February 2004 - Fractint - mailman.xmission.com

Re: FOTD 18-02-04 (Where is the Seahorse [5])
by Jim Muth 18 Feb '04

18 Feb '04

At 10:57 AM 2/18/04 -0600, Paul Lee wrote: >Sorry for the lateness of putting up Jim's current FOTD >image, but I when it rendered in about 2 seconds, I >figured something was not quite correct. I did not realize that an earlier version of the formula existed with the same name. The image on the web site is the correct one. I have renamed the new version of the formula SliceJulibrot2 as Paul suggested. Jim M.

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FOTD 18-02-04 (Where is the Seahorse [5])
by Jim Muth 18 Feb '04

18 Feb '04

FOTD -- February 18, 2004 (Rating 5) Fractal visionaries and enthusiasts: Since yesterday, I have reworked the Julibrot rotation formula and given it a new name. The only change is that the angles of rotation are now entered as degrees rather than fractions of pi. This makes it easier for me to work with. It's hard enough trying to think in four dimensions without doing the conversion math. The new formula is included in the parameter file at the bottom of this letter, but the [frm:] that I have inserted in front of the formula name must be removed before the formula can be copied into a formula file. Using the new formula, today's image takes us to the area we know and love so well -- Seahorse Valley of the Mandelbrot set. But where are the seahorses? Actually, they are in the picture, but they are distorted to such a degree that they have become totally unrecognizable. The thing we know as Seahorse Valley is actually nothing more than a particular part of a two-dimensional slice down the center of the four-dimensional Z^2+C Julibrot figure. This slice is known as the Mandelbrot set. But Seahorse Valley is not limited to two dimensions. It actually extends off into two more dimensions, both of which are perpendicular to the familiar Mandelbrot aspect of the valley, making the entire valley a true four-dimensional object. These two extra dimensions, when displayed on the screen, create the familiar Julia set associ- ated with Seahorse Valley. A slightly distorted version of this Julia set may be seen by making one full outzoom from today's image. The Julia set is distorted because it is not a true Julia set. The orientation of the image on the screen has been slightly rotated in four different directions from the true Julia orientation. The spirals appearing on the tips of the valleys are Julia features which are familiar enough, but what is that straight- edged border cutting diagonally through the scene? It is not part of a Julia set, nor is it a part of the Mandelbrot set. It is the edge of something entirely new, which I call a bridge, a true 4-D object totally impossible for mere 3-D beings to visualize. These straight edges are one of the most common features of the odd slices of the Julibrot, and make up