June 2009 - Fractint - mailman.xmission.com

FOTD 25-06-09 (Seahorse Valley-25 [Not Rated])
by Jim Muth 25 Jun '09

25 Jun '09

FOTD -- June 25, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image is a scene on the east side of the north branch of the twelfth valley out the negative stem of the Mandelbrot set, eleven valleys beyond Seahorse Valley. This valley has no name, and I intend to give it none. I arrived at the remote scene while I was searching for a limit. The more remote the valleys become, the more they start to look the same. Today's image shows what I assume to be the limit of the scenery in the higher-order valleys. Similar scenes first appear around the 4th valley out, and the scenes change little in the valleys beyond there. The ridiculous maxiter of 20-million is no mistake. All these iterations are actually necessary to fully resolve the scene. By comparison, a similar scene in the 4th valley would require a maxiter of only 100-thousand, and would calculate in a minute or two. The three brilliant yellow areas are filled-in peanut holes. It can be seen that the center filled-in hole in the peanut hole is actually the 'star' at the end of the filament extending from the bud. The two 'bulbs' on either side of the center are end- less spirals on either side of the star. I also see some kind of animals in the scene, though I'll not try to identify them. They're clearly not elephants, but they're not seahorses either. Maybe they're spider monkeys. I could hardly give a rating to an image with so little to offer and so much time required for the calculation. But I will say that 50 minutes may be saved by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a high temperature of 88F 31C and a hot sun, things were a bit too warm for absolute comfort here at Fractal Central on Wednesday. The fractal cats were skittish because of the noise of work being done on a neighboring house, but this did not keep them from checking often to see exactly what was happening. My day was busier than average but still well under control. I'll be taking a short trip back to Old Fractal Central on Thursday to do a little porch maintenance, so the FOTD for June 26 might be late. Until whenever, take care, and never doubt the word of science. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_valley-25 { ; time=0:50:55.84-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.4011550420563\ 79/+0.00000000901429934/4.398626e+009/1/-88/0 params=0/0 float=y maxiter=20000000 inside=255 logmap=-87270 periodicity=10 colors=000UYzU_zUazUczUezUgzUizUkzUmzUozUqzUnzTjzS\ dhQaZPRPOMKNIKNDKN7KM1KL0KK1KI7LGDMEJNCPOCUPDYQDaR\ EeSEiTFmTFpTJkUNfURaVVYVZTVbOWfJWjFWnAXr5Xv1X_MHDf\ 2Qj8UnDYqIapGepFipEmpDmpCmoBmoAmo9mo8mo7mn6mn5mn4c\ n3cn2cn1eo3ho4ko6no7qo8tpAwpBzpCzpEzpFzqHzqIzqJzqL\ zqMzqNzrRzsVztZztazudzvgzwjzwmzxpzyszyvzxtzwrzvpzu\ nztmzqoznpzkqzhrzeszbtz_uzXvzUwzRxz`tzjpztlzsmzsmz\ smzsmzsmzsmzsmzsmzsmzsmzsmzsmzqkzpjzohzngzmezldzkb\ zjazi_zhZzgXzfWzeUzdTzcSz_UzXVzUXzRYzNZzK`zHazEbzH\ ZzJWzLTzNQzPNzRKzTGzVDzXAzZ7z`4zb1z_2zY3zW3zT4zR5z\ P5zM6zK6zI7zF8zD8zB9z8Az6Az4Bz2Bz7GzCKzHOzMSzRWzW`\ z`dzehzjlzopzmnzklzijzghzfgzcdz`bzY_zVYzSVzQTzNQzK\ OzHLzEJzBGz9EzFIzLLzRPzWSzaVzgZzmazrdzlbzf`zaZzWXz\ QVzLUzQWzUXzZZzb_zf`zkbzoczsdzrdzqdzpdzodzmezlezke\ zjeziezhezffzeUzjVzpWzuXzjaz_ezQjzFnz5rzBizHazFWzE\ QzDLzCFzBAzATz9kz6Xz3XK0P } END PARAMETER FILE=========================================

