September 2006 - Fractint - mailman.xmission.com

FOTD 16-09-06 (Circle With Horns [5])
by Jim Muth 16 Sep '06

16 Sep '06

FOTD -- September 16, 2006 (Rating 5) Fractal visionaries and enthusiasts: OK. So today's FOTD is 8 hours late. What of it? If I needed an excuse, I would point to the small but urgent job that came in unexpectedly yesterday morning. The missing FOTD discussion is probably for the best, since I had a long statement about reality planned for the Philofractal list, which would likely have spoiled my already tarnished reputation. (After all, nothing upsets rational-thinkers more than the suggestion that the foundation of their world view, the real physical world of nature, might not be as real as advertised.) As it is, we will have no philosophy today. (It might come later.) We must settle for a brief description of today's image, which is a view in the Oblate direction of a Seahorse Valley. But it is not the familiar valley. To find today's valley we must go to the large midget at -1.75 of the Mandelbrot set and then find that midget's largest sub-midget, which is located around -1.785 of the M-set. Today's image shows a side view of the Seahorse Valley of this sub-midget. The scene was stretched in the vertical direction by a factor of 30 to bring it to its state of viewability. (Actually, this is measured by a compression factor of 0.033 in the horizontal direction.) If the image were not manipulated, we would see nothing more than a series of featureless horizontal stripes. I gave the result a rather surreal name -- "Circle with Horns". That's what I see when I look at it. I rated the image at a 5. It had far too little effort put into it to rate anything higher. Rendering the image will demand very little valuable time. The included parameter file finishes in 27 seconds. The unlucky ones with over-qualified computers can find the image on the fotd web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Things got unexpectedly very busy here at New Fractal Central on Friday, with a job that had to be delivered by the week-end. The fractal cats became sulky when they got too little atten- tion. They didn't concern themselves with the mostly cloudy day and the occasional light showers. Toward sunset a perfect rain- bow formed in the east, which went completely un-noticed by the duo, who were chasing each other madly up and down the long hall- way at the time. In my department, the job was finally finished and delivered. And nothing more is in sight, at least at the moment. It looks like the next FOTD will appear in around 16 hours. Until then, take care, and be glad you are real. (Or are you?) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Circle_With_Horns { ; time=0:00:27.19--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/0/1840.308/0.033 params=0/90\ /2/0/0/0/-1.78575/0 float=y maxiter=50000 inside=0 logmap=23 symmetry=xyaxis periodicity=10 colors=000QmbYnddpflrhscjlahe`gZYfTXdMXcFYe9_aFaXL\ cSMeNKcKD`EEYCERBEM9EG8EB6E65HD6JJ7MQ7OW8Qb9Th9VoA\ XuAYmDZfFZZI_SK_KN`DP`6RfDSkJTpQUuWVzaVteSnhQhkObo\ MXrKRuILxGInVFeiJfbNgXRhRViLZjFaj9blCbmEcoGcpIdrKd\ sMeuOevQ`wVWwZRwcMwgHwkCwp7wt2wx8srDplIlfNi`SeVXbP\ a_JgaLldNqfPpdRobTo`UnZWmXYmVZlU`lSakQcjOejMfiKhiJ\ ijKhjLgkLfkMfkMelNdlNdmOcmObmPbnPanQ`nQ`lRZkSXjTVh\ TTgURfVPdVNcWLbXJ`XH_YFZZDYZBZ_DZ`EZaFZbHZbI_cJ_dK\ _eM_fN_fO`gP`hR`iS`jT`jUbQSQVUDZWPTP_OJ`dV`ufKfLQw\ NCGuSPdgXOwd7wOQw8gp9Zj9Qd9HeGOfMUgT_hZekYamYYoYUq\ YQlWZgUgcTpS`hGg`4nTXR`y3gf2ZO2Q62HK8FXEEjKCwPBS_2\ EP91FGcN9R_BFkD3wE2pO2iX2bf2XoqZXRQtLpDMm_WsKTpXQm\ i__GJsWKpbLniMlpuG8iRPY`eC1_IOkzjGfja0qs6otCmuIkvp\ H0fRKX`cBdiEfmHgpKisSf4QhNOidCFvGQvK`v5nGBlVHkh`s3\ 3tCApSHmgaKNUYdALQT0DRGTPWgrFEbV`JJFLTUMahuP6c_Xex\ 5hDj`PnU_rdcl_eoWgqBiZJk` } 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 15-09-06 (A Whatsit Midget [6])
by Jim Muth 15 Sep '06

