February 2004 - Fractint - mailman.xmission.com

Re: [Fractint] FOTD 12-02-04 (Unwatched Watchtower [4])
by Fr. Jim Lacasse 13 Feb '04

13 Feb '04

Jim, The Unwatched Watchtower in view is about an 8. Great color. Have a good day. Fr. Jim >>> jamth(a)mindspring.com 02/12/04 07:08AM >>> 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================================== _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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[Fractint] Jim Muth's Feb 10, '04 FotDay with arbitrary precision math
by Hal Lane 13 Feb '04

13 Feb '04

################################################################ [I like this image a lot, Jim. It shows many classic fractal elements, despite not having a visible miniature Mandelbrot set.] When I rendered Jim Muth's Feb 10, '04 Fractal of the day - 'Order from Chaos' at 1024 x 768 I thought I could see the effect of Jim's turning off arbitrary precision math. To confirm this I turned it on and rendered the image. Some rectangular-looking patches of color now varied smoothly in size. This improvement came at the cost of a 27 hour compute on my P400, but visibly improved the image. Long compute time images can be done conveniently as Disk/RAM 'Video' images. My rendition below includes: - my longtime favorite color map: Leather Gem - arbitrary precision math I obtained the Leather Gem color map from an entry to a Fractal Art contest. It seems to have slightly more muted colors than Fractint automatically generates. It also has smooth color gradations that do not show banding between adjacent iterations for most of its range of colors. To get Jim's 5 minute render, turn the arbitrary precision math off -- as Jim did -- by adding: mathtolerance=/1 to the parameter file below. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START 20.0 PAR FILE================================ Order_fm_Chaos2 { ; time=26:51:35 CPU=P400 1024x768 Jim Muth's ; Feb 10,'04 Fractal of the day with the ; Leather Gem color map and arbitrary ; precision math turned on. - Hal Lane reset=2003 type=mandel passes=1 center-mag=-1.77551631029264878/0.004553217222571274/3.305215e\ +013/1.0404/13.9106570650115682/-0.977835246052904727 params=0/0 float=y maxiter=80000 bailout=9 inside=0 periodicity=10 sound=off colors=YD0Q82O61M41<3>Q71R81S91fM5<3>iO5jP5kQ6<9>UB3S92Q82<3>I\ 10931A00<3>VK0_P0dU0<3>zm0<3>zb0z_0zX0zU0<3>`F0UC0O80H40<2>A47\ 73A73C<3>56K47M48O39Q2AS<8>9QaASbATc<3>E`hFbiGdi<3>JklKmmJkj<7\ >CURBSOAQM<3>6GB5E86G9<9>EWHFYIGZJ<2>JdMKfNLhM<5>bmDenBhoA<3>t\ s3wt1sr2<5>Zf8Vd9SbA<3>DVF<4>CPCCNBCMA<2>BI9BH8BH8<3>AE79D6DE6\ <3>UI9YJAaLBeMCgODjQF<9>tgGuiGvjG<2>ypGzrFzrK<3>yufxukxvqwww<3\ >rhh`F0`F0<5>UA0T90S80R80Q70P60<3>L30K30J20I10I10<16>UB2UB2VC2\ <3>YE3<2>S92 } END 20.0 PAR FILE================================ ################################################################ --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com) Version: 6.0.581 / Virus Database: 368 - Release Date: 2/9/04

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The Face Of Wegner (Tim's Error)
by SherLok Merfy 12 Feb '04

12 Feb '04

Tim's_Face { ; He looks even more ghastly as a negativ. reset=2003 type=tim's_error function=tanh center-mag=-0.0868849/-9.46742e-005/2.491917/1.5675/90/3.8857805861880\ 4789e-016 params=0/0 float=y maxiter=255 inside=maxiter potential=255/255/0 colors=0000001zz<28>XggYggZff<2>bddcccf__<3>oIIrEEu99w55z00<34>H0iG0jF\ 0k<3>90q70s60t<2>20x00z01y<46>0s70t60u5<2>0x20z02z2<23>mzmozoqzq<2>wzw\ zzzzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz00\ 0zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00f\ zz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0f0zzz000zzU00fzz000z0\ f0zzz000zzU00fzz000z0f0z }