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FOTD 24-06-09 (Seahorse Valley-24 [Not Rated])
by Jim Muth 23 Jun '09

23 Jun '09

FOTD -- June 24, 2009 (No Rating) Fractal visionaries and enthusiasts: At first glance, today's image is a disappointing and not very inspiring debris-filled Julia set, but it is an image that is intended to be tweaked, so don't hesitate to start changing the real(p1) and real(p2) parameters. I have seen rumors circulating around the list lately that the fourth spatial dimension doesn't exist. Of course it doesn't exist. The orbits of the planets, among many other things, definitely obey the mathematically rigid inverse square rule of three-dimensional space. But does this prove anything. After all, we invented math ourselves and designed it specially to work with what we observe with our senses. Does the fourth dimension exist then? There is a big difference between not existing and being impossible. There is nothing at all impossible about four-dimentional space with time as the fifth dimension. There is no impenetrable barrier beyond the third dimension other than the inability of our minds to visual- ize spaces higher than the familiar everyday 3-D space. One- two- and three-dimensional objects can be mathematically modeled and manipulated by computers. With some additional complexity, four-dimensional objects can be modeled and manipula- ted by computers just as well. The problem here is that a three- dimensional screen surface would be needed to properly display the resulting images of 4-D objects, and this 3-D surface would need to be viewed from the fourth dimension. Since our minds have evolved to interpret our sensory input as a true image of a surrounding space having three spatial dimensions, we will never be able to visualize a fourth dimension, but this in no way pre- vents us from knowing what we would observe if we were able to do so. Two of the more curious possibilities in 4-D space are absolute perpendicularity and double rotation. Two planes are absolutely perpendicular when they intersect in a point, with every line in one plane perpendicular to every line in the other. Double rotation exists when a 4-D object is subject to two independent rotations at the same time. The points in the object move in a circular hyperhelix, somewhat like a slinky toy stretched out and curved into a circle with its ends connected. When the two rotations are equal, as with today's scene, all the points except the stationary point at the center move in circular arcs. Don't try to picture this motion. I've been trying for years with no success yet. In today's FOTD we have double rotated around the point at +003i in the north branch of Seahorse Valley, and stopped only 1/500th of one degree from the Julia direction, which is absolutely per- pendicular to the Mandelbrot. To see the 4-D double rotation in action, decrease real(p1) and real(p2) toward 