February 2005 - Fractint - mailman.xmission.com

FOTD 14-02-05 (Shattered Shells [9])
by Jim Muth 14 Feb '05

14 Feb '05

FOTD -- February 14, 2005 (Rating 9) Fractal visionaries and enthusiasts: Today's fractal image is so different, so striking, that little can be said about it. The image speaks for itself. I am not going to speculate about where the voice comes from, but when the image is viewed, the fractal voice will be heard. To find the image, I made a slight change in the parent fractal that I have been using for about a week. I increased the portion of Z^(-1.26) from 5 to 9, a change that causes the whole fractal to shrink while keeping most of its overall features intact. I then searched along the southeast shoreline of the large circular bay. This bay is unusual in that it has no obvious buds along its shoreline, but as today's image shows, it does have midgets. When I found today's scene, I tried the usual tricks on it. I tried all the 'outside' options and found the 'tdis' option works best. Then I evaporated the image and found that none of the 'inside' options makes as good an image as the unevaporated outside=tdis version, though the 'bof60' option works best. Finally, I set the escape radius to 500,000,000, which results in a half-evaporated image. I kept the outside parts set to 'tdis', the inside parts set to 'bof60', and the result was the skeletal framework of today's image. The final step was finding a color palette that brings out the best in an image that is only half there. Though Fractint has only 256-color capability, it gives maximum versatility to those limited colors, and after a half hour or so I had worked up the palette that makes today's image one of the few FOTD's that can honestly be said to rate a 9. When it came time to name the image, I studied it a few minutes, then saw a collection of colorful broken shells scattered on a fractal beach. I named the image "Shattered Shells", the name it will carry for all time. The render time of 7-1/2 minutes is quite reasonable for one of the best FOTD fractal images. But rendering may be avoided entirely by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The enlightening and informative, (at least IMO), philosophy continues in the philofractal version of today's FOTD discussion. The weather on Sunday was partly cloudy with a high temperature of 46F 8C. The fractal cats, who most certainly eat food other than tuna, spent about 2 hours lurking in the holly thicket, looking for excitement than never happened. When they came inside, a small treat of tuna eased their disappointment. (The tuna is only a special treat. The dynamic duo's main diet is the variety of food that all well-fed cats eat.) But today is starting cold and rainy. I see a bad day coming up for the duo. For me, the commercial work is average, but there is that next installment of philosophy to start work on. The next FOTD will appear in 24 hours; the next philosophy will take several days longer. Until tomorrow, same time same place, take care, and be ready for anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Shattered_Shells { ; time=0:07:24.73--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.38892447657072300/-0.704796288496714\ 20/20019.17/1/125/-4.43365483215885092e-011 float=y params=9/-1.26/0.5/-12.6/0/500000000 maxiter=1000 inside=bof60 outside=tdis periodicity=10 colors=000WqoWrpmb7U`2Wa3Xb3Yb4_c4`d4ad5ce5df5ef6f\ g6hh7ih7ji7lj8mj8nk8ol9ql9rmAsnAunAvoBwpBxpBoiFgcI\ _XLRROJKRBEUDDSFCQHBOIAMK9KM8IN7HP6FR5DS4BU39W27X1\ 6XFHRSROd`MqjOolPmm000UiiXghZefacdcacf_ahY_kWZmUXp\ SVrQUnP`kOfhNliMmjLmjKmkKmkJnlInlInmHnmGonGonFooEo\ oEomFolGojHoiIohJofKoeLodMobNoaOo`PoZQoYRoXSoVToUU\ oTUofHUs58kFGcPNWZVOhaSkbVncYqd`tecwffyggwfhvfiuej\ teksdlrdmqcnpcnoconbpmbqlarkasj`ti`uh_vg_vf_se`qe`\ od`mdakcaicagbaebbcbb`abZacX`cV`cT_cR_dPZdNZdLZdM_\ eM_fM_fM_gN_hN_hN_iN_jN_jO_kO_kO_lO_mO_mP_nP_oP_oP\ _pP_pOaqNbqMcqMdrLerKgrKhrJisIjsIksHlsGntFotFptEqt\ DruDsuCuuBvuBwvAxv9yv9uv8sp8oj8ld8j_8hU8gO8fJAeLCe\ MEeNGePIfQKgRMhTOiUQiVSiXUiYWiZXi`Zia`hbahdcheehfg\ hghhijgjlgkmgmngnpgoqgpofomfnlfmkflifkhfjffidficfh\ afg`ffZfeXfdWfcUfcSfbRfaPf`Nf_MfZKfYJfYIeZIdZIcZIb\ ZIa_I`_XecXgeXigXkiWmkWom } 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 13-02-05 (A Repeated Scene [7])
by Jim Muth 13 Feb '05

