March 2009 - Fractint - mailman.xmission.com

FOTD 17-03-09 (The Faces of Fear [6])
by Jim Muth 16 Mar '09

16 Mar '09

FOTD -- March 17, 2009 (Rating 6) Fractal visionaries and enthusiasts: The name of today's image, "The Faces of Fear", sounds something like the name of one of those 'shocking' reality shows that fill the TV programming. But the name is fully justified. The first thing I noticed when I saw the finished image was the ring of stylized but terrified profiles of human faces surrounding the central minibrot. These profiles are most obvious in the lower left part of the image. All this fear was generated when I combined 7.5 parts of Z^(-0.5) with 0.75 part of Z^(-5), added (1/C) and iterated the mixture with a bailout radius of 40. The parent fractal is little more than an empty circle with something that looks like a lobster claw on its northeast shoreline. There is an obvious mandel-type bud in this claw however, with a curving filament extending from it. Today's scene is located far out on this filament, near the point where it terminates. The rating of a 6 is near what I think the image is worth. The calculation time of only 39 seconds makes running the included parameter file quite a bargain. But the best bargain of all can be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image already has been or soon will be calculated and posted for immediate viewing pleasure. The temperature of 54F 12C was fair enough here at Fractal Central on Monday, but the cloudy skies totally failed to satisfy the fractal cats, who spent most of the day in the living room, sulking conspicuously. The treat of tuna cheered them some, though they still would have preferred an afternoon in the sun on their sun shelf. My day was average, which means just enough work to keep boredom away. I'll post the next FOTD in 24 hours. Until then, take care, and when one is young, science has the all answers. But the older one grows, the fewer questions science can answer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Faces_of_Fear { ; time=0:00:39.41-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.3338053113603147/+0.0914822065138245\ /3.05e+010/1/-22.5/0 params=7.5/-0.5/0.75/-5/0/-60\ /0/0 float=y maxiter=1600 inside=253 outside=tdis logmap=17 periodicity=10 mathtolerance=0.05/1 colors=000x3ON7s53z79u9FqBLmDRiFXeHaaQdeYgifjlnmpv\ os6Yu7Vq8Tm9QjAOfBMb00KTJOSFOCERkSnoZosdpzzzzzzzoX\ weBwYHtRMlLSbHXZDbVAgPGZJMQDSHczcZjfadie_khUnlPpoJ\ srEujLvbRwVXzObxGhy8nz1tz9frGTjNFbU2VX5T_8RbBQeEOh\ HMjJLiPZhUlgZzfXtfWzfUhfTcfRYfQSfOMfNHXPTORcSPYWOS\ _NNcLHgKCkJ6nI1TqAMnFFlK9jPBeSCaVDYYEU`GQcHMfIIiJE\ kLIiMLhOPgPSfQVdSZcTabUdam2Xm3Ym3Ym4Ym4Ym4YeB_ZH`S\ OaLUbE`c7fd0le2gf3cf5_g6Wg8Sh9OhBKiCGiLW_UkRazIawQ\ atXaqcankakrahybfwbdubcsbaqb`obZmbYlgXhlXeqWbuW_Wg\ f6smHpdSmWbjNmgExe5rcBlaHg_NaZSXXYRVcMUhLThJSgHRfG\ QfEPeCOdBNd9Mc7Lb6Kb4Ja2I`1H`DBkP6uJBdDGO7L8AI9CGA\ FEAHBBK9BM7CP4CR2DT0DSAKRJRWghNkcEp_6tWEoYMk_Ugaac\ ch_eYhdNqcDzbHtcLncPhcSbcWXc_RcbLccIVdGMeEDeC4`ICW\ NKRTSMY_IbfHdhGejFflEgnDhpCirCjtEisGisIisJisIloHnl\ GpiFsfaRZcYXVSRMNMDIG4DBFKAQR9`Y8kd7vk6tfDsaJrXQqS\ WpOahVd``fUfhiNYZfzeaNkfH } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 16-03-09 (Beige Blunder [5])
by Jim Muth 16 Mar '09

