April 2008 - Fractint - mailman.xmission.com

FOTD 11-04-08 (Renormalization [Rating Normal])
by Jim Muth 10 Apr '08

10 Apr '08

FOTD -- April 11, 2008 (Rating Normal) Fractal visionaries and enthusiasts: Today's image is yet a third view of the scene that appeared two days ago on April 9. But whereas in yesterday's reimage we tore the original image to shreds, in today's view we 'renormalize' it into a reasonably symmetrical object. I named today's image "Renormalization". As far as I know, renormalization is something physicists do when the numbers behind their theories add up to infinity or zero, or something else absurd. They simply insert arbitrary terms into their formulas, which result in the formulas accurately describing the ideas they are trying to prove. I'm not sure if this band-aid approach actually proves anything, but it sure eliminates a lot of headaches for the theorists, especially those still searching for that elusive theory of (almost) everything. In today's image I renormalized things by simplifying the orientation parameters to 90,0,0,90, which conveniently draws the 'Rectangular' direction, defined by the imag(c) and imag(z) axes. After much stretching and skewing, this simplification produced a near-symmetrical pattern around the hole at the center, which once was a perfect minibrot. Since the scene was renormalized, the rating could be nothing but 'normal'. But things in the image are not quite as normal as they first appear. Today's orangish pattern has only two rounded points, whereas the Mandelbrot version of the same scene has four points. Where did the other two points go? Most likely, they rolled off into the fourth dimension. The calculation time of today's image is a blessedly brief 34 seconds, fast enough to bring joy even to the hearts of those who don't get the point of fractals. The trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is equally fast. With a high temperature of 72F 22C, gentle winds, and brilliant sun, Thursday was the best day so far this spring. The fractal cats must have agreed. They got into a spat over who should sit in the sunniest window. My day was moderately active. Tomorrow will probably be the same. The next FOTD image will be created sometime during the next 18 hours and posted in 24 hours. Until that semi-glorious moment breaks upon the waiting world, take care, and renormalize yourself. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Renormalization { ; time=0:00:34.74-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=+0.000000003\ 13126323/-0.0000000643364187/2.29769e+007/1.4265/\ -86.5334566310032614/83.7362695773166621 logmap=181 params=90/0/0/90/-1.749446905449293/6.834887985e-0\ 07/-1.749446905449293/6.834887985e-007/2.0000001/0 float=y maxiter=1800 inside=0 periodicity=10 colors=0000850966A79B8BC9ED9HEAKFBOFBRGCWHD`IDeNEl\ TFoaOuiYvrVzxSzxQzyNzyXzzgzzpzzzI00GA0EK0BUT9_O6_K\ 4_F2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcH\ bbIVaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIzzzzzztwso\ rnkieg`XkSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePD\ bMELhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH\ 4fH5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBo\ jCmgCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM\ `JIsSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__e\ Y_bW_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCT\ YCUWDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSS\ bPNaMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOL\ JRLIVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCd\ cDceEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzf\ UzXYzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtz\ rozhjzZezPDzrHzkLzdPzZTzS } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 10-04-08 (All Hell Breaks Loose [!!])
by Jim Muth 10 Apr '08

10 Apr '08

FOTD -- April 10, 2008 (Rating !!) Fractal visionaries and enthusiasts: Look at what has happened to the perfect minibrot of yesterday's image. Not only has it stretched beyond recognition, it has come apart. But this is what happens in the four-dimensional Julibrot when the Mandelbrot scene is double-rotated and sliced at a critical angle. In this case, the angle defined by the real(p1) parameter is the critical one. A change as little as 0.1 degree makes a world of difference. I was so surprised at the result that I rated the image at a !! This is a most unusual rating indeed. And I must apologize for the name "All Hell Breaks Loose". The image is not really that violent, and I doubt that any fractalists believe in the literal existence of that legendary hot place down below. As for a description of the motion known as double rotation, I am working on it, but at the same time I am finding it extremely difficult to put into words. Those in a hurry will find the calculation time of 34 seconds quite reasonable. Those even more hurried may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With a temperature of 63F 17C, Wednesday was mild enough here at Fractal Central in central Pennsylvania, but the clouds kept it from being ideal. The fractal cats live in an ideal world, so they were not disturbed by the grayness. My day was moderately busy, but we were irritated by an irate customer who claims he didn't get what he wanted and refuses to pay his bill. Thankfully, fractals do not incur bills, and even if they did, they would never refuse to pay. The next FOTD will be posted in 24 hours. Until then, take care, and keep going in hypercircles, whatever they are. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AllHellBreaksLoose { ; time=0:00:34.64-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=+0.000000006\ 15716237/+0.00000013555853479/1.861013e+008/0.0130\ 8/92.6807800722809247/-33.0516955361447415 params=-92.5/162/147/-42/-1.749446905449293/6.8348\ 87985e-007/-1.749446905449293/6.834887985e-007/\ 2.0000001/0 float=y maxiter=1800 inside=0 logmap=181 periodicity=10 colors=0003966A79B8BC9ED9HEAKFBOFBRGCWHD`IDdNEkTFl\ aOikYftVmzSrzQvzNzzK_PHNYnLYjIYeGZaEZXBZT9_O6_K4_F\ 2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcHbbI\ VaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIXNHzzztwsornk\ ieg`XcSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePDbME\ LhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH4fH\ 5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBojCm\ gCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM`JI\ sSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__eY_b\ W_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCTYCU\ WDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSSbPN\ aMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOLJRL\ IVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCdcDc\ eEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzfUzX\ YzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtzroz\ hjzZezPDzrHzkLzdPzZTzSXzL } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 09-04-08 (Perfect Proportions [6.5])
by Jim Muth 09 Apr '08