13 Feb '05

FOTD -- February 13, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a repeat of the theme of yesterday's fractal, where a midget is surrounded by concentric closed paths. But in today's image the scene has been evaporated and the remnants made visible by the 'bof61' inside fill, which is the only inside option that produces a worthwhile effect when applied to today's, and most other, evaporated scenes. The parent fractal is the same one that we have been working with for about a week now. To find today's image I examined one of the isolated areas of chaos that surrounds the main body of the fractal like an electron cloud surrounds an atom. (An electron cloud is where an atom's electrons might be located. Electrons have no definite locations in an atom until we deter- mine their locations by observing them.) The overall effect of the image is one of a lush tropical rain forest, and this is what I would have named it if I had not already named it "A Repeated Scene". But, bearing the best name or not, the image still rates a 7, and it renders in under 2 minutes. The image is available, already rendered, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A brief flurry of snow an hour before noon on Saturday did not deter the duo, for when the snow passed off, the sun returned and the temperature rose to 50F 10C. This is not exactly balmy, but the cats took their coats with them when they went out. After a pleasant and uneventful afternoon, they returned indoors to enjoy their evening tuna. Today is starting much like yester- day, though I see no signs of snow showers. I expect a good day. I see little in store for myself today except fractals and TV. A do-nothing day is welcome now and then, but we would not want every day to be idle. I still have the philosophy to shape up however. So I'll set the chances at 50 percent that the next installment of philosophy will appear in the philofractal version of tomorrow's FOTD -- 80 percent that it will appear by Tuesday. But the chance that the next FOTD will appear in 24 hours is 99.99 percent. Until then, take care, and search for the light in a sea of darkness. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Repeated_Scene { ; time=0:01:43.64--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+7.37986268072519800/+0.388743317939182\ 40/7.894345e+007/1/-115/-2.35870500803342376e-005 params=5/-1.26/0.5/-12.6/0/1e+100 float=y maxiter=750 inside=bof61 periodicity=10 colors=0000zT0zo0zz0xz0vz0mz1iz3cz3_z4Tz6vz6Jy7Fx7\ Ax6Fr4Jm4vi3Sd3X`1`X1dY0iO0lP7gLDcQJ`MPPMVSO`gOgmG\ mzAozFoyIouLooPojSodVo_YpVapPdpLgpFjp9op4rp0up0xuJ\ Myf0vd0uc0sc0ra6p`Ao`Fm_LlYPjYTiX_gVcfVgdTmcSraSv`\ Tr`Vm_Vi_Xd_XaaXdcXffXggXijXjlXmoXopXpsXruXsvXusVr\ rTooSlmQjjPgiOdfMcdL`aJY`IXYGTXFQVDPXGMXJJXMGXODXQ\ CXT9XV6YY3Y`0Yc0Yd0Yg0Yj0Yl0Vl0Sl0Ql0Ol0Ll0Jl0Gl0F\ l0Cl09l07l04l01l00l00l00l00j11i44i77gCAfFDfIGdMJcP\ LcSOdQPfPSfOTgOXgMYiL`iLajJdjIflIilGjmFlmFfpLarQXs\ XSuaOvgIxmDys7zy3zz0zz3xz7rzClzGgxJauOXrSSoXMl_Gic\ Cfg6cl0`o0Yl0_i0_f0_c0_`0`Y0`V0`S0`P0aM0aJ0aG0aD0c\ A0c70c40c30a30a30a10a10a10`00`00`00`00`10Y30V40T60\ Q70P90MA0LC0ID0GF0DG0CI09J07L04M03L36J67I79GACFCDF\ FFDIICJJAML9OO7QP7SQAPTDMVGJXIGYLD_OCaP9cS6dV3fX0g\ _0ja0lc0mf0oi0pj0rl0lm0fo0`o0Vp0Pr0Jr0Ds07u11u30dC\ 0PJ3AQ69S99TA9VD9XF0u70x7 } 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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Re: [Fractint] FOTD 12-02-05 (The Right Path [7])
by Fr. Jim Lacasse 12 Feb '05