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Latoocarfian parameters (last part)
by Gerald K. Dobiasovsky 11 Feb '04

11 Feb '04

For what it's worth, here is the rest of the bunch of the Latoocarfian parameters... Gerald ;------------------ Start of PAR --------------------- Number_31 { ; reset=2001 type=latoocarfian function=cos/sin/sin/cos corners=-4.953885/4.521355/-3.675321/3.431109 params=-1/-1/2/-2 float=y maxiter=1000 colors=(a)chroma.map } Number_32 { ; reset=2001 type=latoocarfian function=sin/cos/cos/sin corners=-6.870226/6.437695/-5.112576/4.868364 params=1/1/3/-3 float=y maxiter=1000 colors=(a)chroma.map } Number_33 { ; reset=2001 type=latoocarfian function=asin/sin/asin/sin corners=-5.681818/5.681818/-4.261364/4.261364 params=3.14159265358979/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_34 { ; reset=2001 type=latoocarfian function=sin/asin/sin/asin corners=-5.126411/6.237226/-1.816774/6.705953 params=3.14159265358979/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_35 { ; reset=2001 type=latoocarfian function=sin/asin/sin/asin corners=-5.737359/5.626277/-1.816774/6.705953 params=2.71828182845905/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_36 { ; reset=2001 type=latoocarfian function=sin/acos/sin/acos corners=-13.02041/0.1814591/-1.771725/8.129679 params=2.71828182845905/3.14159265358979/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_37 { ; reset=2001 type=latoocarfian function=cos/asin/cos/asin corners=-3.924439/-2.621505/2.5883915/3.5655919 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_38 { ; reset=2001 type=latoocarfian function=cos/asin/cos/asin corners=-5.015268/-1.530677/1.77027/4.383713 params=2.71828182845905/2.71828182845905/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_39 { ; reset=2001 type=latoocarfian function=acos/sin/acos/sin corners=-5.120538/1.324287/0.6601826/5.493801 params=2.71828182845905/2.71828182845905/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_40 { ; reset=2001 type=latoocarfian function=acos/sin/acos/sin corners=-3.975715/7.109383/-2.655415/5.658409 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_41 { ; reset=2001 type=latoocarfian function=acos/cos/acos/sin corners=-3.975715/7.109383/-2.655415/5.658409 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_42 { ; reset=2001 type=latoocarfian function=cos/asin/sin/acos corners=-10.72341/10.51473/-4.929214/10.99939 params=2/2/-2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_43 { ; reset=2001 type=latoocarfian function=cos/asin/sin/acos corners=-3.351484/3.50045/-1.772775/3.366175 params=2/2/-1/0.5 float=y maxiter=1000 colors=(a)chroma.map } Number_44 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-2.435012/5.283331/-1.395576/4.393181 params=2/2/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_45 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-1.236156/4.537164/-1.194501/3.135489 params=2/1/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_46 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-2.859903/6.16091/-1.930376/4.835234 params=3/1/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_47 { ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-5.692019/8.993026/-2.515938/8.497845 params=3/2/2/2 float=y maxiter=1000 colors=(a)chroma.map } Number_48 {;a and b control the Lissajous coefficients ; reset=2001 type=latoocarfian function=acos/sin/cos/acos corners=-2.591823/5.749282/-1.572917/4.682912 params=3/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_49 { ; reset=2001 type=latoocarfian function=acos/sin/sin/log corners=-6.161078/9.721416/-8.4665/3.44537 params=1/1/1/1 float=y maxiter=1000 colors=(a)chroma.map } Number_50 { ; reset=2001 type=latoocarfian function=acos/sin/sin/cos corners=-2.755082/5.694404/-3.349552/2.987563 params=2/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } Number_51 { ; reset=2001 type=latoocarfian function=acos/sin/sin/cos corners=-3.592511/6.331539/-3.86708/3.575958 params=1/2/2/1 float=y maxiter=1000 colors=(a)chroma.map } ;------------------- End of PAR -----------------------

