February 2005 - Fractint - mailman.xmission.com

FOTD 28-02-05 (Fantas-a-Stick [8])
by Jim Muth 28 Feb '05

28 Feb '05

FOTD -- February 28, 2005 (Rating 8) Fractal visionaries and enthusiasts: After the two highest rated consecutive FOTD fractals of all time, today's image, with its rating of an impressive 8, actually seems disappointing. But a rating of 8 is still much above average, and today's image must be given the recognition it deserves. The image is an evaporated scene in the fractal that results when 4 negative portions of Z^(-1.4) are combined with 0.4 negative portion of Z^(-14) before (1/C) is added. Evaporated fractals, like the physical vacuum, are not as empty as they first appear. The physical vacuum, though it contains no matter, is still filled with energy fields, which can be seen as an exchange of quantum particles; an evaporated fractal, though it contains no visible escaping points, is still filled with trapped points whose activity can be revealed by an inside fill such as the 'bof61' fill that in today's image makes the invisible visible. I gave today's image the nonsense name "Fantas-a-Stick". The reason for such a name is that I felt like doing it. The render time of under 3 minutes continues the recent trend of showing that great fractals do not necessarily need to be unbearably slow. Curiously enough, the fractal lady, who has often commented that I under-rate my fractals, and remarks that I never give a rating of 10, now tells me that I have over-rated the fractals of the past two days, which I did rate at a 10, implying that I don't know the value of my own fractals, and presumably anyone else's, fractals. I think she would like to see me spend a bit less time in fractal land and a bit more time in 'real' land. But if I don't find these images, who will? No one will. And the world is already filled with those who, unlike myself, totally ignore the world of fractals. What difference would it make if I added myself to the multitude who ignore fractals? Today's image may be viewed by running the included parameter file or by downloading the finished GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of sun and a temperature of 37F 3C gave the cats ample time Sunday in the holly thicket at the bottom of the yard. They would have preferred it a little warmer, but seemed satisfied with what they had. Only the normal serving of tuna was needed. This morning I see snow in the forecast, but no snow in the air. Could our weather 'experts' once again be wrong? The duo seems unconcerned. Maybe they know something the experts don't. The work for me is light, and I'm on a fractal hot streak. How long can the good luck last? Tomorrow's FOTD is but 24 hours away. Until then, take care, and a fractal a day keeps one healthy, maybe not wealthy, but certainly wise. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fantas-a-Stick { ; time=0:02:53.95--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.92489902336127200/+0.004753031337121\ 92/129217.4/1/-20/-1.52742572478992145e-008 params=-4/-1.4/-0.4/-14/0/1e+100 maxiter=300 float=y inside=bof61 outside=tdis periodicity=10 colors=000z0rs0kn0dg0Za0SV0LP0FV5GZFGcOGhWIldIplIl\ gOiaTgWYcQc`LhYFlJDe4D`0DV1ASC8PO7MY5Jb4IT5L57O07V\ 1FMFPJSTGdXDpeAzl7zr4zoIonTckePipCmz0ez0Su0Dc00L78\ Fcm8WQ2gZzrg0dSAQDSC0hD5kDClFIoFOpFVsG`uGexGkyQZkZ\ MZg8MFzgOscWl`deWkZTsSPzLMzDJzGzzIMxJzuLPpMQnOzkPS\ iWYicaiighpkhxphzuhzyazuVzpOzlGzhAzd0zWMgneJzhAak2\ 7sYPpVSnSTkQVhOYeLZcJ`iGWpFSxCOzAJlCMYCPICQMFWPIaS\ JeVMkYOocMahMPnLCrL000zZ8zzSzzWzyZprcgkeWdiLYlAWiJ\ VgQVdYTadSZkSWrMduGlxAuz4zzDzzMyzVxzcvzksysryzpxzo\ xzhzvczperZoZGyF0z00y10p80hG0aO0TV0La0Ch04o4IkCThJ\ deQocYz`czYdzVevSgoPhgMi`JkTGkMDVVTFch0ix0cd0WM0P2\ 0WJ0cZ0il0pz0vzLa8VY5dT4nP1xL0zG0zC0zM2sW8heFZnLLY\ 57I0IJ8QJPZLdgLsoLzv0rvazzdhzgSziAePvWPpMPlCPh1Pd0\ Y40V80SC0PF0MI0JL0GO0DQ0OJAWCLd5Vl0du0aVFgZClc8rg5\ xk2zo0zr0hd0JQ00C05J0IP2VV5e`8peCzd2zc0zZAnVPaQcPM\ pDJzCGzADz8Az77z54z51z84z } 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 PARAMETER FILE=========================================

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FOTD 27-02-05 (Tessellation-II [10+])
by Jim Muth 27 Feb '05

