June 2009 - Fractint - mailman.xmission.com

FOTD 14-06-09 (Seahorse Valley-14 [No rating])
by Jim Muth 14 Jun '09

14 Jun '09

FOTD -- June 14, 2009 (No Rating) Fractal visionaries and enthusiasts: Whenever the FOTD for Sunday is late, as it is today, it usually means a surprise antiquing trip erupted on Saturday, the day I find the Sunday image and write the discussion. This Saturday's trip took us to Carlisle, a town about 20 miles, 32km, west of Harrisburg. Luckily, FL found nothing absolutely necessary to our survival. The venitian blinds in today's image really are part of the 4-D Seahorse Valley complex. To save time, I'll not try to describe the direction in which the north branch of the valley complex was cut to give the effect. Since the area is four-dimensional, the words would have little meaning. But I will say that the open black strips are buds seen from the side, and I'll add that in 4-D space certain angles can have two independent values. I have posted similar images several times in the past, so I could not give today's image a rating. Another problem is that the image takes almost 1/2 hour to calculate on the 2000mhz machine, but this problem may be solved by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it will soon be, if it is not already, posted. A few showers were around the area on Saturday, but it stayed dry back here at Fractal Central, giving the 4-D fractal cats a hopefully pleasant day while their humans were away. I survived -- enough said. The next FOTD will be posted in 24 hours. Until then, take care, and measure your angles. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-14 { ; time=0:28:48.50-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=0/+0.004335/12072/0.000333 params=90/30/2/0/0/0/-0.750035/0 float=y inside=0 maxiter=25000 symmetry=yaxis periodicity=10 colors=000ulhukiukiukjukjukjtkktkktkltkltkmtjmtjnt\ jntjotjotjptjptjqtjqtjrtirtististittittiutiutivtiv\ tivdemQadBZWAa_9cc8eg7hk6jo5ls3mw4nw4nw4nw4nw4ow4o\ w4ow4ow4ow4pw4pw4pw4pw4qw4qw4qw4qw4qw4rw4rw4rw4rw4\ sw4sw4sw4sw4sw4tw4tw4tw4tw4uw4uw4uw4uw4uw4vw4vw4vw\ 4vw4vw7us9upCtmEtjHsgJsdMraOrZRqWTqTWpQYpN`oKcpGbo\ HanIamJ`mJ_lK_kLZkLYjMYiNXiNWhOWgPVgPUfQUeRTeRSdSS\ cTRcTRbUQaVP`WP`WO_XNZYNZYMYZLX_LX_KW`JVaJVaIUbHTc\ HTcGSdFReFReEQfEPgDOhCOhCNiBMjAMjALk9Kl8Kl8Jm7In6I\ n6Ho5Gp4Gp4Fq3Er2Er2Ds1Ct0Bu1Ct1Dt1Dt2Et2Et2Ft2Ft3\ Gt3Gs3Hs3Hs4Is4Is4Js4Js5Ks5Ks5Lr6Mr6Mr6Nr6Nr7Or7Or\ 7Pr7Pr8Qq8Qq8Rq8Rq9Sq9Sq9Tq9TqAUqAVpAVpBWpBWpBXpBX\ pCYpCYpCZpCZoD_oD_oD`oD`oEaoEaoEbo4_v9arEboJckOdhT\ edXfaahYfiVkjRpkOulKznGymHymHxmHxmIwmIwmIvmIvlJulJ\ ulJtlKtlKslKslKrlLrkLqkLqkMpkMpkMokMokNnkNnjNmjOmj\ OljOljOkjPkjPjjPjiQiiQiiQ } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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FOTD 13-06-09 (Seahorse Valley-13 [8])
by Jim Muth 12 Jun '09