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FOTD 28-01-04 (The Quintessential Midget [8])
by Jim Muth 11 Feb '04

11 Feb '04

FOTD -- January 28, 2004 (Rating 8) Fractal visionaries and enthusiasts: Unless I am mistaken, today's FOTD is the third consecutive one that rates an 8. Combined with the render time of 19 minutes, its overall value is 41. This unexpected spate of excellence might have been equalled sometime in the past, but at the moment, I cannot recall when. But how did this excellence come about? Surely the extra time available for fractal exploration, due to the bad weather and resulting lack of work, is largely responsible. When I saw the golden ratio mentioned on the list, having nothing else to do, I was inspired to venture into the fractals that this mysterious number can produce. Turning to the MandelbrotMix4 formula, I checked the fractal that results when 0.8 parts of Z^(1.618) are subtracted from 0.8 parts of Z^(-1.618) and (1/C) is added. This fractal is an oversized thing consisting of three main Mandeloids, the largest of which barely appears in the southwest corner of the default screen. In today's scene I ignored this giant Mandeloid, which is mostly off the screen, and turned instead to the larger of the two Mandeloids that fit entirely onto the screen. This Mandeloid appears to be in what I call a condition of stress, as though it were ready to be cut off by a too-small escape radius. But stressed as it might be, the midget still has some interesting areas to check. The area I chose is the interior of the west branch of the valley leading to the large southern bud of this midget. Hidden there, deep in a cut-off area of interest, I found the midget that appears in today's image. And what a splendid midget it is. It is so splendid in fact that I named it "The Quintessential Midget", a title that is too long to fit into the allotted space in the parameter file. Actually, the midget looks as though it could use a few more iterations. This could easily be done, but if I raised the maxiter, it would mess up the color palette, which is what really makes the image. The render time of 19 minutes is a small price to pay for such a fine example of a midget. And there is even better news -- the completed GIF image is available for download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Freezing drizzle prevailed all day Tuesday here at Fractal Central, making the area roads an ice-skating rink. The drizzle did not stop until it was replaced by heavy snow around sunset. With a temperature of 25F -4C, the day was a true winter wonder- land. Unfortunately, the fractal cats do not enjoy wonderlands, and passed the day indoors by the heat. I have lost track of the snow depth this morning. It appears to be around 1 foot in the U.S. measuring system, or 30cm in the rest of the world. Whatever the exact amount of snow, the dynamic duo will have another indoor day. For me, the work appears to have come to a halt, probably because everyone is snowed in. This means a good opportunity to find more great fractals. Any success I might have in Fractal Land will appear as tomorrow's FOTD. Until then, take care, and keep those fractals iterating. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ QuintesentialMidgt { ; time=0:00:00.00--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.39979361592270500/-0.608017365655577\ 00/4795150/1/-75/-1.8414457056414868e-008 params=-0.8/1.618034/0.8/-1.618034/0/0 float=y maxiter=2400 inside=0 logmap=305 periodicity=10 colors=000HEZJEVLERMENRCTVBY_9bc8gh6ll5qj6sh7tf8ud\ 8vTIoHRi5_c4`a4a_4bY4bX3cV3dT3eR3eQFdZQdg`dodephep\ keqoeqreqUmaSgdQbgPYjNTmLOpKJsIEvH9xLBwPDwTFwXHw`I\ wkBmv4duB_tHWtNSsTNrZJrdFnaLk_RgYXdWb`UhYSnUQtROzT\ LxUJvVGtWErYCpZ9n_7l`5kD7y9Bq6Fi3Ia4Oe5Th6Yl7bo6Xi\ 5Rc4LY3FS29MfspiodllToiIq`FrSCsJ9tA6u23t45s67s79r9\ BrADqCFqDHpQJzzzzzmzwMxgGsUHn9Ii8Jd8J_7KV7LQ6ML6MK\ INKTOKdPKoPK_WKKbK5hzPkrabjmUcyMWvSOtXGrb8pg0nlAqq\ KtvUwzUwzUwzUwzUwzUwzDP6W9IG49icjYUZNKNBABDqoftncb\ RaM3TK4LJ5CH64G7HQJUZVfgepTgzEhjFlWGpHHt2HxQnkYsPd\ w2J7DRc1DK0gXnC5a9gLxmGcXAKG5H`yBOd5CKdBrF5LfzMWeG\ LSBAE5cu7Uf5KT3N4VH5ZB5a56e06h0IW0UJ6QGBNEGKBMH9RE\ 6WB4YH7_M9aRCcWEe`HfeJidPkcUmb_oadr`it_ovZtxYyuZwr\ ZvoZum_tj_sg_re_qZ`iTaaNaUTeVYhVckVhnVkqUnsWqvYtx_\ wzaxzcyzezzgzzizzkzzmzzozzqzzszzuzzvzzwzzxzzyzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 11-02-04 (Watchtower [8])
by Jim Muth 11 Feb '04