09 Apr '08

FOTD -- April 09, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Although the minibrot at the center of today's image looks like a quadratic one, it is not. The parent fractal was generated by the formula Z^2.0000001+C rather than the classic Z^2+C. On the surface, the parent cannot be distinguished from a perfect clas- sic Mandelbrot set, but down deep, especially along the negative X-axis, things are quite different. The little minibrot in today's image lies at the edge of the infinitely divided X-axis in the vicinity of East Valley of the large minibrot at -2.475 on the X-axis. Yes, I know that the large minibrot is centered at -1.75 of the negative X-axis, and not -2.475, but today's parent is not the standard Mandelbrot set. It is the fractal I call the shadow Mandelbrot set, which lies in the same Julibrot figure as the classic M-set but is double rotated 45 and 45 degrees toward the Julia orientation. This less-familiar shadow set has twice the area of the classic set, and the linear dimensions are therefore 1.414 times those of the classic set. As for double rotation, don't waste mental energy trying to picture it. It's a four-dimensional thing im- possible to visualize in three dimensions except in a projection. With its near-perfect square pattern, the minibrot in today's image is quite striking in its own right. Enjoy it while you have it, for we will see another view of it in tomorrow's FOTD, when we see what a difference a little rotation can make. The image rates a not-too-bad 6-1/2. The name "Perfect Propor- tions" refers to the strikingly perfect square pattern, which will not remain perfect for long however. The calculation time of only 35 seconds makes running the included parameter file a pleasure. Equally pleasurable is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant viewing. A dull, dreary morning gave way to a brilliant blue sky at noon, followed by a balmy sunny afternoon with a temperature of 63F 17C. The cats enjoyed the balminess from their shelf in the front window. My day was busy, but still well under control. The next FOTD, a shocking scene indeed, is already in the bag and will be posted in 24 hours. Until then, take care, and be ready for the big change. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= PerfectProportions { ; time=0:00:34.89-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 center-mag=0/0/\ 2.154207e+008/1/-179.25/0 params=45/0/45/0/-1.749\ 446905449293/6.834887985e-007/-1.749446905449293/\ 6.834887985e-007/2.0000001/0 float=y maxiter=1800 inside=0 logmap=181 periodicity=10 colors=0003966A79B8BC9ED9HEAKFBOFBRGCWHD`IDdNEkTFl\ aOikYftVmzSrzQvzNzzK_PHNYnLYjIYeGZaEZXBZT9_O6_K4_F\ 2_B7XCCVDHTDMQEOXCROEWMFewcdoZcgUb_PaSKfEsdGjcHbbI\ VaJNI`RKZQLYPNXOOWNPUMRTLSSLTRKVQJWOIXNHzzztwsornk\ ieg`XcSOzXLvVLqSHjOFeMF_ic``V`SNo_9lXAjUBgSCePDbME\ LhzNevOcrPanR_jSYfTWbVUZWSVXQRZON_MJiF0hG2gG3fH4fH\ 5eH6dI7dI9cJAbJBbJCaKD`KEL5kTDVxy9vvAtsArpBqmBojCm\ gCldCjaDhZDfWEeTEcQFaNF`7l`9h`Ad`C``DX`FU`GQ`IM`JI\ sSNoQLkOJgNIcLGjzJgoIedHbUGYtjZqgZoeZlcZjaZg__eY_b\ W_`T_YR_WP`TN`RL`OJ`MHLk9MiANgAOeBPdBQbBR`CSZCTYCU\ WDVUDWSEXREYPEZNF_LFkmzjjuigqhdlgbhf_deX_dUWcSSbPN\ aMJlVFjTFhRFfQFeOFcNFaLF0OR4NP7NOBMNEMMHMLLLKOLJRL\ IVKHYKGxQ0vP1uP2sO3rO4pP5oQ6mS7lU8jW9iYAg_BfaCdcDc\ eEagFiicgk_fmWeoTcqPbsMauIUwIWxHXyHYzGZzG_zFQzfUzX\ YzORzuSzqTzmUzjVzfWzcWz_XzWYzTZzP_zM`zICzzPzbtzroz\ hjzZezPDzrHzkLzdPzZTzSXzL } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 08-04-08 (Fierce Fiery Scene [7])
by Jim Muth 07 Apr '08

