August 2008 - Fractint - mailman.xmission.com

FOTD 31-08-08 (Orderly Disorder [6.5])
by Jim Muth 30 Aug '08

30 Aug '08

FOTD -- August 31, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image comes from the same general area of the same parent fractal as yesterday's image. It's actually a very rich area, especially since the minibrots that fill the area are almost all cubic ones surrounded by unusually extensive patterns with both cubic and quadratic characteristics. I named the image "Orderly Disorder". That's what fractals are. Then I rated it at a 6.5, which includes a questionable 1/2 point for my coloring efforts. The included parameter file calculates in just under 1 minute, that is after the file is set up to run. This is about the same time required to hop over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the completed image there. The clouds hung around on Saturday here at Fractal Central, but it stayed dry, and the temperature of 75F 24C was not at all bad. The fractal cats were much more relaxed, which means that the intruder cat was not in the area. My day was peaceful enough, and if all goes well, tomorrow will be the same. I'll be taking a brief trip back to Old Fractal Central tomorrow, so the next FOTD fractal image might be late. But the image is assured. I already have it in cold storage, ready to go. Until then, take care, and be with fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Orderly_Disorder { ; time=0:00:58.35-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 float=y center-mag=-3.944756829565295/+0.000377496511276/\ 1.105404e+007/1/-115/0 params=0/0/0/0/0/0/0/0/3/3 maxiter=750 inside=0 logmap=91 periodicity=10 colors=000TcnRcoSeoTfoUgoVioWjoXkoYmoZno_oo`qoarob\ socuodvoewofxohwpjwqlvrnvspvsruttuuvtvxtwztwvorskm\ pfimbdjZ`gUWdQSaMNZHJWDET9APG8LM6HT5DZ39e16k0Bl4Fl\ 8JmBNmFRnIWnM_oQcoTgpXkp_ngToZNoRHoIBqA5nE4lI4jM4j\ Q4kT4iX4g`4dd4bh4`k4Zo4Xs4Vw4Tz4Wx6Yw7_v9btAdsCfrD\ ipFpoGrnIuqJwpLyoMziNuaMtULsMKrEJq6Jo8HnAGlCFkEEiG\ DhICfKBeMAdO9XNNQM_JLlCKyBJvBIsBHpAHmAGjAFg9Fd9Ea9\ DZ9DWDGXGJYJMYNPZQSZTV_WY`_``bcaefahibllcoocrrdutd\ opbjlaei__eZVbXQZWKWUFSTAPSCQRESRGUQHVQJXPLYPN_OPa\ ORbNTdNUeNHkf4qzCmxKjwSgv_ctg`soYrlWnjVkhUhfTddSaa\ QZ_PWYOSWNPUMMSLJTMKTMKTMKUMKUMKUNKVNKVNKVNKVPKXQJ\ ZTI`WHbZGd`GfcFhfEjiDlkDilGgmJenMcoOapR_qUYrWWsZUt\ aSudQvfOwiMxlKynPzkTzhXze`z`dzWhzRkzNgzMdzLazLZzKW\ zKTzJUzIZzIczHhzHmzGrzGvzKzzOzzSzzWzz_zzczzgzzazzX\ zzRzzMzzGzzBzzDzzEzzFzzGzzHzzIzzJzzLzzMzzNzzOzzPzz\ QzzRzzTzzUzzWzzXzzZzzkzzm } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 30-08-08 (A Cubic Conundrum [7.5])
by Jim Muth 30 Aug '08