27 Feb '05

FOTD -- February 27, 2005 (Rating 10+) Fractal visionaries and enthusiasts: No one but no one is perfect, and I am not Mister No-One. I made a minor error when I posted yesterday's 'Tessellation' image. I had calculated and made parameter files of two versions of the same scene, one with the functions set to flip/ident, the other with the functions set to ident/flip. I inadvertently included the wrong parameter file in yesterday's FOTD. The flip/ident image, which was drawn by yesterday's parameter file, rates a 9.5, which I rounded off to a 10. The ident/flip image, which is drawn by today's file, rates a 9.7, which also rounds off to a 10. Today's image is basically the same as yesterday's, but the overall form is in a different orientation and the tessellation in the upper half is even more impressive. The problem is that I gave yesterday's image a rating of 10, which is the highest possible rating, yet today's image is slightly better, and there is no such thing as a rating of 11. (Such a rating would be as meaningless as the claim that one owns 10 square kilometers of land 100 miles north of the north pole.) This is why I have always been conservative in my ratings. But I had to do something to show that today's image exceeds yesterday's, so I gave today's image a rating of 10+ and left it to the viewer to decide exactly what such a rating means. I could have named today's image something like, "Son of Tessellation" or "The Return of the Tessellation" or "The Curse of the Tessellation" or "The Tessellation Strikes Again". But in keeping with the current trend in the film industry, I named it "Tessellation-II". The render time of 12 minutes may be avoided by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> As expected, I was away all Saturday afternoon, looking at the things that other people had discarded. As a result, the fractal cats could not go out. They were forced to enjoy the warm sun and temperature of 46F 8C from their window shelf. When we returned in the evening, the duo was rightfully irate, and loudly demanded extra tuna. Only when the tuna was delivered did they settle for a quiet evening. This morning is starting sunny and calm, but cold. I hope the duo has time enough in the yard today. More snow is forecast for tomorrow. I expect a slow day. Slow days make great fractals, so check back tomorrow to see what happens. It will not be another repeat. Until then, take care, and be rational but wise. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Tessellation-II { ; time=0:12:16.61--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multXYZWcompjb-min function=ident/flip passes=1 center-mag=-0.0315473/0.306062/0.9536765/\ 1/45/-3.77822773067748585e-014 params=89.8/90/1.2/\ 0/1.1/0/0/0/0/0.814 float=y maxiter=1000 inside=bof61 logmap=yes periodicity=10 colors=000P0zK0zk0WzW0W00z00W00s00Q00S02U03W05Y06_\ 09a0Dc0He0Kg0Ni2Rk5Um9XoA`qDdtHhvInuSwmbzhkzcqzduz\ dxzdyzdzzfzxfztfzqfznhzihzfhzchz`izWizSizPizMhzKfz\ IfzHdzFdzDczCcxAbv9`t6`q5Zp3Zm2Xk0Xh0Wf0Wd0U`2SW9R\ SFPNMNKSMFZKCcMFdMIdMKdMNdMRdNSfNWfNXfN`fNcfPdhPhh\ PkhPmhPphPqhWfcbX`hNWmDSs3Ny0Kz0Hv5MnPRfhWZz`RzcRz\ WRzNRzFRz6Rz0Rz0Rz0Sz0Uz0Wv2Xq6ZmD`hIbcPcZUdU`fPdh\ KkiFp`IdRMWINK9RA0U00W00X00X00Z02Z03`06`29b3Cb5Fc6\ Hc9KdCMdDPfFRfHUhIWhKSfMPdMMcMIcMFbMC`N9ZN6ZN3XN0W\ N0UP0UP0SP0RP0RP0PR0NR0MR0MR0KR0IR0HR0HR0FS0DS0CS0\ CS0AS09S06S06S03S02S00S00S00S00S00S00S02`CIfPZm`ns\ UhpNbmHWiAPf5IcAWsDhzmzzmzzmzzmzzmzzmzzmzzmzzmzzmz\ zmzzmzz0zz0zz0zz0zt0xq0vp0tn0sm0qk0pi0nh0mf0kd0hc0\ fb0d`0cZ0bX0`W0ZU0XS0WR0SP0000RN0PM0NK0MI0KH0IF0HD\ 0FC0CA0A909606505303202000000000000000000000P00S20\ W60ZD0bI0dP0hW0kS2cf2qk3z } frm:multXYZWcompjb-min {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5, q=(c^(p3-1)): z=(-z)^(p2)*(q)+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 26-02-05 (Tessellation [10])
by Vortex Swirling 27 Feb '05

27 Feb '05

Hey Folks, What was the other FTOD that rated a 10? It was: http://home.att.net/~Fractals_2/FotD_00-10-10.html Two have been rated 9.5: http://home.att.net/~Fractals_2/FotD_01-08-02.html http://home.att.net/~Fractals_3/FotD_04-10-29.html -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.302 / Virus Database: 266.5.0 - Release Date: 2/25/2005

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FOTD 26-02-05 (Tessellation [10])
by Jim Muth 26 Feb '05