16 Mar '09

FOTD -- March 16, 2009 (Rating 5) Fractal visionaries and enthusiasts: I named today's image "Beige Blunder" when something went wrong with the coloring. The parent fractal was created when I combined 7.5 negative parts of Z^(-1.3) with 3.25 positive parts of Z^(-3.3) and added (1/C). This parent fractal is basically a huge 'fan'. In fact, that's just about all there is to it. Actually, I think I have a tendency to color my fractal images a bit too intensely, so the more subdued colors of today's image might not be as big a blunder as I implied in the name. Today's scene is located in a tiny valley near the origin of the parent. I rated it at a 5, which might be a bit conservative. The calculation time of 13-1/3 minutes is slow, so I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday began cloudy but soon turned clear and sunny here at Fractal Central. The hazy, sunny afternoon with a temperature of 59F 15C seemed almost like a day in mid-autumn. The fractal cats, well settled after Saturday's excitement, passed the afternoon on their shelf in the sunny window. I passed the day doing as close to nothing as I could manage. FL thought of an antiquing trip, but when I began discussing quantum mechanics, soon forgot it. I'll post the next, but far from the last, FOTD in 24 hours. Until then, take care, and together we can save the world from something. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beige_Blunder { ; time=0:13:21.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+4.253333487671743/+0.3674515879141611/\ 6e+007/1/122.5/0 params=-7.5/-1.3/3.25/-3.3/0/0/0/0 maxiter=18000 inside=0 outside=tdis periodicity=10 colors=000zruWMLWLLWLMWKNWKNWJOVINWJOWJOWKPWKPXLPX\ LQXLQXMRXMRYNRYNSYNSYOSYOTZPTZPUZPUZQUZQV_RV_RW_SW\ _SX_SZ`T_`Tc`Ue`Ug`UkaVoaVvaW_dY_cY`dY_dZZeYZeZYdZ\ YcYXaXW`VW_UV_TVZSUZRTZQTYPSYOSYNRXNQXMQXLPXJPWOOW\ OOWNNVNMVMMVMLVLLULKULJUKJTKITJITJHSJGSIGSIFSHFRHE\ RHDRGDQGCQFCQFBPE8QFAQFBRFDRFERGGSGHSGJTGKTGLTHNUH\ OUHQVHRVITVIUWIVWIXXIYXJ_XJ`YJbYJcYJdOCQB59E6BG6DI\ 6FK6HM7JO7LQ7NS7PU8QW8SY8U_8Wa9Yc9_e9ag9ciAdkAfmAh\ oAjqBlsBnuBpwBryBsxCrxDrxErxErxFrxGrxGrxHrxIrxIrwJ\ qwKqwKqwLqwMqwMqwNqwOqwPqwPqvQpvRpvRpvSpvTpvTpvUpv\ VpvVpvWpuXouXouYouZou_ou_ou`ouaouaoubotcntcntdnten\ tentfntgntgnthntintinrjoqjopjonjomkolkokkoikohlpgl\ pflpdlpclpbmp`mp_mpZmpYnqWnqVnqUnqToqRoqQoqPoqNnrO\ oqOoqPoqPoqQoqQopRopRppRppSppSppTpoTpoUpoUpoVqoVqo\ VqnWqnWqnXqnXqnYqmYrmZrmZrmZrm_rm_rl`rl`rlaslaslbs\ lbskbskcskcskXOIXOJXNJWMK } 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 14-03-09 (Beyond all Limits [5])
by Jim Muth 14 Mar '09

