October 2011 - Fractint - mailman.xmission.com

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

09 Oct '11

FOTD -- October 08, 2011 (Rating minus 6) Fractal visionaries and enthusiasts: Today's image is not as bad as its rating would suggest. The image has a negative rating of -6 because it's a negative image. Most fractals, with their bright pinks and yellows, produce a feeling of positivity and elation; but today's image, with its somber blues and purples, creates a feeling of negativity and depression, thus the negative rating. The name "Deep-Purple Scene" describes the image quite thoroughly. The depression the image evokes is due to the colors. With more cheerful colors, the image would be not at all depressing. The image is simply a near-Julia set of a point in the north branch of Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set. It is only a 'near' Julia set because the Julibrot slice is double rotated 0.2,0.2 degrees from the true Julia direction. It is impossible to imagine such a double rotation, but by actually doing the rotations, one can observe that the double rotation does exist. The somber deep blue wedge slicing through the middle of the open Julia shape is actually a grossly enlarged view of the Mandelbrot aspect of the area. It is possible to enlarge the 4-D Mandelbrot shapes to infinity because the stuff Mandelbrot shapes are made of is compact in the Mandelbrot 'C' planes but extends to infinity in the Julia 'Z' planes. The calculation time of 3-3/4 minutes is perhaps a high price to pay for such a downer of an image. Once again, thank goodness for the FOTD web site, which I believe is back in action again. The official FOTD web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high definition version of the image is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> After a gray and foggy start, today turned into near perfection here at Fractal Central. The sun shone constantly, while the temperature reached 72F 22C, which made the fractal cats happy and sent them scrambling to their sunny shelf in the southwest window. With the real work winding down, the humans took it easy doing other things. The next FOTD is due to be posted in 24 hours, but from the way things have been going lately, I would not be surprised if it was sooner or later. Until whenever, take care, and there's a new world coming, where time travel into the past is an everyday reality. (Want to bet?) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Deep-Purple_Scene { ; time=0:03:42.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=t center-mag=0/0/6.666667 params=89.8/0/89.8/120/\ -1.7685524/0.0008063/0/0 float=y maxiter=16000 inside=0 logmap=6 periodicity=0 colors=000002002002003113223335447859A6BC7DD7EF8GH\ 9IJAKLBMNCOOCPQDRSETUFVWGXYHZZH_`IabJcdKefLghMiiMj\ kNlmOnoPpqQrsRttRurTtpUtnVtlWtkXtiZtg_te`tcatbbt`c\ tZesXfsWgsUhsSisQjsOlsNmsLnsJosHpsGqsHpqIooJnmKmkL\ liMkgNjeOicPhaQg_RfYSeXTdXUcYVcZWcZXc_Yc`Zc`_ca`ca\ acbbbcbacb`dc_ecZecYfcXfdWgdVhdUhdTieUjeUjeUkeVkfV\ lfVmfWmfWngWogXogXphYqgXpgXpgXpfYpfYpfYoeYoeZoeZoe\ _odZod_nd_nc_nc_nc_nb_nb_mb_mb`ma`ma_ma`m``l``l`al\ ``l``laalaakabkbckdckddkfdkfejedkbej`fjZdjWbiW_iWZ\ iVXiVWiVViUVhUVhUUhUUhTThTShTRgSPgSOgSNgRNgRNgRNfR\ MfQMfQMfQMfPMfPLePLeOLeOLeOLePMdOLeOLeOLeOLfNLfNLf\ NKgNKgNKgMKhMKhMKhMJiMJiLJiLJjLJjLHjLHkKHkKHkKHkKH\ lKHlJGlJGmJGmJFmJFnIFnIEnIGoICoIAoHApHApHApHAqHAqG\ AqGArGArGArFAqGArGArGArGArGArG0rG0rG0sG0sG0sG0sG0s\ G0sG0sG0tG0tG0tG0tG0tG0tG0tG0tG0uG0uG0uG0uG0uG0uG0\ uG0vG0vG0vG0vH0vH0vH0vH0v } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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