an entire world in themselves. We will be seeing many more of them as we delve deeper into the hyperspace of four dimensions. Today's image, which consists mostly of gaudily colored spirals and a straight edge, has been named "Where is the Seahorse". The name was inspired by the fact that, though the scene is Seahorse Valley, no seahorses are recognizable. The comb-like fringes throughout the image are true features, and not artifacts. These fringes are also very common in the odd slices of the Julibrot, especially in the areas associated with Mandelbrot valleys. Sometimes these odd slices are rather unpleasant appearing, as illustrated by today's image, which I could rate at only a 5. Taking the render time of 23 minutes into consideration gives an overall value of 21. Today's hyper-image may be seen by starting the parameter file and sitting back to watch the fun, or by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> thereby saving time but missing the fun. The temperature reached 36F 2C and the clouds increased threateningly on Tuesday here at Fractal Central, but the forecasted snow never arrived. The cats not only approved of the situation, they actually found the courage to endure over 1/2 hour in the yard at the warmest time of the day. And when evening came, no treat was needed. Today is starting sunny and milder. It should be an even better day for the local cats. For me it will be an average day. Most days are. And when I start pondering the fourth dimension, that will also be part of an average day. Until next FOTD, take care, and where does one look to find this fourth dimension we hear so much about? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ WhereIsTheSeahorse { ; time=0:23:49.82--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot passes=t center-mag=-1.11565/-0.0388942/7.803134/1/-35.0000\ 000000000142/3.85524945301085609e-014 params=86/89/89/89/-0.75/0.03/0/0 float=y maxiter=65000 inside=0 logmap=yes periodicity=10 colors=000bOScNQdMPeMNfLMgKLhKJiJIjIGkIFlHEmGCnGBo\ F9pE8qD6rE7qF8oG9mG9kHAiIBgJCeJCcKDaLE_LEYMFWNGUOH\ TOHRPIPQJNRKLRKJSLHTMFUKGTMGSNGROGQPGPQGPRGOSGNTGM\ UGLVILWKKUMKSOLUQMWSMXUNZWN`YOa_OcaPdcPfeQhgQiiRkk\ QkmRloSmpTnnUolVojWpiXqgYreZsc_sa`t_auYbvWawXcvXev\ YgvYhvZjvZlvZmv_ov_qv`sv`tvavvaxv`zyayvbxscxpdwmev\ jfvgfudgtahtZisXjsUkrRkqOlqLmpInoFooCpn9pn7okAohDo\ eFobIoRKoQNoPPoNSoMUoKYoIaoFbo9coIcnNblRajU_hWZfYY\ d_WbaV`cUZeVXgWVgWTgXRfXRfYTfYUfZVe_Xe_Ye`Ze``daad\ abdbddceccfcdhcdiceicejceigZhkTfpMetFey8dx9dwAdvAd\ uBdtBdsCdrCdqDdpDdoEdnEdmFdlFclGckGcjHciHchIcgIcfJ\ ceJcdKccKcbLcaLc`Mc`MdaNdaOdaPebQebRebSecSfcTfcUfc\ VfdWgdXgdXgeYgeZhe_he`hfahfaifbigcigdigejgfjhfjhgj\ hikikkimkioljqkiskhukhwkgxkgzkfzjezjezjdzjdzjczjbz\ ibziaziazi`zi_zi_zhZzhZzhYzhXzhXzhWzgWzgVzgUzgUzgT\ zeSzgTzhTziUzkQzmQzmPzmOz } frm:SliceJulibrot {; 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 20.0 PAR-FORMULA FILE==================================