14 Mar '09

FOTD -- March 14, 2009 (Rating 5) Fractal visionaries and enthusiasts: Today's image is as far as we can go into the center of the Hyper-Mandelbrot thing that appeared as yesterday's FOTD. Even at the incredible magnitude of almost 2*(10^14) there is no end in sight to the bottomless pit, which appears to go on to infini- tesimal infinity, with new scenery all along the way. The math- tolerance entry in the parameter file is necessary to assure that the image calculates at the extreme magnitude, which is actually a little beyond the limit of full definition. I named the image "Beyond all Limits" because there appears to be no end in sight. Then I gave it a rating of a 5. It's hard to give a higher rating to the third consecutive view of the same object. The calculation time of 3-2/3 minutes is easy to live with, as is the trip to enjoy the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A rather pleasant but slightly chilly late winter day prevailed here at Fractal Central on Friday. The fractal cats enthusiasti- cally approved the brilliant warm sunlight that flooded their window shelf all afternoon, while I interrupted my work several times to also enjoy the cheerful show. Unless some weekend distraction, such as an antiquing trip, arises, I'll post the next FOTD in 24 hours. Until then, take care, and what will we turn to when we outgrow science? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beyond_all_Limits { ; time=0:03:41.07-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 center-mag=+0.2527592\ 487851626/-0.0002262879051008/1.578045e+014/1/-87/0 params=0/0/0/0/-4.085/0/1e-015/0 float=y inside=0 maxiter=2400 logmap=1319 periodicity=0 mathtolerance=0.05/1 colors=0009iZAgWBdSCaPDYLEVIFSEGPBHN7HL4GK7FKAELDD\ MGCNJBOMAQP9RS8SV7TY6U`5Vc4We8Z_C`VGcQKeKOhFRjAQlD\ PnGOoJNqMMsPMtSOuRPuQRuQSuPUvOVvOXvNYvM_wM`wLbwKcw\ KPQnIANCBO6CPADQEGRHISIKTJMUKOVLQWDSX5VY6Y_6``6ca6\ fX7iS7lN7oI7qEBoFFlGJhHNcIRZJVUJZPKbKLfFMjANn5Or1O\ q2Mp3Lo3Ko4In4Hm5Gl5El6Dk6Cj7Ai79i88h86g95g94iG5kN\ 5lT6n_6oe7ql7rr7giIY`SNSbDJl3BvSnEZoCeqBls9rt8TkC3\ bFDaJN`NWaRe`Vo_ZsaXucUwdLyfCzh4ze3za2zY1zT0xPHsJI\ jKKhILzzMSJOVHPZFQaDSeBTh9Ul7Wo5Xs3Yv1Zw2_w3`w3aw4\ bx4cx5dx5dx6ex7fy7gy8hy8iy9jy9jqDijHhcLgXOgVQhTShR\ ViPXjNZkL`lJbmHdnFfoDhoSRue9zdCwcFubIsaLq`Oo_RmZUj\ YXhX_fWbdVebUh`UkZPaXLSWGIVC8UF7VH7WJ7WL6XO6YQ6YS6\ ZU5_W5_Z5``4ab4ad4bf4bTNNFd8IXKLQzOczRBz0gH4hG8hGB\ iGFiGJjGMjGQkFTkFXlF`lFcmFgmFjmFcXyZasUemPihKnbFrX\ BvSAzUAzWmzXzzZzz_zzazzbzzdzzezzgzzhzzjzzkzzmzznzz\ lzzjzzhzzgzzfzzezzezzdzzc } 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 13-03-09 (On the Inside [7])
by Jim Muth 12 Mar '09

12 Mar '09

FOTD -- March 18, 2009 (Rating 7) Fractal visionaries and enthusiasts: In yesterday's brief discussion I commented that the center of yesterday's image looked interesting. Since then, a quick inspection has shown that the center of yesterday's image is indeed interesting. Today's scene is a blow-up of the eye-shaped object at the center of yesterday's image. At first glance it appears to have 6-way symmetry around the center, but a closer examination will reveal that the symmetry is actually 3-way, with only the opposing arms being similar. An even closer exam will show that there is no symmetry at all. The whole thing is an illusion. So enjoy the illusion of symmetry while it lasts. I suspect that even more interesting things lie deeper in the center of today's image, and I'll check there later today. Unfortunately, we are already near the limit of resolution, so I'm not sure how much deeper I'll be able to go. The rating of a 7 is based mostly on the unusual mathematical aspects of the image. The name "On the Inside" indicates the location of the image with respect to yesterday's image. The calculation time of 1-1/2 minutes is reasonable enough to please a rationalist who enjoys fractals. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will please the more credulous. Winter staged a sudden return here at Fractal Central on Thursday. The fractal cats staged a fine show of sulking when the sun failed to shine on their window shelf in the afternoon. Cassie asked me to turn on the sun; Nicholas just sulked. An extra large treat of tuna restored their normal cat moods. For me the day was busier than I would like to have seen, but not so busy that things got hectic. The next FOTD is due in 24 hours. I expect that it will actually be posted at that time. Until then, take care, and if we found extraterrestrial life, would it prove the believer's view that the universe was inten- tionally created to generate life, would it prove the skeptic's view that extremely unlikely things sometimes do happen, would it prove none of the above, would it prove both of the above, or would it prove nothing at all? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_the_Inside { ; time=0:01:28.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 periodicity=0 center-mag=+0.25275924878512120/-0.000226287905106\ 45/2.05197e+011/1/172.5/0 params=0/0/0/0/-4.085/0/\ 1e-015/0 float=y maxiter=1850 inside=0 logmap=840 colors=000XNsWOsVPsUQsTRsSSsRTsQUtPVvOWxNZvMbuLetK\ gsMjrOkqQlpSloUopUppWrp_tpcupgwpkxpozpszpwzpvzovyn\ uxmuwltukttjssisrhrqgrofqneqmdplcpkcoj_niXmhTlgQpj\ KlgNidQfaTbYW_VZWTaURcRPfOMiLJlIGoFDrCCr8Fr9IrALrB\ OrCTrDYrDbtEgvFlxGqzHvzIzzIzzHamGZhFWcET_DQYEOaFMd\ FKgGIjHGmHEpOHqPKpQKoRInSGmTElUFkWGjYHiaIheJhiKhmL\ hpLkmMlkNliOmgOmePncQnaQn`Ug`Ya_aW_eQfiKmmEsqAqoKo\ mUmkckimigcgeUecLcaQa_UaYZcWchUhmSlrQevO_zTUzYNzbH\ zgBzY5NYCKYIIYPFYVCY`AYg7Ym5YsCXnJXiPWdkH8dIGZINSJ\ VLKbFKiEIcDHZCFTCEODDMDDLEDJEDIFDGFDFGDDGDCGDBHD9H\ D8ID6ID5JD3JD2JD1zzQzzPzzOzzNzzNzzMuzLmzKdvKcrJbmI\ ahH`eH`eH`eI`eJ`eJ`eK`fL`fL`fM`fN`fN`fO`fOadNacNab\ NaaNa`Na_zbZzbYzbmzbzzbzzbzzbzzczzczzczzczzczzczzc\ zzdzzezzfzzgzzhzzizzjzzkzzlzzmzznzzozzmzzlzzkzzjzz\ izzhzzgzzezzdzzczzbzzazz`zz_zzZzzXzzWzzVzzUzzTzzSz\ zwzzvzzvzzuzztzzszzrzzrzz } 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 12-03-09 (The Fourth Dimension [Rating 6])
by Jim Muth 12 Mar '09