08 Oct '11

FOTD -- October 07, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows one of the forgotten sets -- those that lie in the Julibrot at orientations other than the Julia or Mandelbrot. Today's image happens to lie in the Oblate direction, which is determined by the imag(c) and real(z) axes of the Julibrot, and is a name of my own invention. The image is a sideways view of Seahorse Valley of the large minibrot on the main spike of the largest minibrot on the main spike of the Mandelbrot set. The scene is not centered in the Mandelbrot plane however. It is located at a distance of -1.786117 in the real(z) direction, which means it is part of the shadow M-set, a phantom set with a linear size 1.4142 times that of the classic M-set. The name "The Forgotten Sets" gives recognition to the sets in the four odd planes of the Julibrot figure, as well as those in the countless rotations. In fact, calling these things 'sets' is basically a mistake. All Z^2+C fractals including the Mandelbrot set are mere 2-D slices through a far more monstrous figure -- the 4-D Julibrot. The rating of a 7 is getting to be boring, but I must rate the fractals as I see them, and today's impresses me as being of only average quality for a FOTD. The calculation time of 54 seconds will pass quickly, even though not in a flash. If the official FOTD web site host can recover from the hack attack, the finished image will soon be posted at: <http://www.crosscanpuzzles.com/Archives.html> It will also be posted, and in high definition at that, at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original and now classic web site may be accessed at: <http://www.Nahee.com/FOTD/> Absolute perfection prevailed here at Fractal Central today. Both the humans and the fractal cats agreed, enjoying the day as much as possible. With a large anticyclone, (one of those things with an 'H' in the center that the TV weather people put on their maps), parked right overhead, not a single cloud was seen and the temperature reached a very pleasant 68F 20C. The next FOTD will be posted in 24 hours. Until then, take care, and if neutrinos really do exceed the speed of light as claimed in a recent issue of 'Time' Magazine, what would happen if we sent a burst of them to the moon, where they would be reflected back to earth? As I see it, they would return a few seconds before they were sent and could then trigger a device that would cause them not to be sent out in the first place. Faster-than-light neutrinos would also give a glimmer of scientific respect to the paranormal claim of precognition, a currently 'impossible' thing that I already know does in fact exist. This does not imply that I put faith in the ramblings of Madam Zucchini, the fortune teller down at the corner. But it does mean I am convinced that, in some strange way, the future may affect the past, thus violating the law of causality. If this makes me a superstitious true-believer in the paranormal, so be it. Now it's time for the useless information of the day. The formula for the hypervolume of the curved 5-D hypersurface of a 6-D hypersphere is very simple -- (pi^3)*(radius^5). Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Forgotten_Sets { ; time=0:00:54.82-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 periodicity=6 center-mag=+0.00010515898520233/0/3801.206/1.2576 params=0/0/90/0/-1.786117/0/-1.786117/0 float=y maxiter=12000 inside=0 logmap=27 symmetry=xaxis colors=000B1QC2QD3QD4RE5RF6SF7SG8TG9THAUIBVICWJDXK\ EYKFZLG_LH`NIaOIbPIcQJcSJcTJcUJcVKcWKcYKcZLc_Mc`Nc\ aNccObdPaePcfQehPfiQgjRgkRglRgmRhmRhmRhmShmSimSimS\ ilSikSijSjiTjhTjgTjfTkeTkdTkcTkcUmbTkbSiaSgaRf`Qd`\ Qb_P`ZP_YOYWNWUNUSMTRLRQLPPKNOKONKMMILLGKKEJJCIIAH\ H8GE6FE4EF8FFBGFFHFIIGLJGPKGSLGVMHZNHaOHdPHhQIkRIn\ SIrTIuUJzVIxUIwUHuUHtTGrTGqTGpTFnSFmSEkSEjSEiRDgRD\ fRCdQCcQCbQB`QB_PAYPAXP9UOAWPBXQCYRD_SD`TEaUFcVGdW\ HeXHgYIhZJi_Kk`LlbLmdMofNphOqjOrlLngJlcHi`FgXCcUA`\ Q8YN6WK8XJ9ZKA_LBaMCbNDcOEdPFfQGgRHhSIjTKjULkVMlWO\ mXQnYSoZUo_Wp`YqaZrb_sc`scarcbqdcp_doOenKfmFfmAgm7\ hm7im8jm8mm9rm9vmAzmAzmBzmBzmCzmBzmCzmDzmDzmEzmEzr\ FzrGzrGzrHzrHzrGzrGzrFzrFzwEzzEzzDzzDzzCzzCzzBzzBz\ zAzzAzz9zz9zz8zz8zz7zz7zz6zz6zzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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