12 Jun '09

FOTD -- June 13, 2009 (Rating 8) Fractal visionaries and enthusiasts: In today's image we slice the 4-D Seahorse Valley complex in the Elliptic direction. This orientation results when the imag(z) axis is perpendicular to the Mandelbrot plane and the resulting three-dimensional slice of the Julibrot is cut in a horizontal direction parallel to the top of the desk. Real(z) and/or imag(c) must be set a bit above or below zero, or else the slice misses Seahorse Valley, passing through the space between the two branches. In today's case, both values are set to 0.06, which eliminates X-axis symmetry in the parent fractal. In this parent, Seahorse Valley appears as a bridge between the north and south shores. Two micro-thin hairlines lie on the west edge of the bridge, with today's scene lying in the thinner hairline closer to the main body of the valley. These hairlines are actually parts of Seahorse Valley sub-buds seen from the side. A look at the crazy values in the parameter file will show that today's image was hugely stretched and skewed to bring it to a recognizable appearance. In fact, I did no actual skewing, but the rotating and stretching I did has the same effect as skewing. I rated the image at an 8. This includes a full point for the coloring, which turned into a study of getting smooth colors from a 256-color palette. The unusual in-to-infinity-and-out- again spiral accounts for the other 7 points. The calculation time of 6-3/4 minutes is barely within reason, so why not take a scenic trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and save the minor effort of setting up this letter so that it will run as a Fractint parameter file. The Friday weather was uneventful here at Fractal Central. The partly cloudy skies and temperature of 81F 27C were so close to normal that little else need be said. The fractal cats slept through most of the non-action. Meanwhile, my day was also close to average, and with any luck, tomorrow will be the same. The next FOTD is due to be posted in 24 hours. Until then, take care, and live in peace with fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-13 { ; time=0:06:44.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=Elliptic center-mag=-0.756516862636129\ 8/-0.3556880339637087/4.796564e+007/0.0006617/89.9\ 81502659185395/-89.0184738672499662 params=0.06/0/\ 0/0.06 float=y maxiter=15000 inside=255 logmap=2708 periodicity=10 mathtolerance=0.05/1 colors=000SEtTFtUGtVHsWIsXJsYJsZKr_Lr`MraNrbOqcOqd\ PqeQqfRpgSpgTqhTrgUrfVqeXpdYocZnb_ma`l`ak_bkZckYdk\ XekWfkVflUflTflSfkRfkQfkQfkQelRelTemVemXdnYdn_dnad\ occoecpfcphcqjbqlbqnbrpbrrastasvatwatwarw`qw_pv_nv\ ZmuZkuYitXgtXfsXdsXbsY`rY_rZYqZWq_Up`TpaRobPocNocM\ ocNncOmcPlcQkcRicSgcTedUceXafZ_g`YgcYfeZeg`ejadlbc\ nccpbboabnabm`bl`ak_ajZaiZahYagY`gX`fX`eW`dV`cV_bU\ _aU_`TZ_UY`TY_TXZTWYTVXTUWTSVTRUSPTSNSSMRSKQSJPSHO\ SGNREMRCLRBKR9JR8IR6HR5HQ6IQ7JP8KP9LOALOBMNCNNDOME\ PMFPLGQLGRLHSKITKJTJKUJLVIMWINXHOXHPYGQZGR_GR_HQ`I\ PaIObJNcKMdKLeLKfMJgMIhNHiNHimTGoTEzmDzTBzmAzUBzmB\ zUCzUCzmCzUDzmDzUEzmEzUEzmGzZIzmKzzLzdNzuPzhRzuSzl\ UzuWzpYzuZzt`zubzsdzuezuczrbzuapj_ngZlcYj_XhWVfSUd\ PTbLS`HQZDPX9OV3JW6NW8RWBVXDZXGbXHdXIeYMdZQdZUd_Xd\ _`d`ddahcakcbocbsccwcczcbyaay_`yZ_yXZyVYxUNCmLCnJB\ pHBrFAtB9vDAuEBuGCuHDuJEt } frm:Elliptic {; Jim Muth imag(z),real(c) z=flip(imag(pixel))+p1, c=real(pixel)+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 12-06-09 (Seahorse Valley-12 [No Rating])
by Jim Muth 11 Jun '09