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FOTD 17-02-04 (A Very Deep Scene [6])
by Jim Muth 17 Feb '04

17 Feb '04

FOTD -- February 17, 2004 (Rating 6) Fractal visionaries and enthusiasts: While working on the Julibrot rotation formula last evening, (I wanted to make a few changes.), I took a short diversion into the very-deep, unexplored depths of the Mandelbrot set, down to where no one has gone before and the patterns around the midgets are all circles. The exact location of today's scene is on a filament of a larger midget, which in turn is on a filament of a still larger midget that lies on a filament extending from the northern shoreline of the large period-2 bud of the M-set. I named the picture "A Very Deep Scene", a name that needs no explanation. When the time came to rate the image, I decided on a 6. All images this deep should be at least a little above average. When the two-hour render time is considered, the overall value drops to a measly 4.9. But the value may be increased immensely by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I sent the image to Paul in a separate e-mail earlier this morning, so it should be posted very soon. Monday, the Presidents' Day holiday here at Fractal Central, passed like any other day. I didn't even realize it had been a holiday until the day was nearly over. Holidays mean little when every day is a holiday, filled with the joy of fractals. Well, there is that slight matter of the design work that must be done on schedule, but that also is more fun than labor. The fractal cats must have agreed, for despite the below freezing temperatures of 30F -1C that kept them indoors, their spirits remained high. This morning is starting cloudy, with possible snow threatening. We'll see what happens with the cats if the conditions deteriorate. For me, the immediate task is to finish the modicum of work so that I can get back to the Juli- brot formula. If I find anything, I'll present it as tomorrow's FOTD. Until then, take care, and though the attributes of the Julibrot are impossible, we explore it anyway. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Very_Deep_Scene { ; time=2:02:27.65--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=-1.013604105547047168538693807702/0.373\ 6435665162143165812429607776/4.737036e+026/1/-177.\ 5/2.03941030729737349e-013 params=0/0 float=y maxiter=7500 bailout=9 inside=0 periodicity=10 colors=000VTzROzSPzTQyUQwVglYej`cic`gfZfiXdlUcoSar\ Q`qPZqOXqNVqMTpLRpKPpJNpJLoIJoHHoGFoFDnEBnD9nC7nC5\ lLDkULjbTik`hsggqefpceobdn`cmZblYajW`iU_hTZgRYfPYe\ OXgRWhTViVUjXUkZTl`SmbRndQofQphR`eRLbUN_XPY_RWbTTe\ VRgXPjZMm`KpbIsdFvfDxhBtdAqaAnZAkWAhT9eQ9bN9_K9XH9\ YJAZKB_LC`MD`NEaOFbPGcQHcRIdSJeTKfULfVMhTViRckPllO\ tfRkaTcXWVSYNN`EIb6Ja7Ja7J`7K`7K_7K_8LZ8LZ8E5YF6ZG\ 8_H8`I9aJ9bKAcLAdMDeNFfOHgPJhQLiRNjSPkTRlUTmVVnVXo\ WZpY`q_as`ctbeudgvejvdmwcpxbsyfuzWT9UVASYCP_DObENe\ GMhHKkIJnKHqLFtMLwPQzRVzT_ZWdUYiQ_nLasHdxCfz8hz4jz\ 8grBekFccI`XMZPPXISVHXUH`UHeTGiTGnSarSfvSkwTmwTowU\ qwUrwUswVtwVuxVvxWwxWxxWyxXuxXqxXmu_knaiichdff_hdV\ jcQleSjgTiiUhkVgnWeqXdtYcwZaz__y`Zy`Zy`Zz`Zz`Zz`Yz\ `Yz`Yz`Yz`Yz`Xz`Xy`Xy`Xy`XzdWzhWzlVzoVzsUzvUzzUzzT\ yzSszSnzVjaYgY`dVcaRfZNiWKlTGoQCrN9tMrdQqgUqjYqm`q\ odqrhqulqxoqzjlzfgzbbzZYz } END PARAMETER FILE=========================================