26 Feb '05

FOTD -- February 26, 2005 (Rating 10) Fractal visionaries and enthusiasts: The rating of today's image is no typo. I feel it is actually worth a 10, making it only the second FOTD image to achieve this supreme rating. Not only is it one of the most unusual fractal images I have yet seen, everything about it excels. The coloring is excellent; the mathematical interest is excellent; the uniqueness is excellent. In short, the image is so close to perfection that when I considered its minor faults, the rating still rounded off to an actual 10. The name "Tessellation" was inspired by the branch-like arms in the upper half of the image, which appear to have been covered with a tile mosaic. By contrast, the lower half of the image consists of a carnival-like riot of brilliantly colored bits and strips of fractal debris. The dividing line between the upper half and lower half is extremely sharp, yet the features still appear continuous across the divide to some degree. The image was created by the formula (-Z)^1.2*(C^0.1)+C, which is the same formula that created the 'No_Cigar' image of Feb 24. In today's image I picked a point near the northern shoreline of the main bay of the parent Mandeloid, but still located some distance offshore, and calculated an almost-Julia set rotated only 0.2 degree from the Julia direction. When this open figure is rendered with the 'inside=0' option, it is blank. Most of the active inside fills work wonders with it however. I chose the 'inside=bof61' option for today's image, but the other inside options are well worth a try. The render time of 10-1/2 minutes is well within reason for such an outstanding image. For extra convenience, the completed GIF image has been posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Limited sun, a temperature of only 36F 2C, and snow-covered ground, kept the dynamic fractal cats safely inside all day Friday here at Fractal Central. They did venture briefly onto the porch to check conditions, but turned back inside before the door was closed, to spend the rest of the afternoon on their comfortable shelf by the window. Today is starting about the same as yesterday. I expect the duo to have a similar day. For me the work is light, but fractal lady is thinking about a browsing trip to one of the local antique and collectible emporiums. Maybe seeing some of the old stuff people have thrown away will give me a few new fractal ideas. The next FOTD will not rate as high as today's, but it will appear in 24 hours. Until then, take care, and don't be disappointed. Some day we might find another FOTD that rates a 10. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Tessellation { ; time=0:10:31.42--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multXYZWcompjb-min function=flip/ident passes=1 center-mag=0.343582/0.0348611/0.8796844 params=89.8/90/1.2/0/1.1/0/0/0/0/0.814 float=y maxiter=1000 inside=bof61 logmap=yes periodicity=10 colors=000P0zK0zk0WzW0W00z00W00s00Q00S02U03W05Y06_\ 09a0Dc0He0Kg0Ni2Rk5Um9XoA`qDdtHhvInuSwmbzhkzcqzduz\ dxzdyzdzzfzxfztfzqfznhzihzfhzchz`izWizSizPizMhzKfz\ IfzHdzFdzDczCcxAbv9`t6`q5Zp3Zm2Xk0Xh0Wf0Wd0U`2SW9R\ SFPNMNKSMFZKCcMFdMIdMKdMNdMRdNSfNWfNXfN`fNcfPdhPhh\ PkhPmhPphPqhWfcbX`hNWmDSs3Ny0Kz0Hv5MnPRfhWZz`RzcRz\ WRzNRzFRz6Rz0Rz0Rz0Sz0Uz0Wv2Xq6ZmD`hIbcPcZUdU`fPdh\ KkiFp`IdRMWINK9RA0U00W00X00X00Z02Z03`06`29b3Cb5Fc6\ Hc9KdCMdDPfFRfHUhIWhKSfMPdMMcMIcMFbMC`N9ZN6ZN3XN0W\ N0UP0UP0SP0RP0RP0PR0NR0MR0MR0KR0IR0HR0HR0FS0DS0CS0\ CS0AS09S06S06S03S02S00S00S00S00S00S00S02`CIfPZm`ns\ UhpNbmHWiAPf5IcAWsDhzmzzmzzmzzmzzmzzmzzmzzmzzmzzmz\ zmzzmzz0zz0zz0zz0zt0xq0vp0tn0sm0qk0pi0nh0mf0kd0hc0\ fb0d`0cZ0bX0`W0ZU0XS0WR0SP0000RN0PM0NK0MI0KH0IF0HD\ 0FC0CA0A909606505303202000000000000000000000P00S20\ W60ZD0bI0dP0hW0kS2cf2qk3z } frm:multXYZWcompjb-min {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5, q=(c^(p3-1)): z=(-z)^(p2)*(q)+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 25-02-05 (Good Versus Evil [7])
by Jim Muth 25 Feb '05

