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FOTD 13-10-11 (1-1/2 Seahorses [8])
by Jim Muth 13 Oct '11

13 Oct '11

FOTD -- October 13, 2011 (Rating 8) Fractal visionaries and enthusiasts: Believe it or not, today's image is a scene in the Seahorse Valley area of the (-Z)^(1.5)+C Mandeloid. Actually, the scene is very close to a Julia set of the valley, being double-rotated only 0.4,0.4 degrees from the true Julia direction. The wedge- shaped feature almost filling the outer figure-8 shape is a grossly enlarged view of the Mandelbrot Seahorse Valley. Iterating (-Z) rather than straight (Z) makes a great difference in the fractals with a fractional exponent of Z between 1 and 2. While positive (Z) results in tiny bean-shaped fractals, negative(Z) produces much larger fractals, with recognizable Seahorse Valleys and much more interesting surrounding semi- chaos to explore. I rendered the scene with the outside set to 'tdis'. Some of the other outside options also produce interesting versions of the scene. The name "1-1/2 Seahorses" refers to the exponent of Z, not to any sliced up seahorses that might be lying around. The rating of an 8 includes a full point for the coloring. This might be a bit excessive, but why not reward myself? I must have put almost an hour into working out the colors. The calculation time of 8-3/4 minutes is on the slow side. Most of this time is caused by the large maxiter of 32767, which was the maxiter limit of early versions of Fractint, and which I still use as a standard setting. But wait! There is no need for the 8-minute delay. Calculation may be avoided by viewing the image already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And by viewing the high-definition version at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds and intermittent showers continued here at Fractal Central on Thursday, while the temperature of 63F 17C was on the mild side for the season. The fractal cats, being warm weather fans, enjoyed the conditions. The humans spent the day doing routine things, which make for a peaceful day to live through but rather dull reporting. The next FOTD is scheduled to be posted in 24 hours, and it might actually be ready. Until next time, take care, and if we ever defeated the terrorists, who would we then blame our problems on. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 1-1/2_Seahorses { ; time=0:08:47.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=t inside=0 center-mag=-0.305312/0.00434276/1.123196 params=89.6/0/89.6/92/-0.742/0.05/0/0/1.5/0 float=y maxiter=32767 outside=tdis logmap=3 periodicity=9 colors=000TL_SKYRJWQIUPHSOGQNFOMEMLDKKCIJBFIACH99G\ 86F73D50C30700800900000000000000000000000000ZVKb`D\ fe6lx_iwaevcbvf_uhWtjTslQsoMrqJqsGpuDpwIqrMrmQshUt\ cYuZauUzMHvJMsGRpDWlA`i7ef4iY3`P2SG1J71BJ4DU6Fd9Ho\ BJzDLwJPtPTqVWn`_kfbhlffridojbmk`jl_hmYenWcoV`oTZp\ RWqPUrORsMPtKMuJKuLMsNNrPPqRQpTRoVTnXUmZWk`XjbYid_\ hf`ghbfjcekddlbelaem`em_emZejachcbfe`cg_aiY_kXXnWV\ pUTrTctRmvQzxPmqNcjMScKSXJTQHUJGRKJOKMLKPJKSGKVDLX\ AL_8Lb5Le2Lh0Lj1Mg1Md2Mb2M_2MX3MV3MS4NP4cc4cc5cc5c\ c6cc6cc6cc6cc6cc6cc6cc6cc6cf6cl6cr9cpBmoDmnGmlImkK\ mjNmhPmgRmfUmdWmcomYcmZ9mgwmuqmmkmfemzkmzgmzcmz4mz\ LmzcmzamzZmz_mz_mz`mzNmzSmzXmzemzcrzarzDrzSrzXrz9r\ zGrzNrzUrz0rzJrzDrzPrzcrzbrzarzmrzmrzmrzmrzmrzmrzm\ rzmrzmrzmrzmrzmwzmrzmrzmrzmrzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot5 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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time theory, addendum
by Sebastien helie 13 Oct '11