0 and 0, keeping the two parameters equal. At (0,0) the Mandelbrot set will fill the screen, with Seahorse Valley at the center. For a quick but dizzying trip through four-dimensional space, check the slices at (90,90) (89.998,89.998) (89.99,89.99) (89.96,89.96) (88,88) (82,82) (75,75) (62,62) (50,50) (30,30) (10,10). Notice that the closer we come to the Mandelbrot orientation, the slower things go. The final (10,10) slice is barely distinguishable from the actual M-set. The scene may also be rotated from the Julia to the Mandelbrot by two simple 3-D type rotations. Gradually reduce real(p1) to zero, which reveals the Oblate aspect of Seahorse Valley. Then gradually reduce real(p2) to zero, which rotates the Oblate aspect back to the Mandelbrot. Doing it this way passes through some quite interesting slices, while introducing quite a bit of stretching distortion. Keeping the real(p1) and real(p2) para- meters equal will prevent this distortion. The passes=t option is needed to avoid major drop-outs. Since the image is actually one in a series of images, I gave it no rating. The calculation time of 2 minutes may be eliminated by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted. Picture perfect weather prevailed here at Fractal Central on Tuesday, with digitally-enhanced blue skies, puffy clouds, and a temperature of 81F 27C. Taking things for granted, the fractal cats slept through most of the day. My day was once again average and uneventful. The next FOTD trip to Seahorse Valley will be posted in 24 hours. Until then, take care, and today's series of images could make an interesting animation, but it would require choosing some carefully measured increments. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-24 { ; time=0:01:54.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0\ /0.7 params=89.998/0/89.998/0/-0.75/0.003/0/0/2/0 float=y maxiter=6400 inside=0 periodicity=10 colors=000QPGDC8MrzGdjBRV5DFTDsL9eE6S73E3gT2XL1ME0\ B7I_F9I7AG3581NPbRRlhJCM96TYzBWv8Og5GT28ExsjheZUSN\ FEBfHIWCDL89A44u0yRvByT8UU2FF13Nj1BNGwvpR4QD2HFteh\ 3SU2EF1wfLhWFULAFA5JsHC`B6I5W9_O6RG4I8294K02A09uV6\ aK3JAsYZ`MNIBBBvO7bG3J8a_UOyoJd9OHiC8NvmObXGJG8LfU\ np5PQ2XjKMVDBF6TACF5f72LW3_keid`CKU4AF2pMLQBAQy_Ji\ RDVI6F9UXwKMcABK49C268134rp5db3RQ2DD1J64C42621iu`f\ OiWIYLCNA6BjVkZN_NFOB7C5pIR2GI1A905RDxI8c94Kx81U40\ gEZDPT8GJ489zP9eG6L83p8`b6RQ4ID29hRrUI_F9IdYRtEqa9\ _J4IqUY_KMIABfaEWSALJ7A93e1WV0OL0GA08qSMREBxWnUGPZ\ k1HO0wEYc9MK4B7507pV1gR0MDEFDuMbTBJUGFKAAA55tlkikT\ NOEkYqOHRtZaeQSSHJE89VsnNeaFSP7ECWtoGSQqqY__MIIBHS\ S8EE1HK08As9pS4QVI7KC4A62sQK`HDI86wSGcIAK95gCOT8GE\ 48Xes`zzXfrTNjQ4c9XZZWLxV7qcOjldctukYnrChkP`e`UZlM\ TxFfFFWVVMjjeaTSPJFPMEC9V2uK1aA0J3Xk2MW1BGmfuPLTKe\ BFV8AL55A2DJw9Eh69U34FbaP } frm:SliceJulibrot4 {; 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=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 23-06-09 (Seahorse Valley-23 [7.5])
by Jim Muth 22 Jun '09