30 Aug '08

FOTD -- Aubust 30, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image shows an unusually rich cubic minibrot, which I named "A Cubic Conundrum". The parent fractal is an oversized Mandelbrot set, just starting to morph into a cubic Mandeloid. Today's scene is located in an extra valley pushing into the second bud along the negative X-axis. The generating formula divides the Z^2 Mandelbtot set by (-Z+3), or something like that. At least I think I've got it right this time. Bur regardless of how it happened, the image, which rates a 7.5, is well worth the 1-1/2 minutes it takes to run the included parameter file. And even this small task may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday turned out to be a strange day here at Fractal Central. The temperature of 70F 21C was fair enough, and the overcast skies were not too bad, but it was too wet to be a dry day and too dry to be a rainy day. The occasional showers of mist kept it undecided. The fractal cats were not undecided however. They definitely want that intruding manx tomcat out of the area for good. My day was definitely not filled with loitering. The work was somewhat heavy, and the leisure, somewhat limited. But the fractal is acceptable, and that's what matters, at least as far as the FOTD goes. The next fractal will be posted in 14 hours. Until then, take care, and what is that heavy feeling in the air? . . . I just realized that Fractal Central is filled with a million tons of dark matter and energy. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Cubic_Conundrum { ; time=0:01:31.56-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=-3.945176537568527/+0.00000000678488286\ /5.016586e+011/1/72.5/0 params=0/0/0/0/0/0/0/0/3/3 float=y maxiter=1800 inside=0 logmap=114 periodicity=10 mathtolerance=0.05/1 colors=00000H00J10M10P10S10U40V60V90VB0WD0XG0ZI0aL\ 0cN0eM0iQ0kR0mT0nU0nV0nT0lR0jP2iN4gL6fJ8dHAcECaBE`\ 8GZ5IY2IW0KV9Uezcezmfzsfzzgzz0zz0zz06zhBzdFzaKwZOu\ WztTzzzzzzzzzzzzzzzzzFzzEzwDzwCzwBbwzawz`wz_wzZwzY\ wzWvzVvzUvzTvzSvzRuzQuzPuzOuzNuzMuzNrzOoTPlTQjTQgT\ RdTSbTT_UUXUUUUVSUWPUXMUXKUXKUZNS_QQaSObVMdYKe_Igb\ GheEjgCkjAll9jj8ii8hh7gg7ff6de6cd5bc5ab4`a4_`4aZ5b\ Y5dX5eW5gU5hT5iS6kR6lP6nO6oN6pM6qL9qLBrLDrLFsLHsLJ\ tLLtLNuKPuKRvKTvKVwKXwKZxK`xKbtIdqHenFgkEhgDidBkaA\ lZ9mW7oS6pP5qM3sJ2tG1uH2qH3mH4iH5fH6bz7Zz8Wz9SzAOI\ zLzzHIzDzzAHzBGzBzzBFzBzzBEzCzzCCzCCbCBdCAgDAjD9mD\ 8pD8sDMv9Zx6lz3yz0qz7jzEbzKWzRPzYzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzVzwVzwWzxWzxXzxXzxY\ zyYzyZzyZzybzyezyizylzypzyszywzyzzyrzvkztczrXzpQzn\ PziPzdOz_OzVNzQNzLMzGMzBLz6Lz2Mz7MzBMzGNzKNzPNzTOz\ YOzaOzeZziizl9zN9zQ9zUAzY } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 29-08-08 (The Underdog Wins [4])
by Jim Muth 29 Aug '08