25 Feb '05

FOTD -- February 25, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal was created with the MandelbrotMix3a formula, which combines 4 different powers of Z but requires that the critical points be calculated manually. In today's image, various portions of Z^(-5.5), Z^(1.5), Z^(2.5) and (1/Z) were combined, and a critical point was entered as (p5) to produce a parent fractal that consists of little more than a scattering of disconnected fractal strings. But some of the strings hold curious little Mandelbrot atoms, one of which is the star of today's sizzling fast image. When rendered in the traditional manner, with the outside set to 'iter', today's image is rather dull. The 'tdis' outside option brings the scene to life however, and earns the rating of a 7. I chose the name "Good Versus Evil" when I noticed the contrast between the strong celestial blue in the center of the image and the lurid red around the edges, which hints at devilishness. Of course, in a theoretical battle of good against evil, the result must always be a stalemate. Both sides are equally powerful. I rendered today's image with the 'passes=b' option, which is the fastest with this particular image. It is also the most fun to watch. The drawback is that it often completely misses some features of the images on which it is used. Though today's parameter file renders fast as lightning, the FOTD web site, where the completed GIF image has been posted, is still fun to visit. The site is located at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Snow fell all day Thursday here at Fractal Central, keeping the fractal cats confined all afternoon to their shelf by the window, where they watched the birds scrounging for food. The duo must have been reasonably contented with their situation, for they were satisfied with the normal serving of tuna. This morning is starting with some sun, but it is still cold and we are deep in snow. I have no idea how the duo will manage the challenging conditions. For me it's another average day with the average amount of work to clear away before tackling the fractal world. The 6 inches 15cm of snow that fell yesterday is not enough to stop normal activity of a rather large city, so I have no excuse to put things off. The next FOTD will appear in 24 hours. The wrap-up of the philosophy will appear a few days later. Until next time, take care, and where is Yukon King? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Good_Versus_Evil { ; time=0:00:56.74--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=b center-mag=+1.295364358/+0.033121647/21027.75/1/16\ 5/7.70038116604254697e-010 params=0.5/-5.5/2/1.5/\ -0.3/2.5/-4/-1/0.8541307166/0 float=y maxiter=256 inside=255 outside=tdis periodicity=10 colors=000YtBXtCWtEVtFUsGTsISsJRsLQsMPsNQoQRkSSgUT\ cWU_YVW_WSaXOcUMgRKkPInMGrJEvHDyLIuPMrTQnXUk`Ygcad\ gfakjYonVsrR0005HDsHJlHIfHH_HGUHENHDHHCAHB4HA6IE7J\ I9JMAKPBLXDLdEMkNPmKSoPVqUYsZ`ultzUghL0`CGS42K9ETE\ PaJ_iE`dAa_5bV1bQ9e_HhhPkqMojKrczzXzzRzzSQzSVhT_cT\ dZUiTUnOVsJVfHiVFw_MmdSciZVndLsjColIknNgoSdqX`saXt\ fTvkQwpyPrx`qwlpvwoc3ieFYgRNibBjn0k`BlNLmAVaMXQYZE\ i`2tb8rcDqdJpeOnfUmgZlhQ_lHOo8Cr5AU3859DHEITKNcPSo\ UXzLi9QeBVaD_YFZULYQQXMVWI`VEeUAjU7oR9jPBeMD`KFWHH\ RFJMCLHANDlLFc_CVmAQoGLpMHqRCsX7tb3ugNV_f4TYCWQJZI\ QaAXdCTTDPHHNLKLONJRRHVUFYXD`_Cc_B``BY`AVa9Sa8Pb7M\ b6Jc5Gc5Db7Fa9H`BJ_CLZENZGPYIRXJSWLUVNWVPYUQ_TSaSU\ cRWeRXfUZeW`dZbcmu0lt2ks4kr6jq8ipAioChoEhnGgmIflKf\ kLejNdiPdiRchTcgVbfXaeZad``cb97vB9tDBsEDrGFqHHpUN`\ NGPG9ELKFQUGVcHZmHUlKQkNLjQHjTCiW8hZ4haDafLWjTQn`J\ rhDvp7zm3Vj00g64eB8bGC000 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 24-02-05 (Close but no Cigar [8])
by Fr. Jim Lacasse 25 Feb '05