15 Sep '06

FOTD -- September 15, 2006 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a most curious fractal hole. But it most certainly is not a Mandelbrot midget. And it certainly is not a Julia set, though it does have some Julia characteristics. Nor is it an Elliptic set, a Rectangular set, a Parabolic set, or an Oblate set. It is actually a set in a slice oriented about half way between the Parabolic and Elliptic directions. As the value of the center point of today's image indicates, the scene is located in the vicinity of the large midget located at -1.75 of the Mandelbrot set. Since we are exploring 4-D space when we examine the Julibrot, it is impossible to describe the exact direction from the -1.75 midget in which today's scene lies. The thin straight yellow line at the edge of the solid inner area is actually one of the Mandelbrot valleys of the large -1.75 midget sliced from the side. It seems counter-intuitive that, from the side, a Mandelbrot valley should appear as a straight line, but the Mandelbrot aspect of the Julibrot is actually shaped like a nest of 4-D hypercylinders, which, like 3-D cylinders, appear straight when sliced parallel to their length. I named today's image "A Whatsit Midget" because I have no idea what else I might name it. The rating of a 6 seems about right for an image that is more a mathematical curiosity than an artistic triumph. The render time of a little over 1/2 minute should make the task of rendering almost enjoyable. And the job of rendering may be eliminated entirely by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, fog on the hills, occasional rain, and a tempera- ture of only 63F 17C made conditions far less than ideal here at New Fractal Central on Thursday. But the fractal cats, who can look outside but are not permitted to go there, do not concern themselves with mundane things like weather. They spent the day searching for trouble. Luckily, they failed to find much of it. My day was near normal, and it looks as though the next week or so will remain uneventful. One of these days I'm going to give up graphic design work and start earning my living by selling fractals. Oh well, we can dream, can't we? The next FOTD will appear in 24 hours. Until then, take care, and the secrets of the universe may be hidden in these fractals -- if only we had the key to unlock the secret door. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Whatsit_Midget { ; time=0:00:38.56--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-xz-yw-new passes=t center-mag=-0.16772097072767390/-1.749397401235292\ 00/514.2573/1.444/-120.75/33.166619765944354 params=0/49.68/2/0/0/0/0/0.0001 float=y maxiter=5000 inside=0 logmap=5 periodicity=10 colors=00000H00M01S02X03V04U05T06S17K28L39M4AN5BO6\ CP7DQ8ERAFSCGTEHUGIVIJWJKXLMYNOZPR_RU`TXaV_`WbaUdb\ SgbQhbPibNjbLlcKncIocGpcFqcDodBndAnd8md6kd5ic4g`3f\ Y3eV2dS2cP1bO1aO0aM0aE7aFEaJKaNN_RQYSTWQWUOZSM`QKb\ OGaME_KCYHAW38U86S78Q6AO50M40K45I6AG8FEAKCBP0ESCHV\ CKYCN`CQcCTfEUfGUfIVfLWfNXfPYgRYgTZgV_gY`m_bradvcg\ zejzgmzjozloznpzpqzrrzrrzpoznlzojzphzqdzrbzrZzrWzq\ UzpWzoYznbzmgzmfzmizmlzmozmrzmszmuzlsykoxjkwigvhcu\ g_tfWseSrdOqeKpeGoeDnfCmfAlg8kg6kg5kh3lh1lh0lg3mg5\ ng8ngAofDofFpfHqfKqeMrePreRseTtdWtdYud`udbvddvectf\ csgcrgcqhcoicnicmjclkcjkcilchmcgncencdoccpbbpbaqb_\ rbZrbYsbXtbVubUubTvbSwbQwbPxbOybNybMwcNvdOtdPseQrf\ RpfSogTngUlhVkiWjiXhjYgjZfk_dl`clabmb`mc`nd_oeZofY\ pgYphZqe_qb`r`arYasWbsTbtRbtOcuLcuJdvGfvEhwBjw9lx6\ nx4py5ry5ty6vy6xy7zy7zy8zy8zy8zy9zy9zyAzyAzyBzyBzy\ CzyCzyCzyDzyDzyEzzEzEBzDB } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 14-09-06 (Fractal Potentia [8])
by Jim Muth 14 Sep '06

