ_ZNWSKPLHJFEFDBC\ F89I56K76I96GB6EC6HE6KG6NH6QJ6UL6SM6QO6OQ6MR6KT6IV\ 6GW6FV8EVADVBDVDCVECVGBVHAVJAVK9VM9VN8VP7VQ7VS6VT6\ UU7TV8SW9SXARYBQYCQZDP_EO`FOaGNaHMbIMcJLdKKeLKeLJc\ MIbMH`NG_NFYOEXODWOCUPBTPARQ9QQ8OR7NR7MR9KUAJXCHZD\ GaFFdGDfICiJAkL9nT8zb6ze5z`4zV9zT8`V7QWBEXK3YL4ZM5\ _N6`O6aP7bV8cW9dX9eTAfZBg_Cg`ChaCjaBkbBmcBncAodAqi\ 9re9se9rdAqdApcAocAnbAnbAmbAmaAlaAmTjmTnmUqmSnmRlm\ PjmKhmIfmGdmEbmC`mAYmAWmAUmASzAUzAUzAUzAUzAczAczAc\ zAczAmzAmzKmzKmzKzzUzzUzzUzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczzcz } 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, esc=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < esc } END PARAMETER FILE=========================================

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FOTD 10-01-13 (Something New [7])
by Jim Muth 10 Jan '13

10 Jan '13

FOTD -- January 10, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the fractal that results when the formula Z^(1.5)+C is iterated 379.2424085207679 levels up the complex hyperladder with no function applied. The odd number of levels indicates that the value was set at random by Fractint's evolver feature. A very similar image could have been found with a far simpler value, though I lacked time to search for it. Actually, the complex logarithm has an infinity of values, but this does not mean that an infinite variety of fractals is possible. The fractals change in a circular manner as the value of 'k' in the complex log formula is changed, and soon begin repeating. I named today's image "Something New". I have never before seen features quite like the dark blue ones in today's image. The filaments extending from them resemble those extending from everyday Mandelbrot buds. And the filaments in the image have identical mini dark blue mini-features lying along them. The rating of a 7 is average. The artistic value is not that great, nor is the mathematical interest. Extra coloring effort might have raised the rating a half point or so however. The calculation takes 2-1/2 minutes to finish. Significant time may be saved by viewing the finished image on one of the web sites. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> High definition variations are or soon will be online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Back images may be found at: <http://www.Nahee.com/FOTD/> Near total sun with a temperature of 45F +7C made today unusually pleasant for the time of year. The fractal cat enjoyed the sun; the humans enjoyed getting the work finished. The next FOTD will be posted in a day or two. Until whenever, take care, and the surest sign of a dysfunctional group is when its members begin fighting among themselves instead of working together to solve their common problems. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Something_New { ; time=0:02:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident inside=0 center-mag=+1.52637522907494/+0.5716577695720915/\ 1.263153e+009/1/-90/0 params=1.85/0/379.2424085207\ 679/0 float=y maxiter=3600 logmap=381 periodicity=6 colors=000E7SF8TG9UHAVIBWJCXKDYLEZMF_NG`OHaPIbQJcR\ KdSMeVOeZQeaSfeVfiXflZgp`gvYbt`esbgrejpglojopkrolq\ nlqmlqllqklqklqjlqilqhmqgmqgmqfmqemqdmqcmqclwcmqcm\ kcnecn`cnVcoPcoJfrGdpFcoEanD`mCZlBYjAWi9Vh8Tg7Vf4S\ f6Re5Rd5Rc5Rb5Qa5Q`5Q`5Q_5QZ5PY5PX5PW5PV5Ya2PV5GO8\ WBG7HABJBFKCJLCNMDQNDUOEYPEaQFdRFhSGlTGpUHxJLuPJsV\ Hq`GofErlDvrBzz8vwAruBnsCkqEloFmlGnjHnhJofKpdLpbMo\ _IkZHhYGeXFbWF_VEXUDUTDRSCORBLQBIPAFO9CN9AQ89T78V6\ 7Y56_45b34d23g12i06h6AgCDgIHfOKeTOeZRddVcjYcoV`kTY\ gRVcPT`NQXLNTJLQGIMEFICCEAAB877643420GWBES9CP8BM79\ J68G56C4493362131iBHeAFb9U_8UW7UT7UQ6UN5UJ4UG3UD3U\ 92K61K30KKTKSEKFNKCJKAFc7Bc57c23cGMm8BmJYmHVzGTzFR\ zEPzDNzBLzAJz9Hz8Ez7Cz5Az48z36z24z12zIYzGUzEQzCMzA\ Iz8Fz6Bz47z23zKKzq`zlXzfTzaQzWMzRIzLEzGBzA7z53z1zz\ 0qz0hz0_z0Rz0Iz09zGazEZzDWzCTzBQz9Nz8Kz7Hz6Ez4Bz38\ z25z12zVrzRlzOgzLazIXzFRz } 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] AOTD Jan 2 & 8 2013
by Hal Lane 10 Jan '13