29 Aug '08

FOTD -- August 29, 2008 (Rating 4) Fractal visionaries and enthusiasts: Everyone is for the underdog, even though the underdog rarely wins. In today's image however, the underdog actually wins. It wins by default more or less. Due to an unexpected rush job, I had no time to explore for a new fractal, so I grabbed an old image that has been lying in the 'maybe' file for months. It is obvious why this image never made it beyond the 'possible FOTD' stage. It has little to show. This is the kind of scene I usually immediately pass over on the way to the final FOTD, but with today's lack of time, it is where I stopped. I'm not going to deceive myself into thinking the image is worth more than a 4. In fact, even the rating of a 4 might be a bit generous. The only thing of note in the image is a minibrot in the upper left corner shaped rather like a peanut. The rest of the scene is a mish-mash of broken-up fractal stuff, some of it arranged into curious patterns, but ultimately dis-satisfying. The parent fractal looks much like the minibrot in today's image; the scene is found in the east branch of a valley leading to the northern period-2 bud. I named the image "The Underdog Wins". In a way, due to the rush, this underdog image actually did win its way into FOTD immortality. The calculation time of 5 minutes is longer than I would have preferred for an image such as today's, but relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-calculated image is posted for immediate satisfaction. The weather was far from perfect here at Fractal Central on Thursday, as the remains of the dissipated tropical storm Fay arrived. Heavy clouds prevailed all day but only a few light sprinkles fell from them, while the temperature hovered around 70C 21C. The fractal cats spent a good part of the day watching for the manx tomcat who is trying to establish his territory in the small field beyond the back yard. The intruder cat never appeared and the fractal duo eventually grew bored watching the rain. My day was unexpectedly busy, which explains the 'filler' fractal. The next FOTD will be posted in 24 hours. Until then, take care, and don't mix the concrete with the abstract. It can lead only to confusion. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Underdog_Wins { ; time=0:05:06.93-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident center-mag=+0.598635449/+0.490200106/2010 params=1.7/0/66/0 float=y maxiter=50000 inside=0 logmap=75 periodicity=10 colors=000cZAbXBbVCaSD`QE_OFZMGYKHXIIWGJWEKXFMYFNZ\ FP_FQ`FRaFTaFUbFVcFXdFYeFZfF`gFagFbeJddNfbQhaUj_Xl\ Z`nX0hW0cV0ZK0NO1OPHKRJFTLAVOFYSK_XPabUdgZflchqhjv\ mjuljuljukjukjujjtjjtijtijthjthjsikrjlqklplmomnomo\ nnomoplpqkqqjrrjrsisthttguUW1UX2UY3VZ4V`5Wb6Wd7Xe8\ Xg8Xi9YkAYlBZnCZpD_qD_qE_rF`rG`rHaqIaqIaqJbqKbpLcp\ McpMdpNdoOdoPeoQeoRfnRfnSWPfMHnC9uDAvEAvFAgGChGCiH\ DjIDkJElJEmKFnLFoMGpNHqNHrOIsPItQJuQJvRKvSKvTLvTLv\ UMvVMvWNvXOvXOvYPvZPv_Qv_Qw`RwaRwbSwvewbSwcTwdUweU\ wfVwfVwgWwhWwiXwiXwjYwkYwlZwlZwm_wn`wo`wpawpawqbwr\ bwscwscwtdwudwvewAZzF_zJ`zO`zSazXbz`bzeczidzndzrez\ `WzbXzdYzfZzh_zj`zk`zmazobzqczsdzueztRzuSzuTzuUzuV\ zHbzFazC`zA_z8ZzAfzCnzDuzHqzKmzNizQezTazWYzZUzaQzd\ MzfPzgRziTzjWzlYzm_zobzpdzrfzsizukzvmzxpzyrzztzvsz\ srzprzmqzjqzkozknzllzlkzmizmhznfznezndzmezlfzkgzkh\ zjizijzikzhhzgfzfdzebzd`z } 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 28-08-08 (Pantominia Coregia [5])
by Jim Muth 27 Aug '08

27 Aug '08

FOTD -- August 28, 2008 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is a quick one, and it shows. The rating of a 5 shows that the image leaves much to be desired. The name "Pantominia Coregia" means nothing at all. I dreamed it up because it sounds kind of like something scientific. The chief advantage of the image is its fireball calculation time of under 15 seconds. It doesn't get much shorter than that. The formula divides Z^2 by (Z^(3)+6) and produces a near- Mandelbrot set, with today's scene located in the northeastern suburbs of the large minibrot on the main spike. When this is done, we see a quintic minibrot surrounded by smaller similar minibrots. There is nothing artistically notable about the image, it is merely interesting to observe. And observe the image is what you'll do if you run the included parameter file or zip over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and peruse the image already calculated and posted there. Despite a thin layer of cirrus clouds that hung over Fractal Central all day Wednesday, the day, with its temperature of 81F 27C, was near perfect. At least the fractal cats must have thought so, for they spent half the afternoon on their shelf by the window, wishing they could go outside, where that tough manx tomcat is lurking and ready for a fight. Needless to say, the duo had no chance to go out and engage the usurper. My day was too busy to be called perfect. Maybe tomorrow will be better. The next FOTD will be posted in 24 hours. Until then, take care, and keep searching for a photon at rest. If you find one, you'll rewrite the physics books. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pantominia_Coregia { ; time=0:00:14.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=-10.48325696865905/+0.09877741090398924\ /3.971914e+010/1/-50/0 params=0/0/0/0/0/0/0/0/5/6 float=y maxiter=316 inside=0 logmap=59 periodicity=10 mathtolerance=0.05/1 colors=000A7LA6MA5OA4PA3R52SADZFNeKXlPfszzzkjBkjBk\ jBeiCZeCQaDIYDATE3PEEWOPbY_igipqUfpFXo0Oo4Ve7aXBhO\ EnFzmKzmzzmzzlZKlcLlhPefTZeXSd`MbdFah8`l2_a3hR4qG5\ yH6qI6iI6bcXmxvxkrv_nt`go`ajaWeaQ`aKXdQRgVMj`HmeBp\ k6sp1ll6ehA_dET`IMXMGUQK_LNeHQkDTq9Wv5RoFMhOIaYzVf\ zOozSgzW_z_SzcLzgFzjAzm5zp0zo7zoEznLznSzmZzmeXzl6z\ 0Uz2pz3hzFazRVzaTzZzzXzzUzzSzzPzzNzzMzzLzzKEzJBzI9\ zH6zG4zG5zL5zP5zT5zX5z`LzT_zLSzMLzNDzO6zODzMKzKRzI\ YzHMzLKz1Jz9JzGJzOIzVIzbIziIzpGzjEzdCzZDz`DzbDzdIz\ bMzaRz_VzZ_zYczWhzVlzUZzdWzfUzhRzjPzkMzmKzoIzpMziP\ zbSzWWzPZzIazBdz5SzXFzxTzwezwrzwSzh1zVCz_NzdYzihzn\ rzsgzVmzWrzXwzXwz_wzawzdwzfwziwzkwzmgzlTzkNzcHzWBz\ O5zGCzEIzDOzCUzB_zARzIIzPNzRRzTVzVZzXczZgz`kzbozcn\ zhnzlnzpnztnzxSzV5z1AzCFzNKzYPzgOzdNzbMz`LzZKzWJzU\ IzSIzQez`ezVezQezKezEez8ez3gz2iz2jz2lz2nz2oz2qz2rz\ 2_z4Hz6Fz4Ez3Dz2mzGgzIazJ } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 27-08-08 (Something from Nothing [6.5])
by Jim Muth 27 Aug '08