11 Feb '04

FOTD -- February 11, 2004 (Rating 8) Fractal visionaries and enthusiasts: In yesterday's FOTD we tried to show what happens in filaments along the shorelines of midgets that lie on the negative X-axis of the Mandelbrot set. This first attempt was only moderately successful. Today we make the second attempt -- one that is somewhat more successful. We jump to a midget on the X-axis a short distance beyond the largest midget, and examine the filaments near its shoreline. The filaments here are covered with tiny nodes which remind me of long fences with watchtowers positioned every kilometer or so. These fractal watchtowers are islands of chaos with smaller midgets at the center. Today's image illustrates one of these watchtowers -- an island of chaos sitting in a prairie of order. I named the image "Watchtower" and rated it at an 8. The rating might be a bit excessive, but I do rather enjoy the image. When combined with the render time of 44 seconds, the image has an overall value of 1067. (I really must bring some consistency to the way I determine the overall value.) The image may be seen by running the attached parameter file and enjoying the lightning-fast rendering show, or by taking a trip to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and downloading the completed GIF image from there. Tuesday turned out to be the best day in over a month here at Fractal Central. The temperature of 52F 11C, gentle breezes, and warm sun, gave the cat duo all they could ask for. They explored the yard from noon until sunset, somehow managing to stay out of trouble for over 5 hours. Today is starting colder, but not extremely so. It remains to be seen what the cats will make of the day. I'm going to make another work day of it. About 4 hours of work waits in the rack beside the desk, and the only way to move it to the finished rack is to get started. So until next FOTD, take care, and how many fractals could fit on the head of a pin? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Watchtower { ; time=0:00:43.45--SF5 on a P200 reset=2003 type=mandel passes=1 mathtolerance=/1 center-mag=-1.86119088257009000/+0.000407298011668\ 70/2.823726e+012/1/-7.27769909978726215/0.00000603\ 84787128533 params=0/0 float=y maxiter=7500 bailout=9 inside=0 symmetry=none periodicity=10 colors=000NleRuhVzkTzlRxmQunOroMopLlpJiqIgrGdsEatD\ ZtBWu9Tv8Qw6Nx5LxJT_W_CUZGTZJRZMQZPOZSNYWLYZKYaIYd\ HYgFXdEXbDW_CWYBWVAVT9VQ8VO7UL6UJ5UH5UI5TJ5TJ7JY7J\ Y7JY7JY7KY7KY7KY7KY7KY6LX6LX6LX6LX6MX6MX6MX6MX6NX6\ NX6NX6NX6NXyHvwIuvItuIttIssIsrIrqIroIqnJqmJplJpkJo\ jJoiJngJnfJmeKldKlcKkbKkaKj_KjZKiYKiXLhWLhVLgULgSL\ fRLfQLePLeOMdNMcMMcKMbAEAAEAAEAAEAAEBAECAEDAEEAEFA\ EGAEHAEIAEJAEKAELCEMFENIEPLGROIURKWUM_WOcZNicMnhLr\ mOwrRywUzzWwwbrrgmmjhmmcmoZmqUmsUnuWowYqyZsz`uzawz\ buvbrqbmlchgcc`cZYcUVdPTeNRfRPgWNh_LicJjgHklFlpDmt\ Bnx9nvHdtPVsXMqdCpl3kk6fj9aiCYhFTgHOfKKeNFdQAcT6cV\ 7bW7aX8`X8_Y9ZZ9YZAX_AX`BW`BVaCUbCTbDScDRdDRdFVgGY\ iHakIdmJhoKkqLgmMcjN_gOWdPSaQOZRKWSGTTCQU8NU5KSISR\ U_PfgOrnNsoNspNsqNsrMssMstMttMtuLtvLtwLtxLtyLtyNnv\ OitPdrQZpRUnSPkTJiUEgV9eW4c87mEEmKLmQSmWZmadmYajV_\ hRXfOVdLSaHQ_ENYBLWFV_Jcb } END PARAMETER FILE=========================================