12 Mar '09

FOTD -- March 12, 2009 (Rating 6) Fractal visionaries and enthusiasts: Due to a hyper work rush, today's scene in the HyperMandelbrot set is being posted 12 hours late. Once again, I have no idea of what's going on here. All I know about the image is that it's something different, which I have never seen in the perturbed two-dimensional M-sets. And that little thing at the center looks interesting also. I might check it later today. If I find anything interesting there, it might appear as tomorrow's FOTD. Today's image rates only a 6. I named it "The Fourth Dimension" because it is obviously a scene in a higher-dimensional object. The calculation time of 2 minutes will pass in a flash for the true fractal fan. The trip to see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will pass in another flash. Due to the work rush, a pleasant late winter day here at Fractal Central on Wednesday passed almost un-noticed by me. The partly cloudy skies and temperature of 63F 17C kept the fractal cats on their window shelf most all afternoon however. With today's FOTD so late, the next FOTD will be due in only 12 hours. Whether it actually is posted is anybody's guess. Until next time, whenever that is, take care, and stick with those stem cells. They can cure anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheFourthDimension { ; time=0:02:08.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 center-mag=+0.2527592\ 50409/-0.000226286238/1.760141e+007/1/-150/0 params=0/0/0/0/-4.085/0/1e-015/0 float=y maxiter=5000 inside=0 outside=real periodicity=0 colors=000XXKceAjm1dg4Zb6TY8NTAHODBJF5EH09JdJlaPm_\ UnXZoVdpSiqQnrOsrMnmKikJdiI`gHYeGVcFSaEP_DMYEKaFId\ FGgGEjHCmHApODqPGpQGoREnSCmTAlUBkWCjYDiaEheFhiGhmH\ hpHkmIlkJliKmgKmeLncMnaMn`Qg`Ua_YW_aQfeKmiEsm9XOuY\ SiZVY_ZM_aB`XG`SLaNQaJUaEZb9cb4hb0l`5eZ9_XDUVINTMH\ RQBQU5NUCKUIIUPFUVCU`AUg7Um5UsCTnJTiPSdWS`bSWhRRmR\ MqRIpNJjJKcFK_BLT7MP4MK9SJEXLIaMNgORlPWqQ_vOcmMghK\ kcKoZKnUKiPKdSK`VKWZKRaKNdKUhK`lKfoKmsJsvMlqOemQZh\ SSdVL_XEWZ7R`1NRHKIWI9jF0yD8hFGSHNaPTjXZscbkZfdVgY\ QeQM_JHdCDg59jABlFDmKFkPGgUIdZKacLZhTcm_hsgmxnrzov\ zrzzzzzzV2MX1HZ0B`06_14_23_32_41_40Yr7ap5en4im3mk2\ qi1uh0QPKaaSln_wzfntbeoZYiVPdRGZN8UJ53L9vxCrpEoiHk\ bJhWMeOOaHRZATW3X_B`cJcfRgjZjmehlgflhdkibkj`kkZjlX\ jmWjn`ajqeAkZReTg7I1MLVaKx_NwZQvXTuWWtVZsUWnUTiTQd\ TN_SKVPDWRFTSHRTIPUKMVMKWNIYNN_NR`NVbN_cNceNggLnfN\ kfOhePfeQcdS`dTZcUWOSUQOU } 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 10-03-09 (Mandelbrot or Not [7])
by Jim Muth 11 Mar '09