12 Feb '05

I think this should be about an 8 or 8.5. I can not wait to put it on the projector for my geometry class next week. Fr. Jim >>> jamth(a)mindspring.com 02/12/05 07:25AM >>> FOTD -- February 12, 2005 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image was named "Most Unusual Midget", but it was not really all that unusual, and rated only a 5. Today's image, which is named "The Right Path", would have been better named if it had been given the name of yesterday's image. It is the more unusual of the two. Today's image is located far to the northeast of the main part of its parent fractal, which is the same fractal that has given us the most recent images. The scene is located in a cut-off bit of circular debris inside a large closed ring that terminates the most prominent filament leading from the main part of the fractal. The image got its name from the narrow, winding path that encircles the central midget like a beltway encircles a city. It is truly a path to nowhere. One could travel it forever and never arrive at an end, for, like infinity, it has no limits. The concept of infinity is a strange thing. It is so easy to see that if one were to start traveling along the path in today's image, they would never come to the end because no end exists. Yet if one tries to imagine a straight line with the same endlessness, they find that their mind cannot grasp the entirety of the thing. Even harder to imagine is a half-line, a straight line with only one end. Is it infinite or not? We can see that a straight line with no ends would be longer, for it would extend into regions where the half-line did not. The answer depends on the direction in which we view the line. In one direction it is infinite; in the other direction it has a certain, though unimaginably great length. This half line situation reminds me of a day in seventh grade religion class in a Catholic school, when the nun was re-re-re- telling of how our souls will be perfectly happy in heaven forever if we obey God's commandments in this life. I asked the good sister how heaven could be fair, since those good people who died long ago have already had more happy time than those now living, and no matter how long we are all in heaven the ones who went there first will always have had more happiness than the late-comers. The sister replied that we will be looking forward to our future happiness when we get to heaven and not back to the hardships of earth life. She explained that everyone will be in heaven forever and will therefore have the same infinite amount of perfect happiness. I started to say, "but . . .", and the sister told me to sit down and shut up. Infinity is strange indeed. Any quantity can be added or subtracted from it and it remains unchanged. It can be multiplied or divided by any quantity, even infinity, and it remains unchanged. It can be raised to any finite power and it remains unchanged. (If it is raised to the power of infinity it might become a higher order of infinity -- I am not sure.) Well, I see myself again wandering from the topic, so it's time to note that today's image rates a pretty good 7 and renders in 2-1/2 minutes. It is available for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Weak sun and chilling winds here at Fractal Central on Friday kept the fractal cats indoors most all day. They did manage a brief 20-minute sojourn to the holly thicket to check for intruders. When they found none, they hurried back inside to watch the world from their shelf by the window. An extra large treat of tuna in the evening eased their disappointment. Today is looking like it will be another blustery one. The duo is braced for more disappointment. For me it looks like an average day coming up. But sometimes average days can be quite interesting. Check back in 24 hours to see if anything of interest appears in before then. Until next FOTD, take care, and if only we knew which path is the right one. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Right_Path { ; time=0:02:25.11--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+5.20383959978280900/+2.454715711010205\ 00/286974.9/1/55/5.08479132410588619e-009 params=5/-1.26/0.5/-12.6/0/0 float=y maxiter=900 inside=0 periodicity=10 colors=000KgOGhPCiQ8jR4kS7lT9lUBmUDmVFmVHnWJnWLoXN\ oXPoYRpYTpZVqZXq_Zq_XhZV`ZUSZSKZRCZkBtiCqgCnfCldCi\ bDgaDd_DbYD_WEYUEUSEPQEMOEKMDIKDGLCECCCDBAEBAGAAHA\ AJ9AK9AM8BN8CP7DQ7ES9FTAGVCHWDIYFJZGKaILcJMfLNhMOk\ OPmPPoRQqSRsTRuXPs`NqdLnhJjkImoGrsEvwDzzBzzzzzzzzz\ wzRrwWmr`omeqhjrcolZjgUfbPbYKZTIUOHQJGMEFI9EECFDEF\ CHGCJGBMGAOHARH9TH8WI8YI7`I6bJ6eJ5gJ5cN9_QDWTGSXKO\ _NKbRGfVCiY8la4od3oc3ob3oa3oa3o`3o_3o_2oZ2oY2oX2oX\ 2oW2oV2oV1oU1oT1oS1oS1oR1oQ1oQ5mT9lWDkZHi`LhcPgfTe\ hXdk`cndaph`sl_voZxm_yk`yjayhayfbyecyccybdy`eyZeyY\ fyWgzVhzThzRizQjzOjzNkzLlzJlzImzGnzFnzIlxKkwMivOhu\ QgtSesUdrWcpYao_`na_mdYlfXkhYjjZhl_gnafpceredtgcvi\ bxkavmbtobrqbpsbnuclwckyciycgzdezdczdazd_zeZzeXzeV\ zeTzfRzfPzfNzfMzfMzdMzcMzaaz5`z4_z6Zz7Yz8Xz9WzAVzC\ UzDTzESzFRzGQzHPzJOzKNzLMzMLzNKzPJzQIzRHzSGzTGzUJz\ RMzOPzMSzJVzHUzGTzFTzESzD } 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========================================= _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 12-02-05 (The Right Path [7])
by Jim Muth 12 Feb '05