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FOTD 10-02-04 (Order from Chaos [5])
by Jim Muth 10 Feb '04

10 Feb '04

FOTD -- February 10, 2004 (Rating 5) Fractal visionaries and enthusiasts: With today's image we tunnel quite deep into the Mandelbrot set. At the end of our trip we find ourselves in a remote valley just off the northwest shoreline of the main bud of the large midget on the negative X-axis. This area consists of areas of wild chaos interspersed with relatively orderly and almost straight filaments. The nature of the general area, with its mixture of order and chaos, is reflected quite well in today's image, which I have named "Order from Chaos". The magnitude of the image is really in the range of arbitrary precision math, but I have forced the program to use the conven- tional math routine by including the 'mathtolerance=/1' entry in the parameter file. In such a chaotic image, the resulting breakdown in resolution is barely noticeable, and the time saved is a sizable part of a day. One result of forcing the use of conventional math is the unwanted stretching and skewing, which is reported on the 'tab' screen of the image. This distortion is barely noticeable, but those who wish to render the image marginally more accurately may be re-enable arbitrary precision math by striking the 'g' key and entering the command 'mathtolerance=/0'. The 'logmap' method of coloring does not work with today's image. The 'tdis' option runs very slowly. The other outside coloring options either create too much chaos or run far too slowly. The best method I found of coloring today's image is also the simplest -- outside=iter logmap=0. When the time came to rate the image, I was undecided whether to consider the overworked nature of the M-set. Is today's image really that unusual? After almost 20 years of exploration, is there anything truly new to be found in the M-set within the range of conventional math? One would think so. At the magni- tude of today's image, the entire M-set would be about as large as the solar system. And except for the X-axis symmetry, no two spots of the M-set are identical. But the differences are often infinitesimal, and for all practical purposes, the major varia- tions have long since been found. Considering all this, I rated today's image at an above-average 6, which, with the render time of just under 5 minutes, gives an overall value of 125. I must get a machine fast enough to make arbitrary precision math prac- tical. Way down deep is where the undiscovered M-set goodies lie. To see the image, run the included parameter file and sit back to watch the fun, or go to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the image from there. The clouds moved in quickly here at Fractal Central on Monday, but the temperature reached 46F 8C, which was mild enough for the fractal cats to enjoy a full 90 minutes in the yard. They must have enjoyed their outing. When the day ended, they were content to settle down without a special treat. Today brings both work and fractals for me. The work I will finish; the fractals will never be finished. I shall return in 24 hours with more goodies, some concrete, some abstract. Until then, take care, and the search for truth is all too often hindered by the difficulty in recognizing and accepting it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Order_from_Chaos { ; time=0:04:50.28--SF5 on a P200 reset=2003 type=mandel passes=1 bailout=9 center-mag=-1.77551631029264878/0.0045532172225712\ 74/3.305215e+013/1.0404/13.9106570650115682/-0.977\ 835246052904727 params=0/0 float=y maxiter=80000 inside=0 periodicity=10 mathtolerance=/1 colors=000_hnaiocjpekqflrdiocgmcekccicagc_ecYccWcc\ UccSccQccOccMccKccIcdGcdEcdCceAce8ce6cf4cf2cf0cg6c\ gCcgIchKchKchKciKcjKckKclKcmKcnHcoCco7cpAcpDcqGcrI\ csLctOcuRcvQewPgxOiyNkzMmzNnzOpzPrzQryRovPosOmpMhm\ LckKZiIUgHPeFKcEFaDA_BAZAAY8AX7AW6AV4AU3AT2AS4AR6A\ Q7AP9AOBANCAMEALGAKHAJJAILAJMAKNALOAMPANQAORAPSAQT\ BRUCSVDTWEUXFVYGWZHX_IY`IZaJ_bK`cLadMbeNceOcgPchQc\ iRajS_kTYlTWmUUnUSmUQlUOjUMhUKgUNeSPcQRbQU`SWZUYYW\ `WZbU`dTbgRdiPfkOhhNgfNfcNeaNd_McXMbVMaSM`QL_OLZLL\ YJLXHLWJNVKOULPUMQTNRTOTSPUSRVRSWQTXQUZPV_PW`OXaOZ\ bN_dM`eMafLbgLchKdiKbgLaeL`cL_aLZ_LYYMXWMWUMVSMUQM\ SPNRNNQLNPJNOHNNFOMDOLBOK9OJ7OI6OK5MM5LO5KQ5IR5HT5\ GV5EX5DZ5C_5BXCEUJHRQJOXMLcOIjRGpTKlVNhXQdZT``XXb_\ TdbPfeLhhIjaMfWPbQTZJWWD_S7bO1eL7gMChNIiNNjOSkOYmP\ bnQhoQmpRrqRnmPjjNfgLbdJZaHWZFSVDOSBKP9GM7EYbGZcI_\ dK`eMafObhQciSdjUekWflYgm } END 20.0 PAR-FORMULA FILE==================================