13 Oct '11

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

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

12 Oct '11

FOTD -- October 12, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image is a blow-up of a tiny hole in the upper right part of the 'infinite ocean' image of October 10. Out of curiosity I checked to see what the hole was about, and to my surprise found the fog shrouded midget car being driven quite recklessly by the driver whose head is clearly visible through the mist. As soon as I saw the driver and his car, I knew the name of the image must be "Reckless Driving". Actually the mini car is a Z^sqrt(2)+C minibrot that exists in its full form in the Mandelbrot aspect of the East Valley of the parent fractal, which resembles nothing quite as much as a kidney bean. The holes in the fog obscuring the mis-shapen car and driver are basically Julia sets of what lies under them. Since the entire image is kind of a joke, and the calculation time is a cumbersome 34-1/4 minutes, I gave it no rating. The calculation may be avoided by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high definition image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site is at: <http://www.Nahee.com/FOTD/> Today's weather left much to be desired here at Fractal Central. Heavy clouds and occasional rain spoiled every outdoor activity, not that any were planned, while the temperature of 57F 14C kept the fractal cats in cold weather mode. The local humans, FL and I, spent the day doing what needed to be done, and did it without powdermilk biscuits. If all goes according to plan, the next FOTD will be posted in 24 hours. If not, who knows? Until whenever, take care, and if we took the money from the top one-percent of wealthiest people in the US and distributed it equally among the rest, how much would each person receive? (Poverty cannot be significantly reduced by making the wealthy people poor.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Reckless_Driving { ; time=0:34:12.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.257646/\ 0.768567/43.47637/1/-55/0 params=89.99/0/89.99/\ -78.25/0.13/0.00037/0/0/1.4142/0 passes=1 float=y maxiter=100000 inside=0 logmap=248 periodicity=10 colors=000m8Jh9KcAMZBOUCQPDSMEUKFVLGWMHXNIYOJZPK_Q\ LaRMcRLdSLeSKfTJgTJgUKgUJgUJgVKgWLiXLkYMlZNmZQmZSl\ ZUj_YiY_hW`fTbeQddMebKgaGh`DhZAiY6kX2jY3kW3lU3lS3l\ Q3mP3nN3nL3nJ4nI4nG4nE4oC4oB4o94o74o54o43p83qC3qF3\ rJ3rN3sQ3sU3tY3t`3sd3rh3qk3oo3mr4jo4gm5ei5cf6ac6_a\ 7Y_7WZ8UX8SU9QS9OPAMNAKKBIIBGFCEDCDBDCDEDEFEFGFGHG\ HIHIJIKKJLLKMMLNNMOONPPORQPSRQTRRUSSVTTWUUYVYZdb_X\ U`YUaZVb_Vd`WeaXfbXgzYKlZidZidZjcYkbYkaXlkXzaXmbWm\ cWmcWncVncVocUocUocUpcTpcTqcTqcSqcSrcRrcRscSscTsbU\ taUt`Uu_UuZUuYUvXUvWUwVUwUUxTUySUzRUzQZzPZzOZzNZzM\ ZzLZzKZzJZzIKmHKmGKmFKmEKmDKmCKmBKmAKm9Km8Km7Km6Km\ 6Km6Km6Km6Km6Km6Km6Km6Km5Km5Km4Km4cz4cz3cz3cz3cz6c\ z8czAczAczAczAczAczAczAczAczAczczzczzczzczzczzczzc\ zzczzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 11-10-11 (Conventional Limits [8])
by Jim Muth 12 Oct '11