27 Aug '08

FOTD -- August 27, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's 6.5 rated image truly gets "Something from Nothing", which is what I named it. To begin, it consists totally of 'inside' stuff, but due to some quirk in the 'fmod' routine, the inside stuff inside the minibrot is more 'inside' than the inside stuff outside the minibrot. Yes, I know it makes no sense, but that's the way it is. (Changing the 'logmap' to 1 eliminates this quirk.) The generating formula divides Z^2 by (Z^(-2.1)+4). The immediate result of this operation is a blank screen, which can be resurrected from the dead by the 'fmod' feature. I really cannot say much more about the image, for I really have no idea what's going on with it. But with its smooth coloring, it's an interesting fractal to study. The calculation time of 1-1/3 minutes should cause no one any grief. The pre-calculated image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely perfect day prevailed here at Fractal Central on Tuesday. Perfection is defined by crystal blue skies, a few puffy clouds for decoration, low humidity, gentle winds, and a temperature of 79F 26C. The fractal cats must have agreed, for they spent much of the day in the window, watching for Max the Manx cat, who is prowling the area, establishing his dominance. My day was busy, which is about all that can be said. The next FOTD, one with more substance, will be posted in 24 hours. Until then, take care, and what does a massless photon become when it sits at rest? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SomethinFromNothin { ; time=0:01:21.46-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=+0.2602484/\ +1.367610189/9214.697/1/92.5/0 params=0/0/0/0/0/0/\ 0/0/-0.1/4 float=y maxiter=1500 inside=fmod proximity=0.25 periodicity=10 colors=000fXYeWXeWXdVWhVYgUYfTYeSXdRXcQWbPWaOV`NV_\ MUZLUYKTXJTWJSVJSUJRTJRSJQRJQQJPPJPOJONJOMJNLJNKJM\ JIMIIMHILGILFIJEHKDHKCHJBHIAGJ9GI8GI7GI6GH5GH4GH3F\ G2GG1FG0GF0FF1FE2FE3EE4ED5ED6ED7EC8EC7DC6DB6DB5CB5\ CA4CA1972A83B94B94CA5CA6DB6DC7EC8ED9FD9FEAGFBGFBHG\ CHGDIHEIHEJIFJJGKJGKKHLKILLIMMJMMKNNLNNLOOMOONPPNP\ QOQQPQRQRRQRSRSTSSTSTUTTUUUVUUVVVWWWXXWXXXYYXYZYZZ\ Y__Z_`Z`a_`a_ab`bc`bcacdacebdfbdfcegcfhdfhdgiegjeh\ jfikfilgjmgjmhknhkoiloimpjmqjnrknrkoslptmptoqupqvr\ rvsrurqtqqtppsopsnormormnqmnqmmpmmpmmomlollnlknlkm\ ljlljllikliklijlhjlhilgilghkfhkfgkegkefkdfkdekdekc\ dkcckbckbbkabjaaj`aj``j``j__j__jZZjZZjYYjYYjXXjXXj\ XWiWViWViVUiVUiUTiUTiTSiTSiSRiSRiSQiRQhRPhQPhQOhPN\ hPNhOMhOMhOLhNLhNKhMKhMJgLJgLIgKJgKKgJLgJMgJNgIOgI\ PgHQgHRgGSfGTfFUfFVfFWfEXfEYfDZfD_fC`fCafBbfBcf6df\ 8ef9ffAgfBheCieDjeEkeFleG } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 26-08-08 (Ultimate Unreality [6.5])
by Jim Muth 25 Aug '08