10 Jan '13

JoTz, Thanks for the great videos! http://www.fractal-animation.net/vid/valentynez.zip http://www.fractal-animation.net/vid/2013.zip Single-stepping thru the rapidly changing areas of the videos let me see all of the great fractals that went by too fast at the default frame rate. In the Windows Media Player V11 you can do this: View > Enhancements > Play Speed Settings Below the Play Speed Settings horizontal slider are two unidentified buttons. If you pause the video, then these two buttons advance and reverse the video one frame at a time, so you can see the many wonderful fractals that are whizzing by -- now frozen for your visual pleasure. The reverse function is buggy -- I've had to kill the Windows Media Player manually using the Task Manager when it appeared to hang when I asked for several reverse steps of a video in a row. (There may have been a patch released that I haven't applied yet.) To go back and see something in the video that has just passed by, I've learned to drag the blue button of the video "progress bar" to the left a bit, and then use the single step Advance button, thus avoiding using the Reverse button... The blue part of the horizontal Speed slider shows the range of speeds where sound is able to be provided. Note that the range of playback speeds between "0" and "0.5" is only the distance between those two labels on the Speed slider... You have a keen nose for parameter sensitivity! - Hal Lane ######################## # hallane(a)earthlink.net ######################## ================================================== > Author: JackOfTradeZ > Date: 2013-01-02 23:47 -500 > To: fractint > Subject: [Fractint] AOTD 1/2/13 > > This really is a "surprise" fractal; it finished way > ahead of what I had calculated. The same interesting > effect is observed with all Julia type fractals > (simple to complex) when animating in one dimension > (linear, along a line in the plane, ie., by varying > one parameter). There are alternating periods of > "slow" activity and motion with fast "explosive" > displays. > > One might think you could isolate the "fast" > segments, then "expand" them by re-rendering the > frames with a smaller increment, but if you do that, > the same alternating slow-fast pattern re-emerges. > I have noticed this over 10 years of Julia > animations. Kinda like a "Cantor Set Line" - as you > magnify it the same pattern keeps occuring. > > In this case it is cool - a small fractal image > slowly morphs and expands with increasing speed and > intensity, and the cycle repeats several times over > the viddie. > > In the original FOTD for 1/1/13 the REAL parameter > (P3) is set to -1.64788477144322. > For the animation it is varied from -1.647853 to > -1.647913 in steps of -0.00000001 to give 6000 > frames. > > It is 6 minutes 11 seconds long, 61 MEG download. > Complete with 12th century soundtrack. > > http://www.fractal-animation.net/vid/2013.zip > > Enjoy! > JoTz ================================================== > Author: JackOfTradeZ > Date: 2013-01-08 22:16 -500 > To: fractint > Subject: [Fractint] AOTD Jan 8 2013 > . > > > Fractal > Animation visionaries > and enthusiasts: > > Today's animation is derived from the FOTD for Jan 4 2013, > "Into The Boondocks", where the REAL portion of the P5 > parameter is varied from -4.01000055420134 to > -4.00999901475165 in steps of 0.0000000005 for 3K+ > frames. > > Perhaps the last one may have been a bit boring, but not > this one. No slow parts, all psychedelic, all cruisin' > all the way! > > The name -- "Valentynez" -- will be evident while viewing. > My rating of 9 for this one makes it one of the best of > the "kaleidoscope" animations. The calculation time of > one day leaves every excuse for those who lack the time > to do the calculation, especially when the finished > viddie is available on my web site: > > http://www.fractal-animation.net/vid/valentynez.zip > > 34 MEG download for 3 min 26 sec viewing pleasure. > > > Clear skies with temperatures in the 40's made today > here at Fractal Animation Central totally typical for > the start of January (in Colorado). > > The fractal coyotes have been silent recently, but > horses and cattle can be heard in the distance at nite > or in the wee hours of morning, adding to the pleasant > environment of the American West, although Colorado is > becoming more infested with liberals every day; I fear > it will soon be New Jersey with a better climate and a > mountain view before too long. > > > The next animation (zoom "Into the Aether") will be > posted when it is finished, in a week or two. Until > then, take care, and I never cease to be amazed at > the emotionally-based but ineffective solutions to > major problems that INsincere people keep inventing. > For example, to make the streets safer, why would any > sensible person be against every free citizen carrying > the firearm of their choice, open or concealed? A wise > philosopher once noted that "an armed society is a > free and polite society", and how right he was! > > Cheers > JoTz ----

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AOTD Jan 8 2013
by JackOfTradeZ＠comcast.net 09 Jan '13

09 Jan '13

. Fractal Animation visionaries and enthusiasts: Today's animation is derived from the FOTD for Jan 4 2013, "Into The Boondocks", where the REAL portion of the P5 parameter is varied from -4.01000055420134 to -4.00999901475165 in steps of 0.0000000005 for 3K+ frames. Perhaps the last one may have been a bit boring, but not this one. No slow parts, all psychedelic, all cruisin' all the way! The name -- "Valentynez" -- will be evident while viewing. My rating of 9 for this one makes it one of the best of the "kaleidoscope" animations. The calculation time of one day leaves every excuse for those who lack the time to do the calculation, especially when the finished viddie is available on my web site: http://www.fractal-animation.net/vid/valentynez.zip 34 MEG download for 3 min 26 sec viewing pleasure. Clear skies with temperatures in the 40's made today here at Fractal Animation Central totally typical for the start of January (in Colorado). The fractal coyotes have been silent recently, but horses and cattle can be heard in the distance at nite or in the wee hours of morning, adding to the pleasant environment of the American West, although Colorado is becoming more infested with liberals every day; I fear it will soon be New Jersey with a better climate and a mountain view before too long. The next animation (zoom "Into the Aether") will be posted when it is finished, in a week or two. Until then, take care, and I never cease to be amazed at the emotionally-based but ineffective solutions to major problems that INsincere people keep inventing. For example, to make the streets safer, why would any sensible person be against every free citizen carrying the firearm of their choice, open or concealed? A wise philosopher once noted that "an armed society is a free and polite society", and how right he was! Cheers JoTz .

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FOTD 08-01-13 (Candy-Drop Tree [7.5])
by Jim Muth 08 Jan '13