07 Oct '11

FOTD -- October 06, 2011 (Rating 7) Fractal visionaries and enthusiasts: In today's FOTD we see the scene I was searching for yesterday when the fractal ship showed up. I named the image "A Seahorse Goes East" because it combines the features of Seahorse Valley with those of East Valley. The outer parts of the scene are clearly of an East Valley nature, while the inner parts reflect the appearance of Seahorse Valley when sliced in the Oblate direction, which is determined by the imag(c) and real(z) axes. The entire image is distorted into a vague triangular shape because it lies at an odd angle in the 4-D Julibrot figure. (As a matter of curiosity, in the German language, the word 'julibrot' means 'bread of July'.) Unlike yesterday's image, which was stretched and skewed beyond verbal description, today's image was stretched only a modest 3-1/2 times in the horizontal direction. The value assigned the real(p4) parameter, which sets real(z) is equal to the real(c) value of the scene in the M-set. This places the actual location of the scene in what I call the shadow Mandelbrot set, a second Mandelbrot set lurking unsuspected at an angle of 45,45 degrees in the Z^2+C Julibrot. The rating of a 7 is an improvement over yesterday's miserable rating of 4, but still leaves plenty room for yet more improvement. The calculation time of a mere 24 seconds will make running the parameter file a breeze. The task of setting up and running the file may be avoided by viewing the image on the web site. The finished image should soon be posted on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> I said 'should be posted' because the last time I checked, the site was refusing access due to a hack attack. The image is also posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> in high definition. The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Strange as it might seem, as the number of hypercube dimensions increases, its diagonal approaches infinity, while the hypervolume of the inscribed hypersphere approaches zero percent of that of the hypercube. BTW, the formula for the hypervolume of a six-dimensional hypersphere is 1/6(pi^3)*(r^6). Not a single cloud spoiled the blueness of the sky over Fractal Central today. The sunrise temperature of 36F +2C was rather chilly, but the unbroken sunshine brought the afternoon tempera- ture to a pleasant 66F 19C, while the near calm winds made the day as close to ideal as we have had in two months. And the best part is that the near perfect conditions are expected to prevail for a week. The fractal cats, always seeking perfection, found it on their shelf in the sunny southwest window. The humans, realizing that perfection never happens, took the day for what it had to offer. The next FOTD will be posted in 24 hours. Until then, take care, and I agree with the angry young protesters. We should abolish poverty. But does anyone know how we might bring about this utopian dream? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_SeahorseGoesEast { ; time=0:00:24.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=0/\ +0.0000003835126177/419409.6/3.4337 params=0/90/0/90/-1.747855067330428/0/-1.747855067\ 330428/0 float=y maxiter=32767 inside=255 logmap=99 symmetry=yaxis periodicity=6 colors=00010S20U30W40Y50_60a70c80e90gA0iA0kA1lC2mE\ 3nH4oJ4pH4oE4mB4j84g84c84_84W75S75P75L64U53c42m3Lu\ cOzclLhsHmzDrz9wzBzzBzzzO7LNAQLDVKG_IJdHMiJQjKTjLW\ jM_jNbjOejPijQljRojSsjTvjUyjXrl_knadpdYr_qNYjPWcSU\ XUSQWQJZOC`oC1E3WM5bU6ia8pi9waJrVTnNajGkf6x_9tbBqe\ DnhFkkHhnLZpJeqHkqFrqExqPng_eZjXQjYOjYMjYKjYJjYHjY\ FxR5qVAjYEsfQkcMc`IWYEOVAGS61dv5XU8Q2FP6LO9SNCYMFd\ LIjKLaOOUSQLWS7aWA`VD_UF_TIZSLYRHfIKaMNYQKZaPWaTTa\ YQaaNa`Q_dXfibmmhsrnzpzzvtzowzpqzmttjopgjodgqaekZb\ iW`gTZeP`gQXdRTbSQ`TMYUJWVFUVCS_HLcDGg9Bk56n12k54i\ 95fD7dH8bLA_PBYTDVXET`GRdHJWFCNE5ED0T`1XY1_V1bT1eQ\ 1hO5kLAnJFqGKtEPwBUz9Zx8cwAhv7mu7mt7ms6mr6oq5qp5so\ 5un4wm4xl4zk5zk5zk6zj6vj6rj7mi7mi7mi8mh8mh9mh9mg9m\ gAmgAmgAmc8m_7mW6mS5mP4mL3lH2rD1xA0eBDOCQ6CaDKaKRa\ RYaYdadkajraksdltfmuhnvjowlpxnqyprzjszdtz_uzXvz_wz\ bxzeyzhzzkzznzzqzztzzw000 } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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