22 Jun '09

FOTD -- June 23, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's scene in Seahorse Valley actually has a seahorse in it. The little sea creature lies near the right edge of the frame, with its tail merging with an elephant's trunk. I have no idea what a ponderous elephant is doing in a valley reserved for sea- horses (and pipefish) but I only report what I see. There the elephant is, and I must show it. The scene lies in the Oblate direction at c=(-0.78), just to the west of the center of Seahorse Valley. The vertical direction has been stretched to about 3 times its normal height to make the seahorse recognizable. A nominal amount of skewing was needed to straighten things out. The rating of 7.5 rewards myself for a modicum of color work. The calculation time of under 11 minutes borders on slowness, but the calculation 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> The weather on Monday here at Fractal Central 60 miles north of Harrisburg was surely the reference standard to which all future claims of perfect weather must be compared. Start with a high temperature of 77F 25C, the middle of the human comfort range, continue with a humidity of 50 percent, again in the middle of the comfort range, go on with kodachrome (now digitally intensi- fied) blue skies and puffy cumulus clouds so clear and sharp it seemed you could reach out and touch them. Mix in a refreshing north breeze and just the right amount of ground moisture to let crops and gardens grow their best. Too bad it was just a bit too cool for a comfortable dip in the pool. The fractal cats slept through it all. My day was average. The next FOTD will appear in 24 hours. In it I will take a one-day break from the Seahorse Valley theme to demonstrate an incremental venture from our normal space into the fourth dimension. Until then, take care as always, and when the weather is perfect, don't cheer up. Remember that it can only get worse. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-23 { ; time=0:10:52.68-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=-0.37431977\ 2688398/+0.1190352122391917/4405.797/0.3045/0/\ 56.4525422252328042 params=0/0/-0.78/0 float=y maxiter=75000 inside=0 logmap=35 periodicity=10 colors=000R7rQ9qQBqPCqPEqOGpOHpNJpNLpMMoMNoLOoLPoK\ QnKRnJSnITnHUnGVmFWnEXoDYpCZqB_rA`rAaqAbpAcoAdnAem\ AflAgkAhhAieBjbBk_BlXCmVCnSCoPDpMDqJDrGDsEEqDEpDFo\ DFnDGlDGkDHjDHiDHgDIfDIeCJdCJbCKaCK`CK_CLYCLXCMWCM\ VCNTCNSBORBOQBORBPSBPTBRUBSVBUWBVXBWYBYZEZ_G_`I`aK\ __MZYOYWQYUSXSUWQWWOYVM_VKaVKcWLeWLgWLiXMkXMmXMoZL\ rXMqWNqVOqUPqTQpRRpQRpPSpOTpNUoLVoKWoJXoIXnHYnGZnE\ _nD`nCamBbmAbm8cm7dl6el5fl4gl3gl4hk5hk6hk7hk8hk9hk\ AikBikCikDikEikFikDkjFikGhkHgkJfkKekLclNblOalP`lQ_\ lSYmTXmUWmWVmXUmYSn_Rn`QnaPnaNobOnbPnbPnbQnbQnbRnb\ SnbSncTncTncUncVncVncWncWncXndYmdYmdZmdZmd_md`md`m\ dameamebmecmecmedmedmeemdfoeemfdkgdjhchhcgibejbdka\ bkaal`_m_Zn_XnZWoZUpYTqYRqXQrXOsWNtVLtVKuUIvUHwTFw\ TExSCySBzR9zR8yU7xX6x_6wb5wd4vg4vj3um2vp1uo2un2to2\ tp2tq2ur2vs2wt2xu2yv3zw3zx3zz3zz3zz3zz3zz3zz3zz3zz\ 4zz4zz4zz4zzJzzJzzJzzVzzf } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Re: [Fractint] The fourth spatial dimension -- in a zoom? (Hal Lane)
by JackOfTradeZ＠comcast.net 22 Jun '09

22 Jun '09

. For one thing, this "4th dimension" stuff is nonsense. There IS no 4th spatial dimension perceivable to human senses; I have never fully understood what people mean when they are talking about it relating to fractals. I have seen those "quat" animations before, Russ Walsmith has done a few, and there are some on youtube. They look intriguing but I never knew how to do it in fractint. (kinda looks like dough in a bread machine). If you (or someone else) can give me some code the fractint formula parser can deal with, and suggest parameter values / ranges, I would be glad to see what I can do with it. In fact, I would welcome this since I have totally run out of ideas for animations! My 4 main systems are chugging away on the E+112 zoom but I'm sure they would welcome a change from the monotony for a while. JoTz .

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FOTD 22-06-09 (Seahorse Valley-22 [No Rating])
by Jim Muth 22 Jun '09