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FOTD 16-02-04 (Triple Point [7])
by Jim Muth 16 Feb '04

16 Feb '04

FOTD -- February 16, 2004 (Rating 7) Fractal visionaries and enthusiasts: This happens every time I start thinking about the fourth dimension. Today's image starts what may prove to be a lengthy journey in the oblique slices of the four-dimensional Z^2+C Julibrot figure. The formula I use for this exploration was developed about five years ago by John Goering and revised slightly by me. I have not posted this particular version previously. Since I will be using it often in the days to come, be sure to remove the frm: from its name and copy it into your formula file. This formula does not draw every possible slice through the four- dimensional figure, but it draws more slices than any other in my vast collection. It can do a smooth rotation from the Julia to the Mandelbrot aspect. And it reveals one of the least known oddities of the world of fractals -- that there are two slices through the Julibrot that produce a Mandelbrot set. One of these slices is drawn when the (p1) and (p2) parameters of the formula are set to zero. I leave it to the intrepid fractalists to find the parameters that reveal the second Mandelbrot set. One hint -- the (p1) and (p2) parameters need to be varied only somewhere between +1 and -1. Today's image is another view of the orange midget of yesterday's image, using the same color palette. I have named it "Triple Point". There is not much to be said about it, except that it is a remote slice of the Julibrot, which appears as though it is being pulled in three directions. The rating of 7 and render time of 7 minutes give an overall value of 84. Starting with tomorrow's FOTD, I'll do some heavy-duty exploration of the fourth dimension. But before that time arrives, save a few minutes by downloading the finished image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday was sunny here at Fractal Central, but the temperature hovered around freezing all day. This was too chilly for the fractal felines, who spent the day indoors, seeking the warmest spots they could find. Thomas managed a few hits at his old playtoy before he settled for the day. Tippy just settled. Today is starting even colder, with a temperature of 14F -10C. The cats, who are growing slower every year, will likely have another inactive day. As for me, when the work is finished, I'll have a fractal day. Until next time, take care, and don't get dizzy trying to figure those Julibrot rotations. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Triple_Point { ; time=0:07:11.60--SF5 on a P200 reset=2003 type=formula formulafile=julibrot.frm formulaname=SliceJulibrot passes=1 center-mag=+0.00000000000130513/+0.000000000008816\ 47/2.524132e+011/0.03598/101.821445919962812/-76.3\ 113167840462694 params=0.83333/0.5/0/0/0.351424051\ 7840664/0.06386667204878391/0.3514240517840664/0.0\ 6386667204878391 float=y maxiter=5000 inside=0 logmap=-820 periodicity=10 colors=00001P02P03P14Q25Q36Q47R58R69R7AQ8BQ9CPADPB\ EPCFPDGQEHRFIQGJRHKSILTJMUKNVLOWMPXNQYNRXOSXPTXQUX\ RVXSWXTYXT_X`bageenkjuonvhgwa`wWUxPNyIGyCAxFBxHCxK\ DxMDwPEwRFwTFwWGwYHv`IvbIveJvgKviKueJtbIs_IrXHqUHp\ QGoNGnKFmHFlEEkBEfDLbERZGXVHbQIeMKgILiEMgCOeBPd9Rc\ 8SbAUcCVcEWcGYcIZcK_dMadObdQcdSfdUheWjeYme_oe`meXk\ iTilPgpLesHcwDZztiTqgVofXleYjd_hc`ebbcaca`eZ_gXZhU\ YjSXkQWmNVnLUpJTqLVmMWjNYgPZdQ``RaYTbVUdSVeOXgLYhI\ ZiFXjHWjIVjJUjKTjLSjMQkOPkPOkQNkRMkSLkTPgSTdRWcQ_c\ PbcOfcNicMmcLpcKtcJwcJscHocFkcEgcCdcA`c9Xc7Tc5Qc4O\ cBMcIKeOIgVGi`EkgCpmAtt9xzCvuEtpGrkIpgKobNqYPsTRuP\ TwKVxFXzBZzL`zVbzc`z_ZzWXzSVzPTzLRzHQzEQzIQzLPzPPz\ SPzWPzZPzbPzeRzcSzbUz`Vz_XzZYzX_zW`zVazTczSdzQfzPc\ zO`zVgzUdzYaz`ZzcXzeVzdTzcVzbYza_zaaz`cz_fzZhzYjzY\ lzXozWqzVszUuzUnzSgzQ`zOUzMOzLVzJ`zIgzHmzGtzFzzEwz\ LtzRrzXozblzhjznczVezThzR } frm:SliceJulibrot {; draws most oblique slices pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1), b=pi*imag(p1), g=pi*real(p2), d=pi*imag(p2), 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 20.0 PAR-FORMULA FILE==================================