07 Apr '08

FOTD -- April 08, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal came about purely by accident as I was using the 'fmod' outside option to search for a minibrot in the Z^(sqrt(2))+C fractal as it appears 4 levels up the logarithmic ladder when no function is applied. I never found a minibrot, though many are certainly nearby, but I did find a strikingly colored scene that consists entirely of 'outside' stuff rendered, of course, with the 'fmod' option. The image uses only a small part of the 256 available colors. In this case however, the lack of the full color palette is hardly noticeable. After a brief moment of indecision, I rated the image at a 7. The name "Fierce Fiery Scene" kind of describes the image, though I could find no signs of flames in the picture. The calculation time of 7-1/2 minutes is a bit slower than I would have preferred, but the image is different enough to be worth the effort. And as always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was dry all day Monday here at Fractal Central, but the heavy clouds and temperature of 48F 9C hardly felt spring- like. The fractal cats spent the day keeping warm by the warmest radiator. I spent the day being busy with work and reading about a certain cat in a quantum box. The fiery fractal ended the day with a moment's satisfaction. The next FOTD, not so fiery, will appear in 24 hours. Until then, take care, and is Schrodinger's cat dead, alive, sick, or none of the above? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fierce_Fiery_Scene { ; time=0:07:37.14-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.6634403428163981/-1.406626216391897/\ 1.641796e+009/1/100/0 params=1.41421/0/4/0 float=y maxiter=1500 inside=0 proximity=0.002 outside=fmod periodicity=10 colors=0003B`3B`3Ba3Ba4Ba4Ba4Bb4Bb4Bb4Bb4Ac4Ac4Ac5\ Ac5Ad5Ad5Ad5Ad5Ae5Ae5Ae5Ae36h48f5Ae5Bd6Dc6Eb7Ga7H`\ 8JZ9LY9MXAOWAPVBRUBSTCURDWQDXPEZOE_NFaMFbLGdJHfIHg\ HIiGIjFJlEIoCJnDJmDJmDKlDKlDKkDLkDLjDLjDMiDMiDMhEN\ hENgENgEOfEOfEOeEPeEPdEPdEQcEQcFQbFRbFRaFRaFS`FS`F\ S_FT_FTZFTZFTZFU`GVaHWbHXcIYeJZfJ_gK`hKaiLbkMclMdm\ NenNfpOgqPhrPisQjtQkvRlwSmxSnyTmzUnzTnySnxSnwRnvQn\ uQntPnsOnrOnqNnpMnoMnnLnmKnlKnkJnjIniInhHngGnfGneF\ ndEncEnbDt_6r`9paBnaDlbGkcIicKgdNedPdeRbfU`fWZgY_j\ Z_l`Yg_WbYUYXSTVQOUOJSLFQMERMERMESNESNESNDTNDTODUO\ DUODUODVPCVPCWPCWPCWQCXQCXQBYQBYRBYRBZRBZRBZRA_RA_\ RBZSCYTDXVDWWEVXFUYFT_GS`HRaHQbIPdJOeJNfKMhLLiMKjM\ JkNImOHnPGpQFrREtSDvTCxUBzUBzUAxTAvSAtRAsQAqQApPAo\ OAnOAmNAkMAjMAiLAhKAgKAeJ9dI9cI9bH9aG9`G9ZF9XE9VE9\ TD9RC9PC9NB9LAAJ9BIACHADGAEIAFKAGMAHNAIOAJPBKQBLRB\ MSBNTBOUBPVBQWBRWCSXCTXCU } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 07-04-08 (Fractal Mark of Doom [6])
by Jim Muth 07 Apr '08