06 Oct '11

FOTD -- October 05, 2011 (Rating 4) Fractal visionaries and enthusiasts: Today's image rates only a 4, hardly up to FOTD standards, but the scene is so funny that I felt obliged to make it FOTD for today. To me the scene shows the ghost of the long-lost ship HMS 'Titanic', barely visible through the mists, sailing calmly over some far-away heavenly sea. Unlike that other ghost ship, the 'Dutchman', a sighting of this ship does not portend disaster. It is an omen of good fortune. The name "The Flying Titanic" gives recognition to both ghost ships. (Well, maybe the ship in today's image does resemble something more like a small destroyer than a mighty ocean liner, but at least it's something better than a tugboat.) The scene is located in the East Valley area of the large minibrot on the main stem of the Mandelbrot set. It is oriented in 4-D space at an angle that would be impossible to describe, and is stretched and skewed beyond imagining, yet here it is, a very recognizable image of a ghostly ship passing silently in the night fog. The image is an example of serendipity. When I stumbled upon the hole that resembles a ship, I was searching for something entirely different. I still am searching in fact, and if I find it, I will make it tomorrow's FOTD. Today's image finishes in 6-2/3 minutes, a little on the slow side for a scene that rates an unusually humble 4. But this is where the FOTD web site comes to the rescue. The web site may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version of the image is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> The space of four dimensions, in which this month's featured fractal object, the Julibrot, lies, is curious in many ways, especially when compared to space of three dimensions. In 3-D space only five regular polyhedrons, the five Platonic solids, are possible: the tetrahedron, with four triangles as faces; the cube, with six squares as faces; the octahedron, with eight triangles as faces; the dodecahedron, with twelve pentagons as faces; and the icosahedron, with twenty triangles as faces. And in space of five dimensions as well as spaces of all higher dimensions, the increasing numbers of lower dimensional elements usually do not match up correctly, and only three regular figures now called polytopes are possible. These are the analogs of the tetrahedron, cube and octahedron. So what about space of four dimensions? Intuition suggests that also in 4-D space, only three regular polytopes are possible, just as in spaces of all higher dimensions. But in this case intuition is wrong. In space of four dimensions, where the polytopes are bounded by three- dimensional boundaries called cells, six regular polytopes are possible: the hyper-tetrahedron, bounded