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FOTD 15-02-04 (Mandelbrot Aspect [7])
by Jim Muth 15 Feb '04

15 Feb '04

FOTD -- February 15, 2004 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's FOTD made such an abomination of such a great scene that I feel compelled to make restitution. I do this by presenting the same scene in its Mandelbrot aspect as today's FOTD. In an attempt to atone for my wrongdoing, I have given the scene a new color palette, one that might be even a bit too intense. But, after what I did yesterday, the midget in question deserves all the help it can get. I named the image "Mandelbrot Aspect" because that's what it is. But let's not forget the five other mutually perpendicular aspects of this four-dimensional scene. The Julia aspect is only one of these. Perhaps I'll see what can be done with today's midget in the other perpendicular directions and present these as the next five FOTD images. I'm once again getting the urge to ponder the fourth dimension, and we all know what happens when I do that. I seem to remember writing in an FOTD discussion about five years ago about a four-dimensional Titanic striking a four- dimensional iceberg. I half finished the description of what a three-dimensional person standing on the deck might see, and then I dropped the topic. Of course, the whole thing might be pure fantasy, since stable planetary orbits are not possible in spaces of four or more dimensions. I originally rated today's image at an 8. Then I noticed that the colors were a bit too strong for comfort, and dropped the rating to a 7. But a seven is still above average, and combined with a render time of 45 seconds gives an overall value of 921. For those who would rather not render, the completed GIF image is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The clouds hung tough on Saturday here at Fractal Central, and the temperature stopped rising before it reached 41F 5C. For proper comfort, the fractal cats demand either full sun or a temperature above 50F 10C. Since neither of these conditions prevailed, the cats were not satisfied, and showed their dis- satisfaction by returning inside only a few minutes after they had gone out and looking as unhappy as they could. I let them look unhappy for a few hours, then gave them a treat of salmon. I hope they enjoyed their special treat, for the salmon is gone and the next treat will be the standard tuna. Today is the seventh day of the week. (Our calendar is wrong. Monday is actually the first day of the week.) It's a day of rest both for the Deity and the created. And, being among the created, I intend on resting. The best source of relaxation I know of is a computer screen on which a fractal is taking shape. I wouldn't be surprised if that's where I find myself in a few hours. Until next time, take care, and if I was not created, I must be a lucky accident. The chances of such an accident must be far greater than one in a googolplex to the googolplex. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Aspect { ; time=0:00:45.70--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=+0.35142405178407020/+0.063866672048795\ 94/3.309344e+011/1/107.500211829640378/-0.00010569\ 7737740419184 params=0/0 float=y maxiter=5000 bailout=9 inside=0 logmap=-820 periodicity=10 colors=00001P02P03P14Q25Q36Q47R58R69R7AQ8BQ9CPADPB\ EPCFPDGQEHRFIQGJRHKSILTJMUKNVLOWMPXNQYNRXOSXPTXQUX\ RVXSWXTYXT_X`bageenkjuonvhgwa`wWUxPNyIGyCAxFBxHCxK\ DxMDwPEwRFwTFwWGwYHv`IvbIveJvgKviKueJtbIs_IrXHqUHp\ QGoNGnKFmHFlEEkBEfDLbERZGXVHbQIeMKgILiEMgCOeBPd9Rc\ 8SbAUcCVcEWcGYcIZcK_dMadObdQcdSfdUheWjeYme_oe`meXk\ iTilPgpLesHcwDZztiTqgVofXleYjd_hc`ebbcaca`eZ_gXZhU\ YjSXkQWmNVnLUpJTqLVmMWjNYgPZdQ``RaYTbVUdSVeOXgLYhI\ ZiFXjHWjIVjJUjKTjLSjMQkOPkPOkQNkRMkSLkTPgSTdRWcQ_c\ PbcOfcNicMmcLpcKtcJwcJscHocFkcEgcCdcA`c9Xc7Tc5Qc4O\ cBMcIKeOIgVGi`EkgCpmAtt9xzCvuEtpGrkIpgKobNqYPsTRuP\ TwKVxFXzBZzL`zVbzc`z_ZzWXzSVzPTzLRzHQzEQzIQzLPzPPz\ SPzWPzZPzbPzeRzcSzbUz`Vz_XzZYzX_zW`zVazTczSdzQfzPc\ zO`zVgzUdzYaz`ZzcXzeVzdTzcVzbYza_zaaz`cz_fzZhzYjzY\ lzXozWqzVszUuzUnzSgzQ`zOUzMOzLVzJ`zIgzHmzGtzFzzEwz\ LtzRrzXozblzhjznczVezThzR } END 20.0 PAR-FORMULA FILE==================================

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Vortex Swirling 15 Feb '04

15 Feb '04

Edwin, Any tips on how to translate one of the .fct files so that that the picture can be generated in Fractint with one of Jim's formulas? I'd just love to generate Kandy Pop and rotate the palette for fun! --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.588 / Virus Database: 372 - Release Date: 2/13/2004

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FOTD 12-02-04 (Unwatched Watchtower [4])
by Jim Muth 15 Feb '04