25 Aug '08

FOTD -- August 26, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image is another ultimately unreal one, which is why I named it "Ultimate Unreality". The generating formula contains an unlikely Z^(-0.5), which, when combined with Z^2, produces a blank screen. But there is action within the blankness. Just as empty space is filled with virtual particles, the blank screen is filled with a virtual fractal, and the energy supplied by the 'fmod' inside fill brings the virtual fractal to fractal reality. In this case, the 'fmod' inside fill is the only one that works. (Since virtual particles also need energy to make them real, I suppose they are also ultimately made of numbers.) Anyway, today's image, composed totally, as it is, of inside stuff, rates a 6.5, 1/2 point of which is a reward for the 20 minutes or so I spent tweaking the colors. The calculation time of 3-1/3 minutes is fast enough to avoid impatience and slow enough to give time for anticipation. Perhaps the easiest way to view the image is to forget parameter files and visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is or soon will be posted in finished form. The near-perfect weather here at Fractal Central on Monday was fully enjoyed by the fractal cats, who slept through most of it. I also noticed the blue skies and temperature of 82F 28C, but I was a bit too busy to enjoy it. The next FOTD, hopefully one with more reality, will be posted in 24 hours. Until then, take care, and never forget that fractals are as real as electrons. (But exactly what is the difference between an abstract electron and a concrete electron?) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ultimate_Unreality { ; time=0:03:22.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 float=y center-mag=+0.4129219397998285/+2.004990460705446/\ 2140000/1/165/0 params=0/0/0/0/0/0/0/0/-0.5/5 maxiter=1500 inside=fmod logmap=yes periodicity=10 colors=000fwAgwAhwAiwAjvAkvAlzAzyzwymtwhrvcquZrtUs\ sPtrKuqFuqAupAupAuoAuoAunAunAumAumAulAulAukAukAujA\ tjAtiAtiAshAshAsgAsgAsfAsfAseAreArdArdAqcApcApbApa\ Ap`Ao`Ao_Ao_AoZAmZAmYAmYAmXAlXAlWAlWAlVAkVAkUAkUAj\ UAjTAjTAjTAjSAiSAhSAhRAhRAgRAgQAgQAgQAfPAfPAfPAfOA\ eOAeOAeNAeNAdNAdMAdMAdMAcLAcLAcLAcKAbKAbKAbKAbKAaK\ AaKAaKAaJA`JA`JA`JA`JA_IA_IA_IA_IAZIAZIAZHAZHAYHAY\ HAYHAYGAXGAXGAXGAXGAY82XB5XE8XGAXJDXLFXOIWRKWTNWWP\ WYSW`UWbXVeZVhaVjcVmfVohVrkVtmUqjTnhTkeShcReaRbZQ_\ XQYVPVSOSQOPNNMLMJJMGGLDELBCMCDMDEMDFMEBMECNFDNFDN\ GENFFNGGOGHOGIOGIOGJOGKOGKPGKPGKPHLPIMPINQJOQJPQKQ\ QKRQLSQLTRMUSMVTNWUOXVOYXPZWPYWQWVQUUPUTOUTXhTYiTY\ jTZkTZkU_lU_mU`nU`oUapRavSatTarUapVanWalXajYaiZag_\ ae_ac`aaaa_baYcaXdaVeaTfaRgaPgaNhaLiaKjaIkaGlaEmaC\ naAoa8pb6oa7oa7oa7oa8oa8na8na9na9na9naAmaAmaAmaAm`\ Bm`Bl`Bl`Cl`Cl`Cl`Dk`DbwI } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 25-08-08 (Pseudo-Fractal [6.5])
by Jim Muth 25 Aug '08