07 Apr '08

FOTD -- April 07, 2008 (Rating 6) Fractal visionaries and enthusiasts: One of the most accessible interpretations of the quantum weirdness is the idea of multiple universes with multiple versions of everything and everyone. But this raises a question that I have never been able to answer. Are those other versions of myself (and everyone else) really conscious, and if they are, who are they? Are they identical twins who are constantly popping into existence complete with my stored memories, and if so, how do I know that I am not merely a twin that popped into existence a second or so ago, complete with a brain filled with the memories of the original me, who or what ever that might be? And at the other extreme, if those other versions of myself are not conscious, then what is the difference? Also, if some supposedly conscious people in alternate worlds are not in fact conscious, how many assumed conscious people in this world are not actually conscious? Finally, perhaps I am the only con- scious being in this entire universe. (Solipsism?) It is pathetically laughable to see intelligent and rational scientists twisting themselves into such knots as multiple universes to explain something that simply does not and can not fit into the classical world-view. I find the concept of a near- infinity of different versions of myself and everyone else in multiple universes a prime example of 'clutching at straws'. And IMO, when reason and logic lead to such an absurdity, it is a sure sign that something monumentally important has been wrong right from the start of the scientific method. It seems as though science is determined to self-destruct. If so, I wish it a pleasant journey. As for today's fractal, it was rendered with the outside set to 'fmod', and the initials of the name, "Fractal Mark of Doom", spell out that option. The scene lies in the Z^(1.99)+C Mandeloid as it appears 0.9 levels up the logarithmic ladder, where it is rotated about 100 degrees, so that the large period-3 north bud intersects the positive X-axis, which in this case is a line of discontinuity. Today's scene is located in the area of this intersection. The bailout radius of 1.79 is critical. The rating of a 6 seems about right. The picture really isn't all that great. The calculation time of just over 1 minute will give no one impatience. And the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday turned into the best day so far this spring here at Fractal Central, as full sun, gentle breezes and a temperature of 61F 16C combined to bring pleasure to all, including the fractal cats, who spent an unusually long time in the afternoon sun. As for me, I did as little work as possible, trying to ignore the grass, which is starting to turn green, but is still a couple weeks from trimming stage. The next FOTD will appear in 24 hours, give or take a few. Until then, take care, and would the real me please stand up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FractalMarkOf_Doom { ; time=0:01:06.42-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.93654970565216/+0.0000009491899/\ 9.489796e+008/1/112.5/0 params=1.99/0/0.9/-98.31 float=y maxiter=1500 inside=0 proximity=0.1412 outside=fmod periodicity=10 colors=000cIQeJQgKQiLRkMRmNRoOSpPSrQStRTvSTxTTzUUz\ VUzWUzXVzYVzZTzYVzXXzWZzW_xVauUcrTeoTflShjRjgQldQm\ aPoZOqXNsUNtRMvOLxLKzHJzJKzLLzMMzONzQOzRPyTQyVQyWR\ xYSxZTw`UwbVwcWveWvgXvhYujZul_um`toatpbsrbstcsudrw\ eryfrzgqzhqzlszhqzeozamzZkzWizSgzPfzLdzIbzF`zBZz8X\ z5Wz6Vz7Vz8Vy9Vy9VyAVxBVxCVxCUwDUwEUwFUvFUvGUvHUuI\ UuITuJTtKTtLTtLTsMTsNTsOTyIPsOTnUXi__dec_kgTqkVpjX\ oiYnh_mgalfbkedjefidghcigbkfale`nd_k`Xoc_sfawhdzkf\ zmhzjfzgezdczabzpWz_azJfz3ky5jw7iv9htBgrCfqEeoGdmI\ clJcjLbhNagP`eQ_dSZbUY`WX_XXYZWW`VVbUTcTReSQbROdQM\ fPNeQNdQNcRObRObROcSPcSPbTPaTDeVP`T`XRlTPxPNzLLzOM\ zQNzSNyUOwWOuZPr`QpbQndRkfRiiSgkTdmTboU_rT`qUaqVbq\ WcqWdqXeqYfqYgqZhp_ip_jp`kpalpampbnpcopcpodqoerofs\ oftoguohvohwoixnjynjznkznlznlznmznnzqqznnzllxjiugg\ reepcbm``jZYgXWdUUaSR_QPXNMULKRJIOGFLEDHE9MHBOJCQL\ DSMEPPGQTHSXIT`JVdKWgMYkN } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 06-04-08 (Frankenfractal [7.5])
by Jim Muth 06 Apr '08