12 Feb '05

FOTD -- February 12, 2005 (Rating 7) Fractal visionaries and enthusiasts: Yesterday's image was named "Most Unusual Midget", but it was not really all that unusual, and rated only a 5. Today's image, which is named "The Right Path", would have been better named if it had been given the name of yesterday's image. It is the more unusual of the two. Today's image is located far to the northeast of the main part of its parent fractal, which is the same fractal that has given us the most recent images. The scene is located in a cut-off bit of circular debris inside a large closed ring that terminates the most prominent filament leading from the main part of the fractal. The image got its name from the narrow, winding path that encircles the central midget like a beltway encircles a city. It is truly a path to nowhere. One could travel it forever and never arrive at an end, for, like infinity, it has no limits. The concept of infinity is a strange thing. It is so easy to see that if one were to start traveling along the path in today's image, they would never come to the end because no end exists. Yet if one tries to imagine a straight line with the same endlessness, they find that their mind cannot grasp the entirety of the thing. Even harder to imagine is a half-line, a straight line with only one end. Is it infinite or not? We can see that a straight line with no ends would be longer, for it would extend into regions where the half-line did not. The answer depends on the direction in which we view the line. In one direction it is infinite; in the other direction it has a certain, though unimaginably great length. This half line situation reminds me of a day in seventh grade religion class in a Catholic school, when the nun was re-re-re- telling of how our souls will be perfectly happy in heaven forever if we obey God's commandments in this life. I asked the good sister how heaven could be fair, since those good people who died long ago have already had more happy time than those now living, and no matter how long we are all in heaven the ones who went there first will always have had more happiness than the late-comers. The sister replied that we will be looking forward to our future happiness when we get to heaven and not back to the hardships of earth life. She explained that everyone will be in heaven forever and will therefore have the same infinite amount of perfect happiness. I started to say, "but . . .", and the sister told me to sit down and shut up. Infinity is strange indeed. Any quantity can be added or subtracted from it and it remains unchanged. It can be multiplied or divided by any quantity, even infinity, and it remains unchanged. It can be raised to any finite power and it remains unchanged. (If it is raised to the power of infinity it might become a higher order of infinity -- I am not sure.) Well, I see myself again wandering from the topic, so it's time to note that today's image rates a pretty good 7 and renders in 2-1/2 minutes. It is available for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Weak sun and chilling winds here at Fractal Central on Friday kept the fractal cats indoors most all day. They did manage a brief 20-minute sojourn to the holly thicket to check for intruders. When they found none, they hurried back inside to watch the world from their shelf by the window. An extra large treat of tuna in the evening eased their disappointment. Today is looking like it will be another blustery one. The duo is braced for more disappointment. For me it looks like an average day coming up. But sometimes average days can be quite interesting. Check back in 24 hours to see if anything of interest appears in before then. Until next FOTD, take care, and if only we knew which path is the right one. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Right_Path { ; time=0:02:25.11--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+5.20383959978280900/+2.454715711010205\ 00/286974.9/1/55/5.08479132410588619e-009 params=5/-1.26/0.5/-12.6/0/0 float=y maxiter=900 inside=0 periodicity=10 colors=000KgOGhPCiQ8jR4kS7lT9lUBmUDmVFmVHnWJnWLoXN\ oXPoYRpYTpZVqZXq_Zq_XhZV`ZUSZSKZRCZkBtiCqgCnfCldCi\ bDgaDd_DbYD_WEYUEUSEPQEMOEKMDIKDGLCECCCDBAEBAGAAHA\ AJ9AK9AM8BN8CP7DQ7ES9FTAGVCHWDIYFJZGKaILcJMfLNhMOk\ OPmPPoRQqSRsTRuXPs`NqdLnhJjkImoGrsEvwDzzBzzzzzzzzz\ wzRrwWmr`omeqhjrcolZjgUfbPbYKZTIUOHQJGMEFI9EECFDEF\ CHGCJGBMGAOHARH9TH8WI8YI7`I6bJ6eJ5gJ5cN9_QDWTGSXKO\ _NKbRGfVCiY8la4od3oc3ob3oa3oa3o`3o_3o_2oZ2oY2oX2oX\ 2oW2oV2oV1oU1oT1oS1oS1oR1oQ1oQ5mT9lWDkZHi`LhcPgfTe\ hXdk`cndaph`sl_voZxm_yk`yjayhayfbyecyccybdy`eyZeyY\ fyWgzVhzThzRizQjzOjzNkzLlzJlzImzGnzFnzIlxKkwMivOhu\ QgtSesUdrWcpYao_`na_mdYlfXkhYjjZhl_gnafpceredtgcvi\ bxkavmbtobrqbpsbnuclwckyciycgzdezdczdazd_zeZzeXzeV\ zeTzfRzfPzfNzfMzfMzdMzcMzaaz5`z4_z6Zz7Yz8Xz9WzAVzC\ UzDTzESzFRzGQzHPzJOzKNzLMzMLzNKzPJzQIzRHzSGzTGzUJz\ RMzOPzMSzJVzHUzGTzFTzESzD } 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 11-02-05 (Most Unusual fractal [5])
by Jim Muth 11 Feb '05

11 Feb '05

FOTD -- February 11, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today's image could well have been named 'The Incredible Shrinking Fractal'. When I first saw it 3 days ago, I consid- ered it an 8, but at every viewing since then, it has appeared less impressive. The rating of a 5 is a gross come-down from the original 8, but if I had waited another day or two before posting the image, I might have rated it a 4 of even a 3. That's how it goes in Fractal Land. Sometimes fractals grow better with age, at other times they turn sour. The image is yet another scene in the same parent fractal that has supplied the past several FOTD's. Today's image is located not too far from where yesterday's image was found, though it lies farther inland and in an area of greater chaos. I named the image "Most Unusual Midget", but I gave it this name when I first saw it and still considered it worth a rating of 8. Right now, a name such as "Somewhat Unusual Midget" might be more appropriate. The most, and perhaps only, notable feature of the image is the sharp contrast between the flat featureless areas and the well-defined areas of near total chaos. The calculation time of 5-1/2 minutes is true on my machine. Calculating may be avoided entirely by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A temperature of 37F 3C, chilly winds and too little sun limited the fractal cats' outdoor time to under an hour on Thursday. But they made the most of the limited time when they ganged up on a prowling cat from up the hill and, with terrifying shouts, sent the intruder scurrying for his life. The resulting satis- faction more than made up for the brief outdoor time. Today is starting with sun, but it is cold, and I doubt that the duo will repeat the victory they had yesterday. My day will include work and fun -- fractal fun, that is. What I find in fractal land will appear as tomorrow's FOTD. Whether the philosophy will be ready is questionable. Until then, take care, and save energy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MostUnusual_Midget { ; time=0:05:32.68--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.06057839712241519/-0.432621869887498\ 30/1.729997e+009/1/-32.5/-6.43962340347789541e-005 params=5/-1.26/0.5/-12.6/0/0 float=y maxiter=900 inside=0 logmap=37 periodicity=10 colors=000kORlOWnN`oNeqNjrNolMjgLfbKbYJZTIUOHQJGME\ FI9EECFDEFCHGCJGBMGAOHARH9TH8WI8YI7`I6bJ6eJ5gJ5cN9\ _QDWTGSXKO_NKbRGfVCiY8la4od3oc3ob3oa3oa3o`3o_3o_2o\ Z2oY2oX2oX2oW2oV2oV1oU1oT1oS1oS1oR1oQ1oQ5mT9lWDkZH\ i`LhcPgfTehXdk`cndaph`sl_voZxm_yk`yjayhayfbyecyccy\ bdy`eyZeyYfyWgzVhzThzRizQjzOjzNkzLlzJlzImzGnzFnzIl\ xKkwMivOhuQgtSesUdrWcpYao_`na_mdYlfXkhYjjZhl_gnafp\ ceredtgcvibxkavmbtobrqbpsbnuclwckyciycgzdezdczdazd\ _zeZzeXzeVzeTzfRzfPzfNzfMzfMzdMzcMzaaz5`z4_z6Zz7Yz\ 8Xz9WzAVzCUzDTzESzFRzGQzHPzJOzKNzLMzMLzNKzPJzQIzRH\ zSGzTGzUJzRMzOPzMSzJVzHUzGTzFTzESzDRzDRzCQzBPzAPz9\ Oz9Nz8Nz7Mz6Mz6Nz9OzCPzFPzIQzLRzORzQSzTTzWTzZUzaVz\ dVzfTzeSzeQzdPzdOzdMzcLzcKzcJzaJz_JzYJzXJzVIzTIzSI\ zQIzOIzNIzLHzJHzIHzGHzEHzDGzBGz9Gz8Gz6Gz4Gz3Ez6Dz8\ BzAAzC8zE7zH5zJ4zL2zN1zP0zR3zS5zS8zTAzTCzUFzUHzUJz\ VMzVOzWRzWTzWczBfzBhzHizM } 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 10-02-05 (E-M-Fields [6])
by Jim Muth 10 Feb '05