25 Aug '08

FOTD -- August 25, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: The parent fractal of today's image divides Z^2 by Z^(-97)+100. Unfortunately, this parent fractal does not exist. It has been totally evaporated by the extreme escape radius built into the formula. With the 'inside' set to the standard numb, the parent fractal is nothing more than a blank black screen. But salvation is at hand, for the active inside fills can often return life to dead images such as the parent of today's scene. In today's case, the 'bof60' fill works quite well. I'm not sure that what results from all this trickery is really a fractal, though it most certainly is a picture. And the picture is more interesting than might be expected from a bland all-inside image. There is a main bay at the bottom, with an imaginary shore line strung with buds. Scattered fields of debris fill the imaginary 'outside' areas, while a most interesting object lies on the left side of the frame. This 'object' is better seen than des- cribed. In fact, it is nearly impossible to describe it. I named the image "Pseudo-Fractal" since I'm not sure that it is really a true fractal. I rated it at a 6.5 to reward myself 1/2 point for my semi-skilled coloring. The calculation time of 3-1/3 minutes is not as short as I would have preferred, but I think the image is worth it. At any rate, the finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A pleasantly warm day prevailed here at Fractal Central on Sunday. The warm sun and temperature of 88F 31C were ideal for outdoor activities of all kinds. The fractal cats limited them- selves to indoor activities however. My day was pleasant also, and F.L.'s new oriental lamp actually looks kind of comforting glowing a soft amber on the living room table. The next FOTD will appear in 24 hours. Until then, take care, and if a thing isn't real, what is it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pseudo-Fractal { ; time=0:03:20.18-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 center-mag=+1.032172008373736/+0.0316130942554965/\ 2352.071/1/95/0 params=0/0/0/0/0/0/0/0/-99/100 float=y maxiter=750 inside=bof60 periodicity=10 colors=000zzUuxUowUkuUesUcpUamU_jUYhUWfUUdUSbUQ`WO\ ZYMX_NUaOScQQfROhSMjTKlUInVGp_HndHmhHkmHjqHhvHgzHf\ vGdrGcnFbkFagF`cE__EZXDXTDWPDVLCUICTEBSABR7BQ7ET7G\ W7IY7K`7Mc7Pe7Rh7Tk7Vn7Xq7ZtJgwpzzhwzZtzRowQltPirO\ fpOdnNbnM_lLXiLUfKSdJPbJMaIJ_HEZHCXNBU000_gcagabg_\ dgZegXggWhgUigTheSgdSgcSfbSeaSe_SdZScYRcXRbWRaURaT\ R`SR_RR_QRZTPYWNYYLX`JWbHWeFVgEVjCUlATo8Tq6St4Sv3T\ s6Uq8VoAWlDWjFXhHYeKZcMZaORXZZJOe6Di7Hl8Kp9OsARwBV\ zCYxAav8dt6hr4kp2oo0rg9i_I`SQSKZJCfAAbB9_B7XB6UB5R\ BXSUxSksQjoPjkOjgNjcMjAnP8tM7yK8uN9rQAoTBlWCiZDfaE\ cdF`gE_PD_7NTHXMQfG_p9hz3qq8shCt`Gug2Nf7MfBLeFKeKJ\ dOIdSHdWGWRPNMYYUVhaSshQE6PK9NPBMUDKZFJcHHhJGmLFgH\ KbDPY9UT5ZO2bK7YHBTDFOAKJ6OE3S90W5P`YRYaTVeVTiXQmY\ OqPPeGQU8RJ9NI9JH9GH9CG98F95FGFCMOASY8Yf6co4dj5ee5\ f`5gW5hR5iM5jH5kD5UHIDLUBF_AAe95kFBbKGUQLMVQD_V5`U\ E`UM`UV`Ub`UjWYcS`YOcSKfM } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 24-08-08 (Seven from Eight [6.5])
by Jim Muth 24 Aug '08