08 Jan '13

FOTD -- January 08, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Those fractal trees must be everywhere. As I was investigating the Julia sets of the (-Z)^(-1.5)+C Mandeloid, I stumbled upon today's fractal tree. I named the image "Candy-Drop Tree" because the tree appears to me made of candy drops. I am certain that fractal trees much more impressive than today's lie in the vicinity, but I had no time to do the necessary checking. The rating of 7-1/2 indicates an average scene on which I put a modicum of coloring effort. The calculation time of 6 minutes borders slowness, but once again the web sites charge to the rescue. To totally avoid calculation problems, check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> and check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of back images are online at: <http://www.Nahee.com/FOTD/> Morning clouds gave way to afternoon sunshine here at Fractal Central today. The temperature of 41F +5C and light winds made the day quite harmless for the season. The fractal cat also had a harmless day, which was enjoyable for him, but makes a rather boring report. The humans got through the day with no major problems arising. The next FOTD will be posted when conditions are right. Until whenever, take care, and according to the news reports, doom is all around us. So be ready to stamp it out as soon as it rears its ugly head. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Candy-Drop_Tree { ; time=0:06:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=t center-mag=0.3\ 99377/0/6.9855/1/90/0 params=90/0/90/0/-1.92748937\ /0/0/0/-1.5/300 float=y maxiter=1900 inside=0 logmap=-100 periodicity=6 colors=000VPUSNQPMMMPNJSOGUPDXQA_R8aRMGONGONGOOGPO\ GPOGPPGQPGQQGQQFRRFRRFRSFSSFSSFSTFTTFThvvkyvcrpWkk\ PdfHY`9RW2KR2sC6qDApEDoFHmGKlHOkISiJVhJZgKaeLedMic\ NlaOp`Ps_PraQqcQpdQofQngQmiQljQklQjnRioRhqRgrRftRe\ uRdwRcxRXtMRqHLmDFj89g4JkJTnYbqlfnmilmljmphmsfmvdm\ q_nlWogSpbOqcTkdYeeb_ffUgkOhpIhtCViHIZM5PR8SQAVPCY\ OF`NHcMJfMMiLOlKQoJTrIVuHXwHVtLUqOTnRSkURhXQe_PcbT\ bdXbf`bhdbjhbllbnobokdnhfnehmbjm_llXnlUpl_qjdqiirh\ nrgsrfKMGfcqddpbep_foYgoWhoXimXjlYjkYkjYkiZlgZlfZm\ e_nd_nc`oa`o``p_apZaqYaqXcrZdr_es`gsahtbitdjuelufm\ vgnvhowjqwkrxlsxmtxnqwlnwjlwiiwggwfdwdawb_waXw_VwZ\ Zrbbmfeijidnl`rpWvsSyrUqqWiqXapZUp_NnYPlWRkUSiSUgQ\ WfOXdMZbK`aIabHibGpaJnaLm`Nk`Pj_Rh_TgZVfZXdYZcY`aX\ b`Xd_fhgolnERyHPwKNvNLuQKtSIsUFrSKqQUpOboMhnKcmInl\ GrlEolCilBhmAgmAem9dm8cn7an6`n5_n5Zn6Uj7Pf7Lc8Ka9K\ `AK_BJZCJYCJXDIWEIVaSaZQY } 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 06-01-13 (Stuck Baghorn [7])
by Jim Muth 06 Jan '13

06 Jan '13

FOTD -- January 06, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Stuck Baghorn". The name has only a little to do with the actual image, which appears as a pentagon with rudimentary staghorns (velvet antlers) jutting from its edges. But these baby antlers reminded me of an old Canadian funny-animals show starring a character named 'Buck Staghorn', who was always stuck in his camper out in some wilderness, observing the antics of the local wild animals and sending messages back to Beatrice at Staghorn Central. And yes, Staghorn Central was the inspiration for Fractal Central, which is equally as real. And as for today's image, it is only half real also, as are all fractals. For a (minor) change, I have switched from the expression Z^(-4.01) to (-Z)^(-5.01). Iterating negative Z instead of positive Z rotates the fractal so that one of the sharp points of the Mandeloid falls on the real positive X-axis rather than in complex territory, where, with two coordinates to adjust, searching for Julia sets is far more troublesome. The SliceJulibrot5 formula might be a new one for the list. I'm not sure. The image itself rates a 7, at least IMO. A bit more detail might have raised the rating to an 8, and I'm certain that better Julia images do exist in this area, but laziness has once again won out, and I made no effort to improve on the scene. (Tomorrow is another day however.) The calculation time of a mere 10 seconds is no typo. The image really does finish almost before it starts. And in addition, the web sites are available to remove even the chore of running the parameter file. The finished image is posted online at: <http://www.crosscanpuzzles.com/Archives.html> with augmented variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of back images may be accessed at: <http://www.Nahee.com/FOTD/> Clouds were plentiful here at Fractal Central today, but the lack of wind and temperature of 41F +5C kept things relatively pleasant for January. With the temperature so far above freezing, the forecast of light snow this evening will probably prove to be a bust however. The fractal cat passed most of the day stretched by the heat, except when he used up excess energy playing with his cat cubes. The humans, (at least we were human the last time we checked), passed the day doing as little as possible. The next FOTD will be posted before long. Until then, take care, and what are fractals but a temporary break from pondering the deeper problems of life? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Stuck_Baghorn { ; time=0:00:10.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=0.0670723/\ 0.206427/0.2693157/1/18/0 params=90/0/90/0/\ 1.528410596/0/0/0/-5.01/3550 float=y maxiter=1500 inside=0 periodicity=0 periodicity=0 colors=000FKYzA8GC8GE8GG8Ec8CG8Ac88z88hzmGC8Gz8GG8\ EG8CG8AGBBGCBGDBGFBGGBGGBFGBDGBCGBBGCBGDBGFBGGBFGB\ 000CABBzBBzzBGDBcFBGGBFGBczcccUKUF00zz000000000000\ 000000e0e00eeUAKe0eeL0eeeLLLLLzLzLLzzzLLzLz000zzz0\ 00555888BcBEEEHHHKKKOOOhccWWW___ccchhhmmmssszzz00z\ G0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0HFHVz0Gz00z00z\ G0zV0zj0zz0jz0VzmrzVVzbVzjVzrVzzVzzVrzVjzVbzVVzbVz\ jVzrVzzVrzVjzVbzVVzVVzbVzjVzrKKKVrzVjzVbzhhzlhzqhz\ uhzzhzzhuzzzzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhzlhzqhz\ uhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70SE0SL0S\ S0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLESOESSES\ SEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLESOESSEO\ SELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKSSKQSKO\ SKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0GG0CG08\ G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0CG08G04\ G88GA8GC8GE8GG8GG8EG8CG8A } 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 05-01-13 (The Great Mystery [7])
by Jim Muth 06 Jan '13