11 Mar '09

FOTD -- March 10, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image might be real or it might be an artifact, but whatever it is, it's interesting. I named it "Mandelbrot or Not?" because it might be a real scene in the Hyper-Mandelbrot set, or it might be an artifact of the rather strange HyperMan- delbrot2 formula that creates it. The scene is located on a filament extending from the northeast shore of the main bay of the large minibrot on the main spike of the parent fractal, which is basically a fancy M-set. The object in the image is a minibrot, or at least it is sup- posed to be one. And at any distance from the minibrot there is nothing unusual in sight, but as the minibrot is approached, something goes awry. The original shore line of the minibrot has become diffuse and spread into the interior, where it forms something entirely new. I guess the thing in the image is better called a hyperminibrot. The rating of a 7 seems about right, considering that this type of effect has appeared several times already in FOTD images. The calculation time of 21 seconds is fast enough to make the effort worthwhile. And as always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies, brisk winds, and a temperature of 54F 12C made Monday a rather pleasant March day here at Fractal Central -- at least the fractal cats thought so. My day was fair enough -- once the work was out of the way, that is. I'll post the next FOTD in 24 hours. Until then, take care, and the best is always yet to come. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot_or_Not? { ; time=0:00:21.44-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 inside=0 center-mag=-1.74593089071/+0.0201490666/328965.8/\ 1/-84.44/0 params=0/0/0/0/-4.18/0/1e-015/0 float=y maxiter=15000 outside=real logmap=55 periodicity=0 colors=000k0Ah0Ae0Ab0A_0AX0AV0AR0BO3CN3IQ3NS3TW3SZ\ AXYHXYJWXLWYJXZHXXGYVFZU8ZR2ZWAa_HdcPggWilclpjotrr\ xytmtlbpdSlXHhP6dHBiJGnLKrNZuelwwbZdTANQFPOJQMNSKR\ THWUF_WDcXBgYVdcnbikhjhnketlTmhGfdI`ZKWUMQPOLKQFFR\ AAgBVxCnvLdtTWr`NqhEceOQcYDagKchQdiWejafkhhlnimtjn\ zknrmpknrdptYqvTrpOskKseFt`BtWptporkoqfnpannYmmTml\ OmkKkjGjjCii8hi4gi0ag2Xe4Rc6Mb7H`9BZB6XD1WEATCIRBQ\ OAYM9eJ8mH7oN6pS6qX6ra6tf6uk6vp6wu6zwEzzMzzTzz`zzh\ zzozzlzzizzfzzgz0gz0cz0oz0zz0zz0zzcMzcVzmXxzWcWVhb\ UmhUrkcvvmzzzUXOJ9LQBIXDFcFCjHAmMCpRDsVE7Qd9WYB`SC\ fMEkGFpAl0zSMlzg_m`TmVNmPHmJBmG9mE7zC6z94z73z51z30\ GeiMOPupqgmoUjmNSzMVxLXvK_tJarIdpHznktD`pPQl`KewIf\ sHgonP1GzJGzOGzTzNYzVbzagzbizcjzzjzzkzzkzzkzzlzzlz\ zgzzjzzkzzlzzEzzJzzNzzSzzWzz_OzdKzhbzpRznkzyUzaNzg\ nz`izbezc`zeXzfTzhOziKzkAzBBzGCzLDzQDzUEzZizLjzSkz\ Zlzemzlnzslztkztjzuizuhzv } 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 11-03-09 (Obscured Ogive [Rating ?])
by Jim Muth 11 Mar '09