10 Feb '05

FOTD -- February 10, 2005 (Rating 6) Fractal visionaries and enthusiasts: In yesterday's philo discussion, I stated that the 'big bang' is estimated to have happened around 12,000,000,000 years ago. No sooner had I sent off the FOTD than the postperson delivered the March issue of 'Scientific American' magazine, which contains an article on common errors about the expanding universe. In the article it is stated that the latest estimate of the age of the universe is now 14,000,000,000 years, and not the 12,000,000,000 years that I assumed. I was off by 2,000,000,000 years. Oh well, with all the other debatable assumptions in my philofrac- tal discussion, 2-billion years is not going to make much of a difference. Today's image is most certainly not an assumptiom. It is an evaporated scene in the same parent fractal that we have been exploring for the past several days and will be exploring for several days to come. I named the image "E-M-Fields" for no particular reason, though these fields, which permeate the modern-day environment, certainly must have quite a few fractal aspects. And BTW, EMF pollution is another of my pet peeves, but that's a story for another day. Today's image is located in a disconnected bit of debris in a minor valley on the southwest shoreline of the large circular bay of the parent fractal. I rated the image at a 6. The soft greenish-grey daisy-like features around the edge of the image are soothing enough, but the too-tight cropping and too-gaudy colors in the spirals give the image a hectic feeling that keeps the rating from reaching a 7, the level where images can start feeling proud of themselves. Images speak louder than words, so don't just read about today's FOTD image. See it...by running the included parameter file or by downloading the completed GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday turned out to be unexpectedly pleasant here at Fractal Central, with some sun and a high temperature of 61F 16C. The dynamic cats had a day that was better than expected also. But this morning is chilly and blustery. The cats' good day will not be repeated. My day should be passably good -- as soon as I get the work behind me, that is. And the next glorious fractal will appear in only 24 hours. Until then, take care, and where were we when the big bang went boom? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= E-M-Fields { ; time=0:10:17.47--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.11693508646745340/-0.461596736962344\ 50/1.962271e+007/1/-47.5/7.17894854646017322e-007 params=5/-1.26/0.5/-12.6/0/1e+100 float=y maxiter=1100 inside=bof61 periodicity=10 colors=000DOVBWY9b`EeZJgXOiVTkTYnRbpPgrNltMjsLirLh\ qLgqLfpLeoLcnLbnLamK`lK_kKZkKYjKWiKViKUhKTgKSfJRfJ\ PeJOdJNcJMcJLbJKaJJaJKbLKbMKcNKcOKdPKdQKeRKeSKfTKf\ UKgVKgWKhXLhZLi_Li`LjaLjbLkcLkdLleLlfLmgLmhLniLnjK\ plLnkLmjLljMkiMjhMhhNggNffNefOdeObdOadP`cP_bPZbQXa\ QWaQV`RU_RT_RRZSQYSPYSOXTNWTLWTKVUJUUIUUHTUGTSEUQD\ VOCWMBXKAYJ9ZH7_F6`D5aB4b93c82d94b95a96_97Z99X9AW9\ BU9CT9DR9FQ9GO9HN9IL9JKBLMDNNFOOHQPJSQLTRNVSPXTQYV\ S_WUaXWbYYdZ_f_ag`ciabpZdjbeefg`jhVnjQrkLvlGzkJvjM\ riPniSjhUggXcg__fbWeeSdgPdjLcmHbpDbrAcoBdmBdkBeiCe\ gCfeCfbDg`DgZDhXEhVEiTEjQFjOFkMFkKGlIGlGGmDHmBHn9H\ n7Io5Io3Ih8JbCJXGKRKKLOLFSLGQKHPJIOJJNIJMIKLHLKGMJ\ GMIFNHFOGEPFEPEDQCCRBCSABT9BT8AU7AV69W58W48X37Y27Z\ 16Z06Y39Y6BY9DYBFYEIYHKYJMYMOYPRYRTYUVXXXXZZXaaXdc\ XfeXigXljXnlXqnXtpXvrVsoTqlSojQmgPkeNibLi_Mg`NeaOc\ bOacP`dQZdQXeGBQH9PH8OFGS } 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 09-02-05 (Fan Blades [6])
by Jim Muth 09 Feb '05