14 Sep '06

FOTD -- September 14, 2006 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows a new view of the large midget at -1.75 on the X-axis of the Mandelbrot set. As far as I know, today's image is the first time this midget has been seen in such an unusual apparition. The image shows the midget as it appears when viewed in the Elliptic orientation. But the question of which part of the image is the actual midget immediately arises. Is the midget the well-defined triangular hole at the center, or is it the broad dark band with bright edges partly visible in the background? Actually, the triangu- lar hole at the center is the midget. The background band shows some of the potential perturbed versions of the midget that become visible when imag(z) is varied. These potential per- turbed midgets are what inspired the name "Fractal Potentia". The rating of an 8 would have been a 5 or 6 if I had not stumbled upon the color palette that works so well with the image. The extremely brief render time of only 11 seconds is one of the best fractal bargains of all time. Those who do not do their own rendering but still enjoy fractals may see the -1.75 midget with its array of potential perturbed midgets by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday started with light rain here at New Fractal Central. The rain ended by 11am, but the clouds persisted for the rest of the day, holding the temperature to 64F 18C. The fractal cats didn't mind the less-than-ideal conditions. They were too busy chasing a ball of aluminum foil all around the first floor. My day was slower, but still a bit busier than I prefer. The next FOTD will appear in 24 hours. Until then, take care, and things may not be as they seem. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Potentia { ; time=0:00:11.48--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=-1.76526/0/2.684939/5.9269 params=90/0/2/0/0/0/0/0.0001 float=y maxiter=1000 inside=0 logmap=18 symmetry=xaxis periodicity=10 colors=000AAF7LV5Qe8RfASfCTfEUfGUfIVfLWfNXfPYgRYgT\ ZgV_gY`m_bradvcgzejzgmzjozloznpzpqzrrztrzpnznlzojz\ phzqdzrbzrZzrWzqUzpWzoYzn_zmgzmfzmizmlzmozmrzmszmt\ zBj6JdGQ_PXUZcPgcOgcMgdKhdJheHieFieDifCjfAjg8kg6kg\ 5kh3lh1lh0lg3mg5ng8ngAofDofFpfHqfKqeMrePreRseTtdWt\ dYud`udbvddvectfcsgcrgcqhcoicnicmjclkcjkcilchmcgnc\ encdoccpbbpbaqb_rbZrbYsbXtbVubUubTvbSwbQwbPxbOybNy\ bMwcNvdOtdPseQrfRpfSogTngUlhVkiWjiXhjYgjZfk_dl`cla\ bmb`mc_ndZoeXofWpgVphWqeWqbXr`XrYXsWYsTYtRYtOZuLZu\ J_vG_vE_wB`w9`x6`x4ay5by5by6cy6dy7dy7ey8ey8fy8gy9g\ y9hyAhyAiyBjyBjyCkyCkyClyDmyDmyEnzEnzFozFpzGpzGqzG\ qzHrzHszIszItzJtzJuzKvzKvzKwzLwzLxzMyzMyzNzzNzzNhx\ YRwhAvs9sq9pp8mo8kn7hm7el7bj6`i6Yh5Vg5Sf5Qe8RbAS`C\ TZFUXHVVJWTMXQOYOQZMT_KV`IX`GYZKZXO_VS`TVaRZaPbbNf\ cLidJmeHqfFuqiEk_DdPCZFCYEEYDGYCHYBJYAKY9MY9NY8PY7\ QY6SY5TY4VY4WS6PN8JIADDB7 } 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 13-09-06 (Side Attraction [6])
by Jim Muth 13 Sep '06