25 Feb '05

Jim, Great fractal. I see a character with many smiles looking at something of great humor. Have a great day. Fr. Jim >>> jamth(a)mindspring.com 02/24/05 09:00AM >>> FOTD -- February 24, 2005 (Rating 8) Fractal visionaries and enthusiasts: To start, I must admit that today's Julia-like image is abysmally slow. And that is not all. It is merely close to being a Julia set. In fact, it is within 1/2 degree of arc of actually being a Julia set. But it is not a Julia set; it is "Close but no Cigar". If the image were a Julia set, it would consist of nothing but the spider-like arms in the foreground. The brilliant, straight-edged, horizontal bar in the background, partially showing through the spider arms, is actually a grossly enlarged and infinitely stretched view of the area of the Mandel- brot set associated with this particular Julia set. The pure Julia version may be seen by changing the imag(p1) parameter from 90.5 to 90. One benefit of this change is that the Julia set renders in 1/10 the time of the 'almost' Julia set. The spidery arms in the pure Julia set are thicker and not nearly as intricate as those of the 'almost' set, especially in the lower part of the image. And unless I am mistaken, there are fewer arms in the pure Julia set. Of course, in the Julia set the straight-edged feature in the background, which adds most of the interest, is totally missing. The very slow render time of today's image is a bit misleading. When I first rendered the image, I used the old version of the multXYZWcompjb-min formula. Since then, I have moved the term (c^(p3-1)) to the initialization part of the formula, which lets it be calculated only once for each point rather than recalcula- ted at every iteration. This cuts the render time almost in half. All previous versions of the multXYZWcompjb-min formula should be replaced with the version that is included in today's parameter file. The 'frm:' that precedes the formula name must be removed before the formula can be included in a formula file. I have rated the image at an 8. This might be a bit overblown, but I rather like the image, and feel that it is worth the 8. But even with the new version of the formula, the image is a slow one that is much more convenient to download. I have sent the image on ahead to Paul, so it should be posted to the FOTD web site, ready for download, shortly after you read this. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday turned out not too bad here at Fractal Central. The sun was visible about half the time and the temperature reached 43F 6C, which is about where it should be at this time of year. The cats spent about an hour in the yard, which is a little below their normal time outdoors. Their evening tuna was near average. But this morning I see light snow falling, with heavy snow forecast for later today. The duo might not have a good day. I expect an average day, but then, even an average day is filled with things of interest. The next FOTD will appear in 24 hours. Until then, take care, and look beneath the surface of the everyday things of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Close_but_no_Cigar { ; time=2:26:36.40--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multXYZWcompjb-min function=ident/flip passes=1 center-mag=-0.419308/3.33067e-016/1.62121\ 2/1/90/3.88578058618804789e-016 params=90/90.5/1.2\ /0/1.1/0/0/0/-0.818/0 float=y maxiter=100000 inside=0 logmap=15 periodicity=10 colors=000PIVPIWOIXOJYNJZNK_MK`MKaLLbLLcKMdKMeJMfJ\ NgINhINiHOjHOkGPlGPmFPnFQoEQpEQqDQrDQsCQtCQuCQvDQw\ DQwDQwEPwEPwEOwENwFNwFMwFMwFLwGLwGKwGJwGJwHIwHIwHH\ wHHwIGwIFwIFwJEwJEwJDwJCwKCwKBwKBwKAwLAwL9wL8wL8wM\ 7wM7wM6wM6wL8wL9wKAwKAwKAwJAwJAwIAwIAwIAwHAwHAwGAw\ GAwGAwFAwFAwEAwEAwEAwDAwDAwCAwCAwBAwCAwDAwEAwFAwGA\ wHAwIAwJAwKAwLAuMAsMAqNAoOAmPAkQAiRAgSAeTCcUEaVG_W\ IYXKWXMUYOSZQQ_QO`QMaQKbQIcQGdQEeQCfQAfQ8fQ6gP5gP5\ hO5hO5hO5iN5iN5iN5jN5jO5kP5kQ5kR5lS5lT5kU4lV5lW6lX\ 6lY8mZAm_Cm`EmaGnbIncKndMneOofQogSohUoiWpjYpk_plap\ mcpneqogqpipqkormnsomtqluskvujwwixyjwzjwzjwzkwzkwz\ kvzkvzlvzlvzlvzluzmuzmuzmuzmuzntzntzntzntzotzoszos\ zoszpszpszprzprzqrzqrzqrzqqzrqzrqzsrztszutzvuzwvzx\ wzyxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:multXYZWcompjb-min {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5, q=(c^(p3-1)): z=(-z)^(p2)*(q)+c, |z| < 400 } END PARAMETER FILE========================================= _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 24-02-05 (Close but no Cigar [8])
by Jim Muth 25 Feb '05