11 Jun '09

FOTD -- June 12, 2009 (No Rating) Fractal visionaries and enthusiasts: It yesterday's image we set the real(z) axis perpendicular to the Mandelbrot plane at the -0.75 limit of Seahorse Valley. In today's image we do the same with the imag(z) axis, which gives us the Rectangular aspect of the valley. The question then immediately arises, which Z axis is actually perpendicular to the Mandelbrot plane. The answer is that they both are. And every other line in the Julia plane is perpendicular to the Mandelbrot plane as well. The two planes are absolutely perpen- dicular to each other, with every line in both planes perpendic- ular to every line in the other. Absolute perpendicularity is one of those strange unvisualizable things that cannot exist in spaces with dimensions less than 4. Seahorse Valley is filled with holes that resemble crossed peanuts, which I call peanut holes. Today's image shows one of these holes in its full glory, with many other holes scattered about. These holes are not true areas of trapped points, but bottomless pits of ever increasing iteration count. In today's image the maxiter is 110,000, but even this value leaves the peanut hole wide open. A much greater maxiter of 1,000,000,000 or so would totally close it however, greatly increasing the already very slow calculation time in the process. The unlikely values in the parameter file show that the image has been greatly stretched and skewed to bring the large peanut hole to a reasonably undistorted state. Such distortion that needs to be undone is very common in the Rectangular and other odd planes. I gave today's image no rating. After all, how could a mere peanut hole earn a rating? In addition, the calculation time of 1-1/3 hours will try the patience of even the most patient fractalist. I strongly recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds blanketed the Fractal Central area on Thursday, but no rain fell during the daylight hours and the temperature hovered around a very comfortable 73F 23C. The fractal cats had nothing to say about things. My day was occupied with work. But the efficiency eventually paid off and the work was finished by 4pm. The next FOTD will be posted in 24 hours. Until then, take care, and no comment at this time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-12 { ; time=1:22:37.96-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Rectangular center-mag=-0.790706186467\ 98470/+0.00044125005017076/5.971931e+007/0.0001521\ /0.0745896617071803714/-89.9801123768401396 params=0/0/-0.75/0 float=y maxiter=110000 inside=0 periodicity=10 colors=000BJDBIEBHFBFGBEHBDIBCJBAKB9LB8MB7N84LB6ND\ 7OF8PH9RJASLBTMCVNDWOEXRFZUH_XI`ZJb`KcbLddMffNghOh\ jPjlQkoQnnRlmRjlRhkRgjSeiSchSbgS`fTZeTXeTWdTUcUSbU\ RaUP`UN_VLZVKYVIXVGVSEXVFZXF`ZGa`GcbHedHgfIhhIjkIl\ mJnozoqKqszsuLuwzvyLtwzsvNqtzpsOnqzmpPlozjmRilzgjS\ fiSdgTcfUbeU`cV_bWY`WX_XKPiQUbWZXacRghLmmFxp4uqzsq\ zqqzoqzmqzkrHirJfrLdrNbrP`sSZsUXsWVsYSs_QtaOtcMteK\ tgItiEwrFunGtkGshHreHpbIo_InXJmUKkQKjNLiKLhHMfEMeB\ Nd8Mb2Nc5Od8OeBPeEPfHQgKRgNRhQSiSSjVTjYUk`UlcVlfVm\ iWnlifjbjlWnnPrpHzsIvqIsoJomJlkKijKehLbfLZdLWcMTaM\ P_NMYNIWOFVOCTP8RP5PQ1QP2OP3NP3MP4LP4KP5JP5IP6GP6F\ P7EP7DO8CO9BO9AOA8OA7OB6OB5OC4OC3OD2OD1QE4RF7SFATG\ CVHFWHIXILYJN_JQ`KTaLWbLYdM`eNcfNfgOhiPkjPnkQqlQrl\ QsiUmfXgc_a`bWYeQVhKOnDQlESkEUjEWhFXgFZfF`dFbcGdbG\ e`Gg_GiZHkXHkWIjWJjWIiVHiVGcVEYWDTWBNWAHWAFWBDWBCW\ ADUADSCDQFDPHDNJDLMEJOEIR } frm:Rectangular {; Jim Muth imag(z),imag(c) z=flip(real(pixel))+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 11-06-09 (Seahorse Valley-11 [8])
by Jim Muth 10 Jun '09

10 Jun '09

FOTD -- June 11, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene in the Oblate aspect of Seahorse Valley. The Oblate aspect is defined by the real(z) and imag(c) axes of the Julibrot. To find the Oblate view, take the point at -0.75 on the negative X-axis of the Mandelbrot set and imagine the real(z) axis cutting perpendicularly through this point, extending in front of and behind the screen. This line is actually the X-axis of the basic Julia set of Seahorse Valley, and when taken with the real and imaginary C axes defines a three-dimensional hyperslice of the four-dimensional Julibrot figure. Now rotate the 2-D image on the screen 90 degrees around the vertical axis, through this imaginary 3-D hyperslice until it sits in an upright position perpendicular to the screen, facing left and right. This is the oblate aspect of Seahorse Valley. It's easier to think about than describe in words. Now that we have our bearings in Seahorse Valley, what we find in there is a whole slew of those things I call peanut holes. In today's image the holes are filled in because of the maxiter of one-million, but they may be seen in their full glory by lowering the maxiter to 7,500. Curiously, these peanut holes appear in all aspects of Seahorse Valley, while the Mandeloid elements such as minibrots vanish soon after we leave the Mandelbrot orientation. I added superfluous detail to the scene by rendering it with the outside set to 'summ', and then I colored it to resemble a scene on some surreal alien planet. I rated it at an 8 because I kind of like scenes on alien planets. The calculation time of under 10 minutes will probably be cut to less than half on a current S.O.T.A. (state-of-the-art) machine, once the machine is taught how handle the Fractint program. Or perhaps it is best to forget teaching a new computer old tricks, and trek electronical- ly out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image in its full glory there. Thickening clouds here at Fractal Central on Wednesday did not dim the spirits of the fractal cats, who spent a good part of the day chasing each other up and down the hallway. The tempera- ture of 84F 29C was just about normal for the end of spring. My day was busy but under control. The next FOTD will be posted in 24 hours. Until then, take care, and does dark energy come from the world of fractals? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-11 { ; time=0:09:51.37-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=-1.18496393\ 032451400/+0.00512773353588221/33113.21/0.6062/\ -1.06803255737970959/-88.8155012674095872 params=0/0/-0.75/0 float=y maxiter=1000000 inside=0 outside=summ periodicity=10 colors=0001_z1Zz1Zz1Zz1Zz2Yz2Yz2Yz2Yz2Xz2Xz2Xz2Xa2\ W`2WZ2WY2WX3VW3VV3VT3VS3UR3TQ3SP3SO3RM3RL3QK3QJ4OI\ 4OG4MF4ME4LD4KC4KA4J94I84H74H64G56H57H58I59J5AI5BJ\ 5CG5DF5EE5GD5HC5IB5JA5KA5LA5NA5QC5TE5WG5YI5`M5cQ5c\ U5cW5cY5c_5cc5ca5c_5cY5cX5eX5gY5iY5kY5lY5kY5jZ5kZ5\ lZ5mZ5nZ5o_5p_5q_5r_5s_5rZ9rZDrZGrYKrYNrYRrYVrXYrX\ arXdrXhrWlrWorWsrWvqVuqVtpVtpVspVsoVroVroVqnVqnVpn\ VpmUomUnlUnlUmlUmkUlkUlkUkjUkjUjjUjiTiiThhThhTghTg\ gTfgTfgTefTezTdzTdzSczSbzSbzSazSazS`zS`mS_mS_mSZmS\ ZhTZgUZfVZcWZcXZcYZcZZc_Zc`ZcaZcbZccZcdZ`AtZCrYDpX\ FnVHlUJjTKiSMgQOePQcORaMT_LVYKXWJYVIUWHUXGVcGVcFVc\ EVcDWcDWcCWcBWcAWcAWc9Wc8Xb5Ya8ZbA_cC`dEadGbeJcfLd\ gNegPfhRgiThjWijYjk_klalmcmmennhoojpplqpnsqptrrurq\ spprnoqlopjnohmnflmdllbkk`jjZiiXihVhgTgfRfePfdNecL\ dbJ`hHdaHgVHjOHnHHqAHw2Et4Hq5Jo6Ml8Oi9QgATdCVbDY_E\ _XGaVHdSIfPKhNLkKMmIOpFPr } 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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FOTD 10-06-09 (Seahorse Valley-10 [6])
by Jim Muth 10 Jun '09