24 Aug '08

FOTD -- August 24, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: Today's FOTD is very late because on Saturday I somehow got involved in another of FL's antiquing expeditions. But all was not lost. We found an oriental-style lamp for $15, which FL claims is worth over $250. To me it looks like an old lamp, but who knows . . . Today's image came about when I divided Z^2 by (Z^(6)+3). The parent fractal resembles a Mandelbrot set starting to morph into the Z^8 Mandeloid. Today's scene is located in some island debris that has appeared in the northwest interior of the large period-2 bud. The image is extremely fast, taking only 24 seconds to run on the fast machine. The name "Seven from Eight" refers to the fact that, though the central minibrot has only 7 lobes, the surround- ing pattern is a series of powers of 8. The rating of a 6.5 could be a little liberal for such a hasty image, but the image is still better than average for one of order-8. The finished image will be available on the FOTD web site as soon as Paul can calculate and post it. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was near perfect here at Fractal Central on Friday. Need anything more be said. The fractal cats enjoyed the great conditions to the best of their ability. My day was busier than expected, yet still within reason. Expect the next FOTD in about 6 hours. But do not be too disappointed if it does not make it. Until next time, take care, and look for those extra iterations. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seven_from_Eight { ; time=0:00:24.58-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=-3.653068462538817/+0.2509654289884953/\ 1.06659e+010/1/-85/0 params=0/0/0/0/0/0/0/0/8/3 float=y maxiter=750 inside=0 logmap=47 periodicity=10 mathtolerance=0.05/1 colors=000GACKAFOAISALWAN_AVcAbgAjkArnGygWo`ccWmUh\ xKztAqp8mjBhfDcbGZ_IUYKPVLKRMGOMKHNOBOS6OXjZayiWjn\ QXsRTpRPnRLlRHiRDgR9eR5cX9XbDQhHJnLCsO5nS5jW5fZ5bb\ 5Ze5aZGdSRgMajFlm9vbFZTLBPLQLLdOOgRQiTSlWUnZXq`Zsc\ `vebxCAyIFtNJpTNkYRgbVcnXEj_LgaRdcXaebZghWinaglgej\ mcisagy_frahlbifck`elVfnPgoOirOluNmxNozMpmLp`KpOJZ\ YIIgI1pM9iPHbTPWWXQ_dJblCes6dtBcuFbvJawO`xS_zWZzUY\ zSXzQWzOVzMUzKTzITzGTzSTzcTzoMzmGzlAzj4ziHzZTzOezD\ qz2NzKmzV7zZ9zSAzLBzEszXdzOQzGSzPMzJHzDSzzMzzHzzkz\ zUzzFzzczzXzzQzzJzzmzz`zzOzzYzzSzzNzzHzz9zzAzzBzz2\ zz7zzQzzUzzazzizzgzzezzdzz`zz`zz`zz`zz`zzgzzlzzqzz\ vzz0zz4zz8zzCzzGzzQzzZzzhzzqzzbzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 23-08-08 (Web of the Spirits [7])
by Jim Muth 23 Aug '08

23 Aug '08

FOTD -- August 23, 2008 (Rating 7) Fractal visionaries and enthusiasts: Another rushed day will make necessary an abbreviated discussion. Fractals are sometimes filled with spider webs, but never have I seen a fractal as web-filled as today's image. To create the parent fractal I returned to one of the earlier versions of the DivideBrot series, the number 4, which has the means to change the escape radius. The parent fractal is better seen than described. All I can say about it is that a minibrot lies near its center, and today's scene is located near the tip of but not exactly on the main spike of the minibrot, which is infinitely divided, making the image kind of a railyard scene. I named the image "Web of the Spirits" because this name sounds better than something like 'web of the spider', and spirits are as mysterious and every bit as real as fractals. I rated it at a 7 because it is pretty good, whatever the word 'pretty' means. The magnitude of an almost off-the-scale 3*(10^13) makes the mathtolerance entry decidedly necessary. But the calculation time of an incredibly brief 32 seconds makes up for the diffi- cult magnitude. And the already-calculated image is or soon will be posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> More near-perfect conditions prevailed here at Fractal Central on Friday. The fractal cats again seemed unconcerned. And once again, my day was too busy to allow a full appreciation of the brilliant sun and comfortable temperature of 84F 29C. The next FOTD will be posted in 24 hours. Until then, take care, and walk with the spirit of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Web_of_the_Spirits { ; time=0:00:32.72-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot4 passes=1 center-mag=-0.064\ 00318711939516/+0.00009960571606727/3.390477e+013/\ 1/-100/0 params=-1.5/0.032/-95.9/0 float=y maxiter=350 inside=0 outside=real logmap=64 periodicity=10 mathtolerance=0.05/1 colors=000SwWPwUMwSJxQGxOExMNmIVcEbUBo08rJDuaIxtMt\ iMpZMlOMbLKTIJKGIJQHIZGHhFGqElzzKr0zzzOdVQY_TRcWKc\ ZDc`6_ZPxXhoVdgTa_RYSPVKNRCLO4JmDzZLmcUmhaFziGXBKU\ CmRDzPDcMEzKEhHFbFFjPRqYbxfn4mvAorGqnMsjSufYwbcxZg\ ybkyeoziszlvzoizoYzoLzo9zoCslEmjHfgJ`eMUbOO`p7eTZd\ 6zcHxbRwaau`kt_usZon`ijacfbYbcSYdMUeGQfBMg41hODngP\ sz`xxWpvSitObrKWpGPnCIl8Bj44bB9VIDNPIFVMXNDmG4nF7o\ F9oFCpFEqFGqFJrFLrFNqEPpERoETnEVmDXlDZkD`jDbkFXkGS\ kHNlIHlJClK7mJ6nU6oU6oU5pU5qc5qc5mc9jcCgmGdmJamNZm\ Q_wU`wYawa_wWYzRzzLzzGzzzzzzzzzzzzzzzFzECzG9zI6zK4\ zMLzJOzPQzUSz_UzdWziYzo_ztazyJz_1zB9zCHzCPzDXzDWzE\ VzFUzFTzGSzHRzHQzIQzI`zGkzFuzEuzEtzFtzFszGszGrzHrz\ HqzIqzIpzJpzJozKozKnzLnzLmzMmzMlzNlzNkzOkzOjzPjzPi\ zQizQhzRhzRgzSgzSfzTfzTezUezUdzVdzVczWczWbzXbzXazY\ azYxzYxzYxzYxzYxzYyz3tz9pzElzKhzPdzV_z_WzeSzjOzpKz\ uGzzJzoLzeNzWPzMQzPYzWVzZ } frm:DivideBrot4 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1), d=real(p2)+100: z=sqr(z)/(z^(-a)+b)+c |z| < d } END PARAMETER FILE=========================================