11 Mar '09

FOTD -- March 11, 2009 (Rating ?) Fractal visionaries and enthusiasts: A tiny bud appears on the east edge of the circular hole at the center of the main bay of the pseudo-minibrot in yesterday's image. This tiny bud is the brilliant background object in today's image. The bright white arc at the bottom of the image is part of the circle that appears in the main bay of the minibrot of yesterday's image. This figure, with its ogive-arch in the background and converg- ing arms in the foreground, is quite prominent in the minibrots of the HyperMandelbrot sets. These scenes appear to be non-crit- ical, yet I have never been able to find any starting points that would clear away the arms and reveal the true shape of one of the arches. Perhaps more investigation is necessary, or per- haps there is no unique 2-dimensional critical Mandelbrot plane in an 8-dimensional Julibrot figure. I named the image "Obscured Ogive" purely as a description. Since I have no idea how successful I was at revealing the true scene, I was unable to give the image a rating. When the image calculates from the parameter file, it starts off as though it will finish in less than a minute. But don't be fooled. The calculation soon slows to a crawl, and a full 15 minutes will be needed for the calculation to finish. I recom- mend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, occasional rain sprinkles and a temperature of 43F 6C spoiled Tuesday here at Fractal Central. The fractal cats sulked and soon turned their thoughts to tuna. In my department things went about average. I'll post the next FOTD in an average time of about 24 hours. Until then, take care, and an ogive is a pointed gothic arch. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Obscured_Ogive { ; time=0:15:25.72-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 outside=real center-mag=-1.74593077988/+0.02015008205/1.95e+007\ /1/5.56/0 params=0/0/0/0/-4.18/0/1e-015/0 float=y maxiter=15000 inside=253 logmap=-534 periodicity=0 colors=000DKdCKeBKfAKg9Kh9Kk9Kj9Ki9KhdKgcKfbKeaKd`\ Kd_KcZKbYKaXK`WK_VKZUKYTJYSIXRHWQGVPFUOEUNDUMCULBU\ KAUJ8TI7SH5RG4QF2PE1OD0NC0MB0LA1K92K83K83K84K85L86\ M77N79O7BP7DQ7FR6GS6HT6IU6IV6JW5KX5LY5MZ5N_5N`4Oa4\ Pb4Qc4Rc3Qc4Rc5Rc6Sc7Sc8Tc9TcAUcBUcCVcDVcDWcEWcFXc\ GXcHYcIYcJZcKZcL_cM_cM`cN`cOacPacQbcRbcSccTccUdcVd\ cVdcWecXecYfcZfc_gc`gcahcbhccicdicdjcejcfkcgkchlci\ lcjmckmclncmncmocnocopcppcqqcrqcsrctrcuscvseztgxsi\ wskvsktsjsshrsgqrforenrcmrblrajr`irZhqYfqXeqWdqUcq\ TaqS`pR_pPZpOXpNWpMVpKTpJSoIRoHQoFOoENoDMoCFp5Is8L\ rBNqDQpGSoIVnLXmN_mQbmTdmVgmYim_lmbnmdmmemmflmglmh\ kmikmijmjjmkimlimmhmnhmnhmogmpglqfkrfjseisehtdhudg\ vcgwcfxcfxbewbewbdwadwacvacv`cv`bv`bv_bu_au_auZauZ\ `uZ`tY`tY_tY_tY_tXZsXZsXZsWYsWYrWYrVXrVXrVXrUXqUXq\ UWqTWqTWqTWpTWpSWpSWpSWpRWoRWoRWoQWoQWoLUnLUmKUmJU\ mIUmHUmGUmFUmEUmszzY_VY_V } 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 04-03-09 (Astro Iterations [6])
by Jim Muth 09 Mar '09

09 Mar '09

FOTD -- March 04, 2009 (Rating 6) Fractal visionaries and enthusiasts: Heaven only knows why I named today's image "Astro Iterations". The parent fractal, which came about when I subtracted 2 parts of Z^(-1.8) from 2 parts of Z^(0.75) and added (1/C), resembles nothing as much as a tiny rubber duck. Today's image is located on the duck's back, at the base of its rather lengthy neck. Much of the figure-eight-shaped network in the image consists of 'inside' stuff made visible by the 'bof60' inside fill. With the regular work being rather heavy here at FC on Tuesday, I had little time to devote to the coloring, limiting the image to a rating of 6. The calculation time of 3-3/4 minutes borders on slowness, so I recommend a speedy trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image at leisure there. Sunny skies made the outdoors appear pleasant here at Fractal Central on Tuesday. But this was true only from indoors. When one went outside, the biting north wind and temperature of 19F -7C brought the truth home -- it is still winter, and will be for almost three weeks. The fractal cats did not worry them- selves about the calendar. They spent the entire afternoon enjoying the warm sunlight streaming in the window and warming their watch-shelf. And I spent the day working. With the work now caught up, the next FOTD is quite likely to be posted in 24 hours. Until then, take care, and walk with confidence. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Astro-Iterations { ; time=0:03:44.91-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.594363042293016/+0.011311085972806/\ 122518.3/1/-150/0 params=2/0.75/-2/-1.8/0/0/0/0 float=y maxiter=950 inside=bof60 periodicity=10 colors=000ZPn_Rm_Tm`Vm`XlaZla`lbblbdkcfkchkdjjdlje\ njepjdqicricshbshbtgaug`vg`vf_wf_xeZyeZyeZqhZljZfl\ Z`oZVqZPsXNoWMlUKiTJfSHcQG`PEXNDUMBRLAOJ8LI7IH6FG5\ GF5GF5GE5HD5HD5HC5IB5IB5IA5JA5J95J85K85K75K65L65L5\ 5L45M45M35M35M57N68O7AP8BQ9DRBESCGTDHUEJVFKWHLXINY\ JOZKQ_LR`NTaOUbPWcQXdRYdSZeTZfUZgV_hV_iW_jX`kY`lZ`\ mZ`mY`nXanWaoVaoPYpKUpFQqAMqBOnCQlDSiETgFVeFXbGY`H\ _ZIaWJcUKdSKfPLhNMiLNkIOmGmrEhnEclEZkEUjEWhEXgEZfE\ _eEadEbbEdaEe`Eg_EhZEjYEkXEmWEnVEoUEpWEpXEqYEqZEr_\ Er`EsbEscEtdEteEufEugEuhEvgFvfFvfFveGveGvdGvdHvcHv\ bHvbIvaIvaIv`Jv`Jv_Jv_JtUGrODpIAnC7l64j02i25i37i4A\ f6Cc7EzUHvPJoKLlFOiDQiFSiGViHXiJZiKaiLciMejNckOblP\ `mQ_mRZnSXoTWpUVpVTqWSrXRsYPsZOt_Nu`LvaKvaJtbKscKr\ cKqdKpdLoeLneLmfLlgMkgMihMhhMgiNfiNejNdkNckOblOalO\ `mO_mOZnNYnNXnNWoMVoMUoMTpLSpLRpLQqRPqdOqzBfzFYzJO\ ANF8PGHRHQTIZVJgXJoYLnZNn } 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 09-03-09 (Abyss of Destruction [No Rating])
by Jim Muth 09 Mar '09