15 Feb '04

FOTD -- February 12, 2004 (Rating 4) Fractal visionaries and enthusiasts: What evil has befallen the splendid midget that appeared as yesterday's FOTD? Where we once had a lovely, perfectly symmetrical pattern, we now have a mis-shapen, distorted thing that is downright stressful to look at. I have used the same color palette, so what could have caused this abomination? Actually nothing evil was done to the glorious scene of yesterday. I simply shifted my point of view, took a 'photograph' of the same scene from a different direction, and named the picture "Unwatched Watchtower". As I have said often in the past, the Mandelbrot set, the perturbed M-sets and the Julia sets are slices of a single four-dimensional object known as the Julibrot. Since this Julibrot object is four-dimensional, it may be sliced in new ways that produce neither Julia nor Mandelbrot sets, but entirely new aspects of the familiar Julia and Mandelbrot scenes. Today's image illustrates what happens to yesterday's "Watchtower" image when it is seen from one of these new directions. Some slices taken in new directions reveal aspects that are virtually the same as the familiar Julia and Mandelbrot aspects; other slices reveal grossly stretched and distorted aspects such as we have in today's image. In order to fully comprehend why this is so, it would be necessary to visualize the entire inside of the Julibrot, which would be difficult for even a four- dimensional person, not to mention a mere three-dimensional one. To try to understand what is happening in images such as today's I reduce the problem to three dimensions and imagine taking a blob of white silly-putty and a blob of black silly putty, and combining them into a single lump. Then I knead the lump slightly, so that the black and white putties just start to blend, forming well-defined arms and filaments that twist and turn through the interior of the combined blob. Then I cut the combined blob in half to reveal inside features much like those in today's image. The features have not really been stretched, the apparent stretching is due to the angle at which some of the twisting and turning features have been sliced. All this stretching and distorting has taken its toll on the superb original image. Today's version is worth no more than a humble 4, which equals slightly below average. Considering the render time of 7-1/2 minutes, this results in an overall value of 52. The 7-1/2 minute wait while the parameter file runs can be avoided by downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather on Wednesday here at Fractal Central was very average, with lots of sun but a chilly temperature of 39F 4C. The cats' behavior was also very average. After an uneventful hour in the yard, they came inside and settled by the heat for a long sleep. Today is starting cloudy and cold, with snow not far to the south. As long as it stays to the south, the cats will not be worried. My only concern is to get the waiting work finished, a task that will take about two hours to accomplish. Then I'll see what I can find in Fractal Land. The best of what I find will appear as tomorrow's FOTD. Until then, take care, and watch for lurking Julibrots. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnwatchedWatchtowr { ; time=0:07:39.12--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000000227835/+0.000000000001655\ 24/9.466954e+011/0.07488/-42.1987606685050665/-86.\ 2801728293503629 params=19.055/-104.667/2/0/-1.861\ 19088257009/0.000407298011669/-1.86119088257009/0.\ 000407298011669 float=y maxiter=7500 inside=0 periodicity=10 colors=000NleRuhVzkTzlRxmQunOroMopL\ lpJiqIgrGdsEatDZtBWu9Tv8Qw6Nx5LxJT_W_CUZGTZJRZMQZP\ OZSNYWLYZKYaIYdHYgFXdEXbDW_CWYBWVAVT9VQ8VO7UL6UJ5U\ H5UI5TJ5TJ7JY7JY7JY7JY7KY7KY7KY7KY7KY6LX6LX6LX6LX6\ MX6MX6MX6MX6NX6NX6NX6NX6NXyHvwIuvItuIttIssIsrIrqIr\ oIqnJqmJplJpkJojJoiJngJnfJmeKldKlcKkbKkaKj_KjZKiYK\ iXLhWLhVLgULgSLfAAAAAAAAAAAAAAAAAAAEAAEAAEAAEAAEAA\ EBAECAEDAEEAEFAEGAEHAEIAEJAEKAELCEMFENIEPLGROIURKW\ UM_WOcZNicMnhLrmOwrRywUzzWwwbrrgmmjhmmcmoZmqUmsUnu\ WowYqyZsz`uzawzbuvbrqbmlchgcc`cZYcUVdPTeNRfRPgWNh_\ LicJjgHklFlpDmtBnx9nvHdtPVsXMqdCpl3kk6fj9aiCYhFTgH\ OfKKeNFdQAcT6cV7bW7aX8`X8_Y9ZZ9YZAX_AX`BW`BVaCUbCT\ bDScDRdDRdFVgGYiHakIdmJhoKkqLgmMcjN_gOWdPSaQOZRKWS\ GTTCQU8NU5KSISRU_PfgOrnNsoNspNsqNsrMssMstMttMtuLtv\ LtwLtxLtyLtyNnvOitPdrQZpRUnSPkTJiUEgV9eW4c87mEEmKL\ mQSmWZmadmYajV_hRXfOVdLSaHQ_ENYBLWFV_Jcb } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 13-02-04 (Whisk Brooms [5])
by Jim Muth 15 Feb '04