09 Feb '05

FOTD -- February 09, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's image returns us once again to a fault line of the parent fractal that was the source of the two most recent FOTD's. We trace the fault line farther from its source in the southern branch of a prominent valley, and follow it to where it begins to disintegrate into chaos. There, very well hidden, lies the midget that forms the nucleus for today's image. Once again, the most satisfactory version of the scene is produced by evaporating it and rendering the ghostly 'inside' remnants with the inside=bof61 option. Fractal evaporation is what happens when fractals created with only negative exponents of Z are calculated with an extremely large escape radius, such as the googol of today's image, in which none of the points will ever escape to infinity. The result is an image composed totally of trapped 'inside' points. In today's image, the central midget is still too small to be seen, but the fault-line arcs that surround it are impressive. These closed arcs remind me of the blades of the exhaust fan on my old, worn-out but still faithful fractal-dedicated machine, which usually need to be nudged into motion by hand when the machine is turned on. I named the image "Fan Blades". The image pleases me about as much as did yesterday's. I therefore rated it at another 6. But it is a rather unusual appearing scene, worth the 9-plus minutes required to render it on my old machine, and the fewer minutes it will take to render on current units. But some current units choke on old 'DOS' programs such as Fractint. For the convenience of those with handicapped computers, the completed image has been posted ready for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The philosophy continues as promised in the philofractal version of today's FOTD discussion. The Tuesday weather here at Fractal central was absolutely perfect, with a spring-like high temperature of 59F 15C and lots of sun. The fractal cats spent most of the afternoon out of sight in the holly thicket at the bottom of the yard, watching the birds clear away the last of the berries. No tuna was needed to make their evening happy. This morning is again starting mild, but it is cloudy and rain is forecast for later today. The duo might have a satisfactory day if they go outdoors early enough. For me the work is average. This means an evening of adventure in Fractal Land. The best of what I find there will appear as tomorrow's FOTD. Until then, take care, and if we can see it, hear it, and touch it, it must be really real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fan_Blades { ; time=0:09:14.25--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.27793976973538160/-1.956885037216322\ 00/1.25203e+012/1/22.5/0.00019039609301178817 params=5/-1.26/0.5/-12.6/0/1e+100 mathtolerance=/1 maxiter=1600 inside=bof61 periodicity=10 float=y colors=000XFSTFTQGTNGTKHUGHUDIVAIV7IVCMZGPbLTePWiU\ ZmYbpbetfhwgguhftierjdqkcplbnmamnalo`jp_iqZgrYfsXe\ tWcuVbuVatY_s_YraXqdVpfUohSnkRmmPloOZiULc_MYUNSOOM\ IPHCUGEZGFcFGhFHXIZLKpPImTHkXFi`EgdDegBckAao9_s7Yw\ 6Wz5UuATqFSmKRiPQeUPaZPVVSOSUHPWAMY3J_8LUDMPINKMOF\ 86CC5GG5KK4NN4RR3VV3YZ2aa2ee1hi1lm0pp0sk2mf4gb5aY7\ WU8QPAKLBFMAINALNAOOAROATPAWQAZQAaRAdRAfSAiTAlTAoU\ ArUAtSGrQMqORpMXoKbnJgmHenFcnEanC_oAYo9Xo8_l7ai7cf\ 6ec5h`5jY4lV3oS3qP2sM2uJ5qI8mHBiHDeGGaFJYFLUEOQERM\ DTICWECVABI35RCMgHWkMenRok`bhbRmrFcnGkkH_gIddJW`JU\ YKSULQRMONNMKNKGOIDPG9QE6RC3RCShCyzDqzDozDlzDetDbs\ DZrDWpESoEPnENlEKkEIjEFhEDgEBfKFkQJpWNu`RyaRvbSsbS\ pcRmdRjdRgeRdfQafQZgQWhPThPQiPNiPKjYGjfDjoAjx7iuCi\ rGioKhlPhiThfXgcag`egYifVnfSrfPvfNzjMtnMnqLiuLcxLZ\ wIWvGTuEQtCNsALr8Iq6Fp4Co29o0774_85b95dA5fB5hC5jD6\ mE6oF6qG6sH6uH6wK8vbER_ES } 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 08-02-05 (Cosmic Ripple [6])
by Jim Muth 08 Feb '05