06 Apr '08

FOTD -- April 06, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's evaporated quickie surprised me when it turned out to rate a 7-1/2 on the Jamth scale of fractal worth. I don't have much to say about it except that it is spectacularly colorful, mostly due to the program, but partly to my efforts. The parent fractal is the same one that gave us yesterday's image, though instead of being located in the snowman's head, today's image is located in a spiral lying beyond his left foot. The name Frankenfractal is a bit of an exaggeration. The fractal is nowhere near as impressive as its namesake monster. With a calculation time of under 2 minutes, today's parameter file should be no problem to run. But in case the unexpected happens, the completed image may be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Variable clouds and a temperature of 52F 11C made Saturday fairly harmless here at Fractal Central. The cats, being of a fractal nature, ignored the outside conditions to find their action inside. My day was fairly lazy. The next FOTD will be posted in 24 hours. Until then, take care, and keep watching that paradigm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Frankenfractal { ; time=0:01:55.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-23.11035411865113/-22.10717055110748/\ 135535/1/156/0 params=-3/-1.3/-1/-3.3/0/1e+050/0/0 float=y maxiter=950 inside=bof61 periodicity=10 colors=000_H0WE0VA0S71P31L01I01H018000000000000015\ 0G30I30K30L10N13P16Q0AS0DT0HV0KW0PY0S_0_Q0eI0lA0s3\ 0q60q80qC0qE0oH0oK0oN0oP0mS0mV0mY0m`0ld0lg0lj0ll0W\ b0IV05N00G00C007103300500600700700C00G00K00P03S07W\ 0C`1Ge5Lj7QmAVsD_xGdzIhzLmzNsz0zt0zo5zhAzdGzYLzTSx\ NYtIdsDjo8qmCjhDeeE_`GVYIQVKKQLGNNCKHHLDLN8QN5VP0_\ Q0dQ0hS0mS0lP5jLDlILmGKoHIqIIsIHtKHvKGxLGzNNzNVzPb\ zPjzQszSzzSzzTzzTzzWzzYzz`zzbzzezzgzzjzzlzzgzzbzz_\ zzVzzSzzNzzKzzGzzDzz8Kz60q10t00q00m00j00g00d00`00Y\ 00T00Q00N00K00H00E00C00800H00Q01_05g0Yz3Vz3Sz1Px1N\ z1czcczczX0zO0z00q00h00`00T00L00I80GI7DVIAdW7qj6wz\ 7wz7wz7wz7wz7mz7mz7bj7_h7Wg7Te7Sd7Pb7L`7K_CIVEHSIG\ PLELQEHTDEWCC`A8d86h81l70q60t50x50tA0sE0oK0mP0lV0h\ _0ge0ej0_e0V`0QY0KT0GQ0CL07I01E00C0070050EL0sd0zv0\ zx0zz0zz0zz0zz0sz0jz0Yz0Tz0Qz0Lz0Iz0Ez1Cz1Gz0Iz0Nt\ 0Qo0Vj0Ye0b`0eW0hT0eP0bL0 } frm:MandAutoCritInZ {; 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)+(p4)), 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 05-04-08 (Angelic Snowman [7])
by Jim Muth 05 Apr '08