25 Feb '05

FOTD -- February 24, 2005 (Rating 8) Fractal visionaries and enthusiasts: To start, I must admit that today's Julia-like image is abysmally slow. And that is not all. It is merely close to being a Julia set. In fact, it is within 1/2 degree of arc of actually being a Julia set. But it is not a Julia set; it is "Close but no Cigar". If the image were a Julia set, it would consist of nothing but the spider-like arms in the foreground. The brilliant, straight-edged, horizontal bar in the background, partially showing through the spider arms, is actually a grossly enlarged and infinitely stretched view of the area of the Mandel- brot set associated with this particular Julia set. The pure Julia version may be seen by changing the imag(p1) parameter from 90.5 to 90. One benefit of this change is that the Julia set renders in 1/10 the time of the 'almost' Julia set. The spidery arms in the pure Julia set are thicker and not nearly as intricate as those of the 'almost' set, especially in the lower part of the image. And unless I am mistaken, there are fewer arms in the pure Julia set. Of course, in the Julia set the straight-edged feature in the background, which adds most of the interest, is totally missing. The very slow render time of today's image is a bit misleading. When I first rendered the image, I used the old version of the multXYZWcompjb-min formula. Since then, I have moved the term (c^(p3-1)) to the initialization part of the formula, which lets it be calculated only once for each point rather than recalcula- ted at every iteration. This cuts the render time almost in half. All previous versions of the multXYZWcompjb-min formula should be replaced with the version that is included in today's parameter file. The 'frm:' that precedes the formula name must be removed before the formula can be included in a formula file. I have rated the image at an 8. This might be a bit overblown, but I rather like the image, and feel that it is worth the 8. But even with the new version of the formula, the image is a slow one that is much more convenient to download. I have sent the image on ahead to Paul, so it should be posted to the FOTD web site, ready for download, shortly after you read this. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday turned out not too bad here at Fractal Central. The sun was visible about half the time and the temperature reached 43F 6C, which is about where it should be at this time of year. The cats spent about an hour in the yard, which is a little below their normal time outdoors. Their evening tuna was near average. But this morning I see light snow falling, with heavy snow forecast for later today. The duo might not have a good day. I expect an average day, but then, even an average day is filled with things of interest. The next FOTD will appear in 24 hours. Until then, take care, and look beneath the surface of the everyday things of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Close_but_no_Cigar { ; time=2:26:36.40--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multXYZWcompjb-min function=ident/flip passes=1 center-mag=-0.419308/3.33067e-016/1.62121\ 2/1/90/3.88578058618804789e-016 params=90/90.5/1.2\ /0/1.1/0/0/0/-0.818/0 float=y maxiter=100000 inside=0 logmap=15 periodicity=10 colors=000PIVPIWOIXOJYNJZNK_MK`MKaLLbLLcKMdKMeJMfJ\ NgINhINiHOjHOkGPlGPmFPnFQoEQpEQqDQrDQsCQtCQuCQvDQw\ DQwDQwEPwEPwEOwENwFNwFMwFMwFLwGLwGKwGJwGJwHIwHIwHH\ wHHwIGwIFwIFwJEwJEwJDwJCwKCwKBwKBwKAwLAwL9wL8wL8wM\ 7wM7wM6wM6wL8wL9wKAwKAwKAwJAwJAwIAwIAwIAwHAwHAwGAw\ GAwGAwFAwFAwEAwEAwEAwDAwDAwCAwCAwBAwCAwDAwEAwFAwGA\ wHAwIAwJAwKAwLAuMAsMAqNAoOAmPAkQAiRAgSAeTCcUEaVG_W\ IYXKWXMUYOSZQQ_QO`QMaQKbQIcQGdQEeQCfQAfQ8fQ6gP5gP5\ hO5hO5hO5iN5iN5iN5jN5jO5kP5kQ5kR5lS5lT5kU4lV5lW6lX\ 6lY8mZAm_Cm`EmaGnbIncKndMneOofQogSohUoiWpjYpk_plap\ mcpneqogqpipqkormnsomtqluskvujwwixyjwzjwzjwzkwzkwz\ kvzkvzlvzlvzlvzluzmuzmuzmuzmuzntzntzntzntzotzoszos\ zoszpszpszprzprzqrzqrzqrzqqzrqzrqzsrztszutzvuzwvzx\ wzyxzzyzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:multXYZWcompjb-min {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5, q=(c^(p3-1)): z=(-z)^(p2)*(q)+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 23-02-05 (Seeing Triple [7])
by Jim Muth 24 Feb '05