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FOTD 09-02-04 (Apples and Oranges [7])
by Jim Muth 09 Feb '04

09 Feb '04

FOTD -- February 09, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us once again to that ultimate fractal reality, the Mandelbrot set, for a brief stay in one of the more remote valleys. I call the M-set the ultimate fractal reality with some misgivings. I am not certain that such a thing as fractal reality exists. As far as that goes, I am not even certain that such a thing as physical reality exists. (I am reasonably certain that I exist however.) But if anything like ultimate fractal reality does exist, the Mandelbrot set comes as close to filling that definition as we have yet come. The scene of today's action lies in a spiral deep in the outer side of the right branch of the valley leading to the large period-4 bud on the northeast shoreline of the main bay of the Mandelbrot set. The features that appear in the image are familiar to those with experience exploring the M-set. This familiarity cost the image one full rating point. But to make up for the familiarity, the coloring is somewhat unexpected, and this originality added one full point to the rating. As a result, we have an image with a rating of a 7 and, due to the short render time, an overall value of 321. I named the image "Apples and Oranges". The tiny orange spots remind me of oranges. The apples were added just to make a more interesting name. There are two ways of viewing the image: first, by running the included parameter file; second, by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> It remained sunny but breezy and quite cold here at Fractal Central on Sunday. The temperature never rose above freezing, which kept Tippy the tabby indoors. Thomas, the rusty, ventured out onto the remaining ice for a few minutes before deciding that comfort was the better part of valor, and hastily retreat- ing back inside. They both ended the day with a treat of left- over salmon. Today is starting milder. Hopefully, it will be better for the duo. For me, it looks like today might be a bit on the busy side. But unless an avalanche of unexpected work arrives, I'll find time to dredge up another fractal worthy of FOTD status. Until tomorrow, when that next fractal will appear, take care, and see you then. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Apples_and_Oranges { ; time=0:02:10.88--SF5 on a P200 reset=2003 type=mandel passes=1 center-mag=+0.25604\ 36923746491/+0.4940656109920195/3.6466e+007/1/177.5\ /1.38515831929475475e-008 params=0/0 float=y maxiter=15000 inside=0 logmap=1560 periodicity=10 colors=000D7WD5YC3ZC2_B4ZB5YB6XB7XB8WA9VAAUABUACTA\ DSAER9FR9GQ9HP9IO9JO9KN8LM8ML8NL8OK8PJ8QI7SI7TH7UG\ 7VF7WF7XE6YD6ZC6_C6`B6aA6b95c95d85e75f65g65h54i44j\ 34k34l24m14n16m37l48l59k6Bk7Cj9DjAEiBGiCHhDIhFJgGL\ gHMfINeJOeLQdMRdNScOTcPVbRWbSXaTYaU_`V``Xa_YbZZdZ_\ eY`fYbgXciXdjWekWflVhnVioUjpUkqTlrTmqSjpRhpQfoPdnO\ bnN`mMZmLWlKUkJSkIQjIOjHMiGKhFIhEFgDDgCBfB9eA7e95d\ 83d81eA3eB4fD6fE7fF8gHAgIBgJDhLEhMFiOHiPIiQKjSLjTM\ jUOkWPkXRlZSl_Tl`VmbWmcYmdZnf_ngaoibojdokepmfunhzo\ izqkzrlztmzuozvpyxrxyswztvyuuzvtzwszxszyszzszzszzs\ zzszzswwsvwsvwsvwsvwquupttossnsrmrplqokqnjpmiolhoj\ gnifmhelgdlfckdbjcajb`ia_h_ZhZYgYXfXWeWVeUUdTTcSSc\ RRbQQaOPaNO`MN_LM_KNZKOYKPYKQXKRWKSWKTVKTVKUUKVTKW\ TKXSKYSKZRK_QKaQKcPKeOKgOKiNKkNKlMKmLKnLKoKKpKKqMK\ rOKsQKtSKuUKvWLwYLx_MyaMzcMzcNzcNzcOzcOzcOzcPzcPzc\ QzcQzcQzcRzcRzcRzcSzcSzcT } END 20.0 PAR-FORMULA FILE==================================

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Fractint version 20.3 patch 1
by Jonathan Osuch 08 Feb '04

08 Feb '04

Fractint and Xfractint version 20.1 patch 1 is now available on the developer's web site. What's new: Fixed the float bailout for the lambdafn fractal type when the EXP function is used so the float and integer images match. Jan Andres contributed Xfractint fixes that allow compiling with newer versions of gcc because varargs.h is no longer supported. Enabled the use of the long double type on Solaris. Moved the getwd() macro definition in prompts1.c after the #include lines, to avoid the mess that happens when the prototype for getwd() is included but it's already defined as a macro. Added some Solaris-specific comments to the Makefile. Fixed the sound in Xfractint so the beep turns off now. Changed lsys.c to use inline1 instead of the reserved word inline. Jonathan

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FOTD 08-02-04 (Jungle Lushness [6])
by Jim Muth 08 Feb '04