05 Apr '08

FOTD -- April 05, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's semi-glorious image lies in the parent fractal that results when 3 negative parts of Z^(-1.3) are combined with one negative part of Z^(-3.3) and (1/C) is added. To make things more interesting the bailout radius was increased to 780,100, which partially evaporated the scene, and the image was rendered with the inside set to 'fmod', which created the excessive sharp angular detail. Both values are critical to the effect. The above-mentioned parent fractal reminds me of an angelic snowman with a halo around his head, which is what I named the image. But do not expect to see a snowman in the image. The oversized parent fractal is the snowman. Today's scene is located on top of the snowman's head. The rating of a 7 might be a bit excessive. The image is too hectic for my taste, but it's still worth a look. That look may be had by running the included parameter file and waiting 1-2/3 minutes, or by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Steady rain and a temperature of 43F 6C here at Fractal Central on Friday made it a day that rated a pathetic 2. The fractal cats gave it a 1. The other aspects of Friday were notably average. The next FOTD will appear in 24 hours. Until then, take care, and don't ask questions that demand too much thought. You might be told to sit down and shut up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Angelic_Snowman { ; time=0:01:41.67-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+5.84307665577121/+5.123185232569579/\ 3964884/1/165/0 params=-3/-1.3/-1/-3.3/0/780000.0/\ 0/0 float=y maxiter=750 inside=fmod proximity=0.016581 periodicity=10 colors=000pkmpanpSopIpjHmdGj_GgUFePFbJE_EEYBCO9AE7\ 959G4AM4CS4DZ4Fd4Gj4Hp4Lr3Os3Su2Vv2RqUOmuMjsKhqIfo\ HdnFalD_jBYhAWgB_kCcoDgrIZpNRoSJmXBla3kd4dg4Yj5Rl5\ KeFL_PLTZMNhMHrMPnGXjBdf6lb1ic6gdAeeFcfJagN_hSYiWW\ i_RjaMkcIleDmg9ni4ok0olX0Sd9QlIOtRMeP`ROnPOkNOhLOe\ JObHO_FOXDOUBOS_3M`7SaBXbFacJfdNkeRpfVunozgozapzVn\ zPmzIjzCqz9hy7jz5Us3cz1QiFTbTYYebTzhagmiwwqbqovpQS\ olMnjGmhBmgT`miOsdWq_coWknRslNzkJsfGlbDeYA_UJYTRWS\ ZUSfSRnQRgSP`UNUWLNYJGZIMWNSURYSWcP_iNdoLhr7St6Sv4\ Tw3Tr6Qm8OhBLcDJZFHXEVVDhUCuLKnxTgyKYyBOqFNjINcLNX\ ONPSNIVNBYN4`NBSWIKdOCl_agoHAeL5XO1qzqtldw_SyNGySJ\ yXMy`PyeSyiVynYyr_phYh_W_QUSHTldNnYLoSJpLHrFFs8Dt2\ BrJDp_FooHfrGZtFRvEOoFLhGIaHFWICPJ9IK6CKFLHOTEW`CQ\ bIKdNEfT8gYvScsP_qMWnJTlHPiEMgBIe9FI2iQ5bX8XdBRkEL\ sHFzJ9qNGhRM_VSRZZIbdAejLhaVkTenKoqByt3xuBwuJvuRvu\ YuuetumtutmvdgwQawBesAhcA } frm:MandAutoCritInZ {; 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)+(p4)), 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 04-04-08 (Fighting the Blues [Fluid Rating])
by Jim Muth 04 Apr '08

04 Apr '08

FOTD -- April 04, 2008 (Fluid Rating) Fractal visionaries and enthusiasts: I recently came upon an article somewhere on the internet that claims we need a new scientific paradigm. Apparently the modern theories of physics are very difficult to fit into the classic Newtonian paradigm, which assumes that there actually is an 'ultimate reality' 'out there', and measuring physical material and energies is as close as we can come to knowing it. All this is very interesting, but if this is not true, I wonder what science would turn to for an ultimate reality if it were forced by its discoveries to admit that the physical universe might not be as real as it appears to us through the indirect means of our senses. Perhaps we would need to turn to numbers and fractals for the ground of our being. Sometimes all this philosophical pondering gets wearisome. I'm no closer to an answer that I was when I read that book about the philosophy of science 40 or 50 years ago. But some things never grows wearisome, and at least for me, one of those things is the universe of fractals. Today's fractal image is named "Fighting the Blues". Its parent fractal came to be when I checked the formula Z^(2.01)+C as it appears 1.5 levels up the logarithmic ladder when no function is applied. At this level the almost-Mandelbrot set is rotated 180 degrees, so that East Valley falls on the negative X-axis, where all the fractal splitting is found. Today's scene is located in this shattered version of East Valley. The image looks as though it were very near the cut-off point of the bailout radius, but this is not so. I raised the bailout to 2100 and it made no difference. The increased bailout does make a difference in the appearance of the image however. I rendered the scene with the outside set to 'tdis', which colors the bands of the image according to the distance the points travel before finally escaping for good. Obviously, a larger area in which to skip about will affect the total distance a point covers before finally escaping. I gave the image a fluid rating. This means I was so uncertain about the quality of the image that I decided to leave it to the viewer to rate the image as he sees fit. I kind of like the moody overall blueness, but at the same time I feel that the image is too flat. One opinion cancels the other and leaves me totally undecided. One thing certain is the calculation time, which on a reasonably fast almost SOTA 2000mhz machine is about 2-1/2 minutes. Or, instead of waiting, the impatient fractalist may speed to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the finished image posted there. Morning sun gave way to afternoon clouds and evening rain here at Fractal Central on Thursday, while the temperature of 52F 11C kept things relatively pleasant. The local fractal cats consi- dered the situation, stretched and went back to sleep. In my department, the day was average. If tomorrow is the same, I'll call it a success. Until then, take care, and watch your paradigms. Whatever they are, they're getting trendy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fighting_the_Blues { ; time=0:03:33.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-0.254450031265811/-0.0000447770940377/\ 2101678/1/45/0 params=2.01/0/1.5/2000 float=y maxiter=1500 inside=0 outside=tdis logmap=old periodicity=10 colors=000cuAguDguDguDguDjuFjuFjuFjuFnuInuInuInuIr\ uKruKruKruKuimuDuu0uu0un0uj0ug0uc0u`0uY5uUDuPKuLTu\ JbuGmuEuuBuu8uuvK0uF0nD0gA0`50U30L20G00B0060030000\ 0000000000000000650PO7gfIvuTvufwwwvuuvuuvtujOuL0u3\ 0uG0uU0uj0qv5XvFFvO20uuv0uv0uv0uv0uv0uv0uv5uuAunIu\ jOucTuYbuUitPtqJumGuiBub6u_3uX0uQ0tO0qK0mI0mD0iA0f\ 70f50OA07F00K00Q00I60DU35vA2vI0vF2vF5vFArFFjFK0Wu0\ WuJFbEFfzzzzzzzzzzzzzpzyfxyXzuPzrIunAuj5uj3ug5uc7u\ `AuYHuWKuROuJRuETu8Vu4Xu0Zu0`u0bu0cu0cu0cu0bu0au0`\ t0Zt0Wy0Vs0Sp0Qn0FW00W00W00WB0W`0tv0uv2uvAuvIivXKv\ _2vb0vf0vi0vt0vu0vu0vu0vu0vu0vu0vu0vu0vuuvuuvuuvuu\ vuuvuuvuuvuuvuuvuuvuuvuuvuuvuuvuu6iu4iu1iu0iu0iu0i\ u0iu0iu0iu0qu0tu0uu0uu0uu0uu0uu0uu0uu0uu0uu0ut0uq0\ ui0uf0ub0uX0uT0uO0uK0uI0uD0uA0u70u50u50u51u56u3Bu3\ Gu3Lu3vuivqKjT3YD0L00J00J00G00G00G00E00E00E00B00B0\ 0B000700720Q30i54u5Eu7RuA } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 03-04-08 (The Rest in Pieces [6])
by Jim Muth 03 Apr '08