10 Jun '09

FOTD -- June 10, 2009 (Rating 6) Fractal visionaries and enthusiasts: The theme of the month of June is Seahorse Valley of the Mandel- brot set. But there are many seahorse valleys other than the one in the M-set. In today's image we go quite deep into the valley that sets off the large bud on the negative X-axis of the Z^4+C Mandeloid. Not surprisingly, we find much of the same type of features that fill the depths of the classic M-set, though down here they come in powers of 4 rather than 2. There is not much more to be said about the image, except that I could rate it no higher than a 6. The calculation time of 15 minutes is a bit too slow to for such a mediocre image. Con- sidering all this, I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday dawned with a spectacular thunder-storm here at Fractal Central, but the rest of the day showed a big improvement, with partly cloudy skies and a temperature of 86F 30C. The fractal cats spent most of the day ignoring the weather while stretched on the floor. I am trying to talk FL into adding an occasional comment to the FOTD discussion to contrast with my rather cynical views, but so far she prefers to remain silently in the background. We'll keep working at it however. In the meantime, fractal cat Cassie says, "purrrrr", and cat Nicholas says, "meow". My day was busy enough to verge on being rushed, but at the end of the day, after ample complaints, everything had worked out to everyone's satisfaction. The next FOTD will be posted in about 24 hours. Until then, take care, and then do it again. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-10 { ; time=0:15:27.31-SF5 on P4-2000 reset=2004 type=mandel4 center-mag=-0.787450771623\ 8988/+0.00135232921300458/3.731695e+012/1/-35/0 params=0/0 float=y maxiter=350000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000cL8eM8gN8fO8bP8_Q8XR8TS8QT8MY2NU8NQENNJN\ JPNGUNC_N9dN5jN2oP4qR6rS8sUAtWCvXEwZGx_HyXIsVImTIg\ RJaPJW3BKDFNNJQWNTzRmzcmzZawYXvXSuWNuWItVDsU8tW2sU\ 4rS5rQ6qP7pN9pLAoJBoICnGEmEFmCGlBHk9Jk7Kj5Li2Kj4Mj\ 6Oj8QjASjCTjEVkFXkHZkJ_kLakNckPekQfhNUeKHdG30rz0mm\ 2hf2dc2``2XY2TW2PT2LQ2IO5HN8GNBGMEFMHELKELNDKQCKTC\ JWBJZAIZ7G_9H`AIaBJbDKcELdFMZ4H`8JbCKdGMfKNgOOiSQk\ WRm_SocUpgVrkWzzzzzzzzvwwrurmsnhqkcogZmcVk`UhXTfTS\ dPRbMQ`IPZEOb8I`9KZAMXBNVCPTDQRESPFTNGVLHWJIYHIZGH\ _FH`EGaEGaDFbCFcCEcBEdADe9Df9Cf8Cg7Bh39o5Ak7Bh9CeB\ DbDE_FFXHGUJHRIHMLIONIPPIRRISUIUWIVYIW_JYaJZdJ`fJa\ hJcjJdp2_n8amDclJekOfjThiZjhckgimfnobwuespgoljkhlg\ doc`q_XtWTwPNvSPuURtWSsZUr`VqbXqdYpg_oiankbmndlpek\ rgZcSel`nwgkthhrhephbmh_khXihUghRdhObhL`hIYhFWhCUh\ 1Wk4Uj7TiAShCRgFQgIPfKOeNNdQMdSLcVKbYJaUIiXIe_IabI\ YeIUhIQSIMUILZIA_IA`JAaKA } END PARAMETER FILE=========================================