08 Feb '04

FOTD -- February 08, 2004 (Rating 6) Fractal visionaries and enthusiasts: I named today's image "Jungle Lushness". Perhaps I should have named it something like "Too Lush". The image has almost too much richness. No jungle on earth was ever as lush as the scene in the image, not even in the deepest depths of the Amazon rain forest. This over-abundance of detail and color has cost the image one full rating point. After careful consideration, I could give the image a rating no higher than a 6, which is still somewhat above average, but falls short of the 7 that I first considered. The parent fractal was created by combining 1 negative part of Z^(-1.1) with 0.1 negative part of Z^(-11) and adding (1/C). This parent is several orders too large to fit on the default screen, but a single outzoom reveals the most interesting parts. The interesting part of the parent consists of an oversized banana-shaped hole with a Mandelbrot set lying at its southwest extremity. The banana-shaped hole splits the East Valley of the M-set as it joins with the set. Today's scene is located on the shoreline of the hole, near the point where it joins the M-set. The traditional equal-iteration-band method of rendering today's scene produces a very interesting image -- almost good enough to be a FOTD. The evaporated version, which appears as today's FOTD, is improved just enough to be the version I chose. As an 'evaporated' image, today's scene consists entirely of trapped inside points made visible by the 'bof61' inside fill. This fill traces quite faithfully the foundation features of the 'real' image that has been evaporated, but adds bells and whistles that the real image never had. Sometimes a humdrum scene can be improved by evaporating it, sometimes not. The only way to find out is to go ahead and evaporate an image and see what can be done with the ghostly remains. There are also 'half-evaporated' and 'extra-condensed' versions of images created by negative exponents of Z, but I have yet to do much investigating in these areas. The render time of today's image is 13-3/4 minutes. Combined with the rating of a 6, its overall value is 44 -- a value that is not too bad. The image may be seen quicker by downloading it from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Saturday turned into a quite pleasant day here at Fractal Central, when sun and an unexpectedly warm temperature of 43F 6C prevailed most of the afternoon. The cats enjoyed the few spots where the sun is now shining above the holly trees in the early afternoon, and ignored the remaining ice. But this morning things are again frozen solid. It once again feels like winter. I doubt that the duo will have a second good day. My day will probably be average . . . most days are . . . that is unless something unexpectedly good or bad happens. Since nothing like this is likely to occur, the day will probably pass with nothing more notable taking place than the appearance of the next FOTD fractal image. When that happens, we will have found tomorrow's FOTD. Until then, take care, and does the brain create the mind, or does the mind create the brain . . . or is it all just one big fractal? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Jungle_Lushness { ; time=0:13:47.67--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.38105363973058900/-5.353386666406572\ 00/1.344518e+009/1/-137.5/0.000903528871152227409 params=-1/-1.1/-0.1/-11/0/1e+100 float=y maxiter=2000 inside=bof61 periodicity=10 colors=000ePadQ`dSZcTXcVVbWUbYSaZQa`O`aN`cL_dJ_eIm\ ulnqmnnnojnogopdop`pqYpqVqrRrrOrsLssHstEttBtmHfAMT\ EKSHIRKGQNEQQCPTAOW8NZ6Na4Md2Lg0LXHNMYPBmQEiTHeVKb\ XMZ_PWaSScUOfXLh_HjaEl_JnZNpYSrXWtW_vUdwThySlyRqyQ\ uyPyyOvyOtyOrwOptOnqOlnOjkNghNeeNcbNa_N_XNYUNWRNUO\ LSPJRPHPPGOQEMQCLQBKQ8KN6KKEEIM8GT3FS6HS8JRALRCMRE\ OQGQQIRPKTPMVPOWRLaSJfTHkVFpWDuXByY9yWAyUBySCyQDyO\ ExMFvKGuIGtGHrEIqCJoAKn8Lm6Mk4Nj2NivEfuHhuJjtLltNn\ tPpsRrsUtrWvrYxr_yqayqcyqeyr`ysXutSouOjvJdwF_xBVxH\ _xNdxThyZmydryjwypyimuVjpGgk1df8_eFVeMQdTLd_GcfBcG\ DyHLyITyI_yJgyJnyOosSokXod`oXeoQioImoBijJeeQb`XZWc\ WRjTQgQPeNOcLNaIM_FLYCKWAJU7IS4HQ2HOKRUa`Zrjcogfle\ hickfamc_p`YrYVuVTwSRyPPyMNyJLyOQyTVyZ_ycdyhiyV_jb\ bhZabflnkomekb_gSUdIQ`HMXHITGEPGDOKDONDNRDNUCMYCM`\ CMdCLgCLkBKnBKrBJuBJyBJyDLsEMkFNcGPWHQOIRGJUKaCTbE\ WcFYdG_eHafIcgJegKgfMeeNc } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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