08 Feb '05

FOTD -- February 08, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's discussion will be terse. While giving the intended philosophical part of today's discussion a final reading before posting, I found so many passages in need of clarification that I decided to basically re-write the whole thing. Unfortunately, I used up most of the FOTD time in the process. It is amazing how obvious the poorly composed parts of a composition become when they are read several days after being written. Today's image is another scene in the same parent fractal that produced the 'Underground' image of yesterday. In fact, it is located in the other branch of the same valley. The main difference is that today's image has been partially 'evaporated' by raising the escape radius to 1,400,000,000 and rendering the scene with the inside set to bof61. The name I gave the image, "Cosmic Ripple", was probably inspired by all the thinking I was doing at the time about the origin of the universe, which is the topic of the philosophical discussion I have been working on. The rating of a 6 seems about right for another of my standard images with a quadratic midget at the center. The render time of 14 minutes is slightly slow, but the slowness may be avoided by downloading the already-rendered GIF image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> I regret that the promised philosophy is not ready in time to be included in today's discussion. But I am in no rush to be considered a great fool -- a lesser fool is acceptable. If I get things right, the philosophy about the origin of the universe will appear in the philofractal version of tomorrow's discussion. If not, it will take a day or two longer. Near perfect weather here at Fractal Central on Monday gave the fractal cats much reason to rejoice. They ended the day happily with their standard treat of tuna. This morning is starting similarly. I expect a similar day for the duo. For me, it looks like a day with only a moderate amount of work, but I still have that philosophy to go over and re-write. The next fractal will appear in 24 hours. Until then, take care, and search for origins, both fractal and otherwise. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cosmic_Ripple { ; time=0:14:36.45--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.09610088547934800/-0.475162969143318\ 10/1.106908e+011/1/-15/0 params=5/-1.26/0.5/-12.6/\ 0/1400000000 float=y maxiter=1600 inside=bof61 periodicity=10 colors=000zDzzDztDzoDziDzdBzZBzVBzQ\ BzKBzGAzAAz6Az0Ay0Ay0Ay0Dz6GzBIzILzQOzWRzVQvTOsTOo\ RNlRNhQLdQLaOKZNIVNIRLHOLHLKGHKGEIEBIE9LL7OR7RY7Vc\ 7Wi7Zo6fv6dz6oz6iz6fz2Vx0Oo0Hh0BZ04U00S0IO00H00M00\ O02P09O6EUBKYGOaLVfQ`kWfoaltfsylxzq0o74q67s4Bt2Et1\ Hv1Lx0Oy0Ty0Wz0Zz0cz0fz0kz0nz0qz0xq6zaKzOZ0t00q10n\ 40k70iA0fD0cG0`I0ZL0WQ0TT0QW0OZ0La0Id0Gh0Ek0Il1Ll7\ QnDTnKWoQ`oWcqafqo00q40q70sA1sD7tHDtKHtNNvQTvVYxYc\ x`ixcnoYniRncLnYGnRAnL4nN7qO9sQBtRDvTGxVHyWIzYLzZN\ z`QzaRzcVzdWzfYzhcziiqkoflvYnzNozElzIizLfzQdzTazYZ\ z`YzcVzhRzkOzoNysKyxHxzGxzLyvRynYzfazZhzRnzKtzDyz7\ stBlnEfhI`aLVVQOOTIIYDD`77c9Bd9Gd9KdANdARdAWdA`dBc\ dBhdBldBod9kf6fh2ai0Yk0Vl0Qn0Lo0Hq0Ds0As0Dv7GxHHyR\ KzcNznOzyRzzTzzQzzNzzKzzHzyEzxBzt9zs7yq4yn1xl0xk0v\ h0vf0td0ti0hl7YoGNtODxY2zf0yk0yn0yq0yt0il9VdRGZkIT\ hLNdNHcQB`T6YV1WW0`W0cY0fY0iZ0lZ0o`0smEz } 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 07-02-05 (Underground [5])
by Jim Muth 07 Feb '05

07 Feb '05

FOTD -- February 07, 2005 (Rating 5) Fractal visionaries and enthusiasts: I had intended on finding a great fractal on Sunday, but you know how it is -- one gets flopped down in front of the TV, the big game is coming on in only an hour, and there is no pressing reason to get up. This happened to me on Sunday. I did not get up, and as a result, today's fractal is not great -- it is merely average -- but it is far better than the fractal with the rating of 2 that passed for yesterday's FOTD. Today's image rates a 5, and it earns its rating. The image is a scene in a valley of the sprawling parent fractal that results when a large portion of Z^(-1.26) is combined with 1/10 as much Z^(-12.6) and (1/C) is added. The area is one where the outside material has partially evaporated, and many 'inside' areas exist beyond the limits of the midget itself. To bring these evaporated areas to life, I have rendered the image with the inside set to 'fmod' and the proximity to 1. The result is a fractal that shows a midget surrounded by what can best be described as squiggly slimy earthworms. Worms might me a suitable name for a cheap horror movie, but not for a high class production such as the FOTD. So I named the image "Underground", which is the place where the squiggly slimy worms are found. With a render time on my worn-out machine of almost 25 minutes, today's image is bordering on slowness. But salvation is at hand in the form of the FOTD web site, where the finished image is available for download. The site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A repeat perfect day here at Fractal Central on Sunday made for continued happy cats. They spent the entire afternoon lurking in the holly thicket, watching for prey to stray too close. No prey strayed close enough to pounce on, and the duo had to settle for their standard evening treat of tuna. Today is starting with some clouds, but there is still a lot of sun and it is still mild. Will the duo notice the weaker sun? Check here tomorrow to find out. My day looks like it will be busier than the past few, but not so busy that the fractals will suffer. The next FOTD will appear in 24 hours. Until then, take care, and stay alert for runaway fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Underground { ; time=0:24:51.78--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.29445314483197500/+0.384470732271648\ 20/6.800512e+008/1/-105/-0.000131802249966776752 params=5/-1.26/0.5/-12.6/0/0 float=y maxiter=1200 inside=fmod proximity=1 periodicity=10 colors=000jTUiSVhRWgRXfQYePZfMaeP_eSZdVYdXXc_WcbVb\ dUbgTajSalR`oQ`rP_tO_wNZzMZzLYzKYzJYzIZzR_wZ`qfakn\ bdwaev`eu_ft_fsZfrYgqYgpXgoWgnWgmVflUgkUfjT`fSthSw\ gRqfQweQpdPpcOobMobOmaPlaQkaSkaTjaUjaViaXi`Yi`Zh`_\ h`ag`bg`cf`df`ff_ge_he_id_kd_lc_mc_nc_lbakabi`ch_d\ gZeeYfdYgbXhaWi`VjZUkYTlWSmVSnURoSQpRPqPOrONsNNtOY\ mPhgQsaQzWPzVOzVOzVNzUMzUmzULzUhxTKsTJqTJpSImSIlSH\ iSGgRGeRFcRFaR2ww3op3hi3ab0T_3VX5XV7ZS9_QBaNDcLGeI\ IfGKhDMjBOl8Nk6Qm6So6Vp6Xr6_t6bx2au6`rA_oDZlHYiLXg\ OWdSVaWUZZTWbTUeQWeNXeKYeH_eE`eBae8ce5de2ee0fe5gf9\ hgDhhHiiLijPjkUjkYklakmelnilommpct1qmpqnpqoprpprqp\ rrpsrpsspsrpsupttptwptupuxpuwpuzpvxpvwpvxpyytuymvz\ mqwiowflubktZjs_is`hs`hragrbfrbfqceqddqddpecpebpfb\ ogaog`oh`ni_niZnjZmkYmkXmlYknYjl_hjaehccge`egZcfXa\ eV`dTZcRXbQWaPU`NS_MQZKPXJNWILUGISFIQDGOCEMA8KBDwQ\ LuPMsONqNOoNPmMQmLRiKSgKT } 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 06-02-05 (Totally Shredded [2])
by Jim Muth 06 Feb '05