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FOTD 22-08-08 (One From Many [6])
by Jim Muth 22 Aug '08

22 Aug '08

FOTD -- August 22, 2008 (Rating 6) Fractal visionaries and enthusiasts: A big rush left little time for fractals on Wednesday, but I did manage to find one in a hurry. The little order-6 minibrot in today's image mixes both quadratic and order-6 elements. It is located on the northeast shore line of the main bud of its parent fractal, which exactly resembles an oversized Mandelbrot set. Since I found the scene almost automatically, I could rate it no higher than a 6. The name "One From Many" had some relevance when I thought of it, but now I can see little meaning in it. The calculation time of 2-1/4 minutes is speedy enough for such a routine fractal. And the already-calculated image has been or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect day went un-noticed by the fractal cats on Thursday, while I noticed the perfection but had no time to enjoy it. The next FOTD will be posted in 24 hours. Until then, take care, and wait with anticipation. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= One_from_Many { ; time=0:02:15.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot passes=1 float=y center-mag=-23.3599216711707/+3.587124300227662/\ 5.186719e+009/1/-158.75/0 params=0/0/0/0/0/0/0/0/6\ /30 maxiter=2200 inside=0 logmap=239 periodicity=10 colors=000h5Ag5Ae5Ac5A`5AY8AVBASEAPHAKKAGNABQ87S6C\ T9GUCKVEOWHTXKXYM`YPdZRi_Um`XqaZubaybctaao`_j_YfZW\ aZVXYTTXROWPJVNFVMIXLLZLN`LQbLSdLVfLXhL_jLakLgmQln\ Vro_wpdunfsmgqkiojjmhlkgmifngdpecqcasa`t`_u_aq_cnZ\ djZfgZgcYi`YkXXlUXnQXoNWqJWsGVtCVv9Vw6Tl8Rb9PTBNJC\ L9DSIBYRAc_9ih8oq7uy6ozEizLczSYzZTzeUqgViiWakWUmhb\ iukfVTNSWMPZLN`KKcJIeIFhHDjGAmF8oFDiKIdOM_TRVXVQa_\ LecGiWJbOMXHPRGSPGUOFXNFZMFaLEcKEfJEhHDkGDmFDpECrD\ CuCCwBFtCHqCJnDLlDNiEPfERdFTaFWZFYXG_UGaRHcPHeMIgJ\ IiHIkJHlKHmLHnNGrOGvPGzNJzLLtJNnIPiGReEUdDWbBY`9__\ 8aaFbcLbeRbgXbibbkhbmnbotbpzbmrajjagbadV`aN`_G`_G_\ _F__F__F__F__FZ_EZ_EZ_EZZEYZEYZEYZDYZDXZDXZDXZDXr5\ _x4Xs9YoDYkHZgLZcPZ_T_WX_S``Od`Kh`Xjdilhumkpngkocf\ p_aqWXrSSsONtKIuGDvC8w84x46y87zB8zFAzIBzMCzPDzTFzW\ Gz_HzbIzeHzfHzfHzfHzfHzfHzfGzgGzgGzgGzgGzgGzgJzdMz\ bPz`RzZUzXXzV_zTazRdzPhzd } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots 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), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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