22 Jun '09

FOTD -- June 22, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image is bogus! Its name is a lie! Today's image is not a scene in Seahorse Valley; it is a scene very deep in East Valley, which is otherwise known as Elephant Valley because the radicals there resemble elephants. While searching around for peanut holes in Seahorse Valley, I got a sudden urge to see whether there are also peanut holes in East Valley. Today's image is a sample of what I found. I found no signs of peanut holes this deep in East Valley. Nor did I find any elephants. What I did find is a whole slew of pinched-off rounded elements, not necessarily arranged symmetri- cally around the minibrot. Since I put very little effort into the coloring, and the image is not even in Seahorse Valley, I could not give the image a rating. But the calculation time of a few seconds over 5 min- utes means that little time will be wasted in the calculation. The task of calculation can be done away with entirely by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 75F 24C made Sunday near perfect for all fathers on Father's Day here at Fractal Central. A few showers sprang up, but they passed so quickly that they were hardly noticed. The fractal cats alternated between sleeping and watching for unwanted cats. My day was fair enough. The next FOTD, a true scene in Seahorse Valley, will be posted in 24 hours, after I make a sincere act of contrition. Until then, take care, and look before you fractalize. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-22 { ; time=0:05:24.94-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=+0.2500\ 000899991309/-0.0000000000415371/3.657298e+012/1/\ 160/0 params=0/0 float=y maxiter=1250000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000j55Y96DHKHEDiJBGH04zTAiLGTEQq0Oc3MQ5OYPN\ QJMJDjE4cD5YD6RC7IRUnx6__7y7ZGsDIhBJYAKN8BvmGZS8EZ\ pIGhGD`FBTD9qjjha``TRe96RJUCTpgNmaViXafSicNp`iwwXb\ iLIXT2O`I8OSSB`kjd0ehNfnSgsXhx`hkah_bhNchBdU9MN7JH\ 5GB3DE6BFkTG8AJA8YCmRCSoV__LL1wu8gdFSO_`_VSQQKGJ4N\ K8FaQDI8GKABw9LmAHcBEUCAUmXPVKfKoZH`SEMN8xMAfLBPsE\ OjDJaDFTCBk5w3QcT2cP7cIL`JI`KGULECoXj_MRz77o97eA7V\ B7j1Ta5LT9EHRALxEL_AtUAbL8GgbyCffqo`fcWXTQMIAT_lUb\ ePVZLNSGFYWjUR`RMROHHxeznYldRZVJL6RfANYEJPIFGeyVZh\ NSSFsmUjcOaVITLCnG2fF4_E5SD6jRccNVYJNRFFlNZeKSZHLS\ EEdKIYHEREAEE0mbJJlIKbFKUCLL93ikCTR`IZVGPQEGRcBPU9\ NL8fbHjFRNerFw9I_8R0zP3lO6ZM9LgBocUzcFzcEzcDzc8zcA\ zcBzcCzcCzcCzcCzc5zcpzcbzcPzcnzcazcPzcSzcwzckzc_zc\ OzcuzcizcZzcNzcbzcZzcTzcNzcHzcEzcbzcUzcLzcozcWzclz\ cbzcUzcLzcxzckzc_zcOzcwzcVzcOzcIzcEzcDzcazc0zc4zc8\ zcyzchzcSzc9zcAzcBzcCzc1z } END PARAMETER FILE=========================================

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Re: [Fractint] infinity
by JackOfTradeZ＠comcast.net 21 Jun '09

21 Jun '09

. "it can be thought in an abstract way as though the closer the scene gets to the singularity, that time is slowing down to the observer of the scene"" . that is exactly what happens when you fall into a black hole (if I understand correctly). the "fallee" will never get to the singularity - he will grow old and die of natural causes or something. but someone outside the event horizon will see him get sucked in real fast. more to the point, the mandelbrot is mathematically connected everywhere (that is theoretically proven now) - even the tiniest minibrot is connected by a very thin fillament ultimately to the main body. so the 2 main bulbs must ultimately be connected at real=-0.75, imag=0. but you need to get to infinity to see it. if you zoom in and see a "bridge" and then up the iterations it again disappears. ad infinitum. maybe the oft hyped (soon to arrive?) quantum computer will be able to do it........... .

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FOTD 21-06-09 (Seahorse Valley-21 [7.5])
by Jim Muth 20 Jun '09