13 Sep '06

FOTD -- September 13, 2006 (Rating 6) Fractal visionaries and enthusiasts: The continuing rush on Tuesday meant anther hurried FOTD image. Today's rather unusual scene is a feature of the Julibrot. It is located some distance to the viewer side of the large midget at -1.75,0 of the Mandelbrot set. It is sliced in he Oblate direction, which is the orientation determined by the real(z) and imag(c) axes of the Julibrot. I named the image "Side Attraction" because it is located to the side of the Mandelbrot set. I rated it at a 6 because it is just interesting enough and colored well enough to deserve that rating. The render time of under 1 minute means that those who rendered the image themselves and are disappointed by it, will not have wasted much computer time. Those who don't render may find the image already rendered on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The cloudy, chilly weather here at New Fractal Central on Tuesday, with a temperature of only 63F 17C, worried the fractal cats not the least. They are showing all signs of being permanent indoor cats, which is the healthiest, but perhaps not the happiest life for a cat to lead. In the evening, they romped and enjoyed their treats of tuna and cheese. For me, the current rush is rapidly coming to a close. The current one went well enought, but I hope these rushes don't come too often. I fear I'm getting too old for this kind of stuff. The next FOTD is quite likely to appear as scheduled in 24 hours. Until that glorious moment, take care, and philoso- phize mightily. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Side_Attraction { ; time=0:00:57.27--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=-1.04707416/+0.005111185/225.2066/0.4584 params=0/90/2/0/0/0/-1.7475/0 float=y maxiter=10000 passes=1 inside=0 logmap=yes periodicity=10 colors=000AVKAYFA_AAb5Ad1Aa4A_7AY9AVCATEARHAOJAMMA\ KOAENAFPAERAASACTAETAGTAIUAKUAMUAOVAQVASV9UX8WX7YX\ 6_XBa`FcbJeeNghSikWkm_mqaoscqzeszguziwzkxzmyzhzzcS\ ZZGQU5IP6HK6HF7HJ7HN7GR8GU8GY9Ga9Fe9FiAFmAFt6CpAFl\ EIiIKeMNaQPZUSVYURaXOeZMdaKccIbfGahF`jD_mBZo9Yr7Xt\ 6XvAWtDVrGUqKToNSnQRlTQkXPi_OhbNfhOdeNecNeaMe_MeYM\ eWLeULeSKcSLeSMfSNhSNiSOjSPlSPmSQnSRpSSqSSrSTtSUuU\ WxSUvRStQQrPOqNMoMKmLIlKGjJEhHCfGAeF8cE6aE5JD5`43n\ C5qL7vJ6tI6rG5pF5nE4mC4kB3i93g82e72dOIacYZsmWaqbLu\ hLuhLvhLvgLvgLvfLvfLveLveLveKtdKwcJxbUyaUz`Uz_UzZc\ zYczXcz0czWmzVmzUmzTmzSwzSwzRwzQwzPzzOzzNzzMzzLzzK\ zzJzzIzzHzzGzzFzzEzzEzzDzzCzzBzzAzz9zz8zz7zz6zz5zz\ 4zz3zz2zz1zz0zzgzzfzzezzezzdzzczzczzbzzazzazz`zz_z\ z_zzZzzYzzYzzXzzWzzWzzVzzUzzUzzTzzSzzSzzRzzQzzQzzP\ zzOzzOzzNzzMzzMzzLzzLzzKzzJzzJzzIzzHzzHzzGzzFzzFzz\ EzzDzzDzzCzzBzzczzZzzUzzP } 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 -- 12-09-06 (Elliptic Elephant [4])
by JimMuth＠aol.com 11 Sep '06