06 Jan '13

FOTD -- January 05, 2013 (Rating 7) Fractal visionaries and enthusiasts: Today's image rates only a 7. Being simply another venture into the Z^(-4.01)+C Julia sets, it deserves no more. But it is still a rather striking image, demonstrating the large variety of Julia sets in this area. The name "The Great Mystery" refers not to the image, but to some other vague mystery only half perceived. Perhaps, it's the old warhorse mystery about the meaning of life, which our over-revered science has so far been helpless to answer. (It punts the question to religion, while implying that the beliefs of religion are only comforting illusions.) The calculation time of one minute will pass in a flash, but when the image appears, it will neither answer the great mystery nor supply a comforting illusion, but it is guaranteed to be at least semi-real. The pre-calculated image is really online at: <http://www.crosscanpuzzles.com/Archives.html> with the high-definition versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Lots of back images are posted at: <http://www.Nahee.com/FOTD/> The string of typical early January days continued here at Fractal Central today, with variable amounts of clouds, breezy west winds, and a temperature of 37F +3C. The fractal cat also had a typical day, taking advantage of the sun when it was out and taking to the heat when the sun disappeared. The humans mostly took it easy. The next FOTD will eagerly be posted when the time arrives. Until then, take care, and we should not propose knee-jerk solutions to our problems. We should instead find effective and workable solutions that everyone will accept. This is why the 99-percent movement went nowhere and the current push for more gun control is futile. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Great_Mystery { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.033113\ /1/45/0 params=90/0/90/0/-1.647906886818445/0/0/0/\ -4.01/0 float=y maxiter=3200 inside=0 periodicity=0 colors=000zzzzz0570450340220110QIWNGTLEQIDNGBKE9HB\ 8E96B748435212_N8UJ6OF5IB4C72631ZG6TD5NA4H83B52521\ NHpIDeDAV96L43ASF2W7tT6oRczP5gM5cK4_I4WG3SD3OB2K9K\ m61q418204CdrA`m9Xh8Tc7QZ6MU5IP4EK3BF27A135X8BS79O\ 68K56G45C34822411KpkHieFb_CXUAQO7JI5DC266alRXeNS_K\ NUGJODEIA9C6463DaKAUG7MC5F8274aRFXODTLBPIALF8GC6C9\ 5zz0h00zczi4b`3VS2NI1F907Pj8Nf7Lb6J_6HW5FS4DP4BL39\ I37E25A1371130gSlcPg_McWKZSHVOFQKCMGAHC7D858424AUm\ 8Qg7Na6KX5GR4DM3AG26B135K35I24H24G24E23D23C13A1291\ 2812HA1D0140120G100zcIzIGrHFnEDg7CZ6AS59N47I36E249\ 13401kRc_KUODKC6AwGcqE_lDWfBTaAPW8LR7IL5EG4AA27513\ XeCT`APW9MS8SsCWsCasBisBosAvzAzzAzhRzXftRvsYczfVqI\ cqRXqMRqOLqQEqS8qT2oV8nXEmZJl`PjbVid_hfeghkfjpcdn`\ _mYUkVPjSJhPEgM8eK3dG2Y9D4D2RA1K61D306Iu7Ei5AY47N2\ 3B1pDXlCUiBSfAQb9O_8MX8KT7IQ6GN5EJ4CG4AD3892661430\ 2GL1EJ0zV0Cb0BF0AE09C08B0 } 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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Albrecht has had computer probs which...
by Hal Lane 06 Jan '13

06 Jan '13

Albrecht has had computer probs which caused the lost of many files but he says he will be back on the forum at a later time. - Hal Lane ######################## # hallane(a)earthlink.net ########################

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FOTD 04-01-13 (The Sound barrier [7.5])
by Jim Muth 05 Jan '13

05 Jan '13

FOTD -- January 04, 2013 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a variation of the 'New Year Surprise' image of January 1. As JackOTZ has already discovered, the parameter values of that image are very critical. (A tiny change makes a huge difference.) To show how critical, I have changed the exponent of Z from (-4.01) to (-4.0100001) and decreased the escape radius from 9 to 2.8. (I have also reduced the magnitude a bit and tweaked a few color registers, but these changes are insignificant.) The tiny change in the exponent makes a huge change in the image, while the tighter bailout radius changes the central rounded square to a kind of rounded letter-X, while narrowing the width of the surrounding bands of chaos. (Increasing the bailout causes the width of the bands to grow, until they finally fill the entire frame with chaos.) As is often the case, the name -- "Into the Boondocks" -- has little relation to the image. The rating of 7-1/2 might be a bit conservative, but I cannot give a super rating to a string of very similar images. The calculation time of 30 seconds leaves no excuse for those who claim to lack the time to do the calculation, especially when the finished image is available on the web sites. For instant viewing, check the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And check the high-definition versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images are posted at: <http://www.Nahee.com/FOTD/> Partly cloudy skies with a temperature of 36F +2C, a breeze from the west, and a 5-inch 12cm pack of snow covering the ground made today here at Fractal Central totally typical for the start of January. The fractal cat passed the afternoon on the shelf in the southwest window, wishing the sun would stop turning off and on so often. The humans passed the day finishing the work. The next variation on the theme will be posted when the neat come home, and around here they come home every day at sunset. Until then, take care, and I never cease to be amazed at the emotionally-based but ineffective solutions to major problems that sincere people keep inventing. For example, to make the streets safer, why would any sensible person be against publish- ing a list of those who have committed crimes with illegally obtained guns, yet be in favor of publishing a list of law- abiding citizens who legally own guns? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Into_the_Boondocks { ; time=0:00:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/\ 0.08621576 params=90/0/90/0/-1.64788477144322/0/0/0\ /-4.0100001/-6.2 float=y maxiter=3200 inside=0 symmetry=xaxis periodicity=0 colors=000000zz0570450340220110QIWNGTLEQIDNGBKE9HB\ 8E96B748435212_N8UJ6OF5IB4C72631ZG6TD5NA4H83B52521\ NHpIDeDAV96L43ASF2W7tT6oRczP5gM5cK4_I4WG3SD3OB2K92\ G61C418204CdrA`m9Xh8Tc7QZ6MU5IP4EK3BF27A135X8BS79O\ 68K56G45C34822411KpkHieFb_CXUAQO7JI5DC266alRXeNS_K\ NUGJODEIA9C6463DaKAUG7MC5F8274aRFXODTLBPIALF8GC6C9\ 5m00zzzzUzi4b`3VS2NI1F907Pj8Nf7Lb6J_6HW5FS4DP4BL39\ I37E25A1371130gSlcPg_McWKZSHVOFQKCMGAHC7D858424AUm\ 8Qg7Na6KX5GR4DM3AG26B135K35I24H24G24E23D23C13A1291\ 2812611501401200100sBInAGi9Fe8D`7CW6AS59N47I36E249\ 13401kRc_KUODKC6AwGcqE_lDWfBTaAPW8LR7IL5EG4AA27513\ XeCT`APW9MS8SsCWsCasBisBosAvzAzzAzdRzQftCvsLczOVqI\ cqRXqMRqOLqQEqS8qT2oV8nXEmZJl`PjbVid_hfeghkfjpcdn`\ _mYUkVPjSJhPEgM8eK3dG2Y9D4D2RA1K61D306Iu7Ei5AY47N2\ 3B1pDXlCUiBSfAQb9O_8MX8KT7IQ6GN5EJ4CG4AD3892661430\ 2GL1EJ0DI0CG0BF0AE09C08B0 } 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 03-01-13 (The Sound barrier [8])
by Jim Muth 03 Jan '13