20 Jun '09

FOTD -- June 21, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Would the real "Seahorse Valley" please stand up. Today's scene, with its unresolved minibrot and well-resolved peanut holes, lies in Seahorse Valley. But this valley is not the obvious one. It is the Seahorse Valley of the large minibrot at -1.75 on the main stem of the Mandelbrot set. It makes little difference however. The smaller version has all the features of the large 'true' valley, and even a few extra things such as filaments thrown in. In fact, today's image is located on one of these filaments leading from a bud on the west side of the parent valley. At a depth of +0.00003i, the scene is quite far down into the valley. Only the super-high-speed type=mandel algorithm enables the image to calculate in an astonishing 35 seconds. I would have switched to arbitrary precision math for a slightly better rendering, but a test showed that this would have increased the calculation time to a very slow 8-1/2 hours, hardly worth the slight improvement. There must be something of worth in the image, or else I would never have rated it at a 7-1/2. The greenish-blue background is of my creation; the program did the rest. If the calculation time of 37 seconds is too fast for comfort, why not zip out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished image there. Saturday began with heavy rain here at Fractal Central. By noon the steady rain changed to heavy showers, which continued on and off into the evening. The temperature hovered around a reason- able 70F 21C all day. The fractal cats slept through most of the wetness, becoming active only at mealtime. My day was average -- enough said. Unless something totally un- expected happens, the next FOTD will be posted in 24 hours. Until then, take care, and with an added space 'nowhere' becomes 'now here'. (I saw it on a church bulletin board.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-21 { ; time=0:00:37.36-SF5 on P4-2000 reset=2004 type=mandel center-mag=-1.7685292334674\ 58/+0.00003283923918143/2.372069e+013/1/12.5/0 params=0/0 float=y maxiter=100000 bailout=6 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000zIizHczHZzKYzNXzQXzZbz_czadzcfzbezbdzbdz\ bczbczmbzaazmaza`za`zm_zm_zmZz`YzmYz`XzmXz`Wz`WzmY\ zYZzW_zV`zmazSczQdzmezNfzMgtLimJjcIkUGlKFmBDo8Cp6A\ q39r18s5Co8FlBIiELfHOcKR`OUXRXUU_RXbO_eLbhIcgJdfKe\ fLfeMgeNhdNidOjcPkbQlbRmaRnaSo`Tp`Uq_Vq_VqZTqYSqXR\ qWQrXOrYNrZMrZKr_Jr`IraHraFrbErcDrcBrdAre9rf8rf6rg\ 5rh4rh3lf7feBacFWbJQ`NL_RKYSJXSIWSHVSGUSFSSERSDQSC\ PSCOSBMTALT9KT8JT7IT6GT5FT4ET3DT3CT5EU6GV7HW9JXAKY\ BMZDO_EP_FR`HSaIUbJWcLXdMZeLadN_ePZeRYeSXfUVfWUfXT\ gZSg`QgaPhcOheNhfLihKijJinJoSQbOTcKVcGXcJ_eMagOciR\ ekTgmWjoZlq`nscpuervgqwhqwiqxjqxkpxlpymqzorzqszstz\ tuzuvzvwzwxzxyzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzczzczzczzczzczzczzczzczzTfATd9Sb8S_8SY7RW6R\ U5RS5PT9NUCMVGKWJIXMHYQFZTD_XC`_Aab8bf7ci5dm3ep2fs\ 7cnCaiH_eMX`RVXWTS`QOeOJjMF`HNRDVH9b75jPMsj2Ti6Qi9\ Ojh`lgenfjpforetteyqdtnco } END PARAMETER FILE=========================================

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FOTD 20-06-09 (Seahorse Valley-20 [8])
by Jim Muth 19 Jun '09