03 Apr '08

FOTD -- April 03, 2008 (Rating 6) Fractal visionaries and enthusiasts: The formula behind today's mischief combines 5 negative parts of Z^(-1.25) with one negative part of Z^(-5.5) then adds (1/C). The resulting parent fractal is a string of three vertically stacked bays, with the largest bay on the southern end of the string. Today's scene lies deep in the eastern branch of the valley separating the large southern bay from the smaller one above it. I tried many tricks to bring the image to a better life, but achieved nothing more than a kind of fractal zombie, appearing to be in a kind of trance. Rendering the scene with the outside set to 'tdis' helped a little, but brought the image nowhere near the potential I at first thought it held. The rating of a 6 is about FOTD average. The name "The Rest in Pieces" has no connection to a chain-saw type movie. It rather indicates that the image is infinitely broken into ever smaller pieces. The calculation time of 8-1/2 minutes is a bit slow for a merely average image, so why not view the image in completed form at leisure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Bright sun but a chilly 50F 10C temperature made Wednesday notably average here at Fractal Central. I kept busy while the dynamic cats took it easy. The next FOTD will be ready in 24 hours. Until then, take care, and be ready for anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Rest_in_Pieces { ; time=0:08:28.22-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=+0.6775879162089047/-2.051238510923745/\ 1.930465e+009/1/67.5/0 params=-5/-1.25/-1/-5.5/0/\ 0/0/0 float=y maxiter=4200 inside=0 outside=tdis periodicity=10 colors=000zzHnUJnVJnVInVInWHnWHnWGnXGnXGnXFnYFnYEn\ YEnZDnZDnZCn_Cn_Cn_Bn`Bn`An`Ana9na9na9o`Ao`Bo`Co`D\ o`Eo`Eo`Fo_Go_Ho_Io_Io_Jo_Ko_LoZMpZMpZNpZOpZPpZQpZ\ QpYRpYSpYTpYUpYVpYVpYWpXXpXYpXZqXZqX_qX`qXaqWbqWbq\ WcqWdqWeqWfqWfqVgqVhqViqVjqVkrVkrVlrUmrUnrUorUorUp\ rUqrUrrTsrTsrTtrTurTvrTwrSxrTwrUwrUwrVvrVvrWvrWurX\ urYurYurZtrZtr_tr_sr`srasrarrbrrbrrcrrcqrdqreqrepr\ fprfprgorgorhorhorinrjnrjnrkmrkmrlmrllrmlrnlrnlrok\ rokrpkrpjrqjrrjrrirsirsirtirthruhrvhrvgrwgrwgrxfrx\ fryfszeryfryfrygrygrygrxhrxhqxhqxiqxiqxiqwjqwjqwjp\ wkpwkpwkpvlpvlpvlpvmovmovmounounounouoouonuontpntp\ ntpntqntqntqmsplrplqpkqokpojoojnninnimnhlnhlmgkmgj\ mfilfilehldgkdgkcfkcekbdjbdjacjabi`bi`ai_`h__hZ_hZ\ ZhYYgYYgXXgWWfWVfVVfVUfUTeUSeTSeTRdSQdSQdRPcROcQNc\ QNcPMbOLbOLbNKaNJaMIaMI`LH`LG`KG`KF_JE_JD_IDZICZHB\ ZHBZIEXJHWKKVKNULQTMTSMWQ } frm:MandAutoCritInZ {; 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)+(p4)), 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 01-04-08 (Flowery Failure [5])
by Jim Muth 02 Apr '08