24 Feb '05

FOTD -- February 23, 2005 (Rating 7) Fractal visionaries and enthusiasts: I enjoy finding well-defined fractal 'objects', such as the mathematical dead-ends for wandering points known as 'midgets' or sometimes 'atoms'. The assemblage illustrated in today's image might or might not be considered a fractal 'object', but it is an interesting collection of fractal things regardless, and it is invisibly filled with the true well-defined 'objects' known as midgets. I named the image "Seeing Triple". The name is an exaggeration of the more common phrase 'seeing double'. The name came about when I noticed that the image had left-right symmetry. Then I looked again and discovered that the opposites were reflections of reflections. They were identical. A third look revealed that the opposites are not reflections or rotations at all -- they are totally different, and no reflection or rotation can ever make them coincide. The parent fractal combines negative portions of Z^(-1.26) and Z^(-12.6). It is a variation of the parent which produced the series of FOTD images that ended about a week ago. The coloring features pastel tints inside the non-symmetrical objects, which contrasts with the intense deep blues of the surrounding environment. I am not sure the rating of 7 is totally earned, but the image does appear to be at least above the FOTD average. The render time of 7 minutes is within reason. If 7 minutes is not reasonable, the wait can be eliminated entirely by down- loading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun broke through in mid-afternoon Tuesday here at Fractal Central, but the temperature reached only 45F 7C, which was a bit too chilly for the paws of the fractal cats, who spent only 45 minutes outside. Their evening was improved however by a generous treat of tuna. Today is starting partly cloudy and colder. It looks rather bleak for the duo. For me the day looks normal -- at least so far. The next FOTD will appear in 24 hours. Until that magnificent moment arrives, take care, but have fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seeing_Triple { ; time=0:07:11.71--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.91423665492388400/+0.003269872083774\ 09/171588.5/1.168/10.7/-2.30992197591817217e-009 params=-5/-1.26/-0.5/-12.6/0/625 float=y maxiter=5000 inside=0 logmap=129 periodicity=10 colors=000G0MG0SG0PG0TG1UG3UG4XG4XG7`GBaGCgGGgGJnH\ KpHOuJSvJKzKXzTWzXazbZzgezj`zjdzjeujdhjcojaKjaXlOJ\ lBvn0Xn0co0`q0Xq4UsBPsGMuMJwUGw`Cyg9yi7yhfyMzqBzj1\ yc0qY0l090060040030010300600900C00H00K00O01S01X03`\ 03c04g04h00h00h00h40hB0hG0cM0`S0XX0Ua0Og0Kl0Hq1Ew3\ 9z66z73zB0zCSg0Vh0Xj0`l1an4do9gqCjsGluJnwOqySszVwz\ YyzczzdzzdzzdwzdnzdgzdYzdSzdOzdOydOwdOudOsdPqdSodU\ ndVldVjdXjdXhdYhg`gh`gjadjaelccnfcodaokaqgaspauobu\ rczwdzuezzfzxgzzhzzizzjzzkzzlzzmzznzzozzpzzqzzrzzs\ zztyzuyzvwzwuzxuzywzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwz\ zwzzwzzwzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzy\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzusz\ qjzlczhXzcOz`HzV9zS3zM0zJ0zE0zB0z70zB0zE0zG0zJ0zK0\ zO0wS1uU4qX7oYBlaEhdGggJcjMalPYoUVsXUu`PycOzgKzjHz\ nGzw0Vw0Uw0Sw0Ow0Mw0Kw0Jw0Hw0Ew0Cw0Bw09w07S0oK06J0\ 7G09E0BB0C90E60G40H10J00K } 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 PARAMETER FILE=========================================

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FOTD 22-02-05 (The Hidden Squid [7])
by Jim Muth 22 Feb '05

22 Feb '05

FOTD -- February 22, 2005 (Rating 7) Fractal visionaries and enthusiasts: With a minor rush lying on the shelf beside me, and a customer coming to pick it up this afternoon, I will have to be terse in today's FOTD discussion. When I saw today's image I was reminded of squid tentacles, yet at the same time, no squid body was visible, leading me to name the image "The Hidden Squid". The image is part of the Julia set that corresponds to the western shoreline of the Mandelbrot fractal created by the formula (-Z)^1.5*(C^0.1)+C. The rating of the image is 7, and most of this rating depends on the striking definition of the tentacles. Almost all the effect of squid tentacles was achieved by arranging the color palette to emphasize the tentacle-like shapes. In themselves, the underlying fractal shapes are hardly worth a rating of 5. To speed up today's formula, I have made a small change in it. The change is minor, and does not affect the running of any parameter files that were created with the earlier version. The render time of 12 minutes is true on my worn-out fractal machine. On my newest unit it renders in just under 2 minutes. But regardless of the speed of the computer, a download of the image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will likely be faster. A bit of hazy sun in the afternoon and a temperature of 50F 10C gave the two fractal cats one acceptable hour in the thicket at the bottom of the yard here at Fractal Central on Monday. When they came inside, they chased each other up and down the stairs like kittens a few times before asking for their tuna. Today is starting cloudy, chilly and damp. Most likely the cats will be once again mildly satisfied. My day is starting in an average manner, and will most likely end in an average manner, with the next fractal appearing almost by magic in 24 hours. Until then, take care, and how did I ever manage to keep this FOTD going for almost 8 years? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Hidden_Squid { ; time=0:12:20.72--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multXYZWcompjb-min function=ident/flip passes=1 center-mag=0.332068/8.60423e-016/15.62891\ /1/90/3.88578058618804789e-016 params=90/90/1.5/0/\ 1.1/0/0/0/-0.7762321652/0 float=y maxiter=6000 inside=255 logmap=51 periodicity=10 colors=000fAaiAVlBPoCItA6rBArCBpEFpGGpHKoKLoLPoNQn\ PUnQVlSYlU_lVbjXdjZgj_iialicnjcridoidlgdigdffdbfd_\ ddWddVbdSbdPadLadI_dFZcB_b7`a6a_AbYDcWFdUIeSLfPNgL\ QiHSgGVfEYdC_bBbaAf_AiYAlWAoVArUAuSAyQAzPAzNAzLAzP\ CzQGzUKzWNz_QzbUzdXzgazjdzngzpkztnzuqzytzzxzzzzzzz\ zzzzzzzzztzzlzrdzjWzaPzUGzLAzD7zD6zD6zD4zD4zD2zD2z\ D1zD1xD0tD0qD0nD0kD0gD0dA0eD0eF4gI7gKDgNGiPKiSPiUS\ kWWkY_kablbglfjngonjrnlupozppzptzquzqyzqzzsyzsyzty\ ztyzvyzvyzxwzxwzxwzywzywzzwzzuzzuzzuzzuzzuzzuwzwtz\ wpzynzyjzygyzdyzaxzYxzVxzSvzPvzLtzItzFtzBsz7sz4qz1\ qz0qz0pz0pz0sz0pz0lz0kz0gz0ey0cw0at1Zp2Xo4Ul6SiAPg\ BNdDKaFH_GEWICULASNAPPALQAKSAGNA7QABUAFWAIYALaAPdA\ SfAViAYlAanAbpAftAiuAlyAozArzAuzAyzZxzcwzhwzmwzmwz\ mwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwymwymwymwymw\ ymwymwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwzmwzm\ wzmwzmwzmwzmwzmwzmwzmwzmw } frm:multXYZWcompjb-min {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p4, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p5, q=(p3-1): z=(-z)^(p2)*(c^(q))+c, |z| < 400 } END PARAMETER FILE=========================================