03 Jan '13

FOTD -- January 03, 2013 (Rating 8) Fractal visionaries and enthusiasts: Today's Z^(-4)+C near-Julia image carries the current theme to the limits. I have double-rotated the orientation of today's slice 0.000001,0.0000001 degree from the true Julia orientation, which totally destroys the 4-way symmetry of recent images. But the resulting image is still notable enough to rate an 8. (A tiny rotation sometimes makes a huge difference in Julia images.) The colors are mostly carried over from yesterday's image, with only a few registers being tweaked. The calculation time of 45 seconds will pass fast, leaving little waste if the image lays an egg. Here is where the web sites can make the viewing even easier. View the finished image online at: <http://www.crosscanpuzzles.com/Archives.html> with hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> and the back images at: <http://www.Nahee.com/FOTD/> After a very chilly morning low of +5F -15C, the brilliant sun raised the afternoon temperature to a comparatively pleasant freezing point. The fractal cat spent the entire afternoon on the shelf in the southwest window, warming himself in the sun. The humans had a routine day getting the work under control. The next FOTD will be posted when I get a round tuit. Until whenever, take care, and I heard a teacher on the local radio the other day claim that the present day children think differently than yesterday's children. I had to agree totally. Yesterday's children were not as helpless as today's lot. They needed no computers to enable them to learn that 2+2=4, etc. They did it all in their heads. And for entertainment they went out, played with their friends and sometimes hurt themselves. Then they came home and read books. Our 'technologically advanced' culture sure is declining. Let's solve the problem with more technology. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Sound_Barrier { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 maxiter=3200 center-mag=6.14828/0/0.09570475 params=89.999999\ /0/89.9999999/0/-1.647884739957274/0/0/0/-4.01/0 float=y inside=0 symmetry=xaxis periodicity=0 colors=000hdrtPvsWczbVqIcqRXqMRqOLqQEqS8qT2oV8nXEm\ ZJl`PjbVid_hfeghkfjpcdn`_mYUkVPjSJhPEgM8eK3dG2Y9D4\ D2RA1K61D306Iu7Ei5AY47N23B1pDXlCUiBSfAQb9O_8MX8KT7\ IQ6GN5EJ4CG4AD38926614302GL1EJ0DI0CG0BF0AE09C08B00\ 00zz0570450340220110QIWNGTLEQIDNGBKE9HB8E96B748435\ 212_N8UJ6OF5IB4C72631ZG6TD5NA4H83B52521NHpIDeDAV96\ L4UzSF2W7tT6oRczP5gM5cK4_I4WG3SD3OB2K92G61C418204C\ drA`m9Xh8Tc7QZ6MU5IP4EK3BF27A135X8BS79O68K56G45C34\ 822411KpkHieFb_CXUAQO7JI5DC266alRXeNS_KNUGJODEIA9C\ 6463DaKAUG7MC5F8274aRFXODTLBPIALF8GC6C95m00HezzUzi\ 4b`3VS2NI1F907Pj8Nf7Lb6J_6HW5FS4DP4BL39I37E25A1371\ 130gSlcPg_McWKZSHVOFQKCMGAHC7D858424AUm8Qg7Na6KX5G\ R4DM3AG26B135K35I24H24G24E23D23C13A129128126115014\ 01200100zBIsAGn9Fh8D`7CW6AS59N47I36E24913401kRc_KU\ ODKC6AwGcqE_lDWfBTaAPW8LR7IL5EG4AA27513XeCT`APW9MS\ 8SsCWsCasBisBosAvzAzzAzdR } 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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AOTD 1/2/13
by JackOfTradeZ＠comcast.net 03 Jan '13

03 Jan '13

. This really is a "surprise" fractal; it finished way ahead of what I had calculated. The same interesting effect is observed with all Julia type fractals (simple to complex) when animating in one dimension (linear, along a line in the plane, ie., by varying one parameter). There are alternating periods of "slow" activity and motion with fast "explosive" displays. One might think you could isolate the "fast" segments, then "expand" them by re-rendering the frames with a smaller increment, but if you do that, the same alternating slow-fast pattern re-emerges. I have noticed this over 10 years of Julia animations. Kinda like a "Cantor Set Line" - as you magnify it the same pattern keeps occuring. In this case it is cool - a small fractal image slowly morphs and expands with increasing speed and intensity, and the cycle repeats several times over the viddie. In the original FOTD for 1/1/13 the REAL parameter (P3) is set to -1.64788477144322. For the animation it is varied from -1.647853 to -1.647913 in steps of -0.00000001 to give 6000 frames. It is 6 minutes 11 seconds long, 61 MEG download. Complete with 12th century soundtrack. http://www.fractal-animation.net/vid/2013.zip Enjoy! JoTz .