19 Jun '09

FOTD -- June 20, 2009 (Rating 8) Fractal visionaries and enthusiasts: Blazing peanut holes, minibrots, and a trip to Seahorse Valley -- they're all present in today's image. The scene lies in the shell of a much larger peanut hole moderately deep in the true Seahorse Valley, which is the one in the classic Mandelbrot set. There is little to be said about the Mandelbrot set that has not often been said, so I will say little. But I do think that the image rates an honest 8, mostly because scenes in peanut holes are not that common. The calculation time of 3 minutes and 50 seconds is true on the P4-2000mhz machine. On the old P-200mhz the image takes 1 hour and 5 minutes to finish. And curiously enough, if the 'outside' is set to 'tdis', which makes an equally interesting image, the calculation takes over 9 hours even on the P4-2000. But why not forget all these timing hassles and hurry on out to the FOTD web site, where the finished image can be seen with no calculation required at all. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday began here at Fractal Central with the threat of rain, but by noon the dark clouds had cleared away, leaving a blue sky speckled with clouds of the altocumulus variety and temperatures around 75F 24C. The fractal cats, unconcerned with clouds or temperature, kept their eyes on two beat-up stray cats prowling the area. When the intruders went away, the resident fractal cats congratulated themselves for a job well done. The next FOTD has a 67-percent chance of appearing in 24 hours. The other 33 percent is the chance that FL will be bitten by the antiquing bug again. Until next time, take care, and science has most all of the answers to some questions and some of the answers to most all the questions, but it never will have all the answers to all the questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-20 { ; time=0:03:50.86-SF5 on P4-2000 reset=2004 type=mandel periodicity=10 center-mag=-0.7499986559107982/+0.0023037519364358\ /1.847007e+010/1/177.5/0 params=0/0 float=y maxiter=1500000 inside=0 logmap=85987 symmetry=none colors=000zzmzwczwmzwcyyUxxKvuKtqKrnLpkFniElgBjeCh\ cCfaDd_IbYJ`WKZUKXSKVQKTOKRMKPKKNIKLGKJEFHKEHKEEKD\ CKKBKKBKKBNNVKcLK`2K4OM8KKAHJBEHCUKKPKKKKWFIMEDECF\ DKKAKKCKKVKKPKPJ`MMOJHI9qFCcDEQbeBPTCYxXqUuGMHDJFJ\ pq_OKakZT`RKQK8Fl9G`AGPxx`_aP1To0gw3`k6U_9NOFMQDKL\ CIH0mC3dD6XD9ODwYeZPRvd55dr7Wd9ORzat`RZz44m77`A9OD\ BqBLfDJWEHLFFEuMC`HVd7LSAL2fG9SeXAVRBLLC8BRAEKcccd\ fIyQLtRQpRUlRY9eJ4`l6nXMrfavpccysUrA`ZgQgXNYMJNwwz\ zzzghYXZRMPKzml`XVyF3vWSNgzK`mHUaENP0QI6LFwoqpHIWG\ FIijGaaEVUCNLDrdM4GcXpPOXj94ZC7NEAzuZG`O`H1zz27g69\ UAzzrPZDIPDmTc`OVOKMc5IU9GKDE1Te5OW8KMWIAQHBzzCGGD\ hoASYCMnGIbFzRE7_VzzBdTCzMDc34U870CcjUmZP`NKPyzn_F\ W_78NzB9kDfYkZTbRPUJKLyfFl_E_TENMDRMsAl`BaTBRLDiyC\ alCV`BNPCFeBGWBGMyi8_VBdaIXWGURKZZPccULhZHmcFrhEvm\ CzrDzvCzzBzz`zzUzzPzzUzzZzzczAhzCmzcrzQvzXzzczzmzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 19-06-09 (Seahorse Valley-19 [7])
by Jim Muth 18 Jun '09