by five tetrahedrons; the hyper-cube, (sometimes called the tesseract), bounded by eight cubes; the hyper-octahedron, bounded by sixteen tetrahedrons; the hyper-dodecahedron, bounded by 120 dodecahedrons; and the hyper-icosahedron, bounded by 600 tetrahedrons. There is also a figure bounded by 24 octahedrons, which has no regular analog in 3-D space, but is related to the semi-regular rhombic dodecahedron. So what would life be like in 4-D space, living on a hyperspherical planet most likely subject to a dizzying double rotation? Would the stars in the 3-D sky trace out helixes? Unfortunately, no such planet would be possible. In 4-D space the force of gravity would obey an inverse-cube law, making stable planetary orbits impossible. A planet would either quickly spiral into its star or sail off into interstellar space. So much for fantasy. The weather here at Fractal Central today was certainly no fantasy. We enjoyed cloudless skies and a temperature of 70F 21C. The fractal cats, now settling into winter mode, found comfort on their shelf in the sunny southwest window. The humans, FL and I, found comfort in the bright sunlight streaming through the windows, which has been pretty scarce the past couple months. Even more comfort will be found when the next FOTD is found and delivered, hopefully in 24 hours. Until then, take care, and the formula for the hypervolome of a five-dimensional hypersphere is 8/15*(pi^2)(r^5). Let me know when this useless bit of information might become important. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Flying_Titanic { ; time=0:06:39.42-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=-0.00048410686492484/+0.089235490629652\ 03/262770.2/0.00651/-90/89.1258940753795486 params=30/90/0/90/-1.7489/0/0/0 float=y maxiter=4200 inside=atan logmap=206 periodicity=6 colors=000GJV_5W_AZ_Ca_Ca_D`_D`_D_ZEZZEZYFYXFYWGXW\ GWVGWUHVTHVTIUSITRITRJSQJSPKROKQOLQNLPMLPLMOLMNKNN\ JNMDONFOMHOMJNMLOMNOMPPMRPMTQLVRLXRLZSL_SLXTMUPORK\ QMJSKKUNKTQKSTOQWTOZWMaXKdYJgYIjZHk_Hm`Gp`FsaEtbDt\ cDtcCtdBueAue9uf9vg8vh7vh6wi5wj5wk4xk3xl2xm1xm1wl2\ wl2vk2vk2uk2uj2tj2tj3si3si3rh3rh3qh3qg3pg3pg4of4of\ 4ne4ne4me4md4md4ld5lc5kc5kc5jb5jb5ia5ia6ha6h`6g`6g\ `6f_6f_6eZ6eZ7dZ7dY7cY7cY7bX7bX7fU0dW4bX7`ZAZ_EY`H\ WbKUcOSeRQfUPgYNi`LjcJlgHmjBsnDqmEpmGnmHmmIkmKjmLi\ mMgmOfmPdmRcmSbmT`mV_mWYmXXmZVm_UmaTmbRmcQmeOmfNmi\ KphLohLngMmgMlgMkfNjfNifNheOgeOgeOfdPedPddPccQbcQa\ bR`bR_bR_aSZaSYaSX`TW`TV`TU_UT_US_USZUXYUaYUfXU`XU\ WWUQWULVUFUUAUU5UUAUUFUUKUUPUUUUUVUUWUUXUUYUUZUU_U\ U`UUaUUbUUcUUdUUdUUcUUbUUaUU`FU`EU_DUZCUYBUYAUXAUW\ AUVAUVAUTAUSAURAUPAUOAUNAUMAUPAUSAUVAUYAU`AUcAUeAU\ cAUbAUaAU`AU_AUZAUXAUdAUd } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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