15 Feb '04

FOTD -- February 13, 2004 (Rating 5) Fractal visionaries and enthusiasts: Today's image was never supposed to be. I announced earlier today that there would be no FOTD for February 13. But the other work went faster than expected, and I managed to find the time for a quick trip into the star of the period-5 radical on the northeast shore of the Mandelbrot set. I stopped at a point on an arm of the star at a magnitude just before the switch over to arbitrary precision math becomes necessary, and zoomed into the nearest midget. The result is pretty much as expected, with spiky filaments radiating and branching from the central midget. For some strange reason I named the image "Whisk Brooms". One benefit of stopping just before the switch over to arbitrary precision math becomes necessary is the extreme speed of the image, which renders in only 17 seconds. Unfortunately, the ordinariness of the scene cut a couple points off the rating, but with a render time of mere seconds, even an image with a rating of a 5 has an overall value of 1786, making it well worth the effort of running its parameter file. As always, the finished GIF image is available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy and chilly day here at Fractal Central on Thursday kept the dynamic cats' outdoor time limited to under 15 minutes. But the brief outing in the 41F 5C degree air seemed to satisfy them, and only a small treat of tuna was needed in the evening to keep their moods livable. The work today was heavy, but the Friday 13th jinx did not appear, and the work was finished faster than at first seemed possible. Until tomorrow's FOTD, which hopefully will appear on schedule, take care, and God made fractals at the same time that he made the universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Whisk_Brooms { ; time=0:00:16.87--SF5 on a P200 reset=2003 type=mandel mathtolerance=/1 center-mag=+0.43792435442605380/+0.341892138828262\ 40/1.312819e+012/1/142.836672263020262/-0.000 params=0/0 float=y maxiter=1500 bailout=9 inside=0 logmap=322 periodicity=10 colors=000HMcINdJMeJMfKMgKMhLMiLLiMLjMLkMLlNLmNLnO\ KnOKoPKpPKqPKrQKsQJsRJtRJuSJvSJwSJxQKyOKzMKzKKzIKw\ GKtFLqDLnBLk9Lh7Le5Lc3Ma4L_4KY4KX4JW4JU4IT4IS5HR6G\ Q7GP8FO9FNAEMBDLCGKCKHDOLESOEWRF_UFcXGg`GkcGofHsiH\ ulHvmKwmNvlQujStiVsgZrfaqdepcioaln`lmallbmlcmldkle\ jlfhlhglhelicljblk`kl_kmZknYkoYkpXkqXkrWksVkuVkwUk\ yXkzUkwRgtPdrM`mKXhHUcFQZCMUAJPCMRDPUFSYGV`IYdJ`gL\ ckMfnOirPluNivMfvLdvKawJZwIXwHUwGRxFPxEMxDJyCHyBEy\ ACyFEvJGsNIpRKmWMj_OgcQdgSaiSYkT_iS`gRaeQccPd`OeZN\ gXLhVKiTJkQIlOHmMGoKFpIEqHDpHDpHDpGCoGCoGCoFCoFBnF\ BnEBnEAmEAmDAmDAmD9lC9lC9lC9lFBhIDdLE`KGXKHTKFQKAM\ K0IK0EM0AP06S03V03Y03`00c13f15i27p59rACtFEvKGxPIzU\ LzZNzcPzhRl5Tk6Wm6Yn6_p7aq7dr7fr8hs8ju5ns8lrAkpCjo\ EinGhlIgkLeiNdhPcgRbeTadV`bYZa_Y`bXZeWYhVYkUXnUZq9\ atBcwDezFgzGizIlzKnzMpzNrzPtzRvzSrzWnzZjzbfzebziZz\ lUzrVzoWzmWzkXziYzgYzeZzc } END PARAMETER FILE=========================================

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FOTD 14-02-04 (Unwhisked Whiskbroom [5])
by Jim Muth 14 Feb '04