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AOTD
by JackOfTradeZ＠comcast.net 03 Jan '13

03 Jan '13

. Hi Hi Hi Droogs - I'm baaaaacck! It's been a long time and I almost forgot how cool it was to have the computers chugging away rendering thousands of frames lighting up my house and making the neighbors ask what are all those flashing colors all night long in your window.... Many of the FOTD for past months have been good, but a lot of fantastic images end up having rather unimpressive zoom-in sequences; I can only determine this by time and trial. And morph animations can be difficult and time consuming especially when there are many parameters with many decimal points. But the FOTD Dec. 28, 2012: "Into the Aether" zoom-in looks pretty cool so far. It is currently rendering; the images are slow and it may be a week or two before I can upload it. Wait for it. Also, I have been investigating the awesome FOTD Jan. 1, 2013: "New-Year Surprise". When I see an image that is not magnified or zoomed in (like a parent fractal), with ONE parameter defined out to MANY decimal places - I think MORPH ANIMATION HERE! And I have found that slight variations of the REAL p3 parameter result in a brilliant sequence of kaleidoscope images, many of which are far better than the original FOTD. (sorry Jim, you understand <g>). I have determined the best range of values and increments to make the animation, it is currently rendering. They render fast so it will have about 6000 frames and run 3 minutes or so. Expect to upload in a day or two. Wait for it. I am simply gonna name it "2013" as the graphical display of total chaos is a reminder of the real doomsday scenario which awaits us in 2013. Cheers. JoTz .

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FOTD 02-01-13 (Wise Butterfly [8.5])
by Jim Muth 02 Jan '13

02 Jan '13

FOTD -- January 02, 2013 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image continues the theme of yesterday's, with a shift upward to an exponent of (-6.01). Since the image is so close to being a repeat, I could not give it an equally high rating, but the rating of 8-1/2 that I did give it is not to be sneezed at. I named the image "Wise Butterflies". I can give no logical reason for such a name. It is simply a phrase that popped into my mind when I shut off my thinking for a few minutes as I studied the image. The calculation time of 12 seconds seems unreal. But that's the time it took for the image to finish on the now ancient 2000mhz unit. It will take longer than this to set up and run the included parameter file. Save the effort of setting up the parameter file by viewing the finished image at: <http://www.crosscanpuzzles.com/Archives.html> And check the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Thousands of back images are posted at: <http://www.Nahee.com/FOTD/> A mix of sun and clouds prevailed here at Fractal Central today, while the temperature of freezing made it feel quite seasonal. The fractal cat spent the afternoon on the shelf in the southwest window while the sun was out, and near the heat when the sun was obscured. The semi-fractal humans had a back-to- work day, which was notably un-exciting. I hear that some people were disappointed when the world did not end on December 21. As for myself, I could not have been disappointed, because I was virtually certain that nothing would happen on doomsday. All predictions of doomsday through all of history have had one thing in common -- they have been wrong. And I saw no reason to expect the latest 'Mayan' doomsday to be any different. IMO, our whole culture is the doomsday scene. I am pretty much a skeptic about most of the strange and unusual things we are given on TV as likely fact. This includes alien spacecraft visiting earth, alien abductions, bigfoots wandering our forests, lake and other monsters, Bermuda triangles, assorted conspiracy theories, and most other things that make no sense. But this does not mean I am a totally boring rational thinker. I do believe in ghosts and invisible 'spirit' worlds, which puts me right up there among the irrational kooks. The next FOTD will be posted soon. Until that earth-shattering moment arrives, take care, and don't give up all hope of doomsday destruction. The media moguls ordaining the public mood will soon invent another looming doomsday for us to worry about. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Wise_Butterflies { ; time=0:00:12.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.1930311 params=90/0/90/0/-1.50078/0/0/0/-6.01/0 float=y maxiter=1500 inside=0 symmetry=xaxis periodicity=6 colors=0000UZzhFKPCGKACF78A5452HGqFFmEEjDDfCCcBB`A\ AX99U88R77N66K55G44D33A226113Zz_zS00RzUozTPUXNS`MR\ cLPcKOcIMcHLcGJeFIgDGeCFcBDaAC_8AW79T67Q56N34K2300\ 0zzevqezuCrsBmqBcoAUlAKj9Ah9Af8Ad8Ab8A_75Y74W64U64\ S53Q53N43L42J42H32F31D21A2181061040020832721721721\ 721621621621621521521511511411411411411310cccz103z\ 021z2002002001001001001000000000008HO5BG258LprJlnI\ hjGdfF`bDYZCUVAXhVWN7IJ6FF4BB377133Ws9L`6AI3J49F37\ B25713301`iRXdOT_LPWIMRGINDEIABD8795342NaqM_nLYlKX\ jJVhIUeHScGQaFP_ENXDMVCKTBJRAHO9FM8EK7CI6BF59D47B3\ 692461340120e10a00Z00V00S00O00L00H00E00A00700300we\ 0sb0p`0mZ0jX0gU0dS0`Q0YO0VM0SJ0PH0MF0ID0FB0C809606\ 4032QpXyvrvsptqnrolpmjmkhkifigdgebec`b`Z`ZXZXVXVTV\ TRqNHnRIlUJjYKh`LedMcgNakO_nPciVgd`j`fnWlrRruNw1D5\ rLtoKqlJniIkgHhdGeaFcZE`XDYUCVRASO9PM8MJ7KG6HD5EB4\ B838525212lyUgsRcnP_iMWdK } 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 01-01-13 (New-Year Surprise [7.5])
by Jim Muth 01 Jan '13