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FOTD 09-06-09 (Seahorse Valley-09 [6])
by Jim Muth 08 Jun '09

08 Jun '09

FOTD -- June 09, 2009 (Rating 6) Fractal visionaries and enthusiasts: While viewing today's image, which is the last time we'll see this particular Seahorse Valley minibrot, I started wondering exactly what a minibrot is. In the Mandelbrot set, minibrots appear as miniature Mandelbrot sets. But at the same time mini- brots extend beyond the Mandelbrot set in 2 perpendicular Julia directions, making it more appropriate when discussing minibrot rotation to consider minibrots as four-dimensional 'minibrot complexes'. The elements in these complexes are very large in the Z-plane directions and small in the C-plane directions. The complexes are open inside and extend throughout the Julibrot figure, appearing here and there until they are ultimately completely cut off by lower-iteration stuff. The great difference in the C and Z dimensions of the minibrot complexes also explains the extreme stretching that so often appears in the odd-plane directions. Today's image is another view of the past two days' minibrot complex, this time sliced in a direction rotated about halfway between the Oblate and Rectangular directions. Conveniently, it has X-axis symmetry, which not only gives a more pleasing appear- ance, but also cuts the calculation time in half. I had to stretch the image quite a bit in the horizontal direction to make it clear. Unfortunately, I could not rate the image at a 9, as Paul wondered, since this is the third consecutive trip to the same minibrot complex. But the rating of a 6 is still a bit above average and makes the 5 minutes required to run the parameter file just barely worth the effort. perhaps the best way to view the image is to surf out to the FOTD web site at <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> but try not to fall into the 4th dimension on the way. If you got turned around there, you would come back as anti-matter and destroy half the continent when you self-annihilate. The fractal cats enjoyed the typical early summer weather that prevailed here at Fractal Central on Monday. The temperature of 86F 30C and the humidity did not bother them at all, but I decided it was time to get the energy-saving fan out of the closet and stir up a breeze or two. The next FOTD will be posted in 24 hours. It will not be just another view of the same minibrot. Until then, take care, and would it be possible for a universe to exist with no conscious observers to observe it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-09 { ; time=0:05:12.20-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=t periodicity=10 center-mag=0/0/108000/50000000/0 params=42.6/90/0/90/-0.7499841692570846/0.01444653\ 20644315/0/0/2/0 float=y maxiter=16000 inside=0 logmap=2000 symmetry=xaxis mathtolerance=0.05/1 colors=000zzzQYxTWwWUvZSuaQudOtgMsjKrmIqmGqkHmiHjg\ HgeIccI`cIYcJUcJRdJOeJLfLKgNJhPIiQHjSGkUFmVEnXDoZC\ p_BqaArc9sd9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\ XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVpaUocUmeUlT`bG\ gT4mJ8rLBvMEzNHzPKzQNvRQrTUmUXjV_iXbiYeiZhh`khanhb\ dg`VgZLgXBgVwpGumFsjEqhEoeDmbCk`CiYBgWBeTAcQ9aO9_L\ 8ZJ8ZO7ZT7ZX7Za7Zf7Zj7YiCXhGWgLWfPVeUUdYUdaYbbaabe\ `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\ Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\ SJGWIH_HIbGJfFKjELnEMqGQmHUiIXfJ`bKdZLgWMkSNoOmr0P\ vzQyzRuzRrzRozRkzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\ NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\ 4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\ F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\ zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 08-06-09 (Seahorse Valley-08 [8])
by Jim Muth 08 Jun '09