14 Feb '04

FOTD -- February 14, 2004 (Rating 5) Fractal visionaries and enthusiasts: After saying that there would be no FOTD for February 13, I went ahead and posted one anyway. If this created a minor bit of confusion, those who were confused have my apologies. This morning I found a note from Paul, suggesting that I post my FOTD's the night before the day on which they are due. This is a good idea. I will resume doing this in the near future. I shifted to morning posting because I am always more alert and energetic in the mornings, and can write better. I will adjust my schedule to write the FOTD's a full day in advance, on the morning of the day before, and post them the evening before. The "Unwatched Watchtower" FOTD of two days ago showed a distorted version of a fine midget in the Mandelbrot set. In a letter with quirky spelling that was posted to the Fractint list on Friday, SherLok Merfy commented that the image was a mixture of Mandelbrot and Julia features. In a way, this is what the image of two days ago is. Today's image consists of the same mixture. It is not a Mandelbrot image; it is not a Julia image. It is not actually a distortion of either of these. It is a legitimate aspect of the Julibrot in its own right. By returning to the default magnitude, keeping the (p1) and (p2) parameters unchanged and changing only the (p3) and (p4) parameters, the entire fractal world glimpsed in today's image can be fixed and thoroughly examined, a world as varied as the Julia and Mandelbrot worlds themselves. But as today's image shows, this new world is not all beauty. Like the 'real' world, it holds scenes that are not pretty. Also like the real world, these not-very-attractive scenes hold a strange fascination, and with a bit of effort can be turned into works of art -- kind of like turning a sow's ear into a silk purse. Today's image demonstrates a bit of this artistic regeneration. The regeneration was not great, but it was enough to raise a total loser to a rating of a 5, which is average. There is actually a fine Mandelbrot midget or Julia set lying at the center of the basin in the image. All that is needed to see one of these aspects is to rotate the point of view to the proper direction. I named today's image "Unwhisked Whiskbroom" because it is a distortion of an area similar to the one that appeared in yesterday's image. The render time of 5-1/4 minutes combined with the rating of 5 produces an overall value of 96. The image can be seen and perhaps enjoyed by running the parameter file or by downloading it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday started very busy here at Fractal Central, but the rush was cleared away far sooner than expected. This made the fractal cats quite happy. (They get jealous when I give the computer more attention than I give them.) The weather was pleasant, with sun and a temperature of 45F 7C. This made them even happier. When they ended the day with their faces in their food dishes, eating a treat of salmon, no less, their happiness was complete. Today is starting cloudy but mild. Anything could happen both in the 'real' world and in the fractal world. Check back in 24 hours to see what the 'anything' turns out to be. Until then, take care, and if you don't find a fractal lying on the side- walk the next time you go out walking, look for a meme. They are almost as rare. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ UnwhiskdWhiskbroom { ; time=0:05:14.61--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000041173934/-0.000000000085871\ 50/2.510428e+010/0.01217/11.9165416490383649/85.78\ 47425758229463 params=90.663/54.828/2/0/0.35142405\ 17840664/0.06386667204878391/0.3514240517840664/0.\ 06386667204878391 float=y maxiter=5000 inside=0 logmap=641 periodicity=10 colors=000FH0GIKHJQIKTJLWKMZLNaMOcNPeOQgQRiSSkUTmW\ UoXVmZUm`SmbQmdOleMlgKiiIhkGfmEenCdmEalGZkHXjJViLT\ iMRhOPgPNfRLeTJeUHdWFcYDbZBa`9aa8Z`AW_CUZDRYFOXGMW\ IJVJGULEUMF`HFfDFm8Fs4Eo3Ek3Dh3Dd2Ca2CY2CV2BR1BN1A\ K1AG09D0990960C84EA8GCCIEGKFKMHOOJRQLVSMZUObWQfYSj\ _Tm`VkaXibZgb`ecacdcbee`egZfhXgjVglThnSipQjqOjsMku\ KlwIlxHjxGhxGfxFdwEbwD`wDZwCXwBVwATwARw9Pw8Nw7Lw7K\ v8Kv8Ku8Ju9Ju9Jt9ItAItALO3LO3LO3LO4LO4LO4LO4NQ8PRC\ QTGSUKTWOVXSWZVY_Z_ab`bfbdjcenegrfhucisairZjpXjoUk\ mSklPljNliKmgImfFndDncAoa8o`Dl_Hj_Lg_Qe_Ub_Y`_aZ_f\ W_jU_nR_sP_wM_zK_zI_zLayObwRctTdrWeoZfmagjchgfjeik\ bll`nmYqnWtoTwpRyqSvrStrSrrTorTmrTkrUirUfrUdrVbrV`\ rVYrWWrWUrWSrURqTRqSRqQQqPQqOQqNPqLPqKPqJOpIOpGOpF\ NpENpDNpBMpAMp9Mp8Mp9Om9Pk9Qi9Rg9Se9TcAUaAV_AWYAXW\ AZTA_RA`PBaNBbLBcJBdHBeFBfDBgBEhAHiAKjANjAQkASlAVl\ AYmA`n9cn9eo9hp9TF6RD4PA3 } 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 20.0 PAR-FORMULA FILE==================================

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No FOTD for February 13
by Jim Muth 13 Feb '04

13 Feb '04

Because of too much real work, which must be done, there will be no FOTD for Feb 13. The fractals will return on schedule on Feb 14. Jim M.

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