11 Sep '06

FOTD -- September 12, 2006 (Rating 4) Fractal visionaries and enthusiasts: I draw attention to today's fractal, which returns us to East Valley, where we check a Mandelbrot midget that lies deep in the trunk-spiral of an elephant. This elephant itself lies fairly deep in the valley. To be a little different, I have calculated the Elliptic view of this midget. Since it is not a Mandelbrot view, I have not violated my promise to have no Mandelbrot midgets during the month of September. At this orientation, the midget appears as little more than a shapeless hole. But the pattern around it remains intact, fairly shouting to the world that this is a scene in East Valley. I named the image "Elliptic Elephant", though no elephants are visible in the frame. I rated it at a meager 4. After all, haven't I already done this kind of thing numerous times? The 6-minute calculation time may be avoided by downloading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Clouds and cool temperatures here at New Fractal Central on Monday bothered the new fractal cats not at all. They spent the day chasing each other up and down the long hallway and occasion- ally checking the window to see if any squirrels or birds were in sight. By 4pm they were ready for their treats -- tuna for Cassie, cheese for Nico. My day was quite busy, which explains the almost-automatically found fractal. The rush will peak tomorrow, which might or might not produce a FOTD for the 13th. But by Wednesday the job will be delivered and the FOTD for the 14th is almost a sure thing. Until next time, which will be in either 24 or 48 hours, take care, and remain fractally correct. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elliptic_Elephant { ; time=0:06:15.34--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip center-mag=0/0/8.073738e+009/0.01316/-89.804935684\ 2955717/89.7960595356130682 params=90/0/2/0/0.2525\ 320556995364/0.0002050585540034/0.2525320556995364\ /0.0002050585540034 float=y maxiter=7500 inside=0 logmap=1032 periodicity=10 colors=000KZEJYFJXFIWGIVGHUHGTIGSIFRJFQJEPKDOLDNLC\ MMCMMELPFLRGKTHKWIKYJJ_KJbLIdMIfNIiOHkPHmQGpRGrSGt\ VIoYKj`MebOaeQXhSSkUNmWJpYEs_9u`5sa8qaAobCmbFkbHic\ JgcLecOcdQadS_dVYeXWeZUe`bZQjSFrM4qO8qPBpQEpRHpTLo\ UOoVRoWUnYYnZ`m_cm`fmbjlcmldplesmbtn`toZtpXtqVtrTt\ sQutOuuMuvKuwIuxGuxEup9si5qb1pd2ke3gg3bh4Zj5Uk5Qm6\ Ln7Ho7DfGFYOGQWIHdJ8lL0tM3qN6nN8lNBiNEfNGdNJaOMZOO\ XORUOUROWPOTQQQQRNRSLRTISUFSVCTWATXj2Ah8CgDEeIGdNI\ bSKaXM`aObcRcdTdfVegXgiZhj`ilcjmelogmpinrkosmnrjnq\ gmpdmoamoZlnWlmTklQkkNkkLhhMeeNbbP__QXXRUUTSRUPOVM\ LXJIYGFZDC`A9a86bB7_E7XH7UK7RN7OQ7MT8JW8GZ8Da8Ad87\ g85dC9bGC`KGZNJXRNUVQSYUQaXOe`MhcNedOcdOadPZdQXdQV\ dRSeSQeSOeTLeUJeUHeSGcRGbPG`OG_MFZLFXKFWIFVHFTFESE\ ERCEPBEOAENEqPHoQJmRMlROjSQhSTgTVeTYdU_bUa`Vd_VfYW\ h_WdbZaeaZgdVjgSnjPqmLtpIwsFzvCzxEztGzpIzmKziMzeOz\ bQzZSzWUzSWzOYzL_zH`zE_zV } 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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Re: FOTD 06_07_31
by jackoftradez＠comcast.net 11 Sep '06

11 Sep '06

I have not explored much East ("elephant") valley, thinking it would be generally lame, as some earlier work suggested a long time ago. Not true! Among other things, it seems to be the only area of the MSET where the "infinite" spirals are NOT! They actually eventually arrive at something, usually a minibrot. And some interesting unique patterns too. I need to check more into this. I dispute the rating of 5 for Jim Muth's FOTD 06_07_31 ; I would give it more. The colors could be better however IMHO. I did a zoom-in to the target image, only thing changed is the color and I used logmap=2 (as always). Loox much better. Posted: http://www.fractal-animation.net/vid/evz320.zip 6.0 MEG http://www.fractal-animation.net/vid/evz640.zip 18.5 MEG Stay Amazed JoTz

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FOTD -- September 11, 2006 (Elephant Trickery [6])
by JimMuth＠aol.com 10 Sep '06