08 Jun '09

FOTD -- June 08, 2009 (Rating 8) Fractal visionaries and enthusiasts: Believe it or not! Today's image shows the same minibrot as yesterday's image. But it is no longer a minibrot. In fact I have no idea what to call it. Apparently, it's a slice through a four-dimensional object that twists and turns in four-dimensional space. But even the 2-4-8-16 series of elements has broken down. All I can say about the image is look at it and make what you will of it. The rating of an 8 is totally due to the mathematical interest. The colors are simply a slight tweaking of yesterday's color palette. Fractint's evolver feature was needed to find this strange angle, which explains the exceedingly critical parameters. The calculation time of 12-2/3 minutes can be eliminated by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather turned slightly muggy here at Fractal Central on Sunday, with a high temperature of 86F 30C. The fractal cats took the warmth stretched out to their full cat lengths. My day was slow, FL wasted a lot of energy trying to talk me into helping with the garden work. I eventually quieted her by lugging a 45-pound (20-kg) bag of mulch out of the shed. The next FOTD, another venture into Seahorse Valley, will be posted in 24 hours. Until then, take care, and see you in the seahorse valley of unimagined delights. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-08 { ; time=0:12:39.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=slicejulibrot4 passes=1 periodicity=10 center-mag=+0.00000000003557236/-0.000000000000080\ 27/2.137415e+012/0.0004748/0.155766213921201102/88\ .7811844407367943 params=-0.433319441053499/0.8160\ 148739585559/90.04358186208685/9.207151535843989/\ -0.7499841692570846/0.0144465320644315/-0.74998416\ 92570846/0.0144465320644315/2/0 maxiter=16000 inside=0 logmap=1850 float=y mathtolerance=0.05/1 colors=000zzzyrywmxuhwscvrcuqctpcsocrncqmcqkcmicjg\ cgecccc`ccYccUccRdcOecLfcKgcJhcIicHjcGkcFmcEncDocC\ pcBqcArc9sc9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\ XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVqaUpcUocUndUme\ VlfWkgXjhYihZhh_gh`fhaeibdiccjdbjeakf`kg_kh`khanh_\ piYrjWtkUukSvjQuhOsgMqfKoeImdGkcEicCgcBecAcc9ac9_c\ 8Zc8Zc7Zc7Zc7Zc7Zc7Zc7YcCXcGWcLWcPVcUUcYUdaYbbaabe\ `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\ Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\ SJGWIH_HIbGJfFK`ELtEMzGQmHUiIXfJ`bKdeLghMkmNorOrvP\ vzQyzRzzRvzRrzRmzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\ NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\ 4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\ F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\ zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 07-06-09 (Seahorse Valley-07 [7])
by Jim Muth 07 Jun '09

07 Jun '09

FOTD -- June 07, 2009 (Rating 7) Fractal visionaries and enthusiasts: The theme for June is Seahorse Valley of the Mandelbrot set. So today's image shows a tiny minibrot deep in the valley, near the limit of resolution. Since there is nothing unusual about Seahorse Valley minibrots, I added a bit of interest by giving the image an unusual color palette. As a result of this coloring effort, I was able to give the image a rating of a 7, which is enough to make the image worth the effort of producing it. The calculation time of 5-5/6 seconds is no mistake. The type=mandelbrot formula runs like a herd of tachyons on the 2000mhz unit. But it's still a lot of fun to roam out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the image posted there. In tomorrow's FOTD we'll check a different view of this same minibrot and see what havoc we can wreak on it. A notable improvement in the weather prevailed here at Fractal Central on Saturday, with lots of sun, gentle breezes and a near- perfect temperature of 79F 26C. The fractal cats, Nicholas and Cassandra, (Nico and Cassie for short), enjoyed the weather, but they would have been more at ease if fewer cats had wandered past their window. We seem to have a thriving cat colony in the area. My day was uneventful. If Sunday is a repeat, I'll have no complaints. The next FOTD will be posted in 24 hours. Until then, take care, and how do we get out of the matrix? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-07 { ; time=0:00:05.50-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.7499841692570\ 8460/+0.01444653206443146/1.046351e+012/1/-31/0 params=0/0 float=y maxiter=16000 inside=0 logmap=1650 periodicity=10 mathtolerance=0.05/1 colors=000zzzQYxTWwWUvZSuaQudOtgMsjKrmIqmGqkHmiHjg\ HgeIccI`cIYcJUcJRdJOeJLfLKgNJhPIiQHjSGkUFmVEnXDoZC\ p_BqaArc9sd9tc8ub7va6w`5x_4yZ3zY3vY8sYDoYIlYNhYSeY\ XaYaZYfVYkSYpOYuLYzOXxQXvSWuVWsXVrZVpaUocUmeUlT`bG\ gT4mJ8rLBvMEzNHzPKzQNvRQrTUmUXjV_iXbiYeiZhh`khanhb\ dg`VgZLgXBgVwpGumFsjEqhEoeDmbCk`CiYBgWBeTAcQ9aO9_L\ 8ZJ8ZO7ZT7ZX7Za7Zf7Zj7YiCXhGWgLWfPVeUUdYUdaYbbaabe\ `ch_ceYZcWU`UQZTLWRGUPCRN7PM3CEM07d66aC6ZH6XN5US5R\ Y5Pb4Mh4Jm4Hi5Ee6Ba69Y76U83Q81P95OA9NBDMCHLDKKEOKF\ SJGWIH_HIbGJfFKjELnEMqGQmHUiIXfJ`bKdZLgWMkSNoOmr0P\ vzQyzRuzRrzRozRkzShzSeLSaMSZNTWOTSPTPQTMRTJSRHQPGP\ NFNLDMJCKHBJF9HD8GB7E96DDBCGFBKJANO9QS8UW7X`6`d5ch\ 4fl3gg5hb6iY7jT8kP9lKAmFBnACo5Dz00z00z00z00z50zA0z\ F0zK0zP0zS0zV0zY0z`0zc0zf0zg0zi0zk0zm0zo0zq0zs0zu0\ zv0zw0zx0zy0zz0zz0zz0zz0zz0zzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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FOTD 06-06-09 (Seahorse Valley-06 [7])
by Jim Muth 05 Jun '09