18 Jun '09

FOTD -- June 19, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today we have a scene very near the Julia set of Seahorse Valley of the (-Z)^(2.5)+C Mandeloid. Actually, the image has been rotated 6 degrees from the Julia orientation toward the Oblate orientation. Instead of being at -0.75 on the X-axis, the seahorse singular- ity in this Mandeloid lies near -0.760037363. To see the pure Julia set, which is far less interesting, change real(p1) to zero and reduce the maxiter to 150 to save time. The first thing I notice about the image is the open slit along the X-axis. This is the area near the singularity between the north and south arms of the valley. Next, I notice the many proto-peanut holes. Most have only two lobes, but the two at the left end of the fractal appear to have developed four lobes, and the brilliant open area on the X-axis just left of center is certainly a peanut hole in the making. Actually, I'm not sure that the image is mathematically correct. The X-axis symmetry might be an artifact of the math routine. To see the problem, set real(p1) to something like 0.0000000001. The image still has X-axis symmetry. Then set real(p1) to zero, and the right half of the resulting fractal totally changes. Such a small parameter change cannot possibly make such a large change in the resulting image. But real or an artifact, today's image rates a 7. The calculation time of 2-1/2 minutes is quite reasonable even for the most fanatical rationalists. And never forget that the finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday started with rain here at Fractal Central, but just after noon the sky brightened and the rain ended. One final sprinkle fell at 2pm, but after that the sun appeared and it was a fine day, with a temperature of 77F 25C. After chasing away a couple unwanted stray cats with their fierce glares and mighty growls, the resident fractal cats spent the day sleeping and ignoring the weather. My day was average. It's not boring; it's peaceful. The next FOTD will be posted in 24 hours. Until then, take care, and be fractalish. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-19 { ; time=0:02:27.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrotMin4 center-mag=-0.056338\ /0/1.03 params=84/0/90/0/-0.760036373/0/0/0/2.5/0 float=y maxiter=50000 inside=0 logmap=yes periodicity=10 colors=000hKdhLehMfhNghOihQjhRkhTmhVnhWphYqh_rh_th\ auhavhcwhcwhcwhdwhdwhewhewhfwhfwhfwhfwhfwT22V68X9D\ ZDI_GNaKScNXdQacP`bP_bO_aOZaOY`NY`NX_NWZMWZMVYMVYL\ UXLTXLTWKSWKRVJRUJQUJQTIPTIOSIOSHNRHMRHMQGLPGLPGKO\ FJOFJNEINEHMEHLDGLDGKDFKCEJCEJCDIBCIBCHBBGABGAAF99\ F99E98E87D87D86C76B75B74A64A63962952851640851951B6\ 2C62E72F73H83I83K84L94N94OA5QA5RB5TB6UB6WC6XC7ZD7_\ E8aF8bG8dH9eI9gJ9hKAjLAkMAmNBnOBpQBqSCsUCt`CvcDwcD\ xhDqmCmmBmmBmmAmlAmk9mj1mi5mh9mgDmfGmeKmaOv_SwYRwW\ RwUQwSQzQPzPPzOPzOOzOOzPNzPNzPMzPMvQMwQLuQLsRKqRKo\ RKmSJkSJiSIhSIhTHgTHfTHfUGeUGeUFdVFcVFcVEbVEbWDaWD\ aWC`XC_XC_XBZYBZYAYYAYYAX_9W`9Va9Uc8Td8Se8Rf8Qh7Pi\ 7Oj7Nk7Mm6Ln6Ko6Mp6Oq7Qr7Ss8Ut8Wu8Yv9_w9axAcyAezAg\ zBizBkzBmzCozCqzDszDuzDwzEyzEzzEzzFzzFzzGzzGzzHzzH\ zzLzzPzzUzzZzzczzhzzmzzrzzvzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrotMin4 {; 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=(-z)^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 17-06-09 (Seahorse Valley-17 [7])
by Vortex Swirling 18 Jun '09

18 Jun '09

Hi Jim, If the scene were calculated closer and closer to point -0.75, the camera could zoom in on it proportionally and keeping the apparent width of the valley the same. What ever the computer, it could do this until it ran out of time to complete the next scene. Interestingly, this shows that while the distance to the singularity is finite, there are an infinite number of increments before getting there. If the scenes get slower and slower to calculate, presumably because the number of digits past the decimal point also approaches infinity, it can be thought in an abstract way as though the closer the scene gets to the singularity, that time is slowing down to the observer of the scene. Actually these statements are probably true of the whole fractal I suppose. I also am wondering if all the buds are pinched off in this manor. Roger > I have also often wondered what lies at the point -0.75 of the > Mandelbrot set. What would we find there if we had a computer > of infinite speed, which would give infinite magnification? I > suspect that, at the -0.75 point, Seahorse Valley is kind of a > singularity with a width of zero, which means that even infinite > magnification would leave it with zero width. But a departure > of an infinitesimal value in the imaginary direction would > introduce an infinitesimal but real width, which an infinitely > fast machine would calculate and magnify to any degree in an > instant. Since infinitely fast machines will always exist only

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