10 Sep '06

FOTD -- September 11, 2006 (Rating 6) Fractal visionaries and enthusiasts: A bit of four-dimensional trickery is displayed in today's image, which tries desperately to be a Julia set of East Valley but never quite makes it. If the imaginary p1 parameter had been 90, we would have had a Julia set. As it is, we have a slice rotated a mere 0.2 degree toward the Elliptic direction, but that tiny rotation makes a world of difference. The basic outer shape of an East Valley Julia set is obvious, and the goofy eyes and noses are well represented, but don't search for elephants. None are there. They have been stretched out of existence, with only their infinitely stretched remains being visible as the vertical stripes inside the outer shell. It is curious how a rotation of only 0.2 degree can make such a large difference in the appearance of Julia sets, while such a rotation makes no difference at all in most Mandelbrot images. It would seem to indicate that the Mandelbrot-shaped parts of the Julibrot are in the form of a nest of four-dimensional hyper- cylinders, with the Julia direction lying parallel to the length of the hypercylinders. As to what such a nest of 4-D hyper- cylinders might look like, I have not the slightest idea. I have seen the Fractint evolver feature mentioned recently on the list. Yes, I do use it. It is one of the most useful features of the program. About one image in three is found with the evolver. But I usually round the evolver's parameters to one or two places before calculating the final image, thereby avoiding such awkward things as an angle of 37.7394877345823114 degrees, which I would enter as 37.74 degrees. BTW, today's image was not found with the evolver. If it had been, I might have let the evolver's (p1) parameters, which determine the angle, remain unrounded. The values are quite critical. Today's image deserves its rating of a 6. In fact a rating of 6-1/2 might have been a better choice. It's a relatively inter- esting if not particularly artistic picture. The name "Elephant Trickery" refers to the tricks the image plays with the Julia set of the central point. Changing the imag(p1) parameter to 90 will reveal the true Julia set, which really is a rather interes- ting one. The calculation time of 12 minutes is true on my tired, worn-out old clunker of a computer. But as long as it boots up DOS when I turn it on, that old warhorse will continue to be my fractal machine. More modern computers are far better on the internet, but some of them go into a panic when a DOS program is loaded. Those fractalists with such sensitive machines may download the finished GIF image of today's fractal from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A few more clouds and lower temperatures made Sunday less than perfect here at New Fractal Central, but the fractal cats don't mind the outside weather, since all they are permitted to do is watch it from their window. In my department, I am barely managing to keep the rush under control. So far it's going according to plan. I'll put the odds at 67 percent that the next FOTD will appear on schedule in 24 or so hours. Until that glorious time arrives, take care and check your world view for hidden errors. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elephant_Trickery { ; time=0:12:05.35--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/0/0.9026217 params=90/89.8/2\ /0/0/0/0.27/0.00593 float=y maxiter=150000 inside=0 symmetry=none periodicity=10 colors=000AMX9NX8OW7PW6QV6RVBSYFS_JSaNScRSeVSgZTib\ UkfXmj_okf_lnKms5on6ph7qb7rY8sV9tS9qSEoQImQMkSQhTU\ fUYdWabXe`YiZXgYWfXWeWVdVVcTUbSTaRT`QS_PSZQR_RR_SR\ _SR`RfZdmarscqtdqtdqtdptepteouemuflufkufiughuggvgy\ vgxvhwvhuvhtwiswiqwipwjjwjhwjbxkaxkVxkUxkMxlIylGyl\ FymDymCymByn9zn8zn7zo5zo4zo3zo5xk7wh9udBtaDrZFqVGo\ SInPKlLMkIOiFQhBSf8Te5kMdUd7Vd8Vc9WcAWcBXbCYbDYaEZ\ aFZaG_`H_`I`_Ja_Ka_LbZMbZNcYOcYPdYReXSeXTfWUfWVgWW\ hVXhVYiUZiU_jU`jTakTblSclSdmSemRfnRgVtLTTgUShUShVS\ hVShWShWShXShXShYShYShZShZSh_Sh_Sh`Sh`ShaShaShbShb\ ShcShcShdRhdRheRheRhfRhfRhgRhgRhhRhhRhiRhiRhjRhjRh\ kRhkRhlRklRnmRqmRtnRwDLzFMzGMzIMzJMzLNzMNzNNzPNzQN\ zSOzTOzUOzWOzXPzZPz_Pz`PzbPzcQzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzYmz_mzamzcmzfmzhmzjmzlmzTmzUmzVmz\ WmzXmzXmzYmzZmz_mz`mz`mzamzbmzcmzcmzdmzemzfmzgmzgm\ zVmzRmzMmzImzEmzDmzCmzBmz } 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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RE: [Fractint] FOTD 10-09-06 (Elephant Run [5])
by Jim Muth 10 Sep '06