05 Jun '09

FOTD -- June 06, 2009 (Rating 7) Fractal visionaries and enthusiasts: Fractals are filled with bottomless spirals. They are probably the most common features in the world of fractals. But how often have we seen a set of concentric fractal rings with a very definite bottom? After viewing today's Seahorse Valley scene, we have seen such a set at least once. But are these rings truly what they appear to be. And for that matter, are the everyday fractal spirals truly what they appear to be. The Mandelbrot set does not exist in isolation. It is a particular slice down the center of a four-dimensional monstros- ity known as the Z^2+C Julibrot. The elements in the Julibrot are 4-D objects that twist and turn in four-dimensions. Those very attractive spirals are actually 2-D slices of 4-D things that cannot be visualized but most likely approximate nested hyperspheres. Today's image is simply a slice in a different direction through one of these nested hyperspheres. The disk at the center of today's image is the next inner shell of the nested hyperspheres, which has not been cut entirely through. A bit of parameter tweaking will punch a hole in the center of the flat central disk, which will then become another ring. I have not yet tried tweaking the parameters, though it should not be very hard to find the right ones. I added a bit of extra life to the scene by rendering it with the outside set to 'summ'. The rating of a 7 is the lowest rating that brings satisfaction for a fractal well done. The calculation time of 8-2/3 minutes is slightly slow. A more efficient way of viewing the sliced nested hyperspheres is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it at leisure there. Solid clouds, steady light rain and a temperature of 61F 16C kept a strict damper on things here at Fractal Central on Fri- day. The fractal cats spent the day catching up on their sleep, though they did have a brief moment of excitement when a bedrag- gled stray cat passed by their window. My day was about average, as are most days. Hopefully, tomorrow will be the same. Unless we get involved in some kind of expedi- tion on Saturday, the next FOTD will be posted in 24 hours. Until next time, take care, and we know that an electron is a unit of energy, but is it a particle, a wave, a wave packet, or none of the above? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-06 { ; time=0:08:42.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 maxiter=2820 center-mag=+1.074127267031372/-0.1217313849462725/\ 6907.325/0.03441/-45.7342470354590063/-52.78617\ 25848204202 params=90.1/46.3/90.9/91.4/-0.75/0/0/\ 0/2/0 float=y inside=0 outside=summ periodicity=10 colors=000bhgchecibdj`ejZekXflUflSgmQhnOhnMioJipHj\ pFkqDkrAlr8ls6mt4nw0mt2lq3ko5kl6ji8ig9idBhbCg_DgXF\ fVGeSIePJdNLcKMbIMcINdIOeIPfIQfIQgIRhISiITiIUjIUkI\ VlIWlIXmIYnIYoIZoI_pI`qIarIarIbJ_GJZGJYGJYHIXHIWHI\ WHIVHHUHHUIHTIHSIGSIGRIGQIGQJFPJFOJFOJFNJFNJHMIJMI\ KMIMLHNLHPLHQKGSKGTKGVJFWJFYJFZIE`IEaIEcHDdHDfHDgG\ CiGCnF9jGCfHFbIHZJKVKNRLPNMSJNVFOXBP_8QaBSaEUaHVaJ\ XaMYaP_aS`aUbaXca_eabexafaagD`fF_fGZeHYeJXdKWdLVcM\ UcOTbPSbQRaSQaTP`UO`VN_XM_YLZZKZ_JYaIYbHXcGXeFWfEW\ gDVhCVjBUkAUlAUmCTlDTlETlFTlGTlHTlITlJTlKTlLTlMTkN\ TkOTkPTkQTkRTkTSkUSkVSkWSkXSkYSjZSj_Sj`SjaSjbSjcSj\ dSjeSjfSjgSjfUkeVkdWkcXkbYkaZk`_l_`lZalYblXdlWelVf\ lUgmThmSimRjmQkmPlmOmmNlnNlnMkoMkoMkoLjpLjpKipKiqK\ iqJhqJhrIgrIgrIgsHfsHfsGetGetGetFduFduDbtFduGfuHhu\ IiuKkuLmuMnvNpvPrvQsvRuvSwvTxvUuwVrwVoxWmxXjxXgyYd\ yYbyZcv_dt_dr`ep`fmafkbgi } 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 05-06-09 (Seahorse Valley-05 [9])
by Jim Muth 05 Jun '09