01 Jan '13

FOTD -- January 01, 2013 (Rating 9.8) Fractal visionaries and enthusiasts: Today's stellar image, the first of the new year, continues the theme of the final two images of the past year. The image is a Julia set of a point on the negative X-axis of the Z^(-4.01)+C Mandeloid. The location is very near the limit of the negative point, which is broadened into a wedge. Considering both the mathematical and artistic aspects, I rated the image at a super-stellar 9.8, one of the highest ratings of all time. The parameter values are extremely critical. The entire image is lost at the slightest change. The name "New-Year Surprise" indicates my surprise when I discovered the appearance of the Julia sets of such negative areas. The very brief calculation time of 40 seconds makes today's image one of the greatest calculation bargains in FOTD history. Start the new year on the right foot by saving even this brief time. View the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And be sure to check the hi-def versions at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> All the FOTD back images are posted at: <http://www.Nahee.com/FOTD/> A blanket of heavy clouds hung over Fractal Central all day today. A few passing flurries of snow amounted to nothing, melting as soon as they fell, with a temperature of 36F +2C. The fractal cat and not-quite-as-fractal humans had a quiet day, which is the best way to start a new year. The next FOTD will be posted in 24 hours if it is ready. If it is not ready, it will be posted sometime later. Until whenever, take care, and I'll make my predictions for the year 2013 in 365 days. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= New-Year_Surprise { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/0.1128405 params=90/0/90/0/-1.64788\ 477144322/0/0/0/-4.01/0 float=y maxiter=3200 inside=0 symmetry=xaxis periodicity=0 colors=000000zz0570450340220110QIWNGTLEQIDNGBKE9HB\ 8E96B748435212_N8UJ6OF5IB4C72631ZG6TD5NA4H83B52521\ NHpIDeDAV96L43ASF2W7tT6oRczP5gM5cK4_I4WG3SD3OB2K92\ G61C418204CdrA`m9Xh8Tc7QZ6MU5IP4EK3BF27A135X8BS79O\ 68K56G45C34822411KpkHieFb_CXUAQO7JI5DC266alRXeNS_K\ NUGJODEIA9C6463DaKAUG7MC5F8274aRFXODTLBPIALF8GC6C9\ 5m00HeHzUzi4b`3VS2NI1F907Pj8Nf7Lb6J_6HW5FS4DP4BL39\ I37E25A1371130gSlcPg_McWKZSHVOFQKCMGAHC7D858424AUm\ 8Qg7Na6KX5GR4DM3AG26B135K35I24H24G24E23D23C13A1291\ 2812611501401200100sBInAGi9Fe8D`7CW6AS59N47I36E249\ 13401kRc_KUODKC6AwGcqE_lDWfBTaAPW8LR7IL5EG4AA27513\ XeCT`APW9MS8SsCWsCasBisBosAvzAzzAzdRzQftCvsLczOVqI\ cqRXqMRqOLqQEqS8qT2oV8nXEmZJl`PjbVid_hfeghkfjpcdn`\ _mYUkVPjSJhPEgM8eK3dG2Y9D4D2RA1K61D306Iu7Ei5AY47N2\ 3B1pDXlCUiBSfAQb9O_8MX8KT7IQ6GN5EJ4CG4AD3892661430\ 2GL1EJ0DI0CG0BF0AE09C08B0 } 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 31-12-12 (Brink of Eternity [?])
by Jim Muth 01 Jan '13

01 Jan '13

FOTD -- December 31, 2012 (Rating ?) Fractal visionaries and enthusiasts: Today's image, the last of the year, is another view of the same Julia set that appeared in yesterday's image. It shows how great a change in a Julia image can be made by such a small change in initial C. The name "Brink of Eternity" has little relation to the image. It refers to the start of a new year, with all its potential for good or evil. The question is which will prevail. (My guess is for a mixture.) I declined to give the image a rating, since it is a virtual repeat of yesterday's scene. With a calculation time of 45 seconds, the image is thankfully a fast one. End the year at leisure by checking today's finished image at: <http://www.crosscanpuzzles.com/Archives.html> Begin the new year by checking the hi-def variations at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Enjoy ten new images every day by checking: <http://www.Nahee.com/FOTD/> where the FOTD back images are online. A mix of sun and clouds with a temperature of 34C +1C made today just about average here at Fractal Central. The fractal cat spent most of the day lounging in the weakened sun coming in the southwest window. The humans made it through the last day of the year without a major problem. The next FOTD will be posted sometime next year. To see exactly when, keep checking back here. Until whenever, take care, and we need to pass a law defining who really are the good guys and the bad guys. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Brink_of_Eternity { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.3569139 params=90/0/90/0/-1.8889971/0/0/0/-2/150 float=y maxiter=5000 inside=0 symmetry=xyaxis periodicity=0 colors=000zAmluPapTRlXGg`2fb5cc8acA_cDYcGWcIUcLRdY\ K9LFANIAPKBRMCTPCVRDXUDZWE`YEb`FdbGfeGhgHjjHllInnJ\ pqJrsKtvKvxLl_L00UgZnDptEpsEpsFpsFprFprGprGpqGpqHp\ qHppHppIppIpoJpoJpoJpnKpnKpnKpmLpmLpmNqiLpmKopJosz\ zuzzwzzzzzrzzpzznzzkzzi000zzezzbzz`zzZzzXzzUzzSzzQ\ zzOHELHEJHFHHFFIGBIHDKIFMJH0LUQNdTLdWJdd5_YHdfz`00\ ZcHeOPKYTR_VTbXVdZXg`Zib`kdbnfdphfsjhuljwmkumismhq\ mfomemmdkmbimagm_emZcmYamW_mVYmTWmSSqRVmRXjRZfRacR\ c_RefU00PzdzrFSrESsCRsBRsAQt8Qt7Pt6Pu4Ou3Ov0Pu2Ot3\ Os5Or6Nq7Np9NoAMnBMmDMlELkGLjHLiIKhKKgLKfMJeOJdPJc\ RIbSIaTI`VH_WHaXDZXHXXLVXPSXTQXXOX`LXdJXhHXlFXpOLh\ V8cXA`YCY_EV`GSaIPcKMdMJdMGeNHeOHeOHfo000XUKc3TU5T\ W8TXATZDT_FTaITbKTdNTfPTgSTiUTjXTlZTmaTocTqfTrhTti\ TuiTwiTwjTxjVvkXulZtm`sRbrMdqHfpCho7in8ij9hfBzz00K\ DhWEgSFgOHgKIfGJfCKf8Lf5Fk7Ap99lF9iL9fR9cX8_b8Xh8U\ n8Rt8OyBSuEWqHZmKbiMefPib } 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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Cloud Service
by Albrecht 31 Dec '12