10 Sep '06

FOTD -- September 11, 2006 (Rating 6) Fractal visionaries and enthusiasts: A bit of four-dimensional trickery is displayed in today's image, which tries desperately to be a Julia set of East Valley but never quite makes it. If the imaginary p1 parameter had been 90, we would have had a Julia set. As it is, we have a slice rotated a mere 0.2 degree toward the Elliptic direction, but that tiny rotation makes a world of difference. The basic outer shape of an East Valley Julia set is obvious, and the goofy eyes and noses are well represented, but don't search for elephants. None are there. They have been stretched out of existence, with only their infinitely stretched remains being visible as the vertical stripes inside the outer shell. It is curious how a rotation of only 0.2 degree can make such a large difference in the appearance of Julia sets, while such a rotation makes no difference at all in most Mandelbrot images. It would seem to indicate that the Mandelbrot-shaped parts of the Julibrot are in the form of a nest of four-dimensional hyper- cylinders, with the Julia direction lying parallel to the length of the hypercylinders. As to what such a nest of 4-D hyper- cylinders might look like, I have not the slightest idea. I have seen the Fractint evolver feature mentioned recently on the list. Yes, I do use it. It is one of the most useful features of the program. About one image in three is found with the evolver. But I usually round the evolver's parameters to one or two places before calculating the final image, thereby avoiding such awkward things as an angle of 37.7394877345823114 degrees, which I would enter as 37.74 degrees. BTW, today's image was not found with the evolver. If it had been, I might have let the evolver's (p1) parameters, which determine the angle, remain unrounded. The values are quite critical. Today's image deserves its rating of a 6. In fact a rating of 6-1/2 might have been a better choice. It's a relatively inter- esting if not particularly artistic picture. The name "Elephant Trickery" refers to the tricks the image plays with the Julia set of the central point. Changing the imag(p1) parameter to 90 will reveal the true Julia set, which really is a rather interes- ting one. The calculation time of 12 minutes is true on my tired, worn-out old clunker of a computer. But as long as it boots up DOS when I turn it on, that old warhorse will continue to be my fractal machine. More modern computers are far better on the internet, but some of them go into a panic when a DOS program is loaded. Those fractalists with such sensitive machines may download the finished GIF image of today's fractal from the FOTD web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html A few more clouds and lower temperatures made Sunday less than perfect here at New Fractal Central, but the fractal cats don't mind the outside weather, since all they are permitted to do is watch it from their window. In my department, I am barely managing to keep the rush under control. So far it's going according to plan. I'll put the odds at 67 percent that the next FOTD will appear on schedule in 24 or so hours. Until that glorious time arrives, take care and check your world view for hidden errors. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elephant_Trickery { ; time=0:12:05.35--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=0/0/0.9026217 params=90/89.8/2\ /0/0/0/0.27/0.00593 float=y maxiter=150000 inside=0 symmetry=none periodicity=10 colors=000AMX9NX8OW7PW6QV6RVBSYFS_JSaNScRSeVSgZTib\ UkfXmj_okf_lnKms5on6ph7qb7rY8sV9tS9qSEoQImQMkSQhTU\ fUYdWabXe`YiZXgYWfXWeWVdVVcTUbSTaRT`QS_PSZQR_RR_SR\ _SR`RfZdmarscqtdqtdqtdptepteouemuflufkufiughuggvgy\ vgxvhwvhuvhtwiswiqwipwjjwjhwjbxkaxkVxkUxkMxlIylGyl\ FymDymCymByn9zn8zn7zo5zo4zo3zo5xk7wh9udBtaDrZFqVGo\ SInPKlLMkIOiFQhBSf8Te5kMdUd7Vd8Vc9WcAWcBXbCYbDYaEZ\ aFZaG_`H_`I`_Ja_Ka_LbZMbZNcYOcYPdYReXSeXTfWUfWVgWW\ hVXhVYiUZiU_jU`jTakTblSclSdmSemRfnRgVtLTTgUShUShVS\ hVShWShWShXShXShYShYShZShZSh_Sh_Sh`Sh`ShaShaShbShb\ ShcShcShdRhdRheRheRhfRhfRhgRhgRhhRhhRhiRhiRhjRhjRh\ kRhkRhlRklRnmRqmRtnRwDLzFMzGMzIMzJMzLNzMNzNNzPNzQN\ zSOzTOzUOzWOzXPzZPz_Pz`PzbPzcQzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzYmz_mzamzcmzfmzhmzjmzlmzTmzUmzVmz\ WmzXmzXmzYmzZmz_mz`mz`mzamzbmzcmzcmzdmzemzfmzgmzgm\ zVmzRmzMmzImzEmzDmzCmzBmz } 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 10-09-06 (Elephant Run [5])
by JimMuth＠aol.com 09 Sep '06