04 Oct '11

FOTD -- October 04, 2011 (6) Fractal visionaries and enthusiasts: A sudden rush descended on FC today, leaving little time for serious fractaling. But the image I found in a hurry is worth at least a cursory look. Today's image takes us to the valley around -1.399 on the negative X-axis of the Mandelbrot set. This is the third valley beyond Scepter Valley. But just to be different, we check the Rectangular aspect of the valley instead of the Mandelbrot aspect, and find today's scene. I named the image "Seeing the Light". The name was inspired by the brilliant white vertical stripe in the center of the image, which is made even more brilliant by the globules spread along it. Having too little time to work on the coloring, I could give the image a rating no higher than a 6. And its calculation time of almost 7 minutes is a bit much to ask for the privelige of viewing an image that rates a mediocre 6. Luckily, the FOTD web site has come to the rescue. The finshed image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> It is posted in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> After a light early-morning sprinkle, the sky brightened today here at Fractal Central. The sun even made a few brief appearances, but it was hardly a sunny day. The fractal cats took the temperature of 66F 19C in stride, giving more attention to the catnip frog that somehow got pulled out from under the book shelves than to the outside weather. FL and I, never fully agreeing on politics, got into a lunch time discussion about the political views of the extreme left and right, with nothing at all being settled between us. (These mildly heated discussions have been going on for many years, and nothing has been settled yet.) One thing firmly settled however is that the next FOTD adventure into the 4th dimension will be posted in 24 hours, when I will begin discussing the six regular polytopes that are possible in four dimensions. Until then, take care, and I know that my political views are correct, but why can't the rest of the world see it? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Seeing_the_Light { ; time=0:06:52.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=1 center-mag=+0/\ -0.02922557903896763/256.4055/4.7933 params=90/90/\ 0/90/-1.399631247361716/0/0/0 float=y maxiter=75000 inside=255 logmap=87 symmetry=yaxis periodicity=6 colors=000HNcHNcHNbHNbHNbHNbHNaHNaHNaHNaHO`HO`HO`H\ O`HP_IP`IQ`IQaIRaJRbJSbJScJTcKTdKUdKUeKVeLVfLWfLWf\ LXgLXgMYhMYiMZjMZkN_lN_mN`nN`oOapOaqObrObsOctPcuPc\ vPcwPcwQdwQdzQdzQdzRezRezRezRezQfzRezRezRezRezRezR\ gzRgzRhzSgzShzShzShzShzShzShzShzThzThzThzThzThzTez\ TezTezUezUezUezUezUezUezUezXezWfzXhzYhzZhz_hz`hiah\ kbhochschwdhwdhwehweiwfiwfjwgjwgkwhkwhlwilwjmmkmml\ mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm\ mmmmmmmmmhhmccmZZmUUmPRmKOkFNiANg5Me5Mc5Lc5Lc5Kc5K\ c5Ja6J`6I`6I`6H`6G`6Fa6Ea6Da6Cb69b7Ab79b78a77`76_7\ 5Z74Y73X72W71V90UB0TD0SF0RH0XJ0VL0TM0RN5POANPFLQGJ\ SHHUHFVIDWIBWJ9WK1XL4YM6ZN8_OA`PCaSEbVGcYId`KecMff\ OgcaheYigUjiQkkMlmJmoFnqBos7pv3qw4rx4sy4tz4vz4xz4z\ z4zz4zz4zz4zz5zz5zz5zz5wz5wz5rz5rzArzFrzKrzPqzUqzX\ pz_pzbpzepzhozkoznozqoztozwmzzmzzmzznzzozzpzzqzzrz\ zszztzzuzzvzzwzzxzzyzzzzz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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My last relative rational
by Sebastien helie 04 Oct '11