05 Jun '09

FOTD -- June 05, 2009 (Rating 9) Fractal visionaries and enthusiasts: Anyone looking at yesterday's image can see at once that nothing interesting lies at the tips of those narrow brilliant diagonal lines inside the central bay of the Seahorse Valley Julia set. But not being 'anyone', I took a look anyway. The going was incredibly slow, but I finally found a scene that rates an honest 9. What I found is a screen filled with spider webs, peanut holes and glowing comets. This is exactly what I found in a recent trip to the deepest depths of the true Seahorse Valley. Today's image is not sliced in the Mandelbrot direction however. It is sliced in a virtual Julia direction, yet it is filled with the stuff normally found in the Mandelbrot direction. I did not check for Mandelbrot minibrots in the scene. The going is simply too slow. But the image has a minibrot feeling to it, and I would not be surprised to find some minibrots hiding in the depths, perhaps only slightly perturbed. And I wonder if this is a way of getting extra magnification for nothing. First we enlarge the valley as I did in yesterday's image, then we can dive into the already enlarged valley and get something for nothing. Of course, it is impossible to get some- thing for nothing, and I suspect that all we're doing here is shifting the decimal point, meaning that breakdown would happen at a much less magnitude. The name of the image is simply a catalog number. The rating of a 9 indicates that I am quite pleased with what I found in such an un-promising location. The calculation time of over 3 hours is no mistake. I very strongly recommend hurrying to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to enjoy the pleasure of seeing the image already calculated. FL asked no interesting questions Thursday, so I have no reason to wax philosophical. (BTW, where is Mister Phil O. Sophical?) The fractal cats had ample reason to complain however. The lack of sun and temperature of only 68F 20C was not to their liking, and they showed their dissatisfaction by tearing apart one of their catnip mice. My day was slightly busy, but otherwise uneventful. The next FOTD will be posted in 24 hours. Until next time, take care, and if we found why there is something instead of nothing, we would solve most other un-answerable questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-05 { ; time=3:01:36.89-SF5 on P4-2000 reset=2004 type=formula formulafile=jim.frm float=y formulaname=ObliqueManPlus inside=255 center-mag=+0.034148955808/+0.034200698652/205344/\ 1/-132.5/0 params=0/0/-0.75/0/0.0075/0.0075 maxiter=7500000 logmap=6129 periodicity=10 colors=000_Ef_Eh_Ej_Dk_Dm_Do_Cp_Cr_CsZDrYErXErXFrW\ FrVGrVGrUHrTHrTIrSIqRJqRJqQKqPLqPLqOMqNMqNNqMNqLOp\ KOpKPpJPpIQpIQpHRpGSpGSpFTpEToEUoDUoCVoCVoBWoAWoAX\ o9Xo8Yo8Yo9Zn9ZnAZnA_nB_nB_nB`nC`nC`mDamDamDamEbmE\ bmFbmFcmFcmGclGdlHdlHdlHdlIelIelJelJflKfkKfkKgkLgk\ LgkMhkMhkMhkNikNijOijOjjOjjPjjPkjQkjQkjQkjRkkSkkSk\ lTklUklUkmVkmWkmWknXknXknQmjJofDqb6sZ0tW1rX1pY2oZ2\ m_3l`3ja4ia4gb5fc5dd6be6af7_g7Zg8Xh8Wi9Uj9TkARlAPm\ BOmBMnCLoCJpDIqDGrDFrCEdBDRBCECDFCDGCDGCEHCEICEICF\ JCFKCFKCGLDGLDGMDHNDHNDHODIPDIPDIQDJQDJRDJSEKSEKTE\ KUELUELVELVEMWEMXEMXENYENZFNZFO_FO_FO`FPaFPaFPbFQc\ FQcFQdFQdGRcGSbHTaHTaIU`IV_JW_JWZKXYKYXLZXLZWM_VM`\ VNaUNaTNbTOcSOdRPdQPeQQfPRgOSgOThNUiMVjMWjLXkKYlJZ\ mJ_mI`nHaoHbpGcpFdqFerEfsDgsChtCiuBjvAkvAlw9mxCnxF\ owKpvPqwUrwUswUtxUuxUvxUwxUzyUzyUzyUzyUzzUzzXzz_zz\ bzzezzhzzkzznzzqzztzzwzzz } frm:ObliqueManPlus {;Jim Muth z=p1+pixel, c=p2+(p3*pixel): z=sqr(z)+c, |z| <=100 } END PARAMETER FILE=========================================

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