02 Apr '08

FOTD -- April 01, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's image is the second consecutive merely average one. Good fractals seem to come in clusters. I named today's evapo- rated image "Flowery Failure" because it just doesn't have that certain something that causes me to feel that 'this is a very good one'. And I can't say what the image lacks. It has enough sparkling emerald detail, and certainly enough contrast. The parent fractal seems promising enough, so why then could I give today's image a rating of only a very average 5? It must be that there have been too many similar fractals in the long history of the FOTD. Regardless, the parent fractal, which was created when I com- bined one negative part of Z^(-1.5) with 0.3 negative part of Z^(-3.3) and added (1/C), is one of those rambling things that cannot be described. basically, it consists of a series of circular bays and smaller sub-bays, with today's scene located in a skeletal valley on the southeast shoreline of a large eastern sub-bay. As I mentioned earlier, the image was evaporated by raising the escape radius to 10^50, which is not one-half of 10^100, but 1/(10^50)th of it. The resulting blank screen was restored to life by rendering the scene with the inside set to 'bof61'. Finally, the calculation time of 2-2/3 minutes may be bypassed by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather absolutely stank here at Fractal Central on Monday. Heavy clouds, drizzle and a temperature of 41F 5C prevailed all day. The local fractal cats checked the outside conditions once, then decided to spend their day, as they do every day -- inside. My day was about as busy as expected, though I was a bit disap- pointed by the gaudy but somehow humdrum fractal. I'll try again for fractal excellence in 24 hours. Until then, take care, and if it is true that nothing is real, what just wrote that nothing is real? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Flowery_Failure { ; time=0:02:41.31-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.32327651312/-1.28247104496/2849086/1\ /-140/0 params=-1/-1.5/-0.3/-3.3/0/1e+050/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 colors=000TNCUNBVNBWNBXPCYQCYRDZSDZTD_UE_VE`WF`XFa\ YF430b_G9w_OkQb`GgL8qO7gQ7qS7pU6pW6pZ6p`6ob5od5of5\ oh5ng7ng8ng9nfBnfCmfDmeFmeGmeHmdIldKldLlcMlcOlcPkb\ QkbSkbTkaUkaVjaXj`Yj`Zj``j_ai_bi_diZeiZfiZghZfgZff\ ZffZeeZz430dZdcZzbZdbZdafc`Zz_Zc_ZzZZbYZbYZaXZaWZa\ X_cWZaWZ`Wf_VZZVZYVZWUZVUZUUZTUZSTZQTfPTfOSZNSZMSZ\ KSfJRZIRZHRZGQZEQZDQZCQZBPfAPZ8PZ7OZ6OZ5OZ4OZ3P_4Q\ _5Q_5R_6R_6S_7430T_8T_9U_9V_AV_BW_BWfCX_CX_DY_EY_E\ Z_F__F__G`_H`_Ha_Ia_IbfJb_J_`KTUKWXKUULSXLQULSXNTU\ OUXPVURWXSXUTYVUYTWYTXYSYYRZYQ`YPaYObYNcYMeYLfYKgY\ MkYKiYJhYIgYGfYFeYEdODQVBaSA_Q9YN7WK6UH5SF4QE5OE6N\ E7ME8LE9KEAJEBIECHEDGEDFEEEEFDEGCEHBEIAFI9GI8HI7IJ\ 6JK5KL4LM3MN2NO1OP0PQ1QR2RS3ST4TU4UV4VW5WX5XY5Y_6Z\ `6_a6`b6ad7be7cf7dh8ei8fj8gl9hm9in9ko9mp8oq8qrAssB\ utBvuCwvDxwDyxEzyFzzFztGznHziHzbIzXJzXIqPIgPHYPHOP\ GLOGMOFNOFOOEPOEQODRNDSNC } frm:MandAutoCritInZ {; 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)+(p4)), 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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