04 Oct '11

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

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

04 Oct '11

FOTD -- October 03, 2011 (Rating 7) Fractal visionaries and enthusiasts: With today's FOTD we find ourselves roaming once again in four- dimensional hyperspace, as we will be all the month of October. Every image this month will be created with the Mandelbrot expression, Z^2+C, but none of the images will resemble the usual Mandelbrot or Julia scenes. Today's image is a view of Scepter Valley, which is the valley at -1.25 on the negative X-axis of the Mandelbrot set. This is the inspiration for the name "Royal Scepter", though the image looks nothing at all like the Mandelbrot or Julia aspects of Scepter Valley. The scene is sliced at an odd angle oriented 75 degrees from the Rectangular direction toward the Julia direction of the Julibrot figure. The brilliant pink vertical stripe in the center of the image is part of the open space between the two branches of the valley, viewed from the side. Though the mathematical interest rates higher than usual in today's image, I could find nothing of artistic value in it that might raise the rating above that of an average 7. I did spend some extra time on the coloring however. In 4-D space, such as the space in which the Julibrot figure lies, there are six perpendicular planes through every point. Every plane is perpendicular in the normal 3-D manner (intersecting in a line) to four other planes, and absolutely perpendicular (intersecting in only a single point) to one other plane. In the Julibrot the absolutely perpendicular pairs of planes are Mandelbrot-Julia, Rectangular-Parabolic, and Oblate-Elliptic. All other pairs of planes lie in the same 3-space and are perpendicular in the normal 3-D manner. Today's image is oriented between the Rectangular and Julia directions, which implies that the rotation is of the normal 3-D kind. In this case, the axis of rotation is the imag(z) line that intersects the M-set at -1.25 of the X-axis. In today's image, the rotation may be seen in progress by varying the real(p2) parameter between zero and 90, which takes us on a trip from the Rectangular to the Julia directions. But be warned, the calculation time increases dramatically as the value of real(p2) gets close to 90. The higher dimensions have always been a mystery, but over the years I have come to see 3-D space as a construct of the mind, and also as an indicator of our level of consciousness. We can not imagine spaces of four or more dimensions because we have not yet reached a level of consciousness where it is possible. Will the human race eventually evolve to a level where higher spatial dimensions are within our grasp? Will we then find ourselves in a world with four or more spatial dimensions? Physicists tell us that the higher dimensions (11 at the latest count) are there, but we cannot percieve them. If this is so, who knows what mysteries the universe yet holds. These questions will not be answered in today's image, but the image does calculate in only one brief minute. The image will make the questions just a bit more significant however. The inconvenience of calculating a parameter file may be avoided by viewing the completed image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image may be enjoyed in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be perused at: <http://www.Nahee.com/FOTD/> Heavy clouds continued here at Fractal Central today, with a very autumnal temperature of 54F 12C. The fractal cats, solidly in cold weather mode, spent the day doing warm things such as curling up on the blankets. FL and I, the local humans, spent the day keeping things running, which is not always as simple as it first appears. The next FOTD will be posted in 24 hours. Who knows where in the Z^2+C Julibrot figure we might find ourselves tomorrow, or what we might find there. Until then, take care, and is three- dimensional physical reality really real? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Royal_Scepter { ; time=0:01:01.24-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 center-mag=0/0.0169994/\ 2.456186/1.1123 params=90/0/75/90/-1.25/0/0/0 float=y maxiter=50000 inside=255 logmap=3 symmetry=yaxis periodicity=0 colors=000agobgocgodgoegnfgmggmhfmgfmgemfdmdcmbaj`\ _gZYcVW_RTWOPSLMOIJLFGHCDE9AA67734334635936C38F3AK\ 3CO3ES3GW3I_4Lc4Nf4Qi4Sl4Xo4Zr4au4bx4dz9dzDdzIczMb\ zR_zQYzPWzOUxNRvMOtMOqNOoNOnNOmOOlOOkPOjPNiPNhQMgQ\ LfRLeRLdSKcSKbSKaTJ`TJ_UJ_UIZUIZVIYVIYWJXWIXXIXXJW\ XJWYJVYKVZKUZKUZLU_LT_LT_MT`MS`MS`MRaMRaLRbLQbLQcK\ PcKPcKOdKOdKOeKNeKNeKMfKMfKLgKLgKKhKKhKKhKJiJJiJIj\ IIjIHjHHkHHkGGlGGlFFlFFmFEmFEnGEnIDoKDoMCoOCpPBpQB\ qRBqSAqTArU9rW9sY8s_8sa3sb4sZ4oU4kP4iK4iF4iA4i85i8\ 5i95i95iA5iA5iA5iB6iB6iC6nC6nD6nD6nD6nE7nE7nF7nF7n\ G7nG7nG7nH8nH8nI8nI8nJ8nJAr9FsAKsAPsAUsAZsAcsAhsBm\ sBrsBvsBzsBzsBzsCzsCzsCzsCzsCzsCzsDzsDzsDzsDzsDzsD\ zsEzsEzsEzsEzsEzsEzsFzsFzsFzsFzsFzsFzsGzsGzsGzsLzs\ LzsLzsMzsMzsMzsMzsMzsMzsNzsNztUzuUzvUzwUzxUzyUzzUz\ zUzzZzzZzzZzzZzzZzzZzzZzzZzzczzczzczzczzczzczzczzc\ zzczzczzczzczzczzczzczxbx } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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