31 Dec '12

Hi, as my web page project has passed away I need a better solution, a free cloud service where I can keep the multifractal images and software available for watching and download even when my computer is offline. Dropbox apparently is no good in that aspect, but there are others. Any help will be appreciated, I need a solution in order to go on- there still is a large amount of new territory to be explored. Thank you! Albrecht

2 1

FOTD 30-12-12 (Spooky Julia Set [7.5])
by Jim Muth 30 Dec '12

30 Dec '12

FOTD -- December 30, 2012 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is another venture into the apparently boring (-Z)^(2)+C Julibrot. This time it is a Julia set of the tip of the sharp Mandelbrot valley pointing directly west. The image is extremely sensitive to changes in some parameters, especially the real parameters. Some changes create surprising variations; others fail miserably. Change any of them at your own risk, but don't say I failed to warn you if a blank screen appears. The Julia set in today's scene is shaped surprisingly like the Julia set of Seahorse Valley of the Mandelbrot set. This is likely a coincidence, though who am I to try to outguess the numbers? The name "Spooky Julia Set" refers to this strange similarity. The rating of a 7-1/2 includes a half-point bonus for the coloring. The adjacent color bands are in no order, but are scattered wildly all over the palette, making coloring quite difficult. The calculation time of 40 seconds will pass rapidly. Setting the symmetry to xyaxis will cut this time by 2/3, but will distort the images with no symmetry that result from changing the parameters. The image is so fast that it will take more time to go to the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> and view the finished image there. But going to the web site will avoid the problem of setting up and running the included parameter file. Augmented variations in hi-def are online at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The back images from as long ago as 1997 are posted at: <http://www.Nahee.com/FOTD/> Yesterday's snow ended at nightfall after dropping a fresh 6 inches or 15cm on Fractal Central. Today was cloudy with a few minor flurries blowing in from the lakes. The temperature of 34F +1C was just about normal. Fractal cat Nicholas spent the day chasing his catnip ball and asking for food. My greatest task was clearing the fractal sidewalk; FL kept busy supplying the hot coffee. The next FOTD will be posted in a reasonable time. Until whenever, take care, and I wonder why happiness in life now comes from purchasing the latest trendy gadgets. Maybe when we're pushing buttons, we don't have time to think about the horrors lurking just beneath the surface of our decaying culture. Jim (always the optimist) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Spooky_Julia_Set { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.3909394 params=90/0/90/0/-1.889/0/0/0/-2/5 float=y maxiter=5000 inside=0 periodicity=0 colors=0000AmYK9LFANIAPKBRMCTPCVRDXUDZWE`YEb`FdbGf\ eGhgHjjHllInnJpqJrsKtvKvxLwzLluPapTRlXGg`2fb5cc8ac\ A_cDYcGWcIUcLRd00UQNdTLdWJdd5_YHdRTiKdnDptEpsEpsFp\ sFprFprGprGpqGpqHpqHppHppIppIpoJpoJpoJpnKpnKpnKpmL\ pmLpmNqiLpmKopJoszzuzzwzzzzzrzzpzznzzkzzizzgzzezzb\ zz`zzZzzXzzUzzSzzQzzOHELHEJHFHHFFIGBIHDKIFMJH0LU00\ ZEHeOPKYTR_VTbXVdZXg`Zib`kdbnfdphfsjhuljwmkumismhq\ mfomemmdkmbimagm_emZcmYamW_mVYmTWmSSqRVmRXjRZfRacR\ c_ReXR00PjQRlMRoJRqFRsCRv8Rx5Rz2Rx3Sw4Sv5Su6Ss7Sr8\ Sq8Sp9SnASmBSlCSkDSiEShESgFSfGSdHScISbJSaJSYIQVHOR\ GMOFLNENMEOLEPKEQJESIETHDUGDVFDXEDYDDZCD_BCaACb9Cc\ 8Cd7Cf6Cg5Bh4Bi3Bk2Bl1Bm0Bn0Ej0Hf0Kb0QZ00XKKc3TU5T\ W8TXATZDT_FTaITbKTdNTfPTgSTiUTjXTlZTmaTocTqfTrhTti\ TuiTwiTwjTxjVvkXulZtm`sRbrMdqHfpCho7in8ij9hfBhb00K\ DhWEgSFgOHgKIfGJfCKf8Lf5Fk7Ap99lF9iL9fR9cX8_b8Xh8U\ n8Rt8OyBSuEWqHZmKbiMefPib } 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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Happy New Year!
by Albrecht 30 Dec '12

30 Dec '12

Hi, as I did this image just for today, I?m posting it, although it?s the last link used. Don?t overdo it! Happy New Year! Albrecht http://www.emarketingiseasy.com/Albrecht/21267.GIF ----------------------------------start-par--------------------------------- 23267 { ; HappyNewYear ; time 1.23.17.36 1600/1200 ; man-bees-man-phoen-newt reset=2004 type=formula formulafile=mfr_10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=6.08751/-0.00145029/6.412837/1/90/-1.23373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/21267.64595702002/14235.4\ 911030602/152048.0404808048/384.1604894048/384.00482000595/128.300768100\ 1/256.3007682001/384.2007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=000<7>000000000<3>000<7>Q0UU0YX0a_0dc0hf0l<2>p0w<4>_0dX0aU0Y<2>K0\ NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<10>2WI2TG2RE<3>4G54D36F5<16>kkammcpoe<3>zwm\ <3>mhZjdVfaS<3>VMCRI8OE4KA0000<43>000<4>000330<6>220220220<3>110000110<2\ >000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0F<3>z0K<6>Z0EV0DR0\ C<3>A08004000<17>000 } frm:multifractal_10 { ; Albrecht Niekamp Jan2005 ;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3 ; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid ; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider ; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp ; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp ;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5 ; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees ;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1 ; Right: 5 Digits_Colour2 5 Digits_Colour3 ;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used) ; Right: 5 Digits_Colour4 6 Digits_Colour5 ;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used) ; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in ;IP4 Left: Inside1_Maxiter ; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1 ;RP5 Left: Inside2_Maxiter ; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2 ;IP5 Left: Inside3_Maxiter ; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord ; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3 ; Altnat: Left: 1_Lake effect enabled (Inside3 disabled) ; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } ---------------------------------------------end---------------------

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