12 Oct '11

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

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

11 Oct '11

FOTD -- October 10, 2011 (Rating 6) Fractal visionaries and enthusiasts: The rating of a 6 that I gave to today's image might be a bit conservative. The image trick is one I have often used before, and this repitition held down the rating a point or two. The outer shape is a Julia set of East Valley of the Z^(1.4142)+C Mandeloid. The chaotic stuff along the 'horizon' inside the Julia set is a grossly enlarged view of the north shore line of the East Valley, rotated so that its edge cuts straight and level across the scene. The sickle-shaped stuff scattered about the lower part of the Julia set is made of the same stuff fractal trees are made of. In fact, only a small tweaking of the parameters will produce a fractal tree. The name "The Infinite Ocean" means just what it implies. The number of fractals is infinite, and the individual fractals are also infinite. This produces a total of (infinity)*(infinity) possible fractals. But do not be too overwhelmed. Infinity multiplied by infinity is still infinity. (Infinity must be raised to the power of infinity to produce a higher infinity.) Today's image finishes on my 2000mhz machine in 13 minutes -- quite slow for an image with a rating of a 6. Visiting the web site defeats this slowness however. The official FOTD web site, now totally back up and running, may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The finished image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic FOTD site is at: <http://www.Nahee.com/FOTD/> The day began with fog here at Fractal Central. The fog lifted by 10am, but the sun was filtered by a veil of higher clouds for the rest of the day. The temperature of 75F 24C left nothing to be desired however. The fractal cats were exhausted by yesterday's boisterousness, and spent most of the day sleeping. The human beings, being human, did human things. The next FOTD, an abstract thing, will be posted in 24 hours. Until then, take care, and I really do enjoy the way this crazy world keeps getting crazier. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Infinite_Ocean { ; time=0:13:02.47-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t maxiter=100000 center-mag=-0.187793/0/0.8130081/1/-90/0 float=y params=89.99/0/89.99/-78.25/0.13/0.00037/0/0/\ 1.4142/0 inside=0 logmap=yes periodicity=10 colors=000D8JE9KFAMGBOHCQIDSJEUKFVLGWMHXNIYOJZPK_Q\ LaRMcRLdSLeSKfTJgTJgUKgUJgUJgVKgWLiXLkYMlZNmZQmZSl\ ZUj_YiY_hW`fTbeQddMebKgaGh`DhZAiY6kX2jY3kW3lU3lS3l\ Q3mP3nN3nL3nJ4nI4nG4nE4oC4oB4o94o74o54o43p83qC3qF3\ rJ3rN3sQ3sU3tY3t`3sd3rh3qk3oo3mr4jo4gm5ei5cf6ac6_a\ 7Y_7WZ8UX8SU9QS9OPAMNAKKBIIBGFCEDCDBDCDEDEFEFGFGHG\ HIHIJIKKJLLKMMLNNMOONPPORQPSRQTRRUSSVTTWUUYVUZWU_X\ U`YUaZVb_Vd`WeaXfbXgcYhdZidZidZjcYkbYkaXl`XlaXmbWm\ cWmcWncVncVocUocUocUpcTpcTqcTqcSqcSrcRrcRscSscTsbU\ taUt`Uu_UuZUuYUvXUvWUwVUwUUxTUySUzRUzQZzPZzOZzNZzM\ ZzLZzKZzJZzIZzHZzGZzFZzEZzDZzCZzBZzAcz9cz8cz7cz6cz\ 6cz6cz6cz6cz6cz6cz6cz6cz5cz5cz4cz4hz4hz3hz3hz3hz6h\ z8hzAhzAhzAhzAhzAhzAhzAhzAhzAhzAmzAmzAmzAmzAmzAmzA\ mzAmzAmzAmzAmzAmzAmzAmzAmzAmzArzArzArzArzArzArzArz\ ArzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAw\ zAwzAwzAwzAwzAwzAwzAwzAwz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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FOTD 09-10-11 (Julia in Mandelbrot [6])
by Jim Muth 11 Oct '11

11 Oct '11

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

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

09 Oct '11

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

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

08 Oct '11

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

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

06 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 05 Oct '11

05 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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