02 Oct '11

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

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

02 Oct '11

FOTD -- October 01, 2011 (Rating 8.5) Fractal visionaries and enthusiasts: I have decided to make the fourth dimension the FOTD theme of the month for October. 4-D hyperspace is not that much of a departure from the 3-D space we are so familiar with, since the Z^2+C Julibrot, (the composite of all the Julia and Mandelbrot sets), is a 4-D figure anyway. Today's image shows a small part of the shore line of the period-4 bud that lies on the northeast lobe of the main bay of the Mandelbrot set. Actually, the scene shows a section of the shore-line as it extends into hyperspace The entire scene has been stretched by a factor of over 57, (the tangent of 89 to be exact), in the direction of the Mandelbrot Y-axis. This stretching was necessary to keep the Mandelbrot ghost buds in their normal near circular shape as the view was rotated from the Mandelbrot orientation to within one degree of the Oblate orientation. The result of all this stretching and the additional skewing that resulted from rotating the image is a scene that vaguely resembles a scene on an alien planet with wispy cirrus-like clouds in the sky. I could have given the image a name such as 'Alien Cirrus' but I decided to name it simply "The Fourth Dimension", which quite nicely leads off a month that will be devoted to Julibrot scenes in 4-D hyperspace and hyper-objects such as the six regular 4-D polytopes. The extra half-point in the rating of 8-1/2 is due to the coloring. My modesty prevents me from granting myself any additional bonus points, even though they were deserved. The calculation time of 13-1/2 minutes is somewhat slow, leaving it to the individual fractalist to decide whether the 4-D scene is worth the wait. To avoid calculation altogether check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And check it in high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic, FOTD web site may be reached at: <http://www.Nahee.com/FOTD/> Today's weather left much to be desired here at Fractal Central. The fractal cats felt that the temperature of 52F 11C was too chilly for comfort, while FL and myself felt that the heavy clouds that blocked the sun and the occasional rain that fell through the day were too unpleasant for the first day of October, which is supposed to bring bright blue weather. The next FOTD will be posted in 24 hours. Until then, take care, and the formula for the hypervolume of a 4-dimensional hypersphere is 1/2(pi^2)*(r^4). How long will it be until someone other than a physicist actually needs this formula? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= TheFourthDimension { ; time=0:13:38.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot2 passes=t center-mag=-0.09254657031508136/+0.561631274103498\ 60/855.02/0.03822/-1.073/-87.9929489969829319 params=0/0/89/0/0.25/0/0/0 float=y maxiter=125000 inside=255 logmap=140 periodicity=6 colors=000UizUhzUgzUfzUezUdzUczUbzUazU`zU_zU`zUazU\ bzUczVdzWezVfzWgzVhzUizThzShzRgzRfzRezQdzQczPczPcz\ OczOczNczNczNczLczLdyJdxJdwHevIeuFetEfsEfrDfqDgpCg\ oCgoBhpBhqAirAisAit9ju9jv8jw8kx7ky7kz6lz6lz4kz5iz6\ gz6fz7ez8ez8dz9cz9czAdzBdyBdyCdxCdxDcxEbwEawFavF`v\ G_vHZuHYuIYtIXtJWsKVsKVsLUrLTrMSrNSsNRtOQuOPvPPyQO\ zQNzRTzRSzSSzSRzSPzSOzSNzSMzSLzSLySLxSLwSLvSLuSLsS\ LqSLqSLqSLqSLqSLqSLqSLqSLpSLoSLnSLmSLlTLkTLjTLiTLh\ TLgTLfTLeTLdTLcTLcTLbTLbTLbTLaTLaTLaTLaTLaULbVLcWL\ dXLeYLfZLg_Lh`LiaLjbLkcLldLmeLnfLogLphLqiKsiKtjKuj\ KvkKwkKxlKylKzmKzmKznKznKzoKzoKzpKzpKzqKzqKzqKzrKz\ rKzsKzsKztKztKzuKzuKzvKzvKzwKzwKzyKzyKzyKzyKzyKzyL\ zyMzyMzzNzzNzzOzzOzzPzzQzzQzzRzzRzzSzzSzzTzzUzzVzz\ WzzWzzXzzYzzYzzZzz_zzazzazzbzzbzzdzzdzzezzfzzfzzgz\ zgzzhzzizzjzzjzzkzzlzzlzzmzzmzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzznzznzzozzpzzpz00H } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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

01 Oct '11

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

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