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FOTD 21-02-05 (Inside-Out [7])
by Jim Muth 21 Feb '05

21 Feb '05

FOTD -- February 21, 2005 (Rating 7) Fractal visionaries and enthusiasts: In today's fractal adventure I tried to duplicate one of the curious rectangles that exist in the Z^2.003+C Julia set with a C value of -1.7435. When I searched the Z^4.003+C Julia sets, I found no more rectangles, but I did find a very interesting Julia set. Today's image is part of this Julia set. The scene has been rendered in the usual way, with the outside set to 'iter' and the inside set to the number zero. The unusually delicate, lace-like effect is part of the fractal and not a result of program trickery. The rating of a 7 might be a bit high. I am not totally pleased with the colors, which are a bit too intense, and create a certain feeling of 'trying too hard'. I named the image "Inside-Out". I can see absolutely nothing in the image that could inspire such a name, but all FOTD images need a name, so "Inside-Out it is. The render time of 18 minutes borders on slowness, but may be avoided by downloading the finished GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A bit of philosophy is included in the philofractal version of today's discussion. Sunday was cloudy and chilly here at Fractal Central, but the over-forecasted snow failed to arrive and the temperature of 41F 5C was just warm enough to give the cats an hour in the holly thicket. They would have preferred more time outdoors however, so a generous treat of tuna was needed to get them back in their usual good moods. Today is starting foggy and drizzly, but it is milder. If things dry out, the duo might have a reasonable day. My day will feature more of the same. The next FOTD will appear in 24 hours, with all the trimmings. Until then, take care, and expect the best. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Inside-Out { ; time=0:18:05.49--SF5 on a P200 reset=2004 type=julzpower passes=1 center-mag=0/-0.0202841/880.7 params=-1.222755/0/4.003/0 float=y maxiter=2000 bailout=9 inside=0 symmetry=yaxis periodicity=10 colors=000zEitKllPodUrXXvPayHgz9lz1ozzUzzXzzXrz_dz\ _UzaHza6za0zg0zi0zo0zr0zv0zy0zz0zz0zz0yz0vz0tz0rz0\ rz0tz0vz0yz0zz0zz0zz0zz0zz4zz9Pz_0oy0to0yg0z_0zS0z\ H0z90z10z00z00z00z01z04z06z09z0Hz0Mz0Sz6XzEazMgzUo\ zatziyzrzzyzzzzzzvzzdzzMzv4ztCzlHzgPzazzU0zP0zKezE\ rw6yu1zs0zu0vv1wrCXdMKSX6Ed04t0Mw0Oz0Sz0Wz0Zz0iz01\ z09y0Hv0Pt0Mt0Hr0Er19r64oC1oH0oM0lS0lX0la0ig0ii0io\ 0dr0at0Xy4UzCPzKMzPHzXEzd9zl6zt1zz0zz0zz9zzMzy_zvl\ ztyztldt_EtM0m00m00m00m00m00m00m10m40d60l900r00i00\ d09_0MS0XM0iH0m00m00_0S0zP0vM0tK0rH0lE4iC9g9Ea6K_4\ PX1US0_P0dM0iH0oEK0gH0dE0aC0_90f66b4MZ1PS0SM0_K0gH\ 0oEUHgMPaHbX9fS4mM3vHbsqfzzizgzv06lXCiaHggMdlKgrHi\ vElzClzCoz9rz6rz4tz1vz1yz0yz0zz0zz0zz0vz0oz0iz0ay0\ Ul0P_0HM09604000000000000000001004604C06K19S4C_4Eg\ 6El6Ht9Kz9MzCPzCPzXSzrUzzXzz_zzSzzKyzClz6at0Pl0Ed0\ 1X00P00H00900S40z1_z6az9g } END PARAMETER FILE=========================================

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