09 Sep '06

FOTD -- September 10, 2006 (Rating 5) Fractal Visionaries and Enthusiasts: The big rush is in full swing, but I still found a few minutes for a trip to East Valley to see the elephants as they have never been seen before. We are actually viewing the pachyderms from the Oblate direction, which is the plane determined by the imag(c) and real(z) axes of the Julibrot. I named this orienta- tion Oblate because when the Jilibrot is sliced through its origin in this direction, an oblate open area appears. In this particular orientation, the elephants are not just sitting there, guarding their buds. They are running as though fleeing a brush fire. As they near the right edge of the image, they scrunch themselves up and dive down out of sight, eventual- ly losing all resemblance to elephants and curving around to become part of the goofy eyes of the Julia sets of East Valley. The straight line across the image around the elephants' feet is what I call a bridge. These straight-edged features never appear in Mandelbrot or Julia sets, but they are quite common in the sets of the four odd planes of the Julibrot. I have no time right now to explain why they are so straight, but I will do so when the rush subsides. Inamed the image "Elephant Run" because I imagined I saw running elephants in it. I rated it at a 5 because I put so little effort into it. As for the fractal cats, they are doing fine, though wondering why they are getting so little attention. If the work keeps moving, the next FOTD will appear in 24 hours. If not, look for it on the following day. Until whenever, take care, and even thinking about the fourth dimension can be hazardous to your health. Jim Muth START PARAMETER FILE==================================== Elephant_Run { ; time=0:06:22.01--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=t center-mag=+0.37097269855928490/-0.003112\ 53640045051/584.8368/0.01431 params=0/90/2/0/0/0\ /0.2615/0 float=y maxiter=50000 bailout=10 inside=0 logmap=yes periodicity=10 colors=000P`KObKNeJMgJLjIKlIJnIIqHHsHGuHFqLEmPEiSD\ eWCaZCAbBAfABiACm9Dp8Et8FwAGsBJpDMmEPjGSgHWdJZaKaZ\ MdVNgSPkPQnMSqJTtGVwDWzAUw9St9Rr9Po8Nl8Mj8Kg7Id7Hb\ 7F_6DX6CV6AS58P57N55K43H42F47J9CNDGRHLVLQZPUbTZfYc\ jagnelriqvmuzqeriQkaBdUZ1tY4uX7uWAuWCvVFvUIvTLvTNw\ SQwRTwRVwQUtQTrQSoQRmQQjQQhQPfQOcPNaPMZPLXPLVPKSPJ\ QPINPHLOGIOGGOFEOEBOD9OC6OB4OB2aVUaVWbWYbWZbW`cWbc\ WdcWedXgdXidXjeXleXneXoZUiSScLQYFOTHPUJQVKRWMSXOTY\ PUYRVZTW_UX`WYaYZbZ_b``cbadcbeecffcfeage`he_heZidX\ idWjdVkdUkcSlcRlcQmcPnbNnbMobLobKpbJpZzzVzzRzzNzzK\ zzGzzCzz8zz4zz1zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zzFzz\ CzzPzzRzzTzzUzzPzzLzzHzzDzzXzz`zzdzzhzzlzzpzztzzqz\ znzzkzzhzzezzczz`zzYzzVzzSzzQzzNzhKziHzjEzkCzlFzkI\ zjLziOziQzhTzgWzgZzfazeczdfzdizclzbnzbjz_fzXbzU_zR\ WzOSzLPzISzGVzFYzE_zDbzCezBgzAdzCczEZzGXzIUzKRzMPz\ NMzPJzRHzTEzVBzX9zYpzNfzT } 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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RE: [Fractint] I used Fractint's evolver to vary both real & imag partsof p1 of FotD 060905.
by Jim Muth 09 Sep '06

09 Sep '06

----- Original Message ----- From: Hal Lane To: Fractint_msg ;Muth, Jim ;Philofractal Sent: 9/8/06 3:43:29 PM Subject: [Fractint] I used Fractint's evolver to vary both real imag partsof p1 of FotD 060905. Jim, what do "O", "E", "R" "P" stand for? O = Oblate E = Elliptic R = Rectangular P = Parabolic and of course M = Mandelbrot and J = Julia These are names I invented for the four unfamiliar perpendicular 2-D planes through the origin of the four-dimensional Julibrot figure. In 4-D space, there are 6 perpendicular 2-spaces through every point. Unfortunately, the big work rush has arrived, and I have no time for further discussion now. There is no FOTD for Sep. 9. I will try to post a FOTD for Sep. 10, but there is no guarantee. Things will be back to good-old normal by this Wednesday, Sep. 13. Jim M.

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