09 Mar '09

FOTD -- March 09, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image with the ominous name was created with the Mystic2 formula, a formula that does God only knows what. I certainly don't know. One thing I do know is that the image consists entirely of 'inside' stuff brought to life by the 'bof60' active inside fill, which colors the points according to how close they come to the origin in their wanderings. The Mystic2 formula draws nothing but blank circles of radius 1. All the action comes from the trapped areas inside the circles. As today's image shows, the things that might be done with the areas inside the circles are endless. The image reminds me of the cover of a cheap "terror" novel so I named it "Abyss of Destruction", a name that might be given to such a story. I gave no rating because I consider it unworthy of one. The image is sensitive to the values of the parameters, particu- larly both parts of the p3 parameter. The fast speed of the image makes experimentation very easy. Changing the function totally changes the image, as does changing the inside fill. So actually, an entire range of images are waiting to be made manifest by tweaking these parameters. The calculation time is only 25 seconds on my P4-2000mhz unit, a time that will bring satisfaction to those, if any, who might be disappointed by the result. Of course, calculation may be entirely avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A partly cloudy springlike day with a temperature of 75F 24C when I left Old Fractal Central at 1:00pm on Sunday turned into a raw overcast drizzly day with a temperature of 48F 9C by the time I reached New Fractal Central at 4:30pm. The new fractal cats greeted me when I arrived, caught a scent of Thomas, the old fractal cat, and asked what I had been doing for the past 32 hours. I answered their question with a double treat of tuna and cheddar cheese. The next FOTD will be posted in about 12 hours. Until then, take care, and let me know when the world ends. I don't want to miss it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AbyssOfDestruction { ; time=0:00:25.45-SF5 on P4-2000 reset=1960 type=formula formulafile=jim.frm formulaname=Mystic2 function=cotan passes=1 center-mag=0.0541584/-0.60902/5.821744 logmap=yes params=-0.065/-5.122/6.003/-6.845/5.664/0.303 float=y maxiter=300 inside=bof60 periodicity=10 colors=000zzzwvptrcpmYlhWhc0dZ0`U0XP0TKFNFKICI8DG0\ DE0DC0BC0CC0DC8DDCEFECFOEGIGMHHOFMTJShM_mQgrTmvZrw\ `uvdwuhwtkrsglrlhqpfpqelmchjbcfa_b`WZZSVYORXKOWFKU\ BGT7LU9QVAVWC`YEeZFj_Ho`ItaKpbMlbNhcPdcR`dSXeUSeWO\ fXKfZGg`Cga8hcFkZ4hdoNXdLSUKOJIK6FF9HGBJGELHHNIKPI\ MRJPTKSVKVXLXZM_`MbbNedOgfOjhPqjRmjQijOdiN`iLXiKTi\ IPiHKhFGhEChCCiBDkADl8En7Eo6Ep5Fr3Fs2Ft1Hu7IuDKuIL\ vOMvTOvZPvcUgT_TJdE8iCAmACr8Er9DrACrBBqCAqD9qE8qF7\ qG6qH5qI4pJ3pK2pL1pM0pM0mO2kP4hR6fS8dT9aVB_WDYXFVZ\ HT_JR`KObMMcOP_NSWMVSLYOL`KKcGJfCIi8HiAIhCJhEKgGLg\ IMfKNfMPfOQeQReSSdUTdWUcYVc_WxoWupWrpWoqWlrWirWfsW\ ctW`tWYuWVvWSvWPwWNwWMtXLqXKnXKlXJiXIfXHcXHaXGZXFW\ XETXERXDOXCLXNZbXkigyohwkjtgkrblpZnnVokRqiNrgJseEu\ bAv`6s`6q_5n_5kZ5iZ4fY4dY3aX3ZX3XW2UW2SW2NR8JMDFII\ BDO79T34YCAVLFSULPaRLjWIsaFs`Hs_Ks_MtZPtYRtXTtXWtW\ YtV_uUbuUduTguSipRjjPkeOl } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END PARAMETER FILE=========================================