06 Feb '05

FOTD -- February 06, 2005 (Rating 2) Fractal visionaries and enthusiasts: Today's fractal is far from great. In fact, with its low-as- they-go rating of 2, it is far from being even average. Maybe I'm getting too interested in philosophy. Maybe I have put so much energy into fractals that I'm beginning to burn out. Why else would I search where I have searched hundreds of times and rarely found anything of even average interest? I don't know why I keep looking along the filaments of very low order Mandeloid fractals for interesting midgets. The midgets are there, but they are so broken by the unavoidable discontinui- ties that they look like they have just gone through a paper shredder. Today's image shows a totally shredded midget that fully deserves its abysmal rating of 2 as well as its name -- "Totally Shredded". The parent fractal is the default Z^1.26+C Mandeloid. I hoped that the cube root of 3 would do something unusual when used as the exponent of Z, but as far as I could tell, nothing out of the ordinary happened. Maybe if I had checked other levels of the logarithmic hyper-spiral, I would have found something more interesting, but somehow I doubt it. I could also have done better with the coloring, but today's earthy palette seems to perfectly capture the futility I felt when working with the image. The parameter file included at the end of this message runs in 7 minutes on my 10-year-old machine with the exhaust fan that needs to be started by hand. But much of that render time may be saved by downloading the fully pre- rendered GIF image from the FOTD web site maintained by Paul at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun was warm, the wind was light, and the temperature reached 54F 12C. It was absolutely perfect here at Fractal Central on Saturday, and the cats made the most of the perfect conditions. They went into the yard before 11am and did not return inside until after 4pm. For some reason they wanted extra tuna for supper, which I gave them. Then they ended the day with one of their rare spells of playfully chasing each other up and down the stairs. Today is starting much the same. Hopefully, the aging duo is not all played out. I have little to do today but watch the big game. If the game is dull, I'll enjoy the over-priced ads. The next fractal will appear in 24 hours, the next philosophy, most likely in 48. Until tomorrow, when the fractal of the day is guaranteed to be an improvement over today's, take care, and there will never be another 2-rated fractal until spammers learn to spell correctly. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Totally_Shredded { ; time=0:07:04.25--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.87536385207072350/+0.898575036268718\ 70/3507503 params=1.26/0/0/0 float=y maxiter=10000 inside=0 periodicity=10 colors=000htNepLblK_hJXeHUaGRYFOUBPVDPVEQVGQVHRVJR\ VKSVLSVNTVOTVQUVRNYYRWVUVSXTQ_SNcQLfPIiNGlMDuO5rM8\ oLBlKDiIGfHJdGLaEOZDRWCTTAWQ9Zer9K3_O8`SD`WIa_MacR\ agWbk`bv`drbcndbjfadlbfgagb`hY_iTZjOYyGckJYYLTKNN6\ PI8NLAMNCLQEKSGJUIHXKGZMFaOEcMGpOEjPDeRC`SAVU9QV8L\ U5HW7GX8GYAF_BF`DEaEEcGDdHDeJCgKChMBiNBkPAlQAmS9nT\ 9mWClYFl`HkbKkeMjgPjjRilUinWjlYkjZli_mganebndcobdp\ `fq_grYhtVkrXiqYgpZfo_dn`cmaakb_jcZidXheWgfUVPpfgT\ heVicXjbZk``l_bnYdoXfpVhqUjrSltRnuPpvOrwMtxLurOlmQ\ chTVcVMZYDU_5WY6YW6_U7`S7bQ8dO8eM9gK9iIAg2DiABjHAl\ P9mW8oc6pj5rr4sy3rx3qw3pw3ov3nu3mu3lt3ks3js3ir3hq3\ gq3fp3eo3do3ep9fpFgpLgpRhpWipaipgjpmkpsquznrykpxhn\ xekwbiw_gvXevUbuR`uOZtMXtpt`hn_ah_Vb_OXZHRZ7ef9WbA\ MZBCVA1TC3SD5RF7QG9PIBOJCNLEMMGLOIKPKJRMIRMJSNISOI\ SPHSQHSRHSSGTTGTUFTVFTWFTXETYETZEWgCDJfGLcIN`LPYNR\ VQTSSVQVXNXZK_`HabEddBsw8 } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(p/(2*PI)) r=real(p2)-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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