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FOTD 07-03-09 (Leftover Goodies [6])
by Jim Muth 06 Mar '09

06 Mar '09

FOTD -- March 07, 2009 (Rating 6) Fractal visionaries and enthusiasts: The curious thing about today's fractal image is that its parent fractal is not there at all. The parent consists of a few lopsided circles and crescents well off the screen to the right. But a deeper investigation reveals tiny clumps of detail around these crescents, and today's image shows that this detail is infinite in the true fractal manner. Despite appearances, the image is not located on the X-axis of its parent. It lies 0.01+ below the X-axis, which therefore re- quires an angle of 178.5 degrees to make the minibrot perfectly horizontal. I named the image "Leftover Goodies" when, studying the boring parent, I had the impression of something that once was there but now is gone, leaving a few splotches to carry on. Then I decided that the splotches were a bit too boring for a rating above an average 6. The calculation time of a mere 28 seconds will waste no one's time even if they find no enjoyment in the result. The finished image is posted, for immediate gratification of course, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun shone and the temperature reached 64F 18C here at Fractal Central on Friday. The fractal cats were totally happy with the conditions. I was a bit too busy to enjoy the early spring however. I'll be back at Old Fractal Central from late Saturday morning until early Sunday evening, keeping Thomas, the one remaining old fractal cat company, while my sister is away visiting an old friend. Because of my absence, the next FOTD will not be posted before March 9, and possibly not until March 10. Until next time, take care, and have a peaceful panic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Leftover_Goodies { ; time=0:00:28.15-SF5 on P4-2000 reset=2000 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+6.014911330674471/-0.0126065468392344/\ 1.536035e+010/1/178.5/0 params=1/1000/-100/-1/\ -0.95/0/0/0 float=y maxiter=300 bailout=25 inside=0 logmap=29 symmetry=none periodicity=10 colors=000bev`mwZkxXtyWzzUgeTVMRJ1U_dXSm_LreEwm7zz\ FzzZzLVEKSEIOFHLFFHFEEFCAFB7FA4F97I8BL7EN6HQ5KT4NV\ 3QY3Tq8PzCLVHGTLCQP8NT4LU8LWBLXFKYIK_MJ`PJaTJbWJbX\ IfZKiaLmcNpeOibMb_JWXHPUEIRCBPACSFDVKEYPF`UGcZHfcI\ ihJlmKorLqvKlsKgqKcnJclJciJcfJcdJcbJc_IcYIcVKcWzcY\ zcZzc_zc`zcbzcczcdzcezcgzchzcizcjzckzcfzdbzeYzeUzf\ PzgKzhGziBzj7zk7zl7zm6zn6zo6zp5zq5zr5zs5zt5zu5zv4z\ w4zx3zy3zz3zzFzzQzzRzzSzzTzzTzzUzzVzzWzzWDzXCzYBzY\ AzZEz`HzbLzdOzfRzgOzcMz_KzX8z8IzTGzPEzMBzI9zE6zB4z\ 72z3BzKAzI9zG7zD6zB4z83z62z41z2gzweztczrazo_zmZzjX\ zhVzeTzcRz`PzZNzWLzUKzRIzPGzMEzKCzHBzF9zC7zA5z73z5\ 1z2XziVzgUzeSzcRz`PzZOzXMzVLzTJzRIzPGzNFzKDzICzGAz\ E9zC7zA6z84z63z41z2YzHWzGUzFSzEQzDKzCMzBKzAJz9Hz8F\ z7Dz6Bz59z47z35z23z11z0RzHKzDDz86z4PzDJzACz66z3gz9\ 1zm1zk1zh1zf1zd1za1z_1zY0zV0zT0zR0zO0zM0zK0zH0zF0z\ D0zB0z90z70z40z